OptSim

Application Notes and Examples

Synopsys, Inc.

Optical Solutions Group

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Ossining, NY 10562

Phone: 914-923-2164
Fax: 914-923-2169

E-mail: info@rsoftdesign.com
Web: www.rsoftdesign.com
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Contents
Chapter 1: Sample Mode Simulations 1
1.1 Getting Started ..................................................................................................................... 1
1.2 Simple Components............................................................................................................. 3
1.2.1 Laser ................................................................................................................... 3
1.2.2 Coupler ............................................................................................................... 3
1.2.3 Mach-Zehnder Modulator................................................................................... 4
1.2.4 Matched Filter .................................................................................................... 4
1.2.5 Sensitivity Receiver............................................................................................ 4
1.2.6 EDFA Amplifier ................................................................................................. 5
1.2.7 Electrical Jitter.................................................................................................... 5
1.2.8 Saturation Model ................................................................................................ 6
1.3 Direct Modulation Laser ...................................................................................................... 6
1.4 Fiber Dispersion................................................................................................................... 7
1.4.1 Dispersion Compensation................................................................................... 7
1.4.2 Dispersion Measurement .................................................................................. 11
1.4.3 Optimum Dispersion Value .............................................................................. 12
1.5 Fiber Linearities................................................................................................................. 12
1.5.1 PMD ................................................................................................................. 12
1.5.2 All-order PMD.................................................................................................. 12
1.6 Fiber Non-linearities .......................................................................................................... 13
1.6.1 Self Phase Modulation (SPM) .......................................................................... 13
1.6.2 Cross Phase Modulation (XPM)....................................................................... 15
1.6.3 Four Wave Mixing (FWM) .............................................................................. 17
1.6.4 Parametric Gain (PG) ....................................................................................... 20
1.7 Fiber-Based Phase Sensitive Amplifier ............................................................................. 21
1.8 Raman Effect ..................................................................................................................... 22
1.8.1 Raman Cross- talk ............................................................................................ 23
1.8.2 Raman Amplifier (RA) ..................................................................................... 25
1.9 WDM systems ................................................................................................................... 27
1.10 EDFA............................................................................................................................... 28
1.11 SOA ................................................................................................................................. 29
1.12 Network Components ...................................................................................................... 30
1.12.1 Optical Add-Drop Multiplexing (OADM) ..................................................... 30
1.12.2 Optical Circulator ........................................................................................... 33
1.12.3 Optical Mu- Demultiplexing .......................................................................... 33
1.12.4 Wavelength Converter .................................................................................... 33
1.12.5 Optical Cross Connector................................................................................. 34
1.12.6 Ring Configuration ......................................................................................... 34
1.13 CATV .............................................................................................................................. 34
1.14 FTTH System with Broadband PON Access Architecture. ............................................. 35
1.15 Soliton Transmission ....................................................................................................... 39
1.16 Duobinary Modulation..................................................................................................... 40
1.17 Chirp ................................................................................................................................ 40
1.17.1 Chirp Measurement ........................................................................................ 40
1.17.2 Chirp Analysis ................................................................................................ 41

OptSim Application Notes and Examples Contents • iii

 1.18 Microwaves on Fiber Optics (MFO)................................................................................ 41
1.19 Signal Regeneration......................................................................................................... 48
1.20 BER Estimation ............................................................................................................... 49
1.21 Relationship Between OSNR and ASE Power Spectral Density in Sample-Mode Models49
DPSK BER Estimator................................................................................................ 49
Optical White Noise Generator ................................................................................. 50
Fixed-Gain Optical Amplifier ................................................................................... 50
Examples ................................................................................................................... 51
1.22 Custom Component Executable (CCE) ........................................................................... 53
1.23 Custom Component for MATLAB (CCM) ..................................................................... 56
1.24 SPICE Co-simulation (CCS) ........................................................................................... 57
1.24.1 SPICE Co-simulation: Sallen-Key Low-pass Filter ....................................... 57
1.24.2 SPICE Co-simulation: Non-linear Laser ........................................................ 59
1.25 VCSEL and Multimode Fiber.......................................................................................... 61
1.26 BeamPROPTM Interface ................................................................................................... 61
1.27 General Purpose............................................................................................................... 62
1.27.1 Iterations......................................................................................................... 62
1.27.2 Parametric Runs.............................................................................................. 62
1.27.3 Recorder & Playback...................................................................................... 62
1.28 Standard OC..................................................................................................................... 63
1.29 DPSK Modulation............................................................................................................ 64
1.30 40 Gbps Systems.............................................................................................................. 64
1.31 DQPSK Modulation: BER curves as function of OSNR ................................................. 68
1.32 Maximum Likelihood Sequence Estimation (MLSE) Receiver for Uncompensated
Transmission System ............................................................................................................... 73
1.33 Polarization-Multiplexed QPSK (PM-QPSK) ................................................................. 75
1.33.1 PM-QPSK with Phase- and Polarization Diversity Receiver ......................... 75
1.33.2 PM-QPSK Modulation and Reception Using Training-sequence based LMS
Receiver..................................................................................................................... 76
1.33.3 PM-QPSK Modulation and LMS Dynamic Receiver..................................... 80
1.33.4 PM-QPSK with External Local Oscillator...................................................... 84
1.33.5 Dual-Carrier PM-QPSK ................................................................................. 86
1.34 PM-BPSK Receiver Sensitivity Analysis ........................................................................ 89
1.35 Polarization-Multiplexed QAM (PM-QAM) ................................................................... 92
1.35.1 PM-16QAM Receiver Sensitivity Analysis.................................................... 92
1.35.2 PM-64QAM Receiver Sensitivity Analysis.................................................... 96
1.36 OFDM Modulation ........................................................................................................ 100
1.37 Burst Mode Transmission in PON Systems Using TDMA............................................ 106
1.38 Dual Rate Burst Mode Receiver in PON systems.......................................................... 110
1.39 DQPSK ROF system ..................................................................................................... 116
1.40 Microwave Photonic Links with Balanced Detection.................................................... 121
1.41 Comparison of Karhunen-Loeve (K-L) Semi-analytical BER Estimation and Direct
Counting of BER via a BER Counter .................................................................................... 125
1.42 Comparison of Karhunen-Loeve (K-L) and Monte Carlo (Chi^2) BER Estimations in 10-
and 40-Gbps Systems ............................................................................................................ 127
Migration from 10 Gbps to 40 Gbps ....................................................................... 129
1.43 Comparison of OSNR sensitivities for Coherent PM-QPSK, RZ-DQPSK and DPSK
systems................................................................................................................................... 130
1.44 Partial DPSK (PDPSK): Influence of MZI delay mismatch in high bitrate dispersive
channels ................................................................................................................................. 132
1.45 In-band Crosstalk in Partial DPSK Systems .................................................................. 136
1.46 All-optical Wavelength Conversion by Nonlinear Polarization Rotation...................... 138
1.47 ROADM Technology Selection and Deployment Testing ............................................ 141
1.48 Unbalanced Mach-Zehnder Modulator with Wavelength Dependent Optical Output... 143

Chapter 2: Block Mode and Transient Simulations 147

iv • Contents OptSim Application Notes and Examples

 2.1 Getting Started ................................................................................................................. 147
2.1.1 10 Gbps Single Channel Link......................................................................... 147
2.2 Transmitters ..................................................................................................................... 150
2.2.1 NRZ, RZ, CRZ and CSRZ Modulation .......................................................... 150
2.2.2 Study of Duobinary Transmitter ..................................................................... 154
2.2.3 Transmitter Band-limiting Filter Study .......................................................... 157
2.2.4 DPSK Modulation .......................................................................................... 159
2.3 Fiber Dispersion............................................................................................................... 162
2.3.1 Dispersion Compensation............................................................................... 162
2.3.2 Chromatic Dispersion: Penalties and Compensation...................................... 166
2.3.3 Chromatic Dispersion Compensation Study................................................... 170
2.3.4 Dispersion Shifted Fiber (DSF) Study............................................................ 172
2.4 Fiber Linear Effects ......................................................................................................... 175
2.4.1 Fiber-induced Loss: Penalties and Compensation .......................................... 175
2.4.2 Fiber PMD Example....................................................................................... 181
2.4.3 Polarization Mode Dispersion (PMD) Induced Penalties in High Bit-Rate
Systems.................................................................................................................... 182
2.5 Fiber Non-linear Effects .................................................................................................. 186
2.5.1 Fiber Four Wave Mixing ................................................................................ 186
2.5.2 FWM Resonance ............................................................................................ 188
2.5.3 Fiber Nonlinearity and Performance of NRZ- and RZ-formats in High-Speed
Links........................................................................................................................ 191
2.6 Fiber Optical Parametric Amplifiers................................................................................ 194
2.6.1 Single-Pump Fiber OPA................................................................................. 194
2.6.2 Dual-Pump Fiber OPA ................................................................................... 195
2.6.3 Fiber-Based PSA ............................................................................................ 195
2.7 Soliton Transmission ....................................................................................................... 198
2.7.1 Soliton in Optical Fiber .................................................................................. 198
2.7.2 Loss-Managed Soliton Link ........................................................................... 201
2.7.3 Dispersion-Managed Soliton .......................................................................... 204
2.8 Raman Amplifier ............................................................................................................. 210
2.8.1 Raman Amplification Tutorial........................................................................ 210
2.8.2 Design of a 40-Channel OC-768 DWDM Link (50 GHz grid) with Multiple
Backward Pumped Raman Amplification ............................................................... 215
2.9 Effective Loss Due to Stimulated Brillouin Scattering.................................................... 218
2.10 EDFA............................................................................................................................. 220
2.10.1 EDFA Tutorial.............................................................................................. 220
2.10.2 EDFA-Based Optical Links.......................................................................... 225
2.10.3 EDFA Design for Dense WDM System ....................................................... 228
2.10.4 Cladding-Pumped EDFA.............................................................................. 231
2.11 EYCDFA ....................................................................................................................... 234
2.11.1 Er-Yb-Based Master-Oscillator Power Amplifier (MOPA) ......................... 234
2.12 OptSim-LAD Interface .................................................................................................. 237
2.12.1 EDFA Gain Compensation via the LAD Interface ....................................... 237
2.13 SOA ............................................................................................................................... 239
2.13.1 Semiconductor Optical Amplifier (SOA) ..................................................... 239
2.13.2 RSOA-based PON with Upstream Remodulation ........................................ 244
2.14 Receivers........................................................................................................................ 247
2.14.1 Receiver Sensivity ........................................................................................ 247
2.14.2 Forward Error Correction and Performance Budget Calculation in
Transmission Link ................................................................................................... 250
2.14.3 Electronic Dispersion Compensation using MMSE-based DFE and FFE.... 252
2.15 Relationship Between OSNR and ASE Power Spectral Density in Block-Mode Models255
2.16 BER Estimation ............................................................................................................. 258
2.16.1 Comparison of IMDD K-L and QA BER Calculations ................................ 258
2.16.2 Monte Carlo BER Estimation in Long-Haul RZ-DPSK Transmission ........ 259

OptSim Application Notes and Examples Contents • v

 References ............................................................................................................... 260
2.17 WDM ............................................................................................................................. 261
2.17.1 10 Gbps 2 Channel WDM Example ............................................................. 261
2.17.2 10 Gbps 4 Channel WDM Example ............................................................. 262
2.17.3 Study of Polarization State Effect in WDM Channels.................................. 264
2.17.4 CRZ Dispersion-Managed Link ................................................................... 267
2.17.5 DWDM Ring with OADM (Optical Add-Drop Multiplexer) Nodes............ 271
2.18 TDM .............................................................................................................................. 276
2.18.1 TDM Link and Demultiplexing in Time Domain......................................... 276
2.19 OCDMA ........................................................................................................................ 280
2.19.1 Optical Code Division Multiple Access (OCDMA) Link with
Encoding/Decoding Based on Pseudo-Orthogonal Code. ....................................... 280
2.20 Free-Space Optics (FSO) ............................................................................................... 285
2.20.1 Free-Space Optical Communication Link .................................................... 285
2.21 Fiber Optic Gyroscope (FOG) ....................................................................................... 292
2.21.1 Interferometric Fiber Optic Gyroscope (I-FOG) ......................................... 292
2.22 CATV ............................................................................................................................ 295
2.22.1 Analog CATV Examples.............................................................................. 295
2.23 FTTH ............................................................................................................................. 303
2.23.1 FTTH System with GEPON Access Architecture ........................................ 303
2.24 Transients....................................................................................................................... 307
2.24.1 Fast Power Transients in EDFA Chains ....................................................... 307
2.24.2 An All-Optical Gain Control Scheme........................................................... 309
2.24.3 Compact Transient EDFA Model Comparisons ........................................... 311
2.25 General Purpose............................................................................................................. 314
2.25.1 How to Create a Block Mode Compound Component (CC) ........................ 314
2.25.2 Compound Component Example.................................................................. 321
2.25.3 How to Co-simulate with BeamPROP.......................................................... 322
2.25.4 BeamPROP Interface Example..................................................................... 329
2.26 Miscellaneous ................................................................................................................ 330
2.26.1 10 Gbps Externally Modulated Single Channel Link ................................... 330
2.26.2 Light–Emitting Diode (LED) ....................................................................... 331
2.26.3 Parallel Optical Bus Example....................................................................... 335
2.26.4 Chirp-Managed Laser (CML)....................................................................... 337

Chapter 3: Multimode Simulations 341

3.1 Laser-Fiber Coupling....................................................................................................... 341
3.2 Spatial Photodetector Coupling ....................................................................................... 349
3.3 Connector Simulation ...................................................................................................... 353
3.4 Multimode Inputs to Multimode Fiber............................................................................. 357
3.5 Linear Multimode Fiber Configuration............................................................................ 363
3.6 Mode Coupling in Multimode Fiber ................................................................................ 367
3.7 Encircled Flux Simulation ............................................................................................... 370
3.8 Differential Mode Delay.................................................................................................. 374
3.9 Spreadsheet Model Comparison ...................................................................................... 378
3.10 Arbitrary Refractive Index Profiles ............................................................................... 385
3.11 Gigabit Ethernet Link Design Based on 1000BASE-SX, -LX Standards...................... 393
3.12 1000BASE-BX (IEEE 802.3ah) Bi-directional EFM System........................................ 399
3.13 10 Gigabit Ethernet Link Design Based on 10GBase Standards. .................................. 402
3.14 Refractive Index Profile Distortions and Multimode Fiber Links Performance -
Cambridge 81-Fibers Statistical Model. ................................................................................ 408
3.15 Vortex Launch to Multimode Fiber Link....................................................................... 418
3.16 MATLAB Cosimulation: Vortex Lens Example ........................................................... 424
3.17 Spatial BeamPROP Interface: Waveguide Example...................................................... 426
3.18 Spatial BeamPROP Interface: Lens Example ................................................................ 430

vi • Contents OptSim Application Notes and Examples

 3.19 Spatial CODE V Interface: Lens Example ..................................................................... 433
3.20 Electronic Dispersion Compensation in multimode link by applying the Forward-
Feedback Equalization Filter ................................................................................................. 435
3.21 25 Gbps Directly Modulated VCSEL ............................................................................ 439
3.22 IEC 60793-1-41: Bandwidth Measurement ................................................................... 442
3.23 IEC 60793-1-49: DMD Test and Measurement............................................................. 445

Index 447

OptSim Application Notes and Examples Contents • vii

Chapter 1: Sample Mode
Simulations

This chapter presents a selection of examples, tutorials and application notes for the sample mode simulations. Several
OptSim examples are located in sub-directories under the /examples directory in the OptSim root installation directory.
Each example is contained in a separate directory and includes the following files:
• the system design, associated parameters and description in file example_name.opf and/or
example_name.moml
• data files for any user-defined components such as the compound_components.opm and/or
compound_component.moml files or other dat files
These examples are an excellent starting point to obtain a practical understanding of the main features of OptSim.

Note
We always recommend that you create a new working directory for each project. Please remember that allowed
characters for directory names are: alphanumerical, "." (dot), "_" (underscore), "-" (dash) and "+" (plus).

The following examples are grouped according to their application focus and they are excellent benchmarks of OptSim
accuracy and speed. Before beginning with your first example, carefully read the chapter 2 “Getting Started” of User
Guide Vol. I to understand how OptSim works and how to build more complex systems.
For each example and for each example group the correspondent path is reported in the gray area.
ProductInstDir/examples/optsim/sample_mode/

1.1 Getting Started

The Getting Started examples are very simple and can be used to gain initial, practical understanding of the OptSim
simulator.
ProductInstDir/examples/optsim/sample_mode/Getting_started

first

ProductInstDir/examples/optsim/sample_mode/Getting_started/First
This example is a single channel 10 Gb/s system.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 1

A 10 Gb/s NRZ optical signal is launched into 50 km of standard single mode fiber. In the receiver section a 980-nm
pumped EDFA is used a preamplifier. The optical signal is filtered and detected using a PIN photodetector.
Measurements include the electrical spectrum, eye diagram and Q estimation.

getting_started_1

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_1
A 9.953 Gb/s NRZ optical signal is launched into 3 spans of Dispersion Shifted Normal fiber, each 50 km in length. The
fiber loss is recovered by 980- nm pumped EDFA before each span and after the third span. The optical signal is passed
through a raised-cosine filter and detected by a sensitivity receiver. The electrical output of the receiver is passed through
a Bessel filter. Measurements include optical spectrum, detected electrical spectrum, eye diagram and Q estimation.

getting_started_2

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_2
The system characteristics for this example are the same as the getting_started_1 example. In this case the parametric run
feature is introduced to show how it may be used to vary the optical attenuation at the receiver.

getting_started_3

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_3
The system characteristics for this example are the same as the getting_started_2 example. In this case the iterate feature
is introduced to show how it may be used to implement multiple fiber spans.

getting_started_4

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_4
The system characteristics for this example are the same as the getting_started_3 example. In this case the compound
component feature is introduced to show how it may be used to create multi-component blocks for the transmitter,
receiver and the optical link section of the design.

getting_started_5

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_5
The system characteristics for this example are the same as the getting_started_3 example. In this case more
measurement components are introduced to show how they may be used to create correlation diagrams.

getting_started_6

ProductInstDir/examples/optsim/sample_mode/Getting_started/Getting_started_6
The system characteristics for this example are similar to the getting_started_4 example. In this case, however, the single
channel configuration is replaced with a 8- channel WDM configuration with 100 GHz channel spacing.

2 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.2 Simple Components
These examples show the behavior of several simple components. Their purpose is to better document the features of the
specific components.
ProductInstDir/examples/optsim/sample_mode/Simple_components

1.2.1 Laser

MQW Laser

ProductInstDir/examples/optsim/sample_mode/Simple_components/MQW_Laser/MQW_Laser.opf
In this example an externally modulated MQW laser is used as source of a single channel system.
The laser is biased at different current levels: below, near and above the threshold. The optical signal is propagated into a
100 km fiber link. At the end of the propagation the optical filtering occurs and a PIN Photodetector detects the signal.
From the measurement blocks it is possible to estimate the performances of the system by mean the Eye Diagram and the
Q value estimation. Moreover the PI curves and the AM curves, available in the OptSim DataDisplay Chart Tree, show
the laser behavior.

Lorentizian Narrow Laser

ProductInstDir/examples/optsim/sample_mode/Simple_components/Narrow_laser/Narrow_laser.opf
In this example is showed the behavior of the Laser CW with a limited Noise Bandwidth.
The Relaxation Oscillation Peak Frequency and Relaxation Oscillation Peak Overshoot are variables (f_res=5,10,20 GHz
and over_shoot=3,9 dB). The comparison among the different cases is made in the spectral domain, after the
transmission and at the receiver section. In fact the signal is propagated into a 150 km fiber link which is divided in 3
span whose length is 50 Km. At the end of each span the signal is received and its spectrum is measured. This kind of
laser model is more realistic compared to the CW one. The noise is limited within a certain band and is more evident the
Relaxation Oscillation contribution and the dispersion effect on them.

Laser Clipping

ProductInstDir/examples/optsim/sample_mode/Simple_components/Laser_clipping/DFB_clipping.opf
This example shows the Laser behavior when the driving current is lower than the Threshold Current. That is the case in
which, whenever the transmitted bit is a logical zero, the Laser is turned off.
In the project the upper and the lower bit levels are variables (they are used in a parametric run), but the Bias Current is
constant.
At the receiver it is possible to see the Eye Diagram for each run. When the Driving Current goes down, below the Laser
Threshold, The Eye Diagram is flattened, in the lower part, on the zero value.

1.2.2 Coupler

coupler

ProductInstDir/examples/optsim/sample_mode/Simple_components/Coupler

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 3

This example is composed of two projects that illustrate the behavior of the optical coupler, tunable and broadband
power meters and cancellation of coherent signals.
The first design is composed of a cascade of two couplers in an interferometric structure. The output port ratio of each of
the two couplers is 50%/50%. A CW optical signal at 193.4 THz with a phase equal to 0 rad is introduced at the input
port 1 of the first coupler while a CW optical signals with exactly same center frequency and phase but with a very low
power is introduced at the input port 2 of the first coupler. Because of the signals are equally split in amplitude and phase
by two couplers, there is no signal at the output port 1 of the second coupler (destructive condition) instead the signal is
completely present at the output port 2 of the second coupler (constructive condition).
The second design is composed of two CW optical signals at different center frequencies (193.4 THz and 193.6 THz)
and same initial phase. These two signals are introduced at the inputs of a single coupler. The output port ratio of the two
couplers is 10%/90%. The power spectrum and total power is measured for the two-coupler outputs. The total optical
power is measured using both a broadband power meter as well as a tunable power meter.

1.2.3 Mach-Zehnder Modulator

MZ_tones_generator

ProductInstDir/examples/optsim/sample_mode/Simple_components/Mach_Zehnder
This example shows how a Mach- Zehnder modulator can be used to generate multiple tones.
If the input to the Mach-Zehnder modulator is a sinusoid at frequency fs, and the modulator is biased at Vpi and driven by
a sinusoidal generator at fm the optical spectrum at the output of the modulator shows tones at the frequencies fs ±
(2n+1)fm (n=0,1,2,...). That is, the carrier is completely suppressed and sidebands appear at frequency offsets equal to the
modulating frequency and its odd multiples. If this optical signal is sent into a photodetector, the square-law nature of the
detector, together with the phase coherence between the generated tones, produces even multiples of the modulation
frequency in the electric spectrum. This phenomenon occurs only when the modulator is characterized by an ideal
extinction ratio. If a finite extinction ratio is introduced, a mixture of even and odd multiple tones occur.

1.2.4 Matched Filter

matched_filter

ProductInstDir/examples/optsim/sample_mode/Simple_components/Matched_Filter
This example compares the behavior of the Matched filter, Raised Cosine filter and Single Pole lowpass filter models.
A 10 Gb/s NRZ electrical signal is amplified by an amplifier (50Ω impedance) and then filtered by the three different
filters. Note that the maximum estimated Q value is with the Matched filter.

1.2.5 Sensitivity Receiver

sensitivity_receiver

ProductInstDir/examples/optsim/sample_mode/Simple_components/Sensitivity_receiver
This example illustrates how to use the Sensitivity Receiver component.
A 10 Gb/s NRZ optical signal is connected directly to the input of the sensitivity receiver. It uses an matched electrical
filter at the output of a PIN photodiode (quantum efficiency equal to 0.75). The optical receiver sensitivity is set equal to
the average input optical power, and the optical test pulse shape is equal to the driver pulse shape. Note that the
estimated Q factor is about 6, corresponding to the desired bit error probability of 10- 9.

4 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.2.6 EDFA Amplifier
The EDFA examples illustrate the performance of the different 980- pumped amplifier models available in OptSim, in
particular the Saturable Gain model and the Physical model.
ProductInstDir/examples/optsim/sample_mode/Simple_components/EDFA

EDFA_saturation

ProductInstDir/examples/optsim/sample_mode/Simple_components/EDFA/EDFA_saturable_gain
This example illustrates the performance of Saturable Gain EDFA model.
A CW optical signal of variable power is amplified by an EDFA set for +7 dBm of output saturation power. The optical
power meter measures the amplifier output optical power vs. the amplifier input optical power. The power out vs. power
in curve shows the amplifier saturation effect.

EDFA_physical

ProductInstDir/examples/optsim/sample_mode/Simple_components/EDFA/EDFA_physical_model
This example illustrates the performance of EDFA Physical model.
The EDFA Physical model used is “Line Amplifier 20 dB Gain”. The optical spectrum computed over a wide bandwidth
shows the typical behavior of this EDFA amplifier model.

1.2.7 Electrical Jitter

Eye_jittered

ProductInstDir/examples/optsim/sample_mode/Simple_components/Jitter/Eye_jittered
The focus of this example is to give to the user a basic understanding of what the electrical jitter block does and show the
effect of jitter modulation at the receiver section.
A single RZ channel at 10 Gb/sec is transmitted over 120 Km of SM fiber. Fiber dispersion is partially compensated
through additional 18Km of DCF fiber (75% dispersion compensation ratio).
The signal are preamplified by an EDFA booster having a noise figure F = 4.5 dB. The average launch power is 0 dBm.
The accumulated fiber attenuation is completely compensated using an EDFA preamplifier having F= 4.5 dB.
From a SPT simulation the optical signal-noise ratio (OSNR) at the end of the link results to be 22.5 dB.
A sensitivity receiver is used to detect the channel. After the detector an electrical jitter block is placed to simulate jitter
modulation. The jitter block is driven by an electrical-wave generator CC where the output signal type can be selected
through parametric run (see EWG CC details). The defined parametric run values allow to analyze system performance
with different jitter conditions.
The first run simulates an ideal clock that has no jitter for the receiver (OptSim default). The resulting eye diagram at
the receiver is widely opened; as a matter of the fact the detected Q factor is about 19.5 dB.
The second and third run introduces a deterministic sinusoidal modulated jitter. In particular for the second run the jitter
is kept low instead in the third run the amplitude of the input jitter signal is increased in order to enhance the jitter effect.
The last two runs introduce a random jitter. In this case the modulated signal is obtained through a noise gaussian
generator followed by a Bessel filter.
At the back-to-back stage two electrical probes are used to display the different jitter signalsalong with the corresponding
eye diagrams. Please note that at the receiver section the evaluated Q factor (optimum threshold) does not change

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 5

significantly introducing jitter. On the other hand we can verify the receiver results more susceptible to the possible
sampling time variations in presence of jitter (plot the " Eye closure vs. Sampling Instant" chart).

1.2.8 Saturation Model

These examples can be used as a reference for the electrical saturation block, using the two predefined compound
components saturable electrical amplifier and saturable photodiode.
ProductInstDir/examples/Simple_blocks/Saturation

Test_saturation_amp

ProductInstDir/examples/Simple_blocks/Saturation
This example shows the comparison between an ideal electrical gain block and an amplifier working in saturation. The
input is a sinewave of amplitude 2 V peak-to peak and a DC level varied through parametric runs from 0 through 2 V.
The signal is passed through an ideal gain block with a gain of 20 dB. In parallel, it is passed through a saturable
electrical amplifier with a small-signal gain of 10 and an output saturation level of 20 V. Comparing the two outputs
clearly shows the saturation phenomenon and strong nonlinear behavior of the saturable amplifier.

Test_saturation_diode

ProductInstDir/examples/Simple_blocks/Saturation
This example shows a PIN photodiode working in saturation. The input is an optical signal modulated with a sinewave
of amplitude 16 mW peak-to-peak and a DC level varied through parametric runs from 8 through 24 mW.
The signal is received by a saturable PIN photodiode. For higher input powers, one can clearly observe the saturation
phenomenon.

1.3 Direct Modulation Laser

These examples can be used as a reference for direct modulation laser schemes. They also illustrate the use of the
predefined rate equation laser models.
ProductInstDir/examples/Lasers/Direct_Mod/

Ageretest

ProductInstDir/examples/Lasers/Direct_Mod/DFB
This example shows the use of a 1310 nm direct modulated laser based on Agere's D1861C laser. In the first set-up, the
laser is driven at 10 Gb/s under typical conditions and transmitted through a single-mode fiber. The fiber length is varied
through parametric runs, from 20 km to 60 km. The signal is received through an APD receiver of sensitivity -27 dB, and
the corresponding eye diagram is displayed in the electrical scope.
In the bottom configuration, we measure the modulation bandwidth of the laser by displaying the frequency response to a
white noise input.

Fujitsutest

ProductInstDir/examples/Lasers/Direct_Mod/DFB
This example shows the use of a 1550 nm direct modulated laser based on Fujitsu's 5F10NP laser diode. In the first set-
up, the laser is driven at 10 Gb/s under typical conditions and transmitted through a single mode fiber. The fiber length is

6 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

varied through parametric runs, from 0 to 50 km. The signal is received through a receiver with a sensitivity of -18 dBm,
before it is displayed in the electrical scope.
The bottom configuration is a bandwidth measurement. In the electrical scope, the user can display the frequency
response to a white noise input.

Fabry_Perot_2_5G_test

ProductInstDir/examples/Lasers/Direct_Mod/FP
This example shows a setup of a directly modulated 2.5 Gb/s Fabry-Perot laser working at 1310. The laser in the
example reproduces the behavior of a Fabry-Perot laser optimized for 2.5 Gb/s direct modulation.
The fiber length is varied through parametric runs. At the output one can observe the effects of chromatic distortion on
the eye, for fiber lengths of 10 km, 20 km, 40 km and 60 km.

Fabry_Perot_10G_test

ProductInstDir/examples/Lasers/Direct_Mod/FP
This example shows a setup of a directly modulated 10 Gb/s Fabry-Perot laser working at 1310. The laser used in the
example is the yy_Fabry_Perot_10G laser available as a predefined model.
The fiber length is varied through parametric runs. In this particular case, the distortion of the eye due to dispersion
limits the fiber length over which this signal can be successfully transmitted. Up to 6 km of fiber, we still have an open
eye, whilst at 20 km the eye is clearly closing.

1.4 Fiber Dispersion

The Fiber Dispersion examples illustrate the well- known measurements and compensation techniques for fiber
dispersion. They also include an example of optimizing dispersion compensation.
ProductInstDir/examples/optsim/sample_mode/Dispersion

1.4.1 Dispersion Compensation

fiber_grating_ideal

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_compensation/Fiber_grating
This example illustrates how to compensate fiber dispersion using the ideal fiber grating component.
A 10 Gb/s NRZ signal is launched onto a 100 km long standard single mode fiber. The dispersion compensation is
performed using the ideal model of the fiber grating component.

fiber_grating_real

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_compensation/Fiber_grating
This example illustrates how to compensate fiber dispersion using the realistic fiber grating component. A 10 Gb/s NRZ
signal is launched onto a 100 km long standard single mode fiber (Fig. 1). The dispersion compensation is performed
using the User- Defined model for the fiber grating component. Virtually any fiber grating transfer function can be
implemented using this User-defined model.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 7

 Figure 1. Topology for FBG as dispersion compensator

Figure 2. Received eye with no compensation (left) and corresponding histogram (right) of electrical samples

Figure 3 shows eye diagram and corresponding histogram of electrical samples for a case where FBG is used as
dispersion compensator.

Figure 3. Eye diagram (left) and histogram (right) with FBG as dispersion compensator

Comparison of eye and histograms of figures 2 and 3 shows marked improvement in link performance due to
compensation of dispersion. This example demonstrated an application of FBG in dispersion compensation.

8 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

ph_conjugator_lin

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_compensation/Phase_conjugator
This example illustrates how to compensate fiber dispersion using the optical phase conjugator component.

Figure 1. Schematic setup for dispersion compensation by phase conjugation.

The schematic setup is given in Figure 1 and combines transmitter, a fiber span consisting of two links, a mid-span phase
conjugator, and receiver. A 10 Gb/s NRZ data stream is sent over a first lossless fiber link where dispersion is set to D =
16 ps/nm/km. The peak power is set to -3 dBm. After 1000 km the eye diagram shows a completely closed eye, due to
the accumulation of chromatic dispersion. Then the signal goes through an OPC, and then to another 1000 km long fiber
link. At the output of the second link the received eye is completely open. Figure 2 demonstrates eye diagrams after
transmitter, first link, OPC, and second link.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 9

 Figure 2. Eye diagrams after transmitter, first link, phase conjugator, and second link.

The principle of operation for OPC block is phase inversion according to

Ein (t) = A(t)e jΦ(t ) and Eout (t) = ηA(t)e− jΦ(t )e jΦSHIFT
where η is device efficiency and Φshift extra constant phase shift. In our example η =1, and Φshift = π/2.

Figure 3. Optical spectrum before and after OPC.

It is known from theory that a phase conjugator placed between two identical spools of fiber can completely compensate
second-order dispersion. This theoretical result is confirmed by this numerical simulation.
In details, the signal is being dispersed in the first half of the span resulting in distorted pulse shapes with the blue light
leading the red light. This dispersed signal is then being phase conjugated. The OPC reverses or inverts the optical
spectrum of the signal so that red becomes blue and blue becomes red. The shape of a pulse remains the same, but now
the leading edge is red and the trailing edge is blue. Now the dispersion in the second half of the span reshapes the pulse

10 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

so that, if the dispersion before the OPC matches the dispersion after it, then the original pulse shape will be restored at
the end of the span. From the optical probes before and after the OPC (see Figure 3), it can be seen that the phase
conjugator near the center of the span reverses the broadening (spectral inversion) and that this allows the broadening to
be zero at the receiver and the pulse shape is restored to its input form. Since the signal spectrum after OPC becomes the
mirror image of the input spectrum, the OPC technique is also referred to as midspan spectral inversion.

ph_conjugator_nonlin

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_compensation/Phase_conjugator
This example illustrates how to simultaneously compensate for both dispersion and non-linearities in fiber, using the
optical phase conjugator component.
The system characteristics are the same as the ph_conjugator_lin example except that the transmitted optical power is
substantially higher (+9 dBm). This power increase in optical power causes non- linearity effects become important. The
eye diagram of the received signal is shown to be completely open even in this case, where there are also the fiber non-
linearity effects.

Dispersion Compensation

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_compensation/DCF/DCF.opf
In this project is showed a Pre-, Post- and Symmetrical Full Dispersion Compensation example.
A 1550 nm single channel is launched onto a fiber link and three different dispersion compensation schemes are used.
In the upper model is presented a pre-compensation. The total link length is about 300Km, which are subdivided into 2
loops. In each loop a 120 Km (D=16 ps/nm/km) fiber span is compensated by a 24 Km (D=-80 ps/nm/km) fiber span
placed before it.
The example in the middle shows a post compensation configuration. The total link is the same of the previous one, but
the 24 Km span is placed after the 120 Km span.
In the lower example is described the correspondent symmetrical configuration. Even in this case, the used DCF fiber is
the same of the 2 other presented configurations.
Performing a linear VBS simulation, it is possible to analyze the compensation effects only. On the contrary, a full VBS
simulation shows the interaction among the dispersion compensation and the non-linear effects. The output Power from
the EDFA is a variable (its values are 5 and 10 dBm). In this way it is possible to understand how changes the
nonlinearity impact on the system.

1.4.2 Dispersion Measurement

disp_measurement

ProductInstDir/examples/optsim/sample_mode/Dispersion/Disp_measurement
This example illustrates one of the simpler methods for measuring the average dispersion of a fiber span, as discussed in
detail in [1].
This method requires measuring the "electrical-to-electrical" transfer function of a link composed of a linear optical
modulator, a fiber span under test and a photodiode. The average dispersion is related to the first zero of the resulting
transfer function.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 11

The following law expresses the resonance frequency fu corresponding to the uth zeros of the transfer function:

c  2 
f u2 L = 2 
1 + 2u − arctan(α )
2 Dλ  π 
where L is fiber length, D is the fiber dispersion and α is the modulator chirp.

1.4.3 Optimum Dispersion Value

optimum_disp

ProductInstDir/examples/optsim/sample_mode/Dispersion/Optimum_disp
This example illustrates how to optimize dispersion compensation.
The system is a 10 Gb/s NRZ single channel. Transmission takes place over 8 amplified spans of normal DS fiber (D=-2
ps/nm/km), 60 km each. Dispersion is compensated before the receiver by employing an anomalous DS fiber span (D=16
ps/nm/km). The optimum dispersion compensation percentage is found to be 83%, corresponding to Q=24.5 dB and to a
compensation fiber length of 50 km.

1.5 Fiber Linearities

The examples illustrate linear fiber effects such as PMD and all-order PMD effects.
ProductInstDir/examples/optsim/sample_mode/Fiber_linear_effect

1.5.1 PMD

PMD

ProductInstDir/examples/optsim/sample_mode/Fiber_linear_effect/PMD/PMD.opf
This example shows the PMD impact on the fiber transmission.
The back-to-back configuration and a 100 Km fiber link are simulated; all the typical effects in the fiber are neglected
(loss, dispersion, non-linearties). Due to the PMD, a pulse, launched in the fiber with a certain polarization has two
components along the X and Y axes, which travel with 2 different velocities during the propagation. Hence, at the fiber
output, they have a Differential Group Delay (DGD) and the received pulse is distorted. Since the PMD is a stochastic
effect, it is significant to perform a Montecarlo simulation. At this purpose the project seed parameter is defined as a
variable that is used in the run definition. Comparing the Eye diagrams in the Sgn_Back_to_back and Sgn_received
blocks it is possible to observe the distortion of the received pulse. Moreover, from the "Input" and “Output” Probes, it is
possible to note the delay between the two components of the pulse.

1.5.2 All-order PMD

AOPMD

ProductInstDir/examples/optsim/sample_mode/Fiber_linear_effect/AOPMD/AOPMD.opf
This example illustrates the use of the AOPMD (LIB) component to simulate Polarization Mode Dispersion (PMD) by
taking into account of its frequency dependence.

12 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The system is composed of a single channel 10 Gb/s NRZ transmitter with optical source at 1550 nm externally
modulated through a Mach-Zehnder modulator. The signal is launched over a linear optical fiber with all polarization
and non linear effects switched off. Then the PMD is introduced as a concentrate effect by mean of the AOPMD block
(available among OptSim LIB blocks under the "Miscellanea" category). At the receiver section the Q-factor and the
eye-diagram can be observed.
In order to verified the random effect of the PMD on the system performance a Montecarlo simulation is performed by
changing the seed parameter of the AOPMD block from 1 to 25 through parametric run. At the end of the simulation it is
possible to display the Q factor versus the seed parameter and then evaluate the mean and standard deviation directly on
the correlation graph. Moreover the value of the Differential Group Delay (DGD) obtained for each statistical case is
directly available as output of the AOPMD block.

1.6 Fiber Non-linearities

The examples illustrating non- linear fiber effects highlight the impairments caused by fiber non- linearities such as self-
phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM), parametric gain and modulation
instability.
ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect

1.6.1 Self Phase Modulation (SPM)

This example illustrates the behavior of Self Phase Modulation (SPM) versus optical power and fiber dispersion.
ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/SPM

SPM_vs_power

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/SPM/SPM_vs_Power

A 10 Gb/s NRZ signal is launched over two DS fiber spans (D=0.4 ps/nm/km) of 50 km, each (Fig. 1). The power at the
input to each span is varied from 10 to 17.5 dBm by using the parametric run feature in OptSim. EDFA noise has been
turned off in order to simplify the analysis of SPM. By increasing the power, SPM grows and depletes the signal, and the
measured power (in a bandwidth equal to twice bit rate) actually decreases with the increasing of the transmitted power
(Fig. 2). Moreover, the channel has been demodulated. The eye diagram highlights the PM- AM conversion due to the
SPM (Fig. 3). Specifically the eye opening decreases with increasing transmitted power. Since there is no noise,
estimation of the Q values is irrelevant.

Figure 1. Topology for studying self-phase modulation (SPM) effects

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 13

 Figure 2. Output power (Y-axis) vs. transmitted power (X-axis).

(a) Back-to-back eye (left) and the received eye (right) for transmitted power = 10dBm

14 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 (b) Back-to back eye (left) and the received eye (right) for transmitted power = 17.5dBm

Figure 3. Eye diagrams – back-to-back and received for two different values of transmitted power

SPM_vs_disp

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/SPM/SPM_vs_Disp
A 10 Gb/s NRZ signal is sent over 4 fiber spans of 50 km each. Dispersion is completely compensated to isolate the
SPM phenomenon. Dispersion values have been varied from -10 to 10 ps/nm/km through the parametric run feature. The
power at the fiber input for each span has been set to 10 dBm. EDFA noise has been turned off. By decreasing the
dispersion modulus, SPM grows and depletes the signal, therefore causing the measured to decrease as in the previous
example. Note that in passing from the normal to the anomalous dispersion regime, the received optical spectrum at first
widens and then narrows.

1.6.2 Cross Phase Modulation (XPM)

XPM_vs_disp

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/XPM
This example shows the effect of XPM on a WDM system versus fiber dispersion.
Two WDM channels are launched over two DS fiber spans of 100 km each (Fig. 1). Dispersion is completely
compensated at each span to better show the XPM phenomenon. Fiber dispersion is varied from 0 to 4 ps/nm/km through
parametric runs. In order to focus on XPM, one of the two channels—the "probe"—has a low power and is sent along the
link together with a stronger "pump" channel. Both probe and pump channels are modulated by digital NRZ signals at 10
Gb/s. The effects of XPM are visible as an enlargement of the received probe spectrum, a distortion of the eye diagram
of the probe signal, and an increase of the power measured by the Receiver Sensitivity.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 15

 Figure 1. Topology for studying cross-phase modulation (XPM) effects

Figure 2 below shows received eye diagram of the probe signal corresponding to dispersion setting of 4 ps/nm/km (left
eye) and 0 ps/nm/km (right eye).

Figure 2. Eye diagrams of the probe signal – fiber dispersion 4 ps/nm/km (left) and 0 ps/nm/km (right)

Figure 3 below compares the received optical spectra of the probe channel for fiber dispersion values of 4 ps/nm/km and
0 ps/nm/km.
The effects of XPM are visible as broadening of the received probe power spectrum (Fig. 3) and as the distortion in the
received eye diagram of the probe channel (Fig. 2).

16 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 3. Optical spectra of the probe channel for fiber dispersion of 4 ps/nm/km (red) and 0 ps/nm/km (green)

1.6.3 Four Wave Mixing (FWM)

These examples illustrate the effect of the Four Wave Mixing (FWM) versus the fiber dispersion and versus optical
signal polarization.
ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/FWM

FWM_vs_disp

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/FWM/FWM_vs_Disp
This example illustrates the production of FWM products in a WDM system versus the fiber dispersion.
Two WDM channels are launched over two DS fiber spans of 100 km, each (Fig. 1). Dispersion is completely
compensated at each span. The fiber dispersion value is varied from 0 to 4 ps/nm/km through parametric runs. The
optical power spectrum of the received signal shows that FWM products decrease with increasing dispersion.

The output results are given in Figs. 2 and 3. Fig. 2 shows optical power spectrum at the fiber input and at the output for
different setting of dispersion. Here the spectrum of the received signal shows that FWM products decrease with
increasing dispersion. Fig.3 shows quantitatively the decrease of FWM product power with increasing dispersion.
In conclusion, we illustrated that FWM products in WDM system are stronger at lower fiber dispersion. At zero
dispersion due to the phase-matching condition the FWM effect is maximized. By increasing the fiber dispersion we
increase the phase mismatch and FWM effect decreases.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 17

 Figure 1. Setup for FWM vs dispersion schematic.

(a) (b)

(c) (d)

18 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 (e) (f)

Figure 2. Optical spectrum: (a) at the fiber input, and at the fiber output for (b) D = 0, (c) D =1, (d) D = 2, (e) D = 3, (f) D = 4
ps/nm/km.

Figure 3. Power levels of FWM product vs. dispersion.

FWM_vs_polarization

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/FWM/FWM_vs_Polarization
This example shows the FWM products on a WDM system versus channel polarization.
Two WDM channels are launched over two DS fiber spans (D=2 ps/nm/km) of 100 km, each. Dispersion is completely
compensated at each span. The fiber dispersion value is varied from 0 to 4 ps/nm/km through parametric runs. The lasers
representing the two channels have the same initial polarization (along the x axis), but polarization for one source is
rotated around the S2 axis of the Poincare' sphere through parametric runs. The FWM products are maximized when the
polarizations are aligned and nearly completely reduced to zero when the two polarizations are orthogonal. To read more
about FWM versus polarization, refer to [2].

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 19

1.6.4 Parametric Gain (PG)
The following five examples illustrate the manifestation of Parametric Gain (PG) as noise enhancement and Modulation
Instability (MI).
ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/Parametric_gain

par_gain

ProductInstDir/examples/optsim/sample_mode/Fiber_nonlinear_effect/Parametric_gain/Par_gain
This example illustrates parametric gain manifested as sideband instability.
A strong CW signal is sent over long optically amplified link (3000 km), with each span composed of 50 km of DS fiber.
The output spectrum clearly shows two sharp peaks, symmetrically located about the CW signal, caused by the
interaction between the CW signal and the EDFA noise. This phenomenon is referred to in the literature as Sideband
Instability, and is related to the periodicity of the link/amplifier chain.

si6dbm

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/Parametric_gain/Si6dBm
This example again illustrates parametric gain manifested as sideband instability.
An ideal CW signal is transmitted together with noise accumulated along an amplified chain. The optical link length is
3000 km. The noise enhancement due to the Parametric Gain effect is evident, just like as the growth of Sideband
Instability peaks 50 GHz apart from the CW frequency.

mi16dbmds

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/Parametric_gain/Mi16dBmds
This example illustrates noise enhancement due to modulation instability (MI).
An ideal CW ideal signal is transmitted over an 80 km long link. Due to the non-linear Kerr effect, the presence of a
strong pump propagating along a fiber can amplify small signals in a bandwidth around the pump frequency. A detailed
theoretical description of this phenomenon may be found in [3], [4] and [5].

mi800

ProductInstDir/examples/optsim/sample_mode /Fiber_non-linear_effect/Parametric_gain/Mi800
This example illustrates the manifestation of parametric gain as SPM and modulation instability (MI).
This example is an 800-km single-channel link at 2.5 Gbit/s, severely impaired by non-linear effects. The fiber is
standard single mode (D=16 ps/nm/km) fiber. The average launch power is +10 dBm that is maintained along the link by
8 in-line amplifiers. By studying the received power spectrum (especially the right-most receiver) it is seen that the
signal spectrum is extremely distorted. Part of the impairment is SPM that, combined with the high fiber dispersion,
brings about a large pulse distortion in the essentially closed eye diagram. Most of the impairment, however, is due to
modulation instability (MI). This effect enhances ASE noise in the proximity of a strong signal. Since MI and SPM
occur together in this example, it is difficult to separate the effects. If the modulated signal is set instead to CW, SPM
will disappear, whereas MI will not.
For this case, see the example mi800cw.moml, below.

20 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

mi800cw

ProductInstDir/examples/optsim/sample_mode/Fiber_non-linear_effect/Parametric_gain/Mi800cw
This example illustrates modulation instability (MI) caused by parametric gain.
This project is derived from the mi800.opf example. The modulation is turned off to eliminate the SPM effect.
Otherwise, all other propagation aspects are unchanged. Note that to obtain the same MI as in the modulated example,
the fixed amplifier output power has been adjusted to obtain the same peak power in the fiber as the previous examples.
The simulation results show the presence of large noise enhancement. The optical power spectrum is very similar to what
is seen in the modulated case. Therefore, one may conclude that indeed most of the signal degradation is due to MI.

1.7 Fiber-Based Phase Sensitive Amplifier

RSoft/examples/optsim/sample_mode/Fiber_OPA/sm_fiber_psa.moml
In a fiber-based phase-sensitive amplifier (PSA), the relative optical phase between pump, signal and an additional idler
wave determines whether four-wave mixing in the fiber leads to amplification or attenuation of the signal. Following the
treatment in [1] and [2] and considering two frequency-degenerate pumps, one signal, and one idler wave, the relative
phase difference θin between the various components at the fiber input is (accounting for the sign convention for sample
mode’s optical signal phase, which is consistent with that used in [2]):

θin = −2φ p + φs + φi

where φp is the pump phase, φs is the signal phase, and φi is the idler phase. By varying the value of θin, we can change
whether the fiber amplifies or attenuates the signal.

Open sm_fiber_psa.moml, whose schematic is illustrated in Fig. 1. This design, based on work presented in [2],
models a fiber-based PSA whose inputs are a single 175-mW cw pump at 1559.83 nm along with two -10-dBm cw
signals at 1560.09 and 1559.57 nm, the latter of which acts as the idler wave. For simplicity, we neglect phase noise in
the optical signals by setting their linewidths equal to zero. The signals are all launched down 1 km of highly nonlinear
fiber (γ = 9 W-1·km-1) with a zero-dispersion wavelength of 1558 nm and a dispersion slope of 0.018 ps/nm2/km. We
neglect SBS and fourth-order dispersion in the fiber. At the output of the fiber, we use a filter to select the 1560.09-nm
signal and then use an Optical Power Meter to calculate the signal power.

To view the PSA amplification as a function of the relative phase difference θin at the fiber input, run the preconfigured
Scan simulation for this topology, which sweeps θin from 0 to 2π radians. At the conclusion of the simulation, you may
view the 1560.09-nm signal output power as a function of θin by right-clicking on Optical Power Meter opowme1,
selecting View Correlation Diagram, and then plotting Optical Power versus Variable phaseIn_rad. The results should
match those shown in Fig. 2. Taking into account the input signal power of –10 dBm, we see good agreement between
our simulation and the published results for amplifier gain from [2]. As can be seen, as θin is varied, the fiber switches
between amplification and attenuation, as you would expect in a phase-sensitive fiber optical parametric amplifier.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 21

 Figure 1. Fiber-based PSA simulation topology.

Figure 2. PSA output power (dBm) for the 1560.09-nm signal as a function of the relative phase difference (radians) at the input.

References
1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers
and their applications,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, no. 3, pp. 506-520, May/June
2002.
2. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-line frequency-nondegenerate phase-sensitive
fiber-optical parametric amplifier,” IEEE Photonics Technology Letters, vol. 17, no. 9, pp. 1845-1847, September 2005.

1.8 Raman Effect

The Raman Effect examples show: the performance of systems affected of the cross- talk induced by the Stimulated
Raman Scattering (SRS); the system performance with the Raman amplification use.
ProductInstDir/examples/optsim/sample_mode/Raman

22 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.8.1 Raman Cross- talk
These examples illustrate the effects of Stimulated Raman Scattering (SRS) on channel cross- talk in WDM systems and
on ASE noise.
ProductInstDir/examples/optsim/sample_mode/Raman/Cross-talk

Raman_on_ASE_wide

ProductInstDir/examples/optsim/sample_mode/Raman/Cross-talk/Raman_on_ASE_wide
This example shows the effect of SRS on ASE noise introduced by a preamplifier.
A CW signal at 194 THz is amplified by an EDFA to +20 dBm output power and launched onto a fiber. The Raman gain
peak in the neighborhood of 180 THz, is due to SRS and this effect is maximum in the spectral region 14 THz below the
carrier.

Raman_tilt_narrow

ProductInstDir/examples/optsim/sample_mode/Raman/Cross-talk/Raman_tilt_narrow

This example illustrates the cross talk induced by the Stimulated Raman Scattering (SRS) as a function of the fiber
Raman gain constant. The setup is shown below:

Figure 1. Setup for Raman cross-talk link

A 16–channel WDM system is launched into 20-km of standard single-mode fiber. All channels are NRZ-modulated at
bitrate 10 Gb/s. Channel spacing is 100-GHz with full bandwidth for all channels of 12 nm. Total input power into the
fiber span is 20 dBm (at 8 dBm per channel). Input spectrum into the fiber is shown in Figure 2.
Raman-induced cross-talk in WDM system leads to power re-distribution between higher- and lower-frequency
channels, i.e. each pair of channels interact as a signal and a pump with the higher-frequency channel, “pump”,
transferring some power to the lower-frequency channel, “signal”. The magnitude of transferred power depends on the
channel spacing, signal input power, and Raman gain coefficient for given wavelengths of “signal” and “pump”. Ideally
one needs to know the spectrum dependence of Raman gain coefficient - these data can be available from measurements

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 23

or fiber datasheets. If not, one can use either a linear slope or Lorentzian shape approximation for Raman gain spectrum
and specify it with a gain peak coefficient, frequently referred to in literature just as Raman (or SRS) gain coefficient gR.

Figure 2. Optical spectrum at the fiber input.

The standard peak value of the Raman gain gR is about 1x10-13 m/W at a wavelength of 1 µm and this value scales
linearly with pumping frequency, so that for 1550 nm it will be about 6x10-13 m/W.

Figure 3. Optical spectrum at the fiber output for scaling coefficients 0.1 (left) and 1.0 (right).

To see the effect of cross-talk at different values of the Raman gain coefficient we introduced the scaling coefficient
Const such that
(gR)new = (Cosnt ) x ( gR) standard
and studied cases with Const = 0.1 and Const = 1.0 through the parametric run.
The optical power spectrum of the received signal (Figure 3) shows the spectral tilting induced by the SRS. The tilting
increases with increasing scaling coefficient (i.e. Raman gain); 10 times higher gain coefficient is expected to produce 10
times larger tilt and we can see from simulation results that tilt goes from ~3 dB for Const = 0.1 ( Figure 3, left) to ~ 28
dB at Const = 1.0 (Figure 3, right).
In conclusion, we illustrated that Raman-induced crosstalk between WDM channels causes the power re-distribution
between higher- and lower-frequency channels and adds a tilt to the fiber output spectrum.

24 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

Raman_tilt_wide

ProductInstDir/examples/optsim/sample_mode/Raman/Cross-talk/Raman_tilt_wide
This example illustrates the cross- talk effect over large bandwidth WDM system.
A 16- channels WDM system is transmitted over 500 km. The channel spacing is 800 GHz, such that the transmission
bandwidth is 12.8 THz. The fiber is DS with anomalous dispersion regime over the spectral region. Dispersion and
dispersion slope are completely compensated before each EDFA using an ideal fiber grating. Power per channel is 0
dBm at the output of each EDFA and the EDFA spacing has been set to 50 km. The SRS induced tilting can be clearly
observed from the optical power spectrum. The OSNR estimation at each fiber span shows the performance degradation
of the lowest channel and the performance improvement of the highest channel.

1.8.2 Raman Amplifier (RA)

The first two examples illustrate the effect of Rayleigh scattering in Raman amplification. The third example explores an
upgrade from a single to a multi- channel system, along with a comparison of using an EDFA and/or a RA.
ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier

simple_noisy

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Simple_noisy
This example illustrates that there exists an optimum pump power for for Raman Amplification and its independence on
the fiber length.
A 10 Gb/s NRZ signal is launched onto 3 separate fiber spans. All of spans have the same characteristics, except for
different lengths (50, 100 and 150 km). The counter- propagating pump power (1454 nm) is varied from +18 to +30
dBm through parametric runs. For each case the optimal pump power (correspondent to the maximum Q-factor value) is
around 28 dBm.

simple_rayleigh_noisy

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Simple_rayleigh_noisy
This example illustrates the importance of considering Rayleigh scattering of ASE noise in the analysis of Raman
Amplifiers.
A 10 Gb/s NRZ signal is launched onto 2 different fiber spans (100 km) with identical characteristics, except for the
Rayleigh scattering factor (“capture factor”). For the first span the noise reflections are not considered. For the second
span, the Rayleigh scattering is considered in a realistic way employing a "capture factor", different from 0, where the
capture factor is the fraction of scattered photons that are back-scattered. The counter- propagating pump power
(1454 nm) is varied from +18 to +30 dBm through parametric runs. If scattering is not considered, the Q value grows
with increasing of the pump power. If the scattering is considered, an optimum value for the pump power is shown at
+28 dBm.

upgrade

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Upgrade
This example demonstrates a possible single- to multi- channel upgrade employing Raman amplification.
In the first system a 10 Gb/s single-channel signal is launched onto a fiber (D= 4 ps/nm/km) link of 150 km. The system
works at the sensitivity limit. To upgrade the system, the power-budget at the receiver must increase employing an
optical preamplifier. Two alternatives are explored: an EDFA or a RA. Two 10-channel WDM systems are shown

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 25

employing respectively an EDFA and a RA. EDFA gain and RA counter propagating pump are determined to obtain the
same optical gain for both the system configurations. A multiple run has been carried on to search the optimum RA
configuration. The simulation results show that the RA with a pump power of about +26 dBm is the optimal
configuration. In this case the Q factor is greater than 20 B for all the three monitored channels. Using a configuration
based on an EDFA preamplifier (NF=3 dB) with equivalent gain=23.5 dB the Q value is 17.9 dB only for the worst
monitored channel.

Multipump

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Multipump
This example shows a comparison between three different Raman configurations.
8 WDM channels at 10 Gb/s and with 100 GHz spacing, are launched simultaneously in three different branches. In each
of them, a 25 km fiber link with loss=0.2 dB/km and D=-2 ps/nm/km is used. In the upper branch, the fiber is pumped by
a 500 mW counter-propagating pump at 1465 nm. In the middle one, it is pumped by two counter-propagating pumps
(P=200 mW @ 1427 nm and P=300 mW @ 1495 nm). Finally in the lower branch, the fiber is pumped by seven pumps
ranging from 1427 nm to 1495 nm. After the simulation it is possible to notice how the Raman gain provided changes. In
the seven pumps case a quite flat gain is obtained in the bandwidth occupied from the 8 channels.

Raman_96ch_3pump

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Raman_96ch_3pump
This example illustrates how to obtain a flat Raman gain in a wide bandwidth using the Raman multipump configuration.
A 96DWDM system at 10 Gb/s with frequency ranging from 185.8 THz to 195.3 THz and channel spacing equal to 10
GHz is simulated. The 96 channels are propagated into 10 fiber spans composed by 70 km of DS Anomalous fiber
Raman pumped and 1.75 km of DCF. A configuration with 3 pumps at 1430 nm, 1475 nm and 1520 nm with
respectively 550 mW, 170 mW and 90 mW is used to provide a flat gain into a broad bandwidth
(10 THz).

Gain_Saturation

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Gain_Saturation
In this example saturation of the Raman gain is observed for input powers exceeding 2 dBm.
A CW signal source, consisting of a laser operating at 1547 nm with a linewidth of 50 MHz, is launched into a 9 km
fiber with D=-2 pumped by a single counter-propagating pump at 1455 nm. For this pump the power is variable (1550
mW, 1250 mW, 1070 mW and 850 mW). Varying the booster output power, from –20 mW to 31 mW, it is possible to
observe how the Raman gain varies and saturates due to the pump depletion.

Raman_Co_Counter

ProductInstDir/examples/optsim/sample_mode/Raman/Amplifier/Raman_Co_Counter
In this example two different Raman configurations are compared. In the first case a fiber pumped with a single counter-
propagating pump is used, in the second one a co-propagating pump amplifies the counter-propagating pump which, in
turn, amplifies the signal launched into the fiber.
The signal consists of two WDM channels at 10 Gb/s with a channel spacing of 100 GHz. The propagation link is
composed by three spans: 100 km of DS Anomalous fiber, 30 km of Raman pumped fiber and an ideal fiber grating to
compensate the dispersion. The Counter-propagating pump is at 1453 nm with a power of 500 mW, the Co-propagating
is at 1365 nm with a power variable from 0 to 500 mW.

26 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.9 WDM systems
The WDM System examples illustrate several WDM configurations that can be designed and simulated in OptSim. By
going through these examples, the user can learn more about the use of the Compound Components, variables and
special simulation techniques.
ProductInstDir/examples/optsim/sample_mode/WDM

WDM_4ch

ProductInstDir/examples/optsim/sample_mode/WDM/WDM4
This is a simple example of a 4-channel WDM system.
Four signals NRZ modulated at the 2.488 Gb/s SONET/SDH rate, are transmitted over a medium haul link with 1 nm
spacing. The four signals are preamplified by an EDFA booster and transmitted over a sequence of two DS fiber spans of
100 Km each. The fiber spans have opposite dispersion signs (D=+/- 2.16 ps/nm/km) resulting in ideal dispersion
compensation at the middle of the simulated bandwidth. A second EDFA is used in the receiver section as a preamplifier.
Two of the four channels are detected and their spectra, eye-diagrams and Q-values are evaluated.

WDM_32ch

ProductInstDir/examples/optsim/sample_mode/WDM/WDM32
This is a simple example of a 32-channel WDM system.
Thirty-two signals, NRZ modulated at 10 Gb/s, are transmitted over a medium haul link. The 32 channels are spaced at
100 GHz. The input signal spectrum occupies a bandwidth of 3.2 THz. The signals are preamplified by an EDFA booster
and transmitted over DS- anomalous fiber of 250 Km. Dispersion and dispersion slope are completely compensated
before each in- line EDFA using an ideal fiber grating. Power per channel is set to 0 dBm at the output of each EDFA
and the EDFA spacing has been set to 50 km. At each span, the optical power spectra and OSNR are evaluated in order
to follow the signal evolution along the transmission path. At the receiver section, the performance of four of the 32
channels is evaluated using the optical spectra, eye diagrams, BER and Q value measurements. Note that the channels at
the highest and lowest ends of the spectrum have the best performance.

WDM_64ch

ProductInstDir/examples/optsim/sample_mode/WDM/WDM64
This is a example of a 64- channel WDM system.
Many of the system characteristics are the same as the WDM_32ch example. In this case the transmitted signal is
composed of 64 channels with a channel spacing of 100 GHz for a total bandwidth of 6.4 THz. The 64 channels are
launched over DS- anomalous fiber of 200 Km. Note the degradation of channel performance compared the WDM_32ch
example.

WDM_96ch

ProductInstDir/examples/optsim/sample_mode/WDM/WDM96/full
ProductInstDir/examples/optsim/sample_mode/WDM/WDM96/channels_2
This is a example of a 96- channel WDM system employing two different Variable Bandwidth Simulation (VBS)
techniques.
The WDM signals are NRZ modulated at 10 Gb/s and transmitted over a sequence of 4 DS fiber spans of 50 km each.
The 96 channels are spaced at 0.8 nm. The signal is preamplified by an EDFA booster. The fiber spans have alternating

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 27

dispersion signs (D=+/- 1.5 ps/nm/km) in order to obtain an ideal dispersion compensation at the middle of the simulated
bandwidth. For each span, the optical power spectra and OSNR are evaluated to follow the signal evolution along the
transmission path. At the receiver section, the performance of 5 of the 96 channels is evaluated using the electrical
Scope.
To make an initial check of the system performance, a simulation is performed over a reduced bandwidth of 2 nm, as
shown in ProductInstDir/examples/WDM/WDM96/channels_2/WDM_96ch.opf. This bandwidth allows a check of only
two channels. In the second case, ProductInstDir/examples/WDM/WDM96/full/WDM_96ch.opf, the whole system
bandwidth is simulated.

nortel4ch2

ProductInstDir/examples/optsim/sample_mode/WDM/Nortel
This example reproduces an experiment that was performed by NORTEL and presented at OFC '97. See post-deadline
paper PD20.
A 4- channel WDM signal at 40 Gbit/s is transmitted over 240 km of fiber. The data is RZ encoded. In the Nortel
experiment, a residual dispersion of –24 ps/nm is present at 1557 nm, whereas the full dispersion compensation is
applied in the OptSim example. The spectrum shows there is no FWM as was reported in the Nortel paper. A fairly low
value of fiber non- linear coefficient is used (1.2 1/W/km) in the simulation. As it turns out, the system is able to
withstand a much higher gamma (try it yourself!). The Q value turns out to be at least 22 dB.

16Ch 4Add-Drop

ProductInstDir/examples/optsim/sample_mode/WDM/16Ch_4OADM/16Ch_4OADM.opf
This example describes a 9.953 Gb/s 16 channels WDM system with a 4-channel OADM put in the middle of the fiber
link.
The transmitter consists of 16 laser sources with wavelength ranging from 193.035 THz to 193.785 THz, the channel
spacing is set to 50 GHz. The optical signal is launched onto a 200 Km fiber link. Along the fiber link, after 100 km, a 4-
channel OADM is used to select and to add channels. The dropped channels are detected by the receivers with an
appropriate electrical filtering. The added Channels are propagated together with the other ones and detected at the end
of the fiber link.

1.10 EDFA
These two examples show practical applications of the predefined EDFAs included in the component library.
ProductInstDir/examples/EDFA

C+L_bands_EDFA

ProductInstDir/examples/EDFA/wideband
This example illustrates the wideband application of EDFA, which includes both C- and L-band.
The predefined compound component models for EDFA for 10 dB gain in C- and L- bands with typical data for gain and
noise figure are used.
The transmitter section consists of two sets of 32-channels transmitters used for in C- and L-band. All channels are NRZ
signals with 100 GHz spacing. In C- bands the channels range is 1537-1562 nm and in L-band - 1575-1600 nm, i.e. total
of 50 nm of bandwidth is utilized.

28 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The combined signal is launched into the transmission link. Before being amplified, the signal goes through a
demultiplexer, which splits it again in C- and L- band portions. Then each part of the signal is amplified by the
corresponding C- or L-band EDFA. Finally both signals are coupled/multiplexed back together.

EDFA_WDM_WithGainEqualization

ProductInstDir/examples/EDFA/GEF
This example illustrates the application of wideband EDFA in WDM systems. The predefined compound component for
EDFA with 10dB fixed gain using manufacturing parameters of OFS HE980 EDF is used.
A 32-channel Transmitter generates 32 NRZ-modulated optical signals with total power 3 dBm with 100 GHz channel
spacing covering 25-nm bandwidth. This optical signal propagates into four spans where each span consists of a fiber
span (50 km long and with 10dB attenuation) and an EDFA. The EDFAs provide a gain across the bandwidth with 10dB
average gain and a gain shape variation peak-to-peak of about 1dB. Hence the accumulated gain variance after 4 spans
will reach about 4 dB and may cause power penalty at the receiver.
To reduce power penalties, an optical filter is used after the last amplifier. This filter is called Gain Equalization (GEF)
and is based on a user-defined data file with spectral shape equivalent to the inverted shape of 4 cascaded amplifiers.
Comparing the optical spectrum after GEF with the one after the last amplifier, one can see that the gain shape variation
reduced from 4 dB to less than 1 dB.
Selected 3 out of 32 channels are demultiplexed and sent to Receivers to demonstrate performance of these channels with
gain equalization.

1.11 SOA
ProductInstDir/examples/SOA

SOA_SingleChan_17dB

ProductInstDir/examples/SOA
This example demonstrates SOA amplification in the single channel case. The SOA model used is the predefined
SOA_26dB component. The SOA provides a gain of 26dB.
With SOA amplification after 90km standard single-mode fiber, the BER tested is around 10-16 whereas the BER without
SOA would be very high.
The detected signal presents intersymbol interference (ISI) due to the chromatic dispersion in the fiber, therefore a
pattern length of 3 is used in the BER estimator.

SOA_SingleChan_26dB

ProductInstDir/examples/SOA
This example demonstrates SOA amplification in the single channel case. The SOA model used is the predefined
SOA_17dB component. The SOA provides a gain of 17dB.
With SOA amplification after 90km standard single-mode fiber the BER tested is around10-17 whereas the BER without
SOA would be very high.
The detected signal presents intersymbol interference (ISI) due to the chromatic dispersion in the fiber, therefore a
pattern length of 3 is used in the BER estimator.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 29

SOA_4ch_WDM_17dB

ProductInstDir/examples/SOA
This example demonstrates SOA amplification in multi-channel situation. The WDM system under study has four
channels covering wavelength from 1547.6 to 1550 nm with channel spacing of 100 GHz The SOA model used is the
predefined SOA_17dB component. The SOA provides a gain of 17dB. All 4 channels have been filtered out and
detected, all showing a bit error rate of 10-13 or better. The detected signal presents intersymbol interference (ISI) due to
the chromatic dispersion in the fiber, therefore a pattern length of 3 is used in the BER estimator.

SOA_4ch_WDM_26dB

ProductInstDir/examples/SOA
This example demonstrates SOA amplification in multi-channel situation. The WDM system under study has four
channels covering wavelength from 1547.6 to 1550 nm with channel spacing of 100 GHz The SOA model used is the
predefined SOA_26dB component. The SOA provides a gain of 26 dB. All 4 channels have been filtered out and
detected, all showing a bit error rate of 10-13 or better. The detected signal presents intersymbol interference (ISI) due to
the chromatic dispersion in the fiber, therefore a pattern length of 3 is used in the BER estimator.

SOA_Switch.opf

ProductInstDir/examples/SOA
This example simulates the SOA as a switch. The SOA uses the default values of all parameters. When the “Bias
Current” is set as very small (say, 1e-20, in this example), the SOA is in the “off” state, which is simulated by the SOA
in the upper arm. When the “Bias Current is set as normal (100mA in this example), the SOA is in the “on” state, which
is simulated by the SOA in the lower arm where the SOA operates as an amplifier. The isolation and amplification the
SOA provides are around 21 and 17 dB respectively. As expected, the BER is very high when the swith is turned off.
When the switch is turned on, the BER measured is around 1e-32.

1.12 Network Components

The Network Component examples illustrate simple applications of the network component available in OptSim.
ProductInstDir/examples/optsim/sample_mode/Networks

1.12.1 Optical Add-Drop Multiplexing (OADM)

These examples illustrate typical uses of the OADM component. It is available in the predefined compound component
library.
ProductInstDir/examples/optsim/sample_mode/Networks/OADM

OADM_simple

ProductInstDir/examples/optsim/sample_mode/Networks/OADM_simple
This simple example illustrates the basic use of the OADM component.
An 8-channel WDM signal is applied to the input of the OADM component, which drops and adds a signal at the fourth
channel. By varying the OADM cross- talk value it is possible to observe changes in the add- drop channel amplitude.

30 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

OADM_net1

ProductInstDir/examples/optsim/sample_mode/Networks/OADM_networks/network1
This is another example of the use of an OADM component.
The system characteristics are the same as the OADM_example, above. However, in this case the OADM is placed at the
20 km point of a 60 km link. The performance of the add- drop channel is compared with the other channels at the
receiver section.

OADM_net2

ProductInstDir/examples/optsim/sample_mode/Networks/OADM_networks/network2
This example illustrates a multi channel add- drop multiplexer component, a more complicated system configuration
than the previous OADM_net1 example.

Figure 1. Topology for OADM in the network

A 16- channel WDM OC- 192 signal is transmitted over a medium haul link (Fig. 1). The 16 channels are spaced at 50
GHz. The signal is pre-amplified by an EDFA booster and transmitted over DS fiber of 200 Km. A four-channel
add/drop is placed in the middle of the link. The transmitter and receiver subsystems are in compliance with the SONET
standard. The fiber dispersion is varied from 0.1 to 4 ps/nm./km through parametric runs. In this way the system
performance can be optimized in terms of fiber dispersion. Channels 13, 14, 15 and 16 are dropped at the OADM and
channels 1, 5, 9 and 13 are detected at the receiver end. At the receiver section, channels are monitored for Q-value in
order to discover the optimum dispersion value of 2 ps/nm/km.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 31

 Figure 2. Received eye (top), corresponding histogram (middle), the Q-factor and eye closure as functions of dispersion coefficient
for Channel 5 (bottom). For the top and bottom sets of plots, the left hand plots correspond to 0.1 ps/km.nm and the right ones
correspond to 2 ps/nm.km

The reader is requested to observe output at each analyzer to understand the corresponding states of signals and spectra.
As an example, Fig. 2 shows an eye diagram, corresponding histogram of samples and the Q-factor plot for Channel 5.

32 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.12.2 Optical Circulator

optical_circulator

ProductInstDir/examples/optsim/sample_mode/Networks/Circulator
This example illustrates the functionality of the optical circulator component as implemented as a predefined compound
component in the OptSim library.
A separate NRZ 10 Gb/s signal is connected to each of the input ports of the circulator. Each signal is at a different
frequency. At each output port the optical power spectrum shows the presence of two different channels. One is the
signal propagated in the clockwise direction toward this output port, the other is the rejection contribution. Note that the
rejection contribution decreases with the increase of the rejection parameter of the circulator component. For more
information see the component description in the OptSim Component Library.

1.12.3 Optical Mu- Demultiplexing

demux

ProductInstDir/examples/optsim/sample_mode/Networks/Optical_Mu-Demultiplexer
This simple example illustrates the use of the demultiplexer component as implemented as a predefined compound
component in the OptSim library.
An 8-channel WDM signal at 10 Gb/s is directly transmitted into the input of the demultiplexer component, in a back-
to- back (no fiber) configuration.

1.12.4 Wavelength Converter

These examples illustrate the simple use of the two wavelength converter components available in the predefined
compound component library.
ProductInstDir/examples/optsim/sample_mode/Networks/Wavelenght_converter

WC-XPM_example

ProductInstDir/examples/optsim/sample_mode/Networks/Wavelenght_converter/WC-XPM
This example illustrates a wavelength converter based on the Cross Phase Modulation (XPM) effects of the
semiconductor optical amplifier and Mach-Zehnder interferometer.
A single- channel NRZ signal (1.25 Gb/s) at 1549 nm is converted to 1550 nm. The comparison of the eye diagrams of
original and converted signal shows a reduction in the extinction ratio (ratio between the high level value and low level
value of the electrical signal). Using the extinction ratio as a figure of merit, a XPM-based converter performs better than
a XGM-based wavelength converter (see WC- XGM_example below). For more information see the component
description in the OptSim Component Library.

WC-XGM_example

ProductInstDir/examples/optsim/sample_mode/Networks/Wavelenght_converter/WC-XGM
This example illustrates a wavelength converter based on the Cross Gain Modulation (XGM) effects of the
semiconductor optical amplifier.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 33

A single- channel NRZ signal (1.25 Gb/s) at 1549 nm is wavelength converted to 1550 nm. The comparison of the eye
diagrams of the original and converted signal shows a reduction of the extinction ratio. The electrical probe shows that
the converted signal is inverted with respect to the original signal: this is the characteristic behavior of wavelength
conversion based on XGM gain saturation. For more information see the component description in the OptSim
Component Library.

1.12.5 Optical Cross Connector

OXC_cross_talk

ProductInstDir/examples/optsim/sample_mode/Networks/OXC
This example illustrates the use of the optical Cross Connector (OXC) component implemented as predefined compound
component in the OptSim library.
Two 4-channels WDM signals at 10 Gb/s are at the input of a 2x2 OXC (an OXC with 2 input ports and 2 output ports).
The total power of the two signals differs for 3 dB. In this way it is possible to recognize at the output ports the origin of
each channel.
The cross-talk parameter is set from 100 to 5 dB through parametric runs. The optical power spectrum at each output
port shows the increase cross-talk effect.

1.12.6 Ring Configuration

Ring Configuration

ProductInstDir/examples/optsim/sample_mode/Ring/Ring.opf
This example illustrates how to simulate a Ring Configuration with an unrolled equivalent configuration using the
iteration feature.
A very low noise feeds an iterate block and each span represents a loop cycle. Increasing the number of iterations it is
possible to improve the simulation accuracy. Three nodes compose the ring and at each node a channel is added and
another channel is dropped. The analysis of results is made by mean of the measurement blocks inserted in the iterate
block. In this way it is possible to analyze the signal evolution (Spectra, Eye Diagrams) at each round in the loop. The
latest iteration represents the most accurate evaluation of the “steady-state” signal.

1.13 CATV
These examples illustrate the available features in OptSim for the modeling and simulation of digitally modulated CATV
links.
ProductInstDir/examples/optsim/sample_mode/CATV

CATV_QPSK

ProductInstDir/examples/optsim/sample_mode/CATV/CATV_QPSK
This example shows CATV transmission using the QPSK modulation format.
A 4- channel transmitter generates QPSK encoded sub-carrier signals at 30 Mb/s in the 1 GHz range. The electrical
signal is sent to an external optical modulator and directly detected, in a back- to- back (no fiber) configuration. The non-
linearity introduced by the external modulator gives rise to clipping effects that can be seen both on the received eye
diagram and received spectra.

34 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

CATV_QPSK_tx

ProductInstDir/examples/optsim/sample_mode/CATV/CATV_QPSK
This example illustrates CATV transmission using the QPSK modulation format.
The system characteristics are the same of the CATV_QPSK model. In this case, however, the optical modulated signal
is transmitted over 2 km of DS fiber. At the receiver section, the scattering diagram is measured. The received scattering
diagram is seen to be rotated due to the fiber propagation.

CATV_16QAM

ProductInstDir/examples/optsim/sample_mode/CATV/CATV_16QAM
This example illustrates CATV transmission using the QAM modulation format.
In this example, the transmitter generates a 16QAM encoded sub- carrier signal at 0.8 Gb/s. The electrical signal is sent
to an external optical modulator and is subsequently directly detected, in a back- to- back (no fiber) configuration. The
sub- carrier channel is filtered and demodulated. This project is a useful example of the use of a QAM demodulator.
Using the Logical Signal Displayer component it is possible to compare the transmitted and received information.

CATV_PSK_subcarrier

ProductInstDir/examples/optsim/sample_mode/CATV/CATV_PSK_subcarrier
This example illustrates CATV transmission using the PSK modulation format.
An 8- channel transmitter generates 4-PSK encoded sub-carrier signals at 50 Mb/s. The electrical signal is sent to an
external dual arm modulator where at one arm a fixed voltage is applied. The signal is directly detected, in a back- to-
back (no fiber) configuration.

CATV_PSK_subcarrier_direct

ProductInstDir/examples/optsim/sample_mode/CATV/CATV_PSK_subcarrier_direct
This example illustrates CATV transmission using the PSK modulation format.
The system characteristics are the same of the CATV_PSK_subcarrier model. In this case the electrical signal directly
modulates the laser, instead of using an external modulator.

1.14 FTTH System with Broadband PON Access

Architecture.
ProductInstDir/examples/optsim/sample_mode/CATV/FTTH

Design and deployment activities for FTTH (fiber-to-the-home) and FTTP (fiber-to-the-premises) access networks are
on the rise in order to support the increasing demands and delivery of new multimedia services to the customer premises
such as interactive video, voice, and high-speed Internet.
There are many types of FTTH technologies; the most popular one is based on the concept of using a passive fiber
distribution network, known as a passive optical network (PON). FTTH employing PON access architecture is the
accepted choice of delivery channel for triple-play services (voice, video and data) from service providers to the home
and business users. Three major PON technologies are currently under consideration as the basis for FTTH
deployments: Broadband PON (BPON), Gigabit PON (GPON), and Ethernet PON (EPON).

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 35

Broadband PON is the most mature and widely used among them to the date. BPON is a set of standards that specify the
service capabilities and network protocols for broadband services over fiber access. It is specified by the ITU-T, and
published in the G.983.x series of ITU-T recommendations.
In a PON, the active optoelectronics are situated on either ends of the passive network. An optical line termination
(OLT) device is installed in the central office (CO), and an optical network termination (ONT) device is installed on the
other end, in or near each home or business site. Fiber distribution is done using a tree-and-branch architecture. A single
fiber connected to the OLT can be split up to 32 times and connected to multiple ONTs.
Current simulation example models a typical BPON FTTH design with 32 subscribers and 20-km reach. Figure 1
depicts the OptSim schematic for example layout. The Central Office is connected through a 15-km standard single-
mode fiber to the first Remote Node with a 1:4 splitter. Each of the four outputs goes through another 4.5-km fiber and
then enters the Remote Node with a 1:8 splitter. Outputs from the 1:8 splitter are connected to eight end-users at the
ONT though drop-off cables of length varying from 100 to 900 feet.
The triple-play service is realized as a combination of data, voice, and video signals. To optimize the bandwidth in
BPON the transmission through the optical fiber path employs the CWDM technique with data and voice component
transmitted at wavelengths in the range of 1480-1500 nm, and video within the 1550-1560 nm range. The high-speed
internet component is represented by a data link with 1.25 Gb/s downstream bandwidth. The voice component can be
represented as VOIP service (voice over IP, packet-switched protocol), which is gaining popularity as an alternative to
traditional PSTN (public switched telephone network) with POTS (plain old telephone service) at the customer end. The
video component is represented as a 16-QAM subcarrier multiplexed (SCM) system. Actually, 64-QAM is more typical
modulation scheme used to carry digital video/data stream in RF channels but we used 16-QAM for simplicity. Also for
simplicity purpose this simulation example models only a downstream link with one ONT unit attached. As an exercise
the reader can add more ONT units and re-run the simulations.
Figure 2 shows the signal spectrum output from OLT with data/voice signal at 1500 nm and video signal at 1550 nm.
Figure 3 demonstrates 4-level logical signal and signal constellation plot for 16-QAM encoder.
The signal from the central office travels though a 20-km long fiber distribution network and arrives at optical network
termination unit. The optical spectrum at the input to ONT is shown at Figure 4. Here the optical signal first
demultiplexed into data/voice and video components. The data component goes to the optical receiver, PIN. Optical
power meters inserted after transmitters and before receivers show that total attenuation from fiber spans and splitters is
about 29 dB and input power to the receiver is about –25 dBm. The receiver eye diagram for data signal is given at
Figure 5. The video component of the received signal enters 16-QAM decoder. Figure 6 shows 4-level logical signal and
signal constellation plot at the received side of 16-QAM decoder. Figure 7 shows multi-level eye-pattern and electrical
signal RF waveform at 16-QAM decoder.

36 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 1. Layout for FTTH BPON system.

Figure 2. Output spectrum from Central Office.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 37

 Figure 3. Signal constellation (left) and 4-level logical signal (right) at 16-QAM encoder.

Figure 4. Received eye diagram for data signal

Figure 5. Received eye diagram for data signal

38 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 6. Signal constellation (left) and 4-level logical signal (right) at 16-QAM encoder.

Figure 7. Eye-pattern (left) and output electrical signal (right) at 16-QAM encoder.

In conclusion, the given example allows user to study various performance characteristics and its dependence of
components characteristics and layout’s specifics in physical layer design for BPON FTTH network.

1.15 Soliton Transmission

These two examples illustrate the possible ways to generate soliton pulses and the evaluate soliton transmission
performance.
ProductInstDir/examples/optsim/sample_mode/Soliton

soliton_generation

ProductInstDir/examples/optsim/sample_mode/Soliton
This example shows two possible ways to generate soliton pulses.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 39

In one case, soliton pulses are generated by applying RZ electrical pulses to an amplitude modulator, which transmits a
CW optical signal. In the second case, an optical pulse generator is used to directly generate the optical soliton pulses.

soliton_transmission

ProductInstDir/examples/optsim/sample_mode/Soliton
This example illustrates the transmission of soliton pulses.
A 5 Gb/s soliton signal is launched onto 20 spans of fiber, each 50 km long. The fiber loss is recovered by a 980- nm
pumped EDFA after each span. The comparison between the received and transmitted signals through their eye diagrams
shows that the fiber propagation does not distorce the transmitted pulses.

1.16 Duobinary Modulation

duobinary_comparison

ProductInstDir/examples/optsim/sample_mode/Duobinary
This example compares a simple IMDD system and a duobinary system.
Duobinary modulation (upper model) is implemented by driving an external dual arm modulator with opposite phase
signals. In the lower model, a NRZ signal is directly generated. In both cases, the modulated optical signals are
transmitted over 100 km of standard single mode fiber. The eye diagram at the receiver section is less distorted for the
duobinary model compared with the NRZ model.

1.17 Chirp
This section groups the OptSim examples on Chirp factor.
ProductInstDir/examples/optsim/sample_mode/Chirp

1.17.1 Chirp Measurement

chirp_measuremet

ProductInstDir/examples/optsim/sample_mode/Chirp_measurement
This example illustrates the measurement of the chirp parameter α of an electro- absorption modulator as illustrated in
[6].
The method employed to measure chirp is based on a small signal bandwidth measurement over a given length of a
standard fiber. The frequency response of the fiber exhibits sharp peaks arising from interference of modulation
sidebands at frequency values that depend on the chirp factor and can be analytically calculated performing a small-
signal computation. This analytical law is reported in [6]. In this example, the modulator chirp factor has stepped through
–1, 0 and 1 using the parametric run feature in OptSim. At the receiver section the electrical power spectrum shows the
peaks in complete agreement with theory.

40 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.17.2 Chirp Analysis

Externally Modulated Laser

ProductInstDir/examples/optsim/sample_mode/Chirp/Chirp_analysis/External_mod/Externally_modulated
_laser.opf
In OptSim it is possible to make a Post-Processing Chirp Analysis using the Optical Probe Data Display Window.
This example shows how to relate the Instantaneous Optical Power, the Instantaneous Phase Deviation and the
Instantaneous Frequency Deviation in order to estimate the Chirp impact on the externally modulated laser.
The laser output is externally modulated using two different Amplitude Modulators. The differences between them are in
terms of Chirp factor value (0 for the No_chirp modulator, 1.5 for the Chirp modulator) and Extinction Ratio value (Ideal
for the No_chirp modulator, Realistic for the Chirp modulator).
In the first Optical Probe (No_chirp) the frequency variations are caused only by the phase noise (depending on the laser
linewidth). This noise appears only when the signal is different by the zero level (check the Power in the Chirp Analysis
section of the Instantaneous Phase Deviation and Instantaneous Frequency Deviation). The phase is almost flat, only the
small random fluctuations are present where the signal is different by the zero level.
From the second Optical Probe (Chirp) it is possible to note that the Optical Spectrum is wider than the previous case.
The Instantaneous Phase varies linearly with the Power, besides the fluctuations depending on the linewidth (check the
Power in the Chirp Analysis section of the Instantaneous Phase Deviation). The Instantaneous Frequency varies
following the well known relation:

1 dφ
∆f = − ⋅
2π dt
where φ is the Instantaneous Phase. When the phase is constant, the frequency deviation is 0, whereas, when the phase
varies, the frequency deviation has a peak, that is positive if the phase goes up and negative if the phase goes down
(check the Phase in the Chirp Analysis section of the Instantaneous Frequency Deviation).

Directly Modulated Laser

ProductInstDir/examples/optsim/sample_mode/Chirp/Chirp_analysis/Direct_mod/Directly_modulated_las
er.opf
This example shows how to relate the Instantaneous Optical Power, the Instantaneous Phase Deviation and the
Instantaneous Frequency Deviation, in order to estimate the Chirp impact on the directly modulated laser.
In this case there are the same two phenomena as it is described in the previous one example (phase noise, frequency
deviation with power slope), but, moreover, are added the direct modulation effects. In fact the lasing frequency depends
on the effective cavity length. By changing the injection current, the refractive index varies and then also the effective
cavity length changes.
The frequency deviation has still the peaks where the power rises or falls quickly, but when the power is constant then it
is not zero anymore (check the Power in the Chirp Analysis section of the Instantaneous Frequency Deviation). The
frequency has two different values, one for the “logical zero” and one for the “logical one”. In The Optical Spectrum it
is possible to observe two peaks corresponding to the stable frequency level.
The difference between the two branches (low_chirp and high_chirp) is in the linewidth parameter. The lower Optical
Spectrum shows a Spectrum with two well distinct peaks, since the linewidth is bigger in this case.

1.18 Microwaves on Fiber Optics (MFO)

These two examples explore the use of Microwaves on Fiber Optics (MFO) using single or multi- tones.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 41

ProductInstDir/examples/optsim/sample_mode/Microwave

MOF_single_tone

ProductInstDir/examples/optsim/sample_mode/Microwave
This example illustrates the analysis of a single- tone MFO system, comparing four different system set- ups. The four
set-ups use a different combination of laser modulation (external or direct) and optical preamplifiers (EDFA or SOA).
MOF system analysis requires the estimation of the electric- optical- electric frequency response in terms of S21 and 2nd
harmonic generation. A single tone modulates a laser output using two different approaches: direct (1549.5 nm) and
external (1550.5 nm) using a Mach- Zehnder modulator. The modulation frequency is varied from 1 to 20 GHz through
parametric run. Propagation is modeled with an attenuator since MFO systems are usually employed over short
distances. At the receiver section, the two channels are splitted, amplified (with an EDFA or SOA) and detected.
To monitor the detected signals an ESA and two narrow bandwidth electric power meters have been placed. The power
meters measure the power at the frequency of the modulating tone and its double. Therefore, sweeping with multiple
runs the modulating tone frequency and then selecting the popup menu command View Chart on the power meters, the
frequency response (S21) can be measured as well as the second harmonic generation.
Using this technique the MFO system can be tested in terms of S21 and multiple harmonic generation.

MOF_multi_tone

ProductInstDir/examples/optsim/sample_mode/Microwave
This example illustrates the analysis of a multi- tone MFO system, again comparing four different system set- ups.
The system characteristics are the same as the MOF_single_tone example. In this case, however, two modulating tones
are employed. The frequency of one tone is varied from 1 to 20 GHz through parametric runs, while the other one is
fixed at 5 GHz. Therefore, in addition to S21 and the 2nd harmonic, the tird-order intermodulation tones and third
harmonic tones may be monitored.

RoF

ProductInstDir/examples/optsim/sample_mode/Microwave

The purpose of this application note is to illustrate how easily OptSim allows simulation of radio-over-fiber transmission
with different but most commonly used approaches and implementation variants.
The layout for this example looks like:

42 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Fig. 1 Layout

The central station (CS) transmits optical intermediate (IF) and local oscillator (LO) signals to the remote node where
amplification and optional wavelength conversion takes place. The demodulated channels are transmitted to remote
antenna stations (RAS) covering each cell that can also be microcells or picocells depending upon the architecture.
This example shows different implementation approaches for transmitting DPSK-encoded multiple data channels and
local oscillator frequencies over a common optical fiber and optionally how to achieve simultaneous wavelength
conversions while keeping crosstalk penalties at minimum. The suggested implementation as shown in above figure uses
a single wavelength converted (thereby reducing component count) based on semiconductor optical amplifier based
Mach-Zehnder Interferometer (SOA MZI). In a similar way, on the receiving side, two approaches are shown – one
where a free-running local oscillator is employed to isolate carrier frequency and to obtain data channel; and the other
where a re-use of the detected oscillator signal is used thereby saving on the number of components (however, the
recovery needs to be jitter free in this case).
IF1 and IF2 are WDM data channels with DPSK-encoded data and modulated using electro-absorption modulators
(EAM). Each data channel transmits 1Gbps data that is DPSK-encoded over 2.5GHz carrier. The WDM architecture is
preferred due to its potential to support a large number of RASs.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 43

Figure 2 shows data (upper) and DPSK-modulated electrical signal (lower) and fig. 3 shows modulated optical signal
(upper) and back-to-back demodulated data (lower) – all for IF2.

Fig. 2 Data signal (upper) and DPSK-encoded Electrical Carrier (lower) at IF2

44 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Fig. 3 Modulated optical signal (upper) and back-to-back demodulated data

At the RN, EDFA-based or SOA-based amplifying scheme can be employed. The layout of fig. 1 shows an optional
wavelength converter using SOA MZI. This wavelength converter acts on all incoming signals including LO signal
(25MHz) which is kept at high power compared to data signals if wavelength conversion is required. LO power can be
scanned to optimize for crosstalk if the user wants and the RAS uses detection schemes as shown in Section A arms of
the project layout. For the rest of the analysis below, since the crosstalk levels due to SOA-MZI are maintained very low,
we use an alternative approach (arms under the Section A) to correctly detect data. In this case, two other options are
available, both of which are simulated. One uses a free-running oscillator and the other uses a low-jitter recovered LO as
inputs to the multipliers. The post-multiplier filters isolate the 2.5GHz electrical carrier which then is fed to the DPSK
demodulator to recover the transmitted data.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 45

For the IF2 cell at the RAS, fig. 4 shows (a) input to the second multiplier (b) output at the second multiplier (note that
the LO is isolated) and (c) filtered output.

(a)

(b)

46 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 (c)

Fig. 4 IF2 cell electrical spectra at (a) the input of second multiplier (b) the output of second multiplier and (c) bandpass filtered
output

Corresponding DPSK-demodulated data are recovered from the free running local oscillator case [Fig. 5(a)] and for the
re-use of recovered LO case [Fig. 5(b)].

(a)

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 47

 (b)
Fig. 5 Received data for (a) free-running and (b) recovered LO cases

Comparing figures 5 to figure 3, we conclude that the radio-over-fiber transmission was successful and error-free.

Reference
Ho-Jin Song, Jeon Seon Lee, and Jong-In Song, “Error-free simultaneous all-optical upconversion of WDM radio-over-
fiber signals,” IEEE Photonics technology Letters, vol. 17, Issue 8, August 2005, pp. 1731-1733.

1.19 Signal Regeneration

OEO_2R

ProductInstDir/examples/optsim/sample_mode/Signal_regeneration
This example illustrates optical- electrical- optical (OEO) signal regeneration using OptSim. In this design, we explore
2R regeneration, i.e. a system that regenerates the signal without clock recovery.
A NRZ single- channel signal at 10 Gb/s is transmitted over 5 spans of standard single mode fiber (D=16 ps/nm/km).
Each span (50 km) is followed by an OEO WC-remodulator. The remodulator is a standard IMDD receiver, which
generates a logical output signal corresponding to the input optical signal level. The conversion is performed by
comparing the electrical signal amplitudes to a threshold level, which results in logical high and low levels. At each OEO
regeneration, the signal is converted to a different wavelength from the set (1549.8, 1550.0, and 1550.2 nm) as may
happen in a practical WDM network. The simulation performs multiple runs with different values for the regenerator
threshold. In this way it is possible to obtain the optimum threshold level corresponding to the maximum Q-factor. It is
worth noticing that, due to fiber dispersion, this system would have a completely closed eye if implemented without
OEO conversion.

48 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.20 BER Estimation
ber_uncertainty

ProductInstDir/examples/optsim/sample_mode/BER
This example shows the accuracy study of BER and Q- factor estimation in the optical system simulation.

1.21 Relationship Between OSNR and ASE Power

Spectral Density in Sample-Mode Models
RSoft/examples/optsim/sample_mode/OSNR/SM_OSNR_singlepol.moml
RSoft/examples/optsim/sample_mode/OSNR/SM_OSNR_dualpol.moml
In sample-mode, different models specify the ASE power spectral density (psd) in different ways. The three models we
will consider here are the DPSK BER Estimator, the Optical White Noise Generator, and the Fixed-Gain Optical
Amplifier.

DPSK BER Estimator

In the DPSK BER Estimator, the ASE is specified via the parameter ASE Power Spectral Density as a dual-sided psd
over a single polarization with units of dB{mW/GHz}. In other words, the ASE is calculated as:

ρ ASE ,1− pol [db{mW/GHz}] = 10 ⋅ log10 ρ ASE ,1− pol [mW/GHz]

We can relate the psd to the measured OSNR using one of three formulas, depending on the polarization settings of the
simulation, and the conditions under which the OSNR was measured.

Single-Polarization Simulation
For a single-polarization simulation, we assume that all quantities, including the OSNR, are calculated over a single
polarization. In this case, the OSNR is

Psig ,1− pol [mW ]

OSNR1− pol =
ρ ASE ,1− pol [mW/GHz] ⋅ ∆ν [GHz]

where Psig,1-pol is the signal power in one polarization and ∆ν is the optical bandwidth over which the noise is calculated.
Thus,

Psig ,1− pol [mW ]

ρ ASE ,1− pol [mW/GHz] =
OSNR1− pol ⋅ ∆ν [GHz]

Converting to units of dB{mW/GHz}, we get

ρ ASE ,1− pol [dB{mW/GHz}] = Psig ,1− pol [dBm ] − OSNR1− pol [dB ] − 10 ⋅ log10 ∆ν [GHz] (1)

Dual-Polarization Simulation, OSNR measured over one polarization

For a dual-polarization simulation in which the OSNR is measured over a single polarization, we can simply use (1).

Dual-Polarization Simulation, OSNR measured over both polarizations

If instead the OSNR is calculated over both polarizations (OSNR2-pol), then

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 49

 Psig ,2 − pol [mW ]
OSNR2 − pol =
2 ⋅ ρ ASE ,1− pol [mW/GHz] ⋅ ∆ν [GHz]

where Psig,2-pol is the signal power in both polarizations. Thus,

Psig ,2 − pol [mW ]

ρ ASE ,1− pol [mW/GHz] =
2 ⋅ OSNR2 − pol ⋅ ∆ν [GHz]

Converting to units of dB{mW/GHz}, we get

ρ ASE ,1− pol [dB{mW/GHz}] = Psig ,2 − pol [dBm ] − OSNR2 − pol [dB ] − 10 ⋅ log10 ∆ν [GHz] − 10 ⋅ log10 2 (2)

Optical White Noise Generator

In the Optical White Noise Generator, the dual-sided ASE is specified in units of dB{mW/THz} via the parameter Dual-
Sided Noise Spectral Density. We can convert from units of dB{mW/GHz} to units of dB{mW/THz} by simply adding
30 dB to the right-hand sides of equations (1) and (2). Furthermore, if the simulation is single-polarization, the
Generator’s ASE psd is specified over a single polarization, whereas in a dual-polarization simulation, it is specified over
both polarizations. In the latter case, the psd over one polarization in dB{mW/THz} can be converted to a value over
both polarizations by adding 10·log102 dB (i.e., 3 dB). Thus, depending on your simulation, and whether the OSNR is
measured over one or two polarizations, you must use a different expression for the Optical White Noise Generator’s
ASE. Below we list three possibilities.

Single-Polarization Simulation
In this case, we simply add 30 dB to expression (1).

ρ ASE ,1− pol [dB{mW/THz}] = Psig ,1− pol [dBm] − OSNR1− pol [dB ] − 10 ⋅ log10 ∆ν [GHz] + 30 (3)

Dual-Polarization Simulation, OSNR measured over one polarization

In this case, we add 30 dB to expression (1), as well as 10·log102 dB to convert to dual-polarized ASE.

ρ ASE ,2− pol [dB{mW/THz}] = Psig ,1− pol [dBm ] − OSNR1− pol [dB ] − 10 ⋅ log10 ∆ν [GHz] + 30 + 10 ⋅ log10 2 (4)

Dual-Polarization Simulation, OSNR measured over both polarizations

In this case, we add 30 dB to expression (2), as well as 10·log102 dB to convert to dual-polarized ASE.

ρ ASE ,2 − pol [dB{mW/THz}] = Psig ,2 − pol [dBm ] − OSNR2 − pol [dB ] − 10 ⋅ log10 ∆ν [GHz] + 30 (5)

Fixed-Gain Optical Amplifier

In the Fixed-Gain Optical Amplifier, instead of specifying the ASE directly, you must specify the noise figure F via the
parameter F. F can be related to the dual-sided ASE in a single polarization via the expression

1
ρ ASE ,1− pol [W/Hz] = ⋅ F ⋅ (G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]
2
where G is the amplifier gain, h is Planck’s constant, and ν is the optical frequency, which, since we are interested in the
ASE near the signal, we assume to be equal to the signal’s center frequency.
Converting the ASE density to units of mW/GHz, we can solve for F:

50 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 2
F= ⋅ ρ ASE ,1− pol [mW/GHz] ⋅10−12 (6)
(G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]
Again, we can relate F to the OSNR using one of three expressions.

Single-Polarization Simulation
In this case, we convert (6) to dB and substitute (1) for the ASE density. The resulting expression is:

F [dB] = Psig ,1− pol [dBm ] − OSNR1− pol [dB ] − 10 ⋅ log10 ∆ν [GHz] −
  G [ dB ]   (7)
10 ⋅ log10   10 10 − 1 ⋅ h[J ⋅ s] ⋅ν [Hz]  + 10 ⋅ log10 2 − 120
 
  

Dual-Polarization Simulation, OSNR measured over one polarization

In this case, we can also use (7).

Dual-Polarization Simulation, OSNR measured over both polarizations

In this case, we convert (6) to dB and substitute (2) for the ASE density. The resulting expression is:

F [dB] = Psig ,2− pol [dBm ] − OSNR2 − pol [dB ] − 10 ⋅ log10 ∆ν [GHz]
  G [ dB ]   (8)
−10 ⋅ log10   10 10 − 1 ⋅ h[J ⋅ s] ⋅ν [Hz]  − 120
 
  

Examples
As examples of these various formulas, we have provided two topologies, SM_OSNR_singlepol.moml and
SM_OSNR_dualpol.moml. Figure 1 illustrates the basic configuration of these two topologies.
First, open SM_OSNR_singlepol.moml. This topology is configured to simulate over a single-polarization (the
Sample-Mode Simulation Parameter Optical Field Representation is set equal to “Single Polarization”). The topology
models a 10.7-Gbps intensity-modulated direct-detection (IMDD) system with three different receiver configurations.
The first uses the DPSK BER Estimator KL_BER set to “IMDD” mode with the single-polarization dual-sided ASE psd
specified using (1). The second configuration uses a Monte Carlo receiver setup with ASE added via the Optical White
Noise Generator Noise. Noise has its single-polarization dual-sided ASE psd set via (3). The third configuration also uses
a Monte Carlo receiver setup with ASE added via the Fixed-Gain Optical Amplifier oampfg with a gain that exactly
compensates the loss introduced by the preceding attenuator. The noise figure of the amplifier is specified using (7). The
single-polarization OSNR is set via Global Symbol OSNR to a value of 16.142856 dB, and ∆ν, set via Global Symbol
delv_GHz, is assumed to be 12.5 GHz, corresponding to an OSA filter bandwidth of approximately 0.1 nm. The signal
power is specified in dBm via the Global Symbol power. The amplifier gain in dB is specified via the Global Symbol G,
Planck’s constant is specified via the Global Symbol h, and the center optical frequency is specified via the Global
Symbol f0, which in turn is calculated from the Global Symbol wavelength, which is specified in nm.
With this in mind, run a single non-scan simulation and first open the Optical Spectrum produced by Optical Probe
probe1. Since this is a single-polarization simulation, by default the spectrum is displayed over one polarization. Next,
set Filter Type to Rectangular and the Resolution to 0.0125 THz. In this way the noise is measured over the 12.5-GHz
bandwidth we assumed earlier. Finally, under the “OSNR and Channel” tab, click “Evaluate OSNR on channels”. The
calculated value of approximately 16.16 dB agrees very well with the value specified by Global Symbol OSNR.
Next, open the Optical Spectrum produced by Optical Probe probe2. As before, set Filter Type to Rectangular and the
Resolution to 0.0125 THz; then, under the “OSNR and Channel” tab, click “Evaluate OSNR on channels”. The
calculated value of approximately 16.21 dB also agrees very well with the value specified by Global Symbol OSNR.
Finally, compare the Optimal BER values calculated by KL_BER and the two BER estimators BER_Chi2_1 and
BER_Chi2_2 (which appear after the receivers that follow the Optical White Noise Generator and Fixed-Gain Optical

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 51

Amplifier, respectively). As can be seen, the resulting values have the same order of magnitude, confirming that the ASE
added by KL_BER, Noise, and oampfg are essentially the same.

Figure 1. Simulation schematic for three different methods of including ASE as a function of OSNR in a sample-mode simulation.

Next, open SM_OSNR_dualpol.moml. This topology is configured to simulate over both polarizations (the Sample-
Mode Simulation Parameter Optical Field Representation is set equal to “Dual Polarization”). As in the single-
polarization case, the topology models a 10.7-Gbps intensity-modulated direct-detection (IMDD) system with three
different receiver configurations. The first uses the DPSK BER Estimator KL_BER set to “IMDD” mode with the single-
polarization dual-sided ASE psd specified using (2). The second configuration uses a Monte Carlo receiver setup with
ASE added via the Optical White Noise Generator Noise. Because the simulation is dual-polarization, and assuming the
OSNR is calculated over both polarizations, Noise has its ASE psd set via (5) (because, as noted earlier, the Optical
White Noise Generator adds the specified ASE to either one or two polarizations depending on the setting of Optical
Field Representation; in this case, the ASE is added to both polarizations). The third configuration also uses a Monte
Carlo receiver setup with ASE added via the Fixed-Gain Optical Amplifier oampfg with a gain that exactly compensates
the loss introduced by the preceding attenuator. The noise figure of the amplifier is specified using (8). The dual-
polarization OSNR is set via Global Symbol OSNR to a value of 13.132556 dB, and ∆ν, set via Global Symbol
delv_GHz, is assumed to be 12.5 GHz, corresponding to an OSA filter bandwidth of approximately 0.1 nm. The signal
power is specified in dBm via the Global Symbol power, the amplifier gain in dB is specified via the Global Symbol G,
Planck’s constant is specified via the Global Symbol h, and the center optical frequency is specified via the Global
Symbol f0, which in turn is calculated from the Global Symbol wavelength, which is specified in nm.
With this in mind, run a single non-scan simulation and first open the Optical Spectrum produced by Optical Probe
probe1. Since this is a dual-polarization simulation, by default the spectrum is displayed over both polarizations. Next,
set Filter Type to Rectangular and the Resolution to 0.0125 THz. In this way the noise is measured over the 12.5-GHz
bandwidth we assumed earlier. Finally, under the “OSNR and Channel” tab, click “Evaluate OSNR on channels”. The
calculated value of approximately 13.28 dB agrees very well with the value specified by Global Symbol OSNR.

52 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

Next, open the Optical Spectrum produced by Optical Probe probe2. As before, set Filter Type to Rectangular and the
Resolution to 0.0125 THz; then, under the “OSNR and Channel” tab, click “Evaluate OSNR on channels”. The
calculated value of approximately 13.16 dB also agrees very well with the value specified by Global Symbol OSNR.
Finally, compare the Optimal BER values calculated by KL_BER and the BER estimators BER_Chi2_1 and
BER_Chi2_2. As before, the resulting values have the same order of magnitude, confirming that the ASE added by
KL_BER, Noise, and oampfg are essentially the same.

1.22 Custom Component Executable (CCE)

The purpose of these examples is to illustrate the implementation of simple CCEs, written either in Fortran or in C. The
first example is a simple attenuator that does not introduce delay. The second example is a simple electro-optical linear
modulator that also does not introduce delay.
ProductInstDir/examples/optsim/sample_mode/CCE

cce_example1
Optical Ideal Attenuator

ProductInstDir/examples/optsim/sample_mode/CCE/CCE_ex1
The purpose of this example is to illustrate the implementation of a simple attenuator CCE written in Fortran. The
attenuator does not introduce delay. The CCE source code shows how to:

manage group delay (the component sets the delay to 0, but the code manages it)
manage electrical inputs and outputs
read and write all files required for CCE execution
read and check parameter values
restrict the CCE definition to a single polarization simulation
write errors and trace messages on the OptSim console
write an .obs file that describes the CCE
The main characteristics of the component are:

one input (electrical)

one output (electrical)
no delay
inear attenuation specified by a parameter
check for polarization mode and abort if double polarization is selected (giving an error message)
write trace messages that show what kind of simulation the CCE has performed
The example CCE files are:

cce_ex1.for
simple_attenuator.obs
Description
This component is a simplified model of an optical attenuator. The input optical signal is multiplied by a factor supplied
as a CCE parameter. Moreover, the following approximations have been made: the modulator introduces neither noise
nor delay.
r r
The optical output signal E out (t ) is related to the optical output signal Ein (t ) through the following relation:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 53

 r r
E out (t ) = Ein (t ) a
where α is the Linear Power Attenuation specified by the parameter.
Inputs: the optical signal injected into the device
Outputs: the attenuated optical signal at the output of the device
Parameters:

Linear Power Attenuation α: allowed values: min 0.; max 1.0; default 1.0
SPT Simulation

Let Pin(f) be the input power spectrum and Pout(f) the output power spectrum. The device transfer function is given by:
Pout ( f )
=a
Pin ( f )
The output peak power is Ppout = a Ppin, where Ppin is the input peak power.
VBS pre-run Simulation
It is the same as SPT Simulation, see above.
VBS Run Simulation
This component is defined only in simple polarization mode, so the optical signal is represented by a single complex
representation.

Let them be ~
xin (t ) the complex envelope representation of the input optical signal and ~
xout (t ) the complex envelope
representation of the output optical signal.
The relation joining input and output representations in the time domain is the following:
~
xout (t ) = ~
xin (t ) a

cce_example2
Electro-Optical Linear Modulator

ProductInstDir/examples/optsim/sample_mode/CCE/CCE_ex2
The purpose of this example is illustrate implementation of a linear electro-optical modulator CCE written in C. The
modulator does not introduce delay. The CCE source code shows how to:

manage optical and electrical inputs and outputs

read and write all files involved in CCE execution
read and check user parameter values
extend the CCE definition to single polarization as well as to double polarization
write errors and trace messages on the OptSim console
write an .obs file that describes the CCE
The main characteristics of the component are:

two inputs (electrical and optical)

one output (optical)
no delay introduced

54 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The example files are:

cce_ex2.c
linear_modulator.obs
Description
This component is a simplified model of an electro-optical modulator with electro-optical linear characteristics.
The input optical signal is multiplied by a factor depending on the input voltage z(t) and on the excess loss introduced
by the modulator. Moreover, the following approximations have been made:

the chirp factor has not been considered

the modulator introduces neither noise nor delay
r r
E
The optical output signal E out (t ) is related to the input output signal in
(t ) and to the input voltage z(t) by the
following relation:


 0 , z(t) < 0
r  r
 p 100
Eout (t ) = 10 −α/ 20 z(t) Ein(t) , 0 ≤ z(t) ≤
 100 p
 r 100
 10 −α/ 20 Ein(t) , z(t) >
p
where α is the modulator excess loss expressed in dB and p is the percentage of input power transmitted when 1 Volt is
applied at input and the excess loss is considered to be zero.
Inputs:
Optical: the optical signal injected in the device to be modulated
Electrical: the electrical signal used to modulate the input optical signal
Outputs:
Optical: the modulated optical signal at the output of the device
Parameters:
Excess Loss α [dB]: allowed values: min 0. dB; max -; default 3. dB
% Transmission per Applied Volt p: allowed values: min 1.; max 100.; default 50.
SPT Simulation
Let it be Pin(f) the input power spectrum and Pout(f) the output power spectrum. The device transfer function is given
by:

Pout ( f ) 1
= A
Pin ( f ) 2
−α / 10
where A = 10 and α is the excess loss in dB.
The output peak power is Ppout = A Ppin, where Ppin is the input peak power.

Note on SPT simulation

The purpose of SPT simulation is to analyze the system in terms of average power per channel and noise level.
Therefore, the only behavior of amplitude modulators that needs to be taken into account for SPT purposes are the
optical spectral modifications introduced on the average power of the channel and the possible introduction of noise. In

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 55

this example the modulator is not supposed to introduce any noise and for simplicity it is moreover assumed that the
average power is reduced by 3 dB during SPT simulation.

VBS pre-run Simulation

It is the same as SPT Simulation, see above.
VBS Run Simulation

Let them be ~
xin (t ) , ~
yin (t ) the two complex envelope representations of the input optical signal and, ~
xout (t ) ,
~
y out (t ) the two complex envelope representations of the output optical signal.
The relationship between the input and output representations in the time domain is given by the following:

 ~xout (t ) = ~xin (t ) M (t )
~
 y out (t ) = ~
y in (t ) M (t )
where M(t) is related to the electrical signal by the following relationship:


 0 , z(t) < 0

 p 100
M (t ) = 10 −α/ 20 z(t) , 0 ≤ z(t) ≤
 100 p
 100
 10 −α/ 20 , z(t) >
 p

1.23 Custom Component for MATLAB (CCM)

The purpose of this example is to illustrate the implementation of a simple CCM, written in MATLAB code. The
example is a simple linear optical electro-absorption modulator.
ProductInstDir/examples/optsim/sample_mode/CCM

ccm_eam
Optical Electro-Absorption Modulator

ProductInstDir/examples/optsim/sample_mode/CCM/CCM_eam
This example is a simple 1-channel, 10 Gbit/s externally modulated transmitter, where the linear amplitude modulator is
a Custom Component for MATLAB.
The single laser source is externally modulated (NRZ modulation format) with power equal to 0 dBm and with frequency
193.4 THz.
The amplitude modulator is a Custom Component for MATLAB with linear electro-optic characteristics (in terms of
output power vs. applied voltage) and signal chirping.

56 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.24 SPICE Co-simulation (CCS)

1.24.1 SPICE Co-simulation: Sallen-Key Low-pass Filter

RSoft/examples/optsim/sample_mode/Spice/Spice_LP_filter_project.moml
In this example we demonstrate the SPICE co-simulation with OptSim using the CCS model to specify the SPICE file.
The electrical circuit that is being co-simulated is a Sallen-Key second-order Butterworth low-pss filter (LPF). Sallen-
Key filters are second order electronic active filters. The low-pass filter for this example uses an operational amplifier
(OPAM) as an emiiter-follower buffer as shown in Figure 1.

Figure 1. Sallen-Key LPF using an OPAM buffer

The cut-off frequency and the Q-factor for this filter are given by:

1 R1 R2 C1C 2
fc = and Q=
2π R1 R2 C1C 2 C1 (R1 + R2 )

1
The passive components are set such that the cut-off frequency is 5 GHz and the Q-factor is equal to . This filter has
2
maximally flat passband response. Figure 2 shows OptSim layout for this project.

Figure 2. The OptSim layout of the project

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 57

The circtuit file, LP_filter.cir lies in the same folder as the project file, and has details on the parameter choice as
shown in Figure 3 below.

Figure 3. The circuit file for the filter being co-simulated

The parameter window of the CCS contains parameters related to the location of the circuit file, options for the SPICE
co-simulation and a flag to save or discard the SPICE workspace as shown in Figure 4.

Figure 4. Parameter window of the CCS model

58 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

Figure 5 shows input to the filter (left) and its output (right).

Figure 5. Input (left) and output (right) at the filter

This example illustrated how to use SPICE co-simulation in OptSim. In the next example, we see another use of CCS
where a laser circuit file is used from the Laser Tool Kit.

1.24.2 SPICE Co-simulation: Non-linear Laser

RSoft/examples/optsim/sample_mode/Spice/Spice_laser_project.moml
In this example we demonstrate the SPICE co-simulation with OptSim using the CCS model to specify the SPICE file.
The electrical circuit that is being co-simulated is that of a non-linear laser model obtained from OptSim’s Laser Tool
Kit.
Figure 1 shows OptSim layout for this project.

Figure 1. The OptSim layout of the project

The circtuit file, Laser.cir lies in the same folder as the project file, and has details on the parameter choice as shown
in Figure 2 below.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 59

 Figure 2. The circuit file for the laser being co-simulated

The parameter window of the CCS contains parameters related to the location of the circuit file, options for the SPICE
co-simulation and a flag to save or discard the SPICE workspace as shown in Figure 3.

Figure 3. Parameter window of the CCS model

Figure 4 shows direct drive to the laser (left) and its output eye diagram (right).

60 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 4. Input drive (left) and output eye diagram (right) for the laser

This example illustrated how to use SPICE co-simulation in OptSim. The Laser Tool Kit can be used to convert data-
sheet parameters into physical rate-equation parameters and corresponding circuit file is gerenated by the toolkit. This
circuit file can be used for SPICE co-simulation as explained in this example.

1.25 VCSEL and Multimode Fiber

ProductInstDir/examples/VCSEL_Multimode
This example shows an 810 nm VCSEL modulated at 1 Gb/s and then transmitted through a multimode fiber. The fiber
length is varied through parametric runs, from 50 up to 200 m. The user can observe the optical signal before and after
the fiber through the optical probe. The received signal is passed to an electrical scope for visualization of the eye
diagram.

1.26 BeamPROPTM Interface

ProductInstDir/examples/BeamPROP
This example is an introduction to using BeamPROP results directly in an OptSim simulation.

BeamPROP_result_example

ProductInstDir/examples/ BeamPROP ProductInstDir/examples/BeamPROP

This example shows the use of a 1x4 WDM optical component designed in BeamPROP. The configuration shows a 4-
channel WDM system demultiplexed by this component. In the optical probes, the spectrum of the signal before
demultiplexing and the signal coming out of each output port can be observed.
The input/output port pairs are characterized by the BeamPROP output file ofsscanall.dat.

BeamPROP_cosimulation_example

ProductInstDir/examples/ BeamPROP

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 61

This example shows, as above, the use of a 1x4 WDM optical component designed in BeamPROP. This time the results
file is not available, so OptSim will launch BeamPROP. Therefore, the user must have BeamPROP installed to run this
example. The configuration shows a 4-channel WDM system demultiplexed by this component. In the optical probes, the
spectrum of the signal before demultiplexing and the signal coming out of each output port can be observed.
The input/output port pairs are characterized by the BeamPROP output file ofsscanall.dat. Since this file is not
available in the directory, OptSim will launch the BeamPROP script ofcscanall.scr to generate the output file.

1.27 General Purpose

This section collects general purpose OptSim examples.
ProductInstDir/examples/optsim/sample_mode/General

1.27.1 Iterations

Iteration

ProductInstDir/examples/optsim/sample_mode/General/Iteration/Iteration.opf
This example illustrates a single channel 10 Gb/s system and the use of the iteration feature.
A 10 Gb/s NRZ optical signal is launched into 1280 km of fiber. Two nested iterated blocks compose the transmission
line. The internal one describes 250 Km of fiber, which are subdivided in 5 loops, whose length is 50 km (D=-5
ps/nm/km). At the end of the each 50 km span an EDFA amplifies the output signal. After 250 Km a 70 Km (D=17
ps/nm/km) span compensates the dispersion which occurs before. The 320 km block previously described is iterated 4
times. At the end of each iterate span the signal is received and displayed in an electrical scope.

1.27.2 Parametric Runs

Parametric Run

ProductInstDir/examples/optsim/sample_mode/General/Parametric_run/Parametric_run.opf
This example describes a 10 Gb/s single channel system and the multiple runs feature.
The signal is launched onto a DS_Normal fiber link and received after the optical filtering, the detection is performed by
a PIN and the electrical filtering. The Input Power in the Laser (P) and the fiber length (L) are variables whose values are
set by the user. From the OptSim Data Display it is possible to see the correlation graphs for the Q and the BER against
P or L and the Eye diagram. Using this approach it is possible to estimate the system performance and to find its best
configuration.

1.27.3 Recorder & Playback

The examples in the Recorder_and_Playback directory (Op_rec.opf, Op_play_el_rec.opf, El_play.opf) illustrate how to
use the Recorder and Playback blocks to export/import OptSim signals into another project or into another tool (for
instance MATLAB).
ProductInstDir/examples/optsim/sample_mode/General/Recorder_and_Playback

Recorder & Playback 1

ProductInstDir/examples/optsim/sample_mode/General/Recorder_and_Playback/Op_rec.opf

62 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

This system is composed by one channel propagated into 100 km Dispersion Anomalous fiber. At the input of the fiber
link the optical signal is split into two branches: at the end of the first it is recorded by an Optical Playback in the
Op_sgn.DAT file; in the second branch the signal is propagated toward the detection section.

Recorder & Playback 2

ProductInstDir/examples/optsim/sample_mode/General/Recorder_and_Playback/Op_play_el_rec.opf
By an optical Playback the optical signal, previously recorded in the Op_sgn.DAT file, is sent into a 100 km Dispersion
Anomalous fiber and is propagated toward the receiver. Then the electrical signal is recorded by an Electrical Recorder
in the El_sgn.DAT file.

Recorder & Playback 3

ProductInstDir/examples/optsim/sample_mode/General/Recorder_and_Playback/El_play.opf
By an electrical Playback the received electrical signal, previously recorded in the El_sgn.DAT file, is measured through
an Electrical Scope and the system performance is measured with a Q value estimator.
The Matlab_Routines.txt file shows how to use one of the four routines to import/export the electrical/optical signal
from/into OptSim.

1.28 Standard OC
OC48 System

ProductInstDir/examples/optsim/sample_mode/Standard_OC/OC_48/OC48test.opf
This example illustrates the use of OC-48/STM-16 standard transmitter and receiver components implemented as
predefined compound component in OptSim library.
The transmitter compound component corresponds to a standard OC-48/STM-16 transmitter at 2.488 Gb/s, based on a
Lucent laser module (D25xx series) directed NRZ modulated. The transmitter operates at 1550 nm with an average
output power of 1 mW.
The receivers compound components correspond to a standard OC-48/STM-16 PIN receiver (lower branch) and to a
standard OC-48/STM-16 APD receiver (upper branch), respectively. For both receivers the parameters setting is chosen
in order to reproduce Lucent P172-type receiver behavior.

OC192 System

ProductInstDir/examples/optsim/sample_mode/Standard_OC/OC_192/OC192_test.opf
This example illustrates the use of OC-192/STM-64 standard transmitter and receiver components implemented as
predefined compound component in OptSim Library.
In the upper system a single channel OC-192/STM-64 transmitter (based on Lucent D2525P-Type) externally modulated
through a Mach-Zehnder modulator is used. In the lower system a single channel OC-192/STM-64 transmitter (based on
Lucent E2560-Type) externally modulated through an Electro-Absorption modulator, is used.
For both systems, the optical link is simply represented by optical attenuators. Then the signal is received by two
different type of receiver: the first one is a single channel OC-192/STM-64 PIN receiver (based on Lucent R192P-Type);
the second one is a single channel OC-192/STM-64 typical APD receiver.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 63

1.29 DPSK Modulation
16 WDM Channels 2DPSK Modulation

ProductInstDir/examples/optsim/sample_mode/DPSK_modulation/16WDM_2dpsk.opf
This example illustrates a 16-channel WDM system with optical 2 Differential Phase Shift Key (2 DPSK) modulation
format.
Sixteen signals, at 40 Gb/s, are transmitted over 5 spans of DS-Anomalous fiber. A parametric run on each span fiber
length is performed (from 25 Km up to 100 Km). The 16 channels are spaced at 200 GHz. The signals are amplified by
an EDFA booster and transmitted over on optical amplified link. Fiber dispersion is compensated after each in-line
EDFA using an ideal fiber grating. At the receiver side, three of the 16 channels are studied.
The single 2DPSK-channel transmitter is composed of a CW laser source externally modulated by a phase modulator.
The single 2DPSK-channel receiver is composed of a raised cosine optical filter followed by an ideal balanced 2 DPSK
receiver LIB block.

Note
Using the datasource directly at the input of 2DPSK channel transmitter the received PRBS will not coincide with the
transmitted PRBS. This fact does not change the performance estimation based on the Q and BER value. In a real
system it is necessary to include a pre-decoder (logic input and output) block between the datasource and the transmitter
and modulate properly the received signal, in order to obtain the same transmitted PRBS.

References
1. F. Devaux, Y. Sorel, and J. F. Kerdiles, Simple measurement of fiber dispersion and chirp parameter of intensity
modulated light emitter, J. of Lightwave Technology, Vol. 11, No. 12, pp. 1937-1940, Dec 1993
2. K. Inoue Polarization effect on four wave mixing efficiency in a single mode fiber, IEEE Journal of Quantum
Electronics, vol. 28, no. 4, April 1992
3. A. Carena, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, New analytical results on fiber parametric gain
and its effects on ASE noise, IEEE Photonics Technology Letters, vol. 9, n. 4, pp. 535-537, Apr. 1997.
4. F. Bentivoglio, A. Carena, V. Curri, P. Ottolenghi and P. Poggiolini, New detailed theoretical and experimental
results on parametric gain and sideband instability for long-haul amplified submarine systems in Proc. of
SUBOPTIC '97, paper THP1-B, San Francisco (CA), May 11-16th, 1997.
5. A. Carena, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, On the joint effects of fiber parametric gain and
birefringence and their influence on ASE noise to be published in IEEE/OSA Journal of Lightwave Technology,
July 1998.
6. F. Devaux, Y. Sorel, J.F. Kerdiles, Chirp measurement and transmission experiment at 10 Gbit/s with Wannier-Stark
modulator, Electronics letters, vol. 29, n. 9, 1993.

1.30 40 Gbps Systems

NRZ, Duobinary, CSRZ-DPSK and RZ-DPSK modulation at 40 Gbps: Optimization of the
Dispersion Map

ProductInstDir/examples/optsim/sample_mode/40_Gbps_systems

64 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

In this example we analyze the performance of four different modulation formats in ultra high spectral efficient WDM
systems. Besides standard NRZ intensity modulation, we analyze Duobinary, DPSK and CSRZ-DPSK and, for each of
them, we optimize dispersion map. We use optimized - in back-to-back condition - transmitter and receiver parameters,
then we study the performance in a multispan scenario, and its dispersion map optimization. Duobinary, DPSK and
CSRZ-DPSK show high suitability for ultra high spectral efficient WDM systems and high resilience to dispersion
compensation tolerances and fiber nonlinearities. These examples were used to obtain results presented in [1].

Figure 1. Transmitter and receiver layouts of the four analyzed modulation formats. From top to bottom, schemes refer to
NRZ, Duobinary, DPSK and CSRZ-DPSK, respectively.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 65

 Fig. 2. System setup used for the back-to-back filter optimization.

Fig. 3. - Layout of the multispan link used for the analysis of the resilience to dispersion map tolerances and to fiber nonlinearities.

Tab. 1. - Filter bandwidths resulting from the optimization process for each of the considered modulation formats

66 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Tab. 2. - OSNR (over 0.5 nm) needed in order to achieve BER = 10-6 (Q = 13.5 dB) for three different back-to-back conditions: the
optimal TX-RX in single channel operation (corresponding to the Quantum Limit), the optimal realistic setup in single channel
operation and the optimal realistic setup in WDM operation.

We consider four modulation formats whose transmitter and receiver structures are pictorially described in Fig. 1. The
structure of the NRZ-IMDD transmitter is shown in the upper part of Fig. 1. The output of a CW operated laser is
externally modulated using a 212-1 Pseudo-Random Bit Sequence (PRBS) by a chirp-free single-electrode conventional
Mach-Zehnder modulator driven in the [0, Vp] range with NRZ pulses. The driving signal is obtained by filtering ideal
rectangular pulses of duration T = 1/Rb, where Rb is the bit-rate, using a 5-pole lowpass Bessel electrical filter. The NRZ
receiver is a standard Direct-Detection (DD) structure composed by a photodetector and a lowpass 5-pole Bessel
electrical filter.
The second modulation format that has been considered is the Duobinary: a three-level line coding applied to the PRBS
output that exploits a mixed amplitude/phase modulation. When using a dedicated precoder, a standard IMDD receiver
can be employed and bit-by-bit decision applied.. A Mach-Zehnder modulator is driven by an NRZ binary signal filtered
by a 5-pole lowpass Bessel electrical filter. The driving voltage is in the [-Vp, Vp ] range. The bandwidth of the filter is a
fraction of the bit-rate (typically around 0.3⋅Rb), thus introducing the bit-correlation needed for Duobinary encoding .
Finally, two different implementations of the promising DPSK have been analyzed: standard DPSK and CSRZ-DPSK.
As it can be observed in last two schemes of Fig. 1, the DPSK and CSRZ-DPSK receivers are based on an interferometer
device - AMZ (Asymmetric Mach-Zehnder) filter with differential delay T - that converts the phase modulation into
intensity modulation and allows the use of a standard DD receiver. Typically, in order to enhance the intrinsic RX
sensitivity a differential receiver scheme is employed instead of the standard single DD receiver: two photodetectors (one
for each output branch of the AMZ) are connected so as to get the difference of the currents. After the differential
receiver, a lowpass 5-pole electric Bessel electrical filter is used for noise reduction. The choice for differential encoding
avoids the need for a coherent detection.
The phase modulation can be applied to a CW operated laser using a standard phase modulator, but it is hard to achieve
an exact π phase shift. This tight requirement on the phase shift comes from the interferometric structure of the receiver.
A viable and experimentally proven solution takes advantage of the intrinsic π phase shift in the Mach-Zehnder
amplitude modulator transfer function. As it is shown in Fig. 1, we based the DPSK implementation on a single-
electrode conventional M-Z modulator, driven in the [-Vπ /2, Vπ /2] range in order to keep the overall voltage variation
within Vπ. The driving signal is obtained by filtering rectangular pulses of duration T, using a 5-pole Bessel electrical
filter.
A variation over the standard differential phase shift keying (DPSK) is obtained by carving RZ pulses in each bit slot
(CSRZ-DPSK). The TX structure is shown in the bottom of Fig. 1. Similarly to the DPSK transmitter, a phase
modulation stage based on a M-Z amplitude modulator is used. Then a second stage applies an alternate-phase pulse
carving to the signal. This second modulation stage stems from the well-known structure extensively used for CS-RZ
modulation, and it is composed by a M-Z modulator driven by a sinusoidal signal with frequency equal to half the bit-
rate and sweeping from –Vπ + Vπ

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 67

For all the modulation formats we assume to use of ideal M-Z modulators with infinite extinction ratio (ER).
Before implementing the examples we considered the realistic TX and RX structures and we optimized some of its
parameters: we assume to operate in ultra high spectral efficiency WDM condition.
The setup used for the optimization process is shown in Fig. 2. We consider three channels in order to include the effect
of linear cross-talk. The channel spacing is 50 GHz. For each modulation format we assume to use an electrical filter –
5th order lowpass Bessel filter with -3 dB bandwidth Bwelt,TX – at the transmitter, a couple of identical optical filter – 2nd
order Supergaussian filters with identical -3 dB bandwidth Bwopt – after the TX and before the RX and an electrical filter
– 5th order lowpass Bessel filter with -3 dB bandwidth Bwelt,RX – after the photodetector. The use of the optical filter at
the TX is necessary in order to achieve high spectral efficiency by narrow filtering.
The bandwidths Bwelt,TX, Bwopt and Bwelt,RX are the parameters optimized. We found the bandwidth values allowing to get
the target performance (BER = 10-6 ⇔ Q = 13.5 dB) with the minimum OSNR for each modulation format. The results
of the optimization process are displayed in Table. I.
The considered link layout used for the examples is shown in Fig. 3. It is composed by a 7 channel WDM transmitter
followed by a multiplexer. Each transmitter uses the ad hoc setup obtained after optimization for each modulation format
under analysis. The channel spacing is set to 50 GHz and the bit rate to 42.65 Gbit/s (40 Gbit/s + typical FEC overhead).
The transmission line is a 5 span periodically amplified fiber link based on NZDSF (Non-Zero Dispersion-Shifted Fiber)
with dispersion parameter D = 4.46 ps/nm/km, dispersion slope S = 0.09 ps/nm2/km and loss adB = 0.22 dB/km. All
values are referred to the wavelength of the center channel of the WDM comb. The length of each span is 100 km. A
variable attenuator is placed at the end of the fiber span in order to set the overall span loss to a fixed value aTOT.
Dispersion management is operated using a Dispersion Compensating Unit (DCU) inserted after the attenuator, between
the two amplification stages. The overall gain per span is set such to completely recover aTOT (transparency condition).
The noise figure F of both the erbium doped fiber amplifiers (EDFA) is equal to 6.5 dB (nsp = 2.23). A further DCU is
placed before the receiver in order to arrange the overall link dispersion. Like the TX structure, the RX is configured as
defined in the back-to-back optimization phase.
For each modulation format, the OSNR at the input of the receiver is set to the one given in Table II, i.e., the one which
gives the target BER of 10-6 in the back-to-back WDM condition. This target OSNR – a different value for each
modulation format (see Table II) – can be achieved by choosing the proper transmitted power, depending on the overall
span loss aTOT.
The resilience of each modulation format to the variation of the dispersion map is tested by varying the amount of
dispersion Din-line and DRX (measured in ps/nm) introduced by the in-line DCU and the receiver DCU respectively. In
order to investigate the impact of fiber nonlinearities, different values of the overall span loss have been considered. The
increasing of the overall span loss, achieved by tuning the attenuators in the link, causes a need for larger launched
powers in order to keep the OSNR constant at the receiver. In this way, with a higher span loss we will have a stronger
nonlinear impact.

References

1. G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, "Modulation Formats Suitable for Ultra High Spectral
Efficient WDM Systems", IEEE Journal of Selected Topics in Quantum Electronics, Vol. 10, No. 2, March/April 2004

1.31 DQPSK Modulation: BER curves as function of

OSNR
ProductInstDir/examples/optsim/sample_mode/DQPSK_modulation

These examples refer to the so-called sensitivity analysis for DQPSK, RZ-DQPSK and CSRZ-DQPSK modulation
formats. It means that such examples give the curve of BER vs. the OSNR measured at the receiver. As OSNR we define
the Optical Signal-to-Noise Ratio considering the amount of noise measured on an equivalent noise bandwidth equal to
the bit-rate. The analysis is carried out using the semi analytical BER estimator based on the Karhunen-Loewe series
expansion of noise [1].

68 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

Topology layout for DQPSK, RZ-DQPSK and CSRZ-DQPSK (first and second version) are pictiorially described in
Figs 1 to 4. In all cases, we consider the transmitter and a booster EDFA. Noise is considered semi-analytically at
various levels within the BER estimator, that includes also simulation of the complete DPSK receiver structure. Layout
of DQPSK receiver is also explicitly simulated in order to obtain the in-phase (Eye_P) and Quadrature (Eye_Q) eye
diagrams. At the transmitter side, a proper data precoding is used in order to differentially precode the two (in-phase and
quadrature) data flows.
For standard DQPSK (Non Return to Zero) the DQPSK modulator is used. Its internal layout is described in Fig. 5. It
can be observed that the optical source is split, and the two signal components are modulated through amplitude
modulators by the in-phase and quadrature data flows. The quadrature signal is properly phase shifted by the phase
modulator driven by the phase-shift bias.

Figure1. Topology layout for DPSK example

The layout for the RZ-DQPSK example can be observed in Fig. 2. The scheme is similar to the DPSK one, but employs
a RZ-DPSK modulator instead of a standard DPSK modulator. Such a component, whose layout can be observed in Fig.
6, is similar to the DPSK modulator followed by a carving stage. This stage is composed by a Mach-Zehnder modulator
driver by a carving signal. In this case, the carving signal is a sinusoidal signal swinging in the range [Voff,Voff + Vπ].

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 69

 Figure 2. Topology layout for RZ-DPSK example

The first version of CSRZ-DQPSK (see Fig. 3) is similar to the standard DQPSK. Carving of the signal is obtained
through an amplitude modulator inserted between the laser source and the DQPSK modulator. This modulator is driven
between Voff -Vπ and Voff + Vπ in order to give opposite phase to subsequent pulse obtaining the carrier suppression
effect.

Figure 3. Topology layout for CSRZ-DPSK example, first version

The second version of CSRZ-DQPSK is pictorially described in Fig. 4. In this case the RZ-DQPSK modulator is used
plugging at the carving input a sinusoidal signal in the range [Voff -Vπ;Voff +Vπ] in order to obtaining the curving effect
and the carrier suppression.

70 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 4. Topology layout for CSRZ-DPSK example, second version

Figure 5. Topology layout for DPSK modulator

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 71

 Figure 6. Topology layout for RZ-DPSK modulator

Figure 7. BER vs. OSNR for the four different “flavors” of DQPSK modulation.

References
[1] J. Lee, C.S. Shim, “Bit error rate analysis of optically pre-amplified receivers using an eigen function expansion
method in optical frequency domain,” IEEE/OSA J. of Light. Tech., Vol. 12, No. 7, pp.1224-1229, Jul. 1994.

72 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.32 Maximum Likelihood Sequence Estimation (MLSE)
Receiver for Uncompensated Transmission System
ProductInstDir/examples/optsim/sample_mode/MLSE_Receiver/MLSE_Receiver.moml

Electronic dispersion compensation (EDC) has been receiving particular attention lately for its potential to correct for
signal distortion in optical communication systems in the electrical domain after photo-detection, thereby promoting
system cost savings and new network configurations with fewer regeneration sites. Types of linear and nonlinear
distortion addressed by EDC include chromatic dispersion, polarization mode dispersion (PMD), modal dispersion and
self-phase modulation (SPM).
The maximum likelihood sequence estimation (MLSE) represents a particularly promising version of EDC. In particular,
this nonlinear equalization technique has performance advantages for the correction of chromatic dispersion distortions
over other algorithms such as feed-forward equalization (FFE) and decision-feedback equalization (DFE). Recent
simulation and experimental results have shown MLSE-based receivers to be capable of supporting uncompensated
transmission over standard single-mode fiber exceeding 1,000 Km at 10 Gbit/s for a total accumulated dispersion of over
17,000 ps/nm. In comparison FFE- and DFE- based receivers have been shown to be limited to dispersion values
between 2,000 and 4,000 ps/nm.
The system of Fig. 1 consists of a 10 Gbit/s (215-1) pseudorandom bit sequence (PRBS) generator followed by a 5-pole
Bessel filter with a –3 dB bandwidth of 7.5 GHz. The signal at the output of the filter drives an ideal Mach-Zehnder
modulator with infinite extinction ratio and zero chirp. The fiber (represented by the FBG model) is 700 Km-long with a
value of dispersion D equal to 16 ps/nm, typical of G.652 standard single-mode fiber at 1550 nm – the continuous-wave
(CW) laser emission wavelength.

Figure1. Topology layout of a direct-detection system with uncompensated transmission at 10 Gbit/s over 700 Km G.652 fiber
deploying a 8192 state MLSE Viterbi processor at the receiver.

The eye diagram appears to be completely closed – See Fig. 2 below:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 73

 Figure 2. Received Eye Diagram

At the receiver there is a second-order super-gaussian optical filter with a –3 dB bandwidth equal to 35 GHz, followed
by an ideal photo-detector and a five-pole Bessel post-detection filter with a – 3 dB bandwidth equal to 7.5 GHz. The
MLSE Viterbi processor uses 8192 states, 4 samples per bit, an A/D decoder with infinite resolution and a delay of 3N
bits before making a bit-wise decision, where N is the number of states. This configuration is sufficient to compensate
11,200 ps/nm of total accumulated dispersion with a –3 dB OSNR penalty. Fig. 3 shows the BER vs. OSNR obtained
with a Monte-Carlo error-counting approach over a million simulated bits and 24 samples per bit. The target BER of
10-4 is reached for an OSNR value equal to 13 dB.

Figure 3. BER vs. OSNR for uncompensated transmission at 10 Gbit/s over 700 Km SMF and 8192 state MLSE Viterbi processor,
calculated with Monte-Carlo error counting over a million simulated bits and 24 samples per bit.

74 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

In conclusion the new OptSim MLSE model enables the user to design and simulate direct-detection systems deploying
MLSE-based receivers. The Monte-Carlo error counting is the only viable approach to calculate the system performance.
OptSim’s unique capability of simulating arbitrarily long bit sequences enables the user to design systems with a line
BER of 10-3 to 10-4, requiring simulations of over 1 million bits.

References
[1] G. Bosco, and P. Poggiolini, “Long-Distance Effectiveness of MLSE IMDD Receivers,” IEEE Photonics
Technology Letters, Vol. 18, No. 9, May 1 2006, pp.1037-1039.
[2] M. Visintin, P. Poggiolini, and G. Bosco, “Long-Haul Optically Uncompensated IMDD Transmission with
MLSE using the M-Method,” IEEE Photonics Technology Letters, Vol. 19, No. 16, August 15, 2007, pp. 1230-1232.

1.33 Polarization-Multiplexed QPSK (PM-QPSK)

1.33.1 PM-QPSK with Phase- and Polarization Diversity Receiver

RSoft/examples/optsim/sample_mode/PM-QPSK/PMQPSK_BER_vs_aspan.moml
High-density optical systems operating at 40 and 100 Gbps require advanced transmission schemes for accurate delivery
of data over long reaches. Towards this end, coherent phase modulation technologies coupled with polarization
multiplexing have been developed. In one such approach, polarization-multiplexed quadrature-phase-shift-keying (PM-
QPSK), four data signals are used to generate a single optical signal, where each of its polarizations supports a QPSK-
modulated data-signal pair. As an example of the utility of this approach, its high spectral efficiency is expected to
provide a solution for implementing 40-Gbps-per-wavelength transmission in existing 10-Gbps architectures [1].
Typically, the receivers necessary for demodulating a PM-QPSK signal must be able to extract the relevant polarization
information from the signal, as well as provide a phase-locked local oscillator. However, recent advances have
demonstrated that the use of digital signal processing (DSP) can dramatically simplify the receiver design [1]-[3]. In a
DSP-based coherent receiver, the local oscillator need not be phase-locked to the signal, nor is complicated polarization
handling required. Instead, receiver circuitry is used to convert the received PM-QPSK signal into electrical signals
representing the in-phase and quadrature portions of each optical polarization. DSP circuitry is then used to accurately
extract the original data, while simultaneously compensating for linear impairments such as dispersion.
This example highlights the OptSim models which support the accurate simulation of these DSP-based phase- and
polarization-diversity receiver technologies. These models include a filtered splitter/combiner for generating the optical
signals to be detected at each photodiode, an electronic dispersion compensation module, a DSP module that implements
a constant modulus algorithm (CMA) for polarization demultiplexing [3], a Viterbi-Viterbi algorithm for phase
estimation [3], and error counting.
As Fig. 1 depicts, these models can be used to implement a PM-QPSK coherent receiver applicable to WDM systems
with data rates over 100-Gbps per wavelength. In this example, the new OptSim models have been used in a 36-channel
PM-QPSK WDM system. Each transmitter generates a single PM-QPSK signal from four 27.9-Gbps data channels
(overhead is included to account for forward error correction). After transmission over 1800-km of fiber (without in-line
dispersion compensation), a DSP-based coherent receiver is used to determine the bit error rate (BER) of one of the
channels. The final block in the receiver, cma_phi4_Jdet, calculates the pre-FEC BER as a function of span loss. The
resulting pre-FEC BER values are on the order of 10-3 for span loss ranging from 20 to 24 dB, and demonstrate the
suitability of this approach for long distance transmission.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 75

 Figure 1. Topology for simulation of a PM-QPSK WDM system with a DSP-based phase- and polarization-diversity receiver.

References
[1] C. Laperle, B. Villenueve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, “WDM performance and PMD
tolerance of a coherent 40-Gbit/s dual-polarization QPSK transceiver,” Journal of Lightwave Technology, vol. 26,
no. 1, pp. 168-175, January 2008.
[2] S. J. Savory, A. D. Stewart, S. Wood, G. Gavioli, M. G. Taylor, R. I. Killey, and P. Bayvel, “Digital equalisation of
40Gbit/s per wavelength transmission over 2480km of standard fibre without optical dispersion compensation,” in
Proceedings of ECOC 2006, Cannes, France, paper Th2.5.5, September 2006.
[3] J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments
mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” Journal of
Lightwave Technology, vol. 26, no. 1, pp. 36-42, January 2008.

1.33.2 PM-QPSK Modulation and Reception Using Training-sequence

based LMS Receiver
ProductInstDir/examples/optsim/sample_mode/PM-QPSK/PMQPSKTrainSeq.moml

High data rates of about 100Gbps per channel can be transmitted over large distances by using advanced modulation
schemes with relatively low Bit Error Rates. The Polarization Multiplexed Quadrature Phase Shift Keying (PM-QPSK)
is one such technique, where the Phase modulation techniques are coupled with the Polarization Multiplexing
technologies. In PM-QPSK, four different data signals are used to modulate a single optical signal. The modulated
optical output consists of two orthogonal polarizations, each representing a data signal pair. Hence, the capacity of the
system can be doubled by using PM-QPSK technology, as compared to an orthodox QPSK modulation. However,
designing a receiver for a PM-QPSK system can be quite complicated and requires some DSP-based techniques for a
simplified receiver design.

In OptSim, there are several models that allow the implementation of DSP-based demodulation technologies at the
receiver. One such vital component is the Training-sequence based LMS receiver model which uses a user-specified
length of training-sequence bits to estimate the inverse of the Jones Matrix of the channel by Least Mean Squares (LMS)

76 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

algorithm and then calculate the Bit Error Rate (BER) of the channel with rest of the bits. This model is useful in almost
all the projects where PM-QPSK is implemented. Other useful models in OptSim for PM-QPSK technology include
Electronic Dispersion Compensation (EDC) model, a DSP-module that implements a Constant Modulus Algorithm
(CMA) for polarization demultiplexing, Viterbi-Viterbi algorithm for phase-estimation and error counting.

In this example, we demonstrate the PM-QPSK modulation and its reception using the training sequence based LMS
receiver. Four data signals with bit rates 10.7Gbps each are used to modulate a single optical signal, which is then passed
through a cascade of simple OptSim models for typical propagation impairments including the birefringence effect on the
polarized optical signal. The schematic of the project is shown in Figure 1.

Figure 1. Topology of the project layout

The first component in the schematic shown above is the transmitter module of the PM-QPSK modulation, which is a
compound component containing three levels of hierarchies as shown in Figure 2.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 77

 Figure 2. Schematic of the compound component tx_pmqpsk_ts1 with its lower heirarchies

The transmitter model generates the PM-QPSK modulated optical signal containing four data sequences of 10.7 Gbps
each. This resultant PM-QPSK signal passes through several intermediate components whose basic functions are listed
below:

• Optical filter
It emulates the presence of a Tx AWG.

• Booster amplifier
It defines the transmitted power level.

• Birefringence emulator
It emulates behavior of a birefringence component or cascade of components. Varying the two angle variables,
all Poincarrè sphere can be explored.

• PMD emulator
It is a PMD emulator. The user can define either the orientation of principal axes or the amount of DGD.

• Dispersive channel
It is an ideal fiber grating, introducing a defined amount of chromatic dispersion.

• Noise loading
It introduces the amount of noise equivalent to N_span EDFAs with noise-figure NF_EDFA, each completely
recovering a span loss equal to A_span.

• Optical filter

78 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 It emulates the presence of a Rx AWG.

• Extra losses

• 90 degree hybrid and local oscillator

This model simulates the 90° hybrid itself and the local oscillator laser affected by Relative Intensity Noise
(RIN).

• Balanced Photodetectors
Balanced PIN photodetectors introducing quantum noise.

• TIAs
Trans-impedance amplifiers introducing thermal noise.

• Low-pass filters
5-pole Bessel filters for noise reduction.

• Electronic Dispersion Compensation (EDC)

Component that mitigates the effects of chromatic dispersion electronically.

Eventually, the PM-QPSK signal is demodulated at the receiver section using the Training sequence-based LMS receiver
model. The length of the training sequence bits used to estimate the Jones matrix of the channel, is specified by the user
under the global parameter Num_PRBS_training. Since the LMS receiver only uses the remaining bits after the Jones
matrix estimation for calculating the BER of the system, the total simulated bit number must be conveniently high even
after the training sequence bits are subtracted, to get an accurate estimation of the BER.

In this example, the total number of bits simulated by each PRBS is 65,536 and the value of Num_PRBS_training is set
to 5 with a PRBS_degree of 11. Hence, the BER is calculated using 65536-(211-1)*5 = 10,235 symbols. The results
showing the BERs for each of the four bit sequences and the total BER with and without differential decoding are shown
below:
BER - Without Differential Decoding
Measurement at rx_pmqpsk_ts1 Run(s): 1

Errors bit 1 = 51
Errors bit 2 = 66
Errors bit 3 = 40
Errors bit 4 = 44

BER bit 1 = 0.7782576E-03

BER bit 2 = 0.1007157E-02
BER bit 3 = 0.6103981E-03
BER bit 4 = 0.6714379E-03

BER tot = 0.7668127E-03

BER - With Differential Decoding

Measurement at rx_pmqpsk_ts1 Run(s): 1

Errors bit 1 = 110

Errors bit 2 = 124

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 79

 Errors bit 3 = 80
Errors bit 4 = 88

BER bit 1 = 0.1678595E-02

BER bit 2 = 0.1892234E-02
BER bit 3 = 0.1220796E-02
BER bit 4 = 0.1342876E-02
BER tot = 0.1533625E-02

References

[1] C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, “WDM performance and PMD
tolerance of a coherent 40-Gbits/s dual-polarization QPSK transceiver,” IEEE/OSA J. Lightwave Technol. 26,
168-175, (2008).

1.33.3 PM-QPSK Modulation and LMS Dynamic Receiver

RSoft/examples/optsim/sample_mode/PM-QPSK/Sensitivity_rx_pmqpsk_dyn.moml
RSoft/examples/optsim/ sample_mode/PM-QPSK/BER_vs_mu_with_lw_rx_pmqpsk_dyn.moml
In these examples we demonstrate the use of PM-QPSK modulation and the LMS dynamic receiver. The transmitter is
followed by an ASE noise generator, a receiver structure based on the 90-degree hybrid component, local oscillator, four
balanced photodetectors and the DSP.

We focus on peculiarities of LMS dynamic receiver with respect to the LMS static receiver. The dynamic receiver
behaves like the static receiver during the training phase(s), then, during the tracking phase(s) presents an additional
option. If the related flag is properly set, during the tracking phase the receiver applies the LMS algorithm based on the
decided bits. The LMS algorithm for this phase is the same as the one used for the training phase but the µ-factor can be
different since the component allows the specifications of two different µ-factor values: one for the training phase(s) and
the other for the tracking phase(s). Therefore, the tracking µ-factor can be properly adjusted in order to “follow” specific
dynamic phenomenon such as, for example, laser phase noise.

When the tracking algorithm is applied, the receiver can be affected by the so-called cycle-slips, i.e., the effect of loosing
the absolute phase reference because of a correction done on the basis of an incorrectly decided symbol. For this reason,
in case of using tracking algorithms, the differential decoding is applied.

The basic layout for this example is shown in Fig. 1.

80 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 1. Project layout

The project file, Sensitivity_rx_pmqpsk_dyn.moml, describes a back-to-back sensitivity characterization of a

single-channel PM-QPSK transmitter/receiver structure at 111 Gbit/s (100 Gbit/s net bit-rate + 11% FEC overhead). The
parametric scan varies the OSNR given by the ASE noise loading in order to get a BER vs. OSNR characterization.
Based on this plot and the target BER, the user can define the OSNR level required in order to obtain the required
performance in case of the absence of any other impairments except the ASE noise. As we can observe in Fig. 2, for a
target BER of 10-3, the required OSNR in 0.1 nm is 13.4 dB for the decision without differential decoding and about 13.9
dB with differential decoding.

(a) BER vs OSNR in absence of differential decoding

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 81

 (b) BER vs OSNR with differential decoding

Figure 2. BER vs OSNR with and without differential decoding

Note that the differential decoding induces the well-known 0.5 dB back-to-back penalty. In this example there are no
dynamic effects, therefore the effect of tracking phase is not relevant and the LMS µ-factors are set to the same values
for both the training and tracking phase.

The project file, PM-QPSK/BER_vs_mu_with_lw_rx_pmqpsk_dyn.moml, demonstrates the effectiveness of tracking

phase in case of presence of some dynamic effects. As a dynamic effect, we considered the transmitter laser phase noise
that we assume is characterized by a 1-MHz linewidth. In order to emulate a realistic training/tracking behavior we
simulated 200,000 symbols subdivided in 10 frames each composed of 20,000 symbols. Within each frame, 1,000
symbols are used for training and the other 19,000 symbols are used for tracking. To be realistic, the error counting is
done starting from the second frame in order to avoid any initial transients. The OSNR is fixed to 15.4 dB supposing 1.5
dB penalty with respect to the required back-to-back OSNR in case of differential decoding. The parametric scan is
performed varying the LMS µ-factor for the tracking phase in the range [10-3.75;10-2.25], while the LMS µ-factor for the
training phase is kept invariant equal to 3⋅10-4. More complex investigations can be done varying also the LMS µ-factor
for the training phase and the training and frame duration. Figure 3 displays the behavior of BER without and with
differential decoding vs. the LMS µ-factor for the tracking phase.

82 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 (a) BER vs the LMS µ-factor in absence of differential decoding

(b) BER vs the LMS µ-factor with differential decoding

Figure 3. BER vs the LMS µ-factor with and without differential decoding with LMS

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 83

First, we can observe that the receiver always gives very-high BER values in case the differential decoding is not
employed. It means that in presence of this amount of phase noise, the use of differential decoding becomes mandatory.
The BER goes down to about BER = 10-3 as µ approaches 10-2. The combined use of differential decoding and tracking
allows the system to operate with a laser linewdith of 1 MHz with about 1.5 dB penalty. This analysis here is limited to
the investigation on the effect of LMS tracking µ-factor given all the other parameters. However, it clearly displays the
effect of tracking phase in presence of some dynamic effect in the simulation setup.

1.33.4 PM-QPSK with External Local Oscillator

The objective of this application note is to demonstrate use of an external local oscillator with the 90-degree hybrid
model for a PM-QPSK system.
The project file is available at:

RSoft/examples/optsim/sample_mode/PM-QPSK/PMQPSK_ExtLO.moml
This example is identical to the previous example of PM-QPSK with training-sequence based LMS receiver. The only
difference is that instead of using 90-degree hybrid model with built-in local oscillator (LO), this example uses a 90-
degree hybrid model with external LO. A separate LO can help user study effects of LO impairments on the PM-QPSK
systems.
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

A CW laser emits power in one polarization by default. Since the local oscillator model expects a dual-polarized light at
the input, a polarization rotator model is added next to the CW laser model. The parameter settings of the polarization
rotator are shown in Fig. 2.

84 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 2. Parameter settings in the polarization rotator model

The pre-FEC BER for the received bits is shown in Fig. 3.

Figure 3. BER of the received data

The CW laser model has parameters to model line-width, initial phase, noise, etc. to help user study effects of LO
impairments on the PM-QPSK systems.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 85

1.33.5 Dual-Carrier PM-QPSK
The objective of this application note is to demonstrate transmission of a dual-carrier PM-QPSK (DC-PMQPSK) system.
The project file is available at:

RSoft/examples/optsim/sample_mode/PM-QPSK/DC_PMQPSK/DC_PMQPSK.moml
The continued push for spectrally efficient high-bitrate transmission has generated tremendous interest in coherent
systems, like PM-QPSK. Using two PM-QPSK carriers, one can reduce transmitter bandwidth requirement to half
compared to standard single-carrier PM-QPSK while still supporting the same total bitrate. Lower bandwidth
components means savings in deployment costs.
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

The total bitrate for the above layout is 40 Gbps. The 100-km of fiber is modeled via a loss element and the fiber
dispersion is modeled by an ideal FBG model. Low transmitted power values in coherent systems typically give lower
nonlinearity-induced penalties. Each sub-carrier is modulated by 21.4 Gbps including FEC overheads. That means, each
polarization of a carrier is modulated by 10.7 Gbps implying the symbol rate of 5.35 GHz.
In order to minimize crosstalk between the two carries, the separation between them is kept at half-the symbol rate. As a
result, when one carrier is at its maximum, the other is at its minimum like in Fig. 2.

86 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 2. Orthogonal carrier separation (half the symbol rate) means minimum crosstalk

The spectrum of the transmitted dual-carrier PM-QPSK is shown in Fig. 3.

Figure 3. Dual-Carrier PM-QPSK Spectrum at the transmitter

In single carrier PM-QPSK, the local carrier frequency is set to the transmitted carrier’s frequency. As a result, the real
and imaginary part of the received electromagnetic field correspond to the baseband signal. However, in DC-PMQPSK,

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 87

since the carriers are apart by half the symbol rate, various settings for the local oscillator frequency exist in the literature
and frequency offsets may appear in the detected signal. For this application note, two local oscillators – each tuned to
corresponding transmitted carrier – are used to avoid frequency offsets at each detected output.
Figure 4 shows BER versus for data from each carrier. Since the equalizer is set to compensate for all transmission
anomalies, the data is received error-free.

Figure 4. BER for each carrier data

The above idea can also be extended for multi-channel (WDM) systems, like in Reference 1.

Reference
1. Torrengo, E., et al., “Transoceanic PM-QPSK Terabit Superchannel Transmission Experiments at Baud-Rate
Subcarrier Spacing ,” ECOC 2010, Digital Identifier: 10.1109/ECOC.2010.5621193, 19-23 Sept. 2010.

88 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

1.34 PM-BPSK Receiver Sensitivity Analysis
RSoft/examples/optsim/sample_mode/PM-BPSK/BER_vs_OSNR_PMBPSK.moml
This application example simulates the sensitivity of the PM-BPSK receiver model named rx_pmbpsk_ts_dyn. The
OptSim project layout is shown in Fig. 1.

Figure 1. OptSim layout of the PM-BPSK system for sensitivity analysis

The PM-BPSK signal is generated with the OptSim Compound Component TX_pmbpsk_1poly. The transmitter layout is
shown in Fig. 2. The two data sources generate the symbols for the X and Y polarization respectively. The polarization
rotator rotates the laser X polarization onto the Y polarization axis.

Figure 2. OptSim layout of the PM-BPSK transmitter Compound Component TX_pmbpsk_1poly

The system symbol rate is 32 Gbaud, the bandwidth 0.512 THz and the number of samples per symbol 20. The OSNR is
measured over a bandwidth of 12.5 GHz, typical for optical spectrum analyzers. The optical noise is injected by the
white noise generator optnoi1. The noise spectral density is calculated as:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 89

   mW 
noise _ spectral _ density dB  = P_T_dBm - OSNR_dB - 10 * log10(0.0125)
  THz 
Where P_T_dBm is the transmitted (signal) power measured in dBm, OSNR_dB is a symbol parameter representing the
target signal to noise ratio in dB, and 0.0125 THz equal to 12.5 GHz is the bandwidth over which the noise is measured.
The transmitted spectrum at the output of the fixed power optical amplifier oampfp1 is shown in Fig. 3.

Figure 3. Transmitted spectrum at the output of the fixed power optical amplifier oampfp1

The amount of noise added to the signal is controlled by the symbol parameter OSNR_dB. In order to study the receiver
sensitivity the OSNR is varied with a parametric scan from 6 to 11 dB. Fig. 4 shows the spectrum with noise before the
coherent reception for OSNR equal to 6 and 11 dB.

Figure 4. Transmitted spectrum with noise for OSNR equal to 6 and 11 dB

90 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The PM-BPSK receiver sensitivity (BER vs OSNR) curve is shown in Fig. 5. The curve confirms that this modulation
format is very resilient to noise and can achieve a target BER of 10-3 with an OSNR value around 11 dB.

Figure 5. PM-BPSK receiver sensitivity (BER vs OSNR)

The scattering diagram at the output of the fixed power optical amplifier and without noise is shown in Fig. 6.

Figure 6. PM-BPSK signal scattering diagram without noise

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 91

 Figure 7. PM-BPSK signal scattering diagram with noise

Fig. 7 shows the scattering diagram for an OSNR value of 11 dB. While the scattering diagram is totally tangled, with
this amount of noise the receiver delivers a BER of 10-3 that is a quite remarkable performance from a noise resiliency
standpoint. On the other hand the data rate is quite low compared to more complexes modulation formats such as
16QAM and 64QAM.

1.35 Polarization-Multiplexed QAM (PM-QAM)

1.35.1 PM-16QAM Receiver Sensitivity Analysis

RSoft/examples/optsim/sample_mode/PM-16QAM/BER_vs_OSNR_16QAM.moml
This application example simulates the sensitivity of the PM-16QAM receiver model named rx_tsdyn_adth_pm16qam.
The OptSim project layout is shown in Fig. 1.

Figure 1. OptSim layout of the PM-16QAM system for sensitivity analysis

92 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The PM-16QAM signal is generated with the OptSim Compound Component tx_pm16qam. The transmitter layout is
shown in Fig. 2. Four data sources generate the PM-16QAM symbol for each polarization.

Figure 2. OptSim layout of the PM-16QAM transmitter Compound Component tx_pm16qam

The system symbol rate is 32 Gbaud, the bandwidth 0.512 THz and the number of samples per symbol 20. The OSNR is
measured over a bandwidth of 12.5 GHz, typical for optical spectrum analyzers. The optical noise is injected by the
white noise generator optnoi1. The noise spectral density is calculated as:

  mW 
noise _ spectral _ density dB  = P_T_dBm - OSNR_dB - 10 * log10(0.0125)
  THz 
Where P_T_dBm is the transmitted (signal) power measured in dBm, OSNR_dB is a symbol parameter representing the
target signal to noise ratio in dB, and 0.0125 THz equal to 12.5 GHz is the bandwidth over which the noise is measured.
The transmitted spectrum at the output of the fixed power optical amplifier oampfp1 is shown in Fig. 3.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 93

 Figure 3. Transmitted spectrum at the output of the fixed power optical amplifier oampfp1

The amount of noise added to the signal is controlled by the symbol parameter OSNR_dB. In order to study the receiver
sensitivity the OSNR is varied with a parametric scan from 16 to 21 dB. Fig. 4 shows the spectrum with noise before the
coherent reception for OSNR equal to 16 and 21 dB.

Figure 4. Transmitted spectrum with noise for OSNR equal to 16 and 21 dB

The PM-16QAM receiver sensitivity (BER vs OSNR) curve is shown in Fig. 5. The curve confirms that this modulation
format is not very resilient to noise and in order achieve a target BER of 10-3 an OSNR around 21 dB is needed.

94 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 5. PM-16QAM receiver sensitivity (BER vs OSNR)

The scattering diagram at the output of the fixed power optical amplifier and without noise is shown in Fig. 6.

Figure 6. PM-16QAM signal scattering diagram without noise

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 95

 Figure 7. PM-16QAM signal scattering diagram with noise

Fig. 7 shows the scattering diagram for an OSNR value of 21 dB. The scattering diagram shows a moderate amount of
noise but, given the adjacency of the symbols in the 16QAM constellation diagram, with this amount of noise the
receiver delivers a BER of 10-3. On the other hand the data rate is four times greater than in the BPSK case.

1.35.2 PM-64QAM Receiver Sensitivity Analysis

RSoft/examples/optsim/sample_mode/PM-64QAM/BER_vs_OSNR_64QAM.moml
This application example simulates the sensitivity of the PM-64QAM receiver model named rx_tsdyn_pm64qam. The
OptSim project layout is shown in Fig. 1.

Figure 1. OptSim layout of the PM-64QAM system for sensitivity analysis

96 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

The PM-64QAM signal is generated with the OptSim Compound Component tx_pm64qam. The transmitter layout is
shown in Fig. 2. Six data sources generate the PM-64QAM symbol for each polarization.

Figure 2. OptSim layout of the PM-64QAM transmitter Compound Component tx_pm64qam

The system symbol rate is 32 Gbaud, the bandwidth 0.512 THz and the number of samples per symbol 20. The OSNR is
measured over a bandwidth of 12.5 GHz, typical for optical spectrum analyzers. The optical noise is injected by the
white noise generator optnoi1. The noise spectral density is calculated as:

  mW 
noise _ spectral _ density dB  = P_T_dBm - OSNR_dB - 10 * log10(0.0125)
  THz 
Where P_T_dBm is the transmitted (signal) power measured in dBm, OSNR_dB is a symbol parameter representing the
target signal to noise ratio in dB, and 0.0125 THz equal to 12.5 GHz is the bandwidth over which the noise is measured.
The transmitted spectrum at the output of the fixed power optical amplifier oampfp1 is shown in Fig. 3.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 97

 Figure 3. Transmitted spectrum at the output of the fixed power optical amplifier oampfp1

The amount of noise added to the signal is controlled by the symbol parameter OSNR_dB. In order to study the receiver
sensitivity the OSNR is varied with a parametric scan from 22 to 30 dB. Fig. 4 shows the spectrum with noise before the
coherent reception for OSNR equal to 22 and 30 dB.

Figure 4. Transmitted spectrum with noise for OSNR equal to 6 and 11 dB

The PM-64QAM receiver sensitivity (BER vs OSNR) curve is shown in Fig. 5. The curve confirms that this modulation
format is not resilient to noise and in order achieve a target BER of 10-3 an OSNR around 30 dB is needed.

98 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples

 Figure 5. PM-64QAM receiver sensitivity (BER vs OSNR)

The scattering diagram at the output of the fixed power optical amplifier and without noise is shown in Fig. 6.

Figure 6. PM-64QAM signal scattering diagram without noise

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 99

 Figure 7. PM-64QAM signal scattering diagram with noise

Fig. 7 shows the scattering diagram for an OSNR value of 30 dB. The scattering diagram shows a moderate amount of
noise but, given the adjacency of the symbols in the 64QAM constellation diagram, with this amount of noise the
receiver delivers a BER of 10-3. On the other hand the data rate is six times greater than in the BPSK case.

1.36 OFDM Modulation

RSoft/examples/optsim/sample_mode/OFDM/OFDM_back2back.moml
RSoft/examples/optsim/sample_mode/OFDM/OFDM_ROF_AM.moml
RSoft/examples/optsim/sample_mode/OFDM/OFDM_ROF_PM.moml
Orthogonal frequency division multiplexing (OFDM) modulation uses orthogonal carriers to transport the phase and
amplitude information of multiple low-rate bit sequences modulated using BPSK, QPSK or QAM. Serial-to-parallel and
parallel-to-serial conversions enable to transmit and receive a single high-rate bit stream.
The OptSim OFDM modulation models are several discrete blocks that can be combined at will with filters and noise
sources to simulate realistic OFDM system setups. Moreover the signal can be monitored at each stage of the modulation
process, making them ideal to study the modulation behaviour details.
OptSim includes convenient OFDM transmitter and receiver Compound Components available in the Sample-
Mode_Compound_Components Transmitters and Receivers categories. These CCs are used in the OFDM radio-over-
fiber project examples using amplitude modulation OFDM_ROF_AM.moml and phase modulation
OFDM_ROF_PM.moml. On the other hand the project example OFDM_back2back.moml use a single level not
hierarchical design with several signal measurement components to show the principia behind OFDM modulation and
the building blocks of OFDM transmitters and receivers.
Figure 1 shows the project example of an OFDM system back-to-back named OFDM_back2back.moml. Graphically the
topology is divided in two horizontal levels, the upper one corresponding to the transmitter section and the lower one
corresponding to the receiver section with eventually three separate terminations to compare the effects of different
options in the model FFTOFDM. A single 10 Gbit/s preudo-random bit sequence is converted into a number of lower
rate bit sequences controlled by the symbol QAM_bit_number. In fact the multiplicity of the serial-to-parallel conversion
corresponds to the number of bits used by the model MQAMIQ to encode one QAM symbol. An intermediate binary to
Gray-code conversion is used in the modulation process. Figure 2 shows the constellation diagram at the output of the
QAM modulator obtained with the component SCATD3_1. Next the model IFFTOFDM converts the QAM symbols in
OFDM symbols with an IFFT operation using a number of subcarriers controlled by the symbol subcarriers_number,
both accepting in input and returning on output baseband in-phase and in-quadrature signals. Figure 3 shows the in-phase

100 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
component of the OFDM signal at scope_2I. Finally the OFDM signal at baseband is RF modulated with a quadrature
mixing upconversion at QUADMIXIQ_UP. Figure 4 shows the OFDM signal RF-modulated at scope_3.
At the receiver section the RF signal is translated to baseband with a quadrature mixing downconversion at
QUADMIXIQ_DOWN. The replica at twice the carrier frequency originated by the downconversion process is filtered
out using two 7-pole low-pass Bessel filters centered at the carrier frequency, 10 GHz in this example. Figure 5 shows
the in-phase component of the OFDM signal at scope_5I connected to the output of the low-pass filter. Finally the model
FFTOFDM extracts the transmitted QAM symbols from the OFDM signal at baseband with an FFT operation. The
OFDM modulation is very sensitive to the sampling instant at the receiver. Not sampling the OFDM symbol at the
optimum sampling instant results in very fast deterioration of the system performance. For this reason the OptSim
models IFFTOFDM and FFTOFDM include the option to use a training sequence to automatically find the optimum
sampling instant. Moreover the model FFTOFDM can also automatically recover the amplitude and phase of the original
QAM symbols, thus facilitating the demodulation into bit streams of the received QAM signal. Figure 6, 7 and 8 show
the received QAM constellation with various combinations of the FFTOFDM options controlling automatic
synchronization and amplitude/gain recovery. Finally the received QAM symbols are converted into low-rate parallel bit
streams at MQADEMIQ1 and into a single high-rate bit sequence with a parallel-to-serial conversion at PARSEV1.
Figure 9 and 10 show the topologies of project examples OFDM_ROF_AM.moml and OFDM_ROF_PM.moml for
Radio-over-Fiber OFDM systems deploying respectively amplitude and phase modulation.

Figure 1. Topology of an OFDM system back-to-back

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 101
 Figure 2. 16-QAM constellation diagram at SCATD3_1

Figure 3. In-phase component of OFDM signal at scope_2I

102 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 4. OFDM signal RF-modulated at scope_3

Figure 5. In-phase component of OFDM signal after RF modulation and demodulation at scope_5I

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 103
 Figure 6. 16- QAM received constellation with automatic synchronization and amplitude/gain recovery at SCATD3_2

Figure 7. 16- QAM received constellation with automatic synchronization only at SCATD3_3

104 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
Figure 8. 16- QAM received constellation with sampling instant greater than the optimal one by 10% of the bit period at
SCATD3_5

Figure 9. Topology of Radio-over-Fiber OFDM system using Amplitude Modulation

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 105
 Figure 10. Topology of Radio-over-Fiber OFDM system using Phase Modulation

References
[1] Agilent WLAN Design Guide, Chapter 1: WLAN Standard.

1.37 Burst Mode Transmission in PON Systems Using

TDMA
ProductInstDir/examples/optsim/sample_mode/BurstMode/BurstModeTx.moml

A burst-mode Passive Optical Network system uses the Time Division Multiplexing technique in transmitting
information from various sources with different bit rates. Each source is thus allocated a specific time slot, in which it
emits a data burst with a specific bit rate.
A data burst is typically made of a Preamble, which consists of a known sequence of data bits followed by the actual
Payload. The Preamble in the burst is used at the receiver for identifying the destination of that particular burst. Two
adjacent data bursts are separated in the time domain by a distance equivalent to the Guard time.
Due to the wide range of models available in OptSim, burst-mode transmission can be easily simulated in the sample
mode of OptSim. A time-division multiplexed logical signal containing data bursts with various bit rates can be created
using various logical component models available in the sample-mode of OptSim, which is then converted into the
optical domain using the optical modulator.
Figure 1 shows the project example of a burst-mode transmission with two different data bursts- one with 10.3Gbps and
the other with 1.25Gbps, respectively.

106 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 1. Topology layout for the project

The graphical topology is divided essentially into four parts: Generation of individual logical bursts, Modulation &
multiplexing, Transmission and Multi-bit rate reception & BER estimation.
The Compound Component used here is the burst_gate_gen.moml, which is very useful for creating logical gate
signals for Preamble and Payload parts of the data bursts. This Compound Component, available in the Sample
mode/Compound_Components category is shown in figure 2.

Figure 2. Topology layout for the compound component “burst_gate_gen.moml"

As can be seen, the burst_gate_gen.moml, when triggered by an external source, gives two output gate signals: one
with a logical “high” for the Preamble generation and the other with a logical “high” for the Payload generation. The
lengths of the preamble gate and payload gate can be varied by changing the global parameters preamble_len and
payload_len respectively.
In the example project, this compound component is used twice for generating two data bursts of 10.3Gbps and
1.25Gbps each, by using two different trigger signals. Figure 3 shows the burst data at the output of the optical combiner:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 107
 Figure 3. Time division multiplexed Burst data at the output of the optical combiner

The Multi-bit rate receiver of the project uses several electrical scopes and BER estimators whose measuring time-span
limits are set for analyzing individual data bursts. This requires us to input a global symbol called the burst_start each
time the simulation parameters are changed. This parameter is nothing but the offset time of the start of the first complete
data burst that can be read from the first electrical scope (total_sim_time block) that measures the signal for the
complete simulated time. Consequently, the project is run twice whenever the simulation parameters (for example, total
simulated time span) are changed. The first run gives us the new burst_start value, which we put in before running the
project for a second time. The total simulated time span for this project is set to be 11.64µs.
The project example here uses a Preamble length of 75ns and a Payload length of 1.28µs. The Guard band length is set to
0.1µs. All these parameters, along with the fiber parameters, can be changed by varying the values in the global symbols
list.
Figure 4 shows the received burst signal for the whole simulation time. The fiber is assumed to be 10-km long with
attenuation and non-linearities included along with dispersion effects.

Figure 4. Received Burst data measured for the whole simulated time span

108 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
Figures 5 and 6 show the eye diagrams for the payloads of 10.3Gbps and 1.25Gbps respectively. The respective Q
factors are measured to be 22.48dB and 22.48dB. The preambles for 10Gbps and 1.25Gbps bit rates are shown in figures
7 and 8 respectively.

Figure 5. Eye Diagram of the Payload for the bit rate 10.3 Gbps

Figure 6. Eye Diagram of the Payload for the bit rate 1.25 Gbps

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 109
 Figure 7. Received Preamble signal for the bit rate 10.3 Gbps

Figure 8. Received Preamble signal for the bit rate 1.25 Gbps

References

[1] Susumu Nishihara, Shunji Kimura, “A Burst-Mode 3R Receiver for 10-Gbit/s PON Systems With High Sensitivity,
Wide Dynamic Range, and Fast Response”, IEEE, Journal of Lightwave Technology, vol. 26, no. 1, January 1, 2008

1.38 Dual Rate Burst Mode Receiver in PON systems

Bitrate Discrimination Circuit (BDC) based dual rate burst-mode receiver using
SPICE cosimulation in OptSim

ProductInstDir/examples/optsim/sample_mode/BurstMode/Project_BDC_BMRx.moml

This example is based on the Burst-mode receiver model reported in the paper in [1] (“Burst-mode Bit-rate
Discrimination Circuit for 1.25/10.3-Gbit/s Dual-rate PON Systems” by Kazutaka Hara, Shunji Kimura, Hirotaka

110 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
Nakamura, Naoto Yoshimoto, and Kiyomi Kumozaki). It basically demonstrates the functioning of an advanced Bitrate
Discrimination Circuit (BDC) based dual-rate burstmode receiver that can be used to detect a time-division multiplexed
composite burstmode signal with dual bitrates and separate out the data bursts of each bitrate. A data burst is typically
made of a preamble, which consists of a known sequence of data bits followed by the actual payload. The BDC-based
burstmode receiver makes use of the unique preamble sequence sent at the start of each burst signal to implement a logic
that generates a gate signal for transmitting that particular burst through.
The main block in this receiver is the Burstmode-Bitrate Discrimination Circuit (B-BDC), which is made up of two BDC
circuits, one for each bitrate. The block diagram of the B-BDC circuit is shown below:

Figure 1. Block diagram showing the Burstmode-Bitrate Discrimination Circuit (B-BDC) unit [1]

Trigger pulses generated by the BDC components by using the preamble sequence of each burst, are converted into
corresponding gating signals by an RS flip-flop as shown in the figure. Each BDC component consists mainly of the
following three circuits:

1) EX-OR Gate
2) Integrator Circuit and a
3) Comparator Circuit
The preamble sequences used for each of the bitrates in this project are:

• Alternating sequence (“010101…”) for the bursts with bitrate of 10.3Gbps

• Cyclic sequence (“01100110…”) for the bursts with bitrate of 1.25Gbps
So the BDC components in this project use an Ex-OR logic gate along with a delay of 97.08ps and 1.6ns (corresponding
to 1-bit delay and 2-bit delay) for the data bursts of bitrates 10.3Gbps and 1.25Gbps respectively.
In OptSim, the BDC-based burstmode receiver can be implemented using the powerful SPICE co-simulation feature
available in the sample-mode of OptSim. Separate CCS components have been used to define individual circuits that
make up the BDC and flip-flop units for easy accessibility if the user wants to make design changes. Using individual
CCS components also helps in keeping constant track of the signal, thus making it easy to debug the project in case of
any issues.
These individual components defined by the SPICE circuit files inside each CCS component are listed below:

• Ex-OR Gate:
The Ex-OR gate is implemented using 4 NAND-gates as shown:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 111
Each NAND gate in turn is made up of a combination of PMOS and NMOS-based switching elements.

• Integrator:
The integrator circuit file actually consists of two cascaded OPAMP circuits -the first OPAMP acts as an inverter to the
incoming signal before inputting it to the actual integrator implemented using the second OPAMP circuit as shown
below:

Note here that we have used a feedback resistor in parallel to the capacitor in the integrating OPAMP circuit to make
sure that the small input offsets are not magnified by the large OPAMP open-circuit gain.

• Comparator:
The comparator again uses an OPAMP in its feedback configuration and a couple of Zener diodes in back-to-back
configuration as shown below:

Since the amplitude of the detected signal is decoupled from the subsequent outputs at the Ex-OR gate itself, the
threshold voltage VREF (or Vth) used in the comparator remains constant for a wide range of values for the incoming
optical power.

• RS flip-flop:
The RS flip-flop implemented here is a basic NAND-latch as shown below:

112 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
There is also a NOT-AND combination gate just before the NAND latch, to make sure the Reset-Set inputs are not active
both at the same time.
Figure 1 shows the layout of the project example “Project_BDC_BMRx.moml” implementing the Burst-mode receiver
below:

Figure 2. Schematic of the example “Project_BDC_BMRx.moml”

On the receiver side, the Burstmode-Bitrate Discrimination Circuit (B-BDC) containing the two arms of 1G and 10G-
BDCs is at the bottom of the schematic. The output gate pulses of this B-BDC are used to separate out the data bursts of
different bitrates shown at the top-right portion of the layout. Notice that the received signal is passed through a delay
element (whose delay time T_delay is just about the guard time) before combining it with the BDC gate outputs, because
the RS flip-flop output switches with some delay (called the response time of the receiver) and thus the gating signal
goes well into the start of the next burst if we do not delay the data signal.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 113
The project simulates dual rate burst packets of 1.25Gbps and 10.3Gbps respectively. The values of the system
parameters used here are:

• Length of each burst (burst_len): 58ns

• Preamble length (preamble_len) of 16ns, Payload length (payload_len) of 30ns and a Guard length (guard_len)
of 12ns
• Fiber Length (length): 10kms
• Dispersion parameter (disp) at the carrier frequency (1550nm): 16ps/nm//km
• Fiber Loss (loss): 0.1dB/km
The project is simulated for a total simulation time span of about 320ns with a VBS Bandwidth of 0.1236THz.
The transmitted composite signal and the received composite signal before the B-BDC component at the receiver are
shown below:

Figure 3. Figure showing the transmitted and the received composite signals

The outputs of the separated 1.25G and 10.3G data burst signals are shown below:

Figure 4. Figure showing the separated burst signals with 1.25 and 10.3Gbps bitrates respectively

The eye diagrams for the separated out 1.25G and 10.3G data burst signals are shown below:

114 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 5. Figure showing the eye-diagrams of the received 1.25Gbps and 10.3Gbps bitrates respectively

The corresponding BER values shown at the bottom of the figures are about 1E-40 for each bitrate, which is almost 0.
To further illustrate the exact working of this BDC based dual rate burst mode receiver, we show below, the outputs of
each of the CCS components implementing the EX-OR gate, Integrator, Comparator and the RS flip-flops respectively
for 1G-BDC.

Output of the 1.25G EX-OR Gate Output of the 1.25G Integrator circuit

Output of the 1.25G Comparator circuit Gating signal for the 1.25G bursts from the RS-FF

Figure 6. Figures showing the outputs of the individual CCS components for the 1.25Gbps signal

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 115
The results show that the response time for the burst mode receiver (time taken to react and distinguish between the
different bitrates) is about 7ns for a burst length of 58ns.
Also, the values of the Resistor (R2) and Capacitor (C1) used in the circuit files of the CCS components simulating the
OPAMP based integrator circuits decide the value of the time constant of the integrator output, and hence might
sometimes require fine-tuning if the burst length specifications are considerably changed.
The BM receiver components can easily be customized for use in any dual-rate burst-mode project with different bitrate
values, by changing the delay time values for the delay elements used just before the first CCS components of both arms
implementing the EX-OR gates. The values for the delay time T_delay must be 1/bitrate for the alternating preamble
sequence (“01010…”) and 2/bitrate for the cyclic preamble sequence (“01100110…”).
In case the preamble sequence is changed, an appropriate logical circuit must be designed for it and implemented using
the first CCS component that implements the EXOR gate currently.

References

[1] Kazutaka Hara, Shunji Kimura, Hirotaka Nakamura, Naoto Yoshimoto, and Kiyomi Kumozaki, “Burst-mode
Bit-rate Discrimination Circuit for 1.25/10.3-Gbit/s Dual-rate PON Systems”, OFC 2009, Optical Society of
America conference (2008).

1.39 DQPSK ROF system

DQPSK modulated radio-over-fiber (ROF) transmission and reception using non-
coherent differential detection

RSoft/examples/optsim/sample_mode/Microwave/ROF_DQPSK.moml
The objective of this application note is to illustrate the implementation of a Differential Quadrature Phase Shift Keying
(DQPSK) modulated Radio signal Over Fiber (ROF) transmission system in OptSim. The project uses built-in library
models to implement the DQPSK modulator in RF domain at the transmitting end. At the receiving end, non-coherent
differential detection is used to demodulate the RF signal. The modulation scheme used in the optical domain is the
standard Intensity Modulation with Direct Detection (IM-DD).
The schematic layout of the project ROF_DQPSK.moml simulating the DQPSK modulated radio-over-fiber system is
shown in figure 1 below:

116 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 1. Schematic of the project layout for ROF_DQPSK.moml

The value of the bit rate of the data sequences used for generating the In-phase (I) and Quadrature (Q) sequences is about
0.128Gbit/s. The DQPSK generation requires that I and Q signals be differentially encoded before being phase
modulated in the RF domain. In OptSim, this differential encoding of the I and Q signals is implemented through a built-
in component called the DQPSK Precoder, whose output Ik, Qk at any stage depends upon the current state inputs ak, bk
and previous state outputs Ik-1, Qk-1 according to the expression:

The output of this DQPSK precoder component thus depends on its current state input bits and the previous state output
bits, which is then sent for the conventional QPSK modulation with an RF carrier, thus producing the DQPSK modulated
RF signal. The block diagram of the logic implemented inside the precoder block is shown in figure 2 below:

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 117
 Figure 2. Block diagram of the logic implemented inside the precoder block

And the truth table for this precoder circuit is also given in table 1 below for clarity:

(Ik-1,Qk-1) = (0,0) (Ik-1,Qk-1) = (0,1) (Ik-1,Qk-1) = (1,0) (Ik-1,Qk-1) = (1,1)

ak bk Ik Qk Ik Qk Ik Qk Ik Qk
0 0 0 0 0 1 1 0 1 1
0 1 1 0 0 0 1 1 0 1
1 0 0 1 1 1 0 0 1 0
1 1 1 1 1 0 0 1 0 0

Table 1. Truth table for the DQPSK precoder circuit

The pre-coded I and Q bit sequences are then used to phase modulate two RF carrier components having a phase
difference of 90° at a signal frequency of 1.28 GHz. The combined signal is then intensity modulated with a laser output
and transmitted over an SMF fiber of length 10kms.
At the non-coherent receiver, the incoming DQPSK signal at the kth symbol period can be represented as:
Rk(t) = I′k Cos(ωt) + Q′k Sin(ωt) (1)
where I′k and Q′k can take any of the values between ±(1/√2) and ±(1/√2) respectively.
In the DQPSK demodulator circuit, the I and Q components are recovered by multiplying the received signal by its bit-
delayed, phase-shifted version and filtering out the high-frequency components. The demodulator part for recovering the
in-phase component is shown in the figure 3 below:

118 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 3. Block diagram of the demodulator circuit for the in-phase component

Let the bit-delayed arm of the differential demodulator introduce a phase-shift of ‘φ’ radians. Then, following equation
(1) above, the inputs to the multiplier look like:

Rk(t) = A*Cos(ωt + m*pi/4)

and R′k-1(t) = A*Cos(ωt + n*pi/4 + φ)

which gives Ir(t) = A2*Cos(ωt + m*pi/4) * Cos(ωt + n*pi/4 + φ)

(or) Ir(t) = (A2/2)*[Cos{2ωt + (m+n)*pi/4 + φ} + Cos{(m-n)*pi/4 - φ}]

where m,n can take any of the four values ±1, ±3 each.

The high-frequency component is filtered out by the low pass filter (LPF), leaving just the offset term Cos{(m-n)*pi/4 -
φ}. To map this filtered output Ir(t) to the transmitted in-phase component I(t), the value of this cosine term must have
only two discrete possibilities for all combinations of the values for m & n between ±1, ±3. It is easy to see with some
trigonometric calculations that only the values of ‘φ = ±pi/4’ satisfy this condition. Further more, from the truth table of
the precoder circuit, it can be deduced that the value of φ = -pi/4 maps the filtered output Ir(t) to the input in-phase
component I(t). Similar argument shows that a value of φ = +pi/4 maps the output of the quadrature arm of the
demodulator to the input quadrature component Q(t). Hence, the phase-shift values used for the in-phase recovery and
quadrature recovery circuits at the demodulator are -pi/4 and +pi/4 respectively.
The project is run for a total simulated time span of 2000ns, corresponding to 256 bits at the reference bit rate. To
validate the working of the non-coherent demodulator, we plot in figure 4 below, the recovered in-phase component
(Ir(t)) along with its corresponding transmitted sequence (I(t)) for the first few bits:

Figure 4. Recovered in-phase (I) component along with the transmitted one

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 119
Similarly the recovered Quadrature component (Qr(t)) with that of the corresponding transmitted sequence (Q(t)) is also
shown in figure 5 below:

Figure 5. Recovered quadrature (Q) component along with the transmitted one

As the above figures show, the demodulated bit sequences match with that of the transmitted sequences bit-by-bit. The
eye-diagram for the demodulated in-phase and quadrature components are shown in figure 6 below:

Figure 6. Eye diagrams of the recovered in-phase and quadrature components at the receiver

The bit error rate (BER) value for the received components is about 1E-40 which corresponds to an error-free
transmission.

References
[1] Lian Zhao, Hari Shankar, and Ariel Nachum, “40G QPSK and DQPSK Modulation”, Inphi Corporation
[2] “Non-coherent differential QPSK demodulator”, Advanced Design System 2008 Update 2, Agilent Technologies,
http://edocs.soco.agilent.com/display/ads2008U2/DQPSK+Demod#TimedComponentsPrintView-DQPSKDemod

120 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
1.40 Microwave Photonic Links with Balanced Detection
RSoft/examples/optsim/sample_mode/Microwave/RF_IMDD_SC_intermod_disto.moml
RSoft/examples/optsim/sample_mode/Microwave/RF_IMDD_SC_fade.moml
As an example of OptSim’s ability to simulate advanced microwave photonic applications, we present here the study of
two microwave photonic link architectures with balanced detection at the receiver, based on the designs described in [1].
The first case is based on intensity-modulation with direction detection (IMDD); Fig. 1(a) illustrates this design’s
OptSim topology in a back-to-back configuration. A pair of RF sources at frequencies f1 and f2 modulates the output of a
1550-nm CW laser via a balanced-bridge Mach-Zehnder modulator (MZM) with a quadrature bias voltage of Vπ/2. At
the receiver, a pair of balanced detectors detects the transmitted microwave signals. Note that the balanced-bridge MZM
model is also based on the work presented in [1].

(a)

(b)

Figure 1 Topologies for simulating back-to-back multi-tone RF transmission using balanced detection: (a) intensity modulation with
direct detection; (b) suppressed-carrier modulation.

The second case uses a suppressed-carrier (SC) link with coherent heterodyne detection provided by a local oscillator
(LO) and a pair of balanced detectors; Fig. 1(b) depicts the OptSim topology of this design, again in a back-to-back
configuration. In this case, the balanced-bridge MZM is biased at the null bias-point voltage of Vπ, and a second CW

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 121
laser acts as the LO whose frequency is offset from that of the source laser by ∆f, thereby producing heterodyne
detection and allowing for down-conversion of the RF source frequencies. As we shall see, this design demonstrates
improved linearity compared to the IMDD case, as well as less susceptibility to distortions due to fiber transmission.
Important measures of a microwave link’s linearity are its higher-order distortion characteristics. In the case of a two-
tone system such as the designs of Fig. 1, one of the third-order intermodulation products appears at the frequency 2f1-f2.
As we increase the modulation of the RF signals, we expect the detected power of the intermodulation product to initially
get worse relative to the detected signal powers and eventually surpass them. To demonstrate this, open
RF_IMDD_SC_intermod_disto.moml which compares the performance of the IMDD and SC designs with f1 = 10
GHz, f2 = 9.5 GHz, ∆f = 8 GHz, and Vπ = 5 V. Run the pre-configured scan simulation, which sweeps the amplitude of
the RF sources from 1.0 to 10.0 via the Global Symbol amp.
We will first compare the detected signal power at f1 to the intermodulation product power at 2f1-f2 for the IMDD design.
To generate a plot of the detected signal power at f1, right-click on Electrical Power Meter epowme1 and select “View
Correlation Diagram”. Then generate a plot of the Electrical Power measured by epowme1 versus the Global Symbol
amp. Next, to generate a plot of the intermodulation product power at 2f1-f2, right-click on Electrical Power Meter
epowme3 and select “View Correlation Diagram”. Then generate a plot of the Electrical Power measured by epowme3
versus amp. To compare the two plots, go back to the plot from epowme1 and in its Edit menu click on Copy. Then
return to the plot from epowme3 and in its Edit menu click on Paste. Figure 2 illustrates the resulting plot. As can be
seen, the intermodulation product power becomes equal to the detected signal power at a value for amp of approximately
3.

Figure 2 Comparison of detected signal power at f1 (orange) and intermodulation product power at 2f1-f2 (green) for the IMDD link.

Next, we will perform the same comparison for the SC design. To generate a plot of the detected signal power at f1
(down-converted by ∆f), right-click on Electrical Power Meter epowme5 and select “View Correlation Diagram”. Then
generate a plot of the Electrical Power measured by epowme5 versus the Global Symbol amp. Next, to generate a plot of
the intermodulation product power at 2f1-f2 (down-converted by ∆f), right-click on Electrical Power Meter epowme7 and
select “View Correlation Diagram”. Then generate a plot of the Electrical Power measured by epowme7 versus amp. To

122 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
compare the two plots, go back to the plot from epowme5 and in its Edit menu click on Copy. Then return to the plot
from epowme7 and in its Edit menu click on Paste. Figure 3 illustrates the resulting plot. As can be seen, in this case the
intermodulation product power becomes equal to the detected signal power at a value for amp of approximately 6. This
doubling of the cross-over amplitude relative to the IMDD case is consistent with the results in [1] and helps demonstrate
the improved linearity of the SC link as compared to its IMDD counterpart.

Figure 3 Comparison of detected signal power at f1-∆f (orange) and intermodulation product power at 2f1-f2-∆f (green) for the SC
link.

Another deficit of the IMDD design is its susceptibility to power fading during transmission over optical fiber due to
chromatic dispersion [1]. To study this behavior, we simulate both the IMDD and SC designs when transmitting over 30
km of fiber, neglecting the effects of loss and nonlinearities in order to focus on dispersive effects. Open
RF_IMDD_SC_fade.moml, which compares the effects of power fading in the IMDD and SC designs. The complete
topology is illustrated in Fig. 4. We transmit a single RF signal over the fiber, with the LO in the SC link set to a
frequency offset that produces a down-converted RF signal frequency at the detector equal to 2 GHz. Furthermore, for
simplicity we transmit each MZM output in the IMDD design over its own fiber. Run the pre-configured scan
simulation, which sweeps f1 from 0.2 to 20 GHz while varying ∆f such that the down-converted frequency in the SC
design remains fixed at 2 GHz. Note that f2 = 9.5 GHz and Vπ = 5 V.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 123
 Figure 4 Topology for simulating the effects of power fading in both IMDD- and SC-based microwave photonic links.

We will now compare the detected signal power at f1 in the IMDD design to that in the SC design (down-converted by
∆f, of course). To generate the plot for the IMDD case, right-click on Electrical Power Meter epowme1 and select “View
Correlation Diagram”. Then generate a plot of the Electrical Power measured by epowme1 versus the Global Symbol
f1_mod_GHz. Next, to generate a plot for the SC case, right-click on Electrical Power Meter epowme2 and select “View
Correlation Diagram”. Then generate a plot of the Electrical Power measured by epowme2 versus f1_mod_GHz. To
compare the two plots, go back to the plot from epowme1 and in its Edit menu click on Copy. Then return to the plot
from epowme2 and in its Edit menu click on Paste. Figure 5 illustrates the resulting plot. As can be seen, in the IMDD
link, power fading leads to a strong variation in the detected power as a function of frequency, whereas the detected
power in the SC link is very uniform due to the coherent heterodyne detection in the design [1].

124 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 5 Detected RF power as a function of source frequency for both IMDD (orange) and SC (green) links over 30 km of fiber.

References
[1] C. Middleton and R. DeSalvo, “Improved microwave photonic link performance through optical carrier
suppression and balanced coherent heterodyne detection,” Proceedings of SPIE - Enabling Photonics Technologies for
Defense, Security, and Aerospace Applications VI, vol. 7700, p. 7700-08, 2010.

1.41 Comparison of Karhunen-Loeve (K-L) Semi-

analytical BER Estimation and Direct Counting of BER
via a BER Counter
The objective of this application note is to compare Karhunen-Loeve (KL) semi-analytical BER estimation with direct
counting of errors.
The project files are available at:

RSoft/examples/optsim/sample_mode/BER/KL_Counter/
Figure 1 shows the schematic layouts for (a) K-L and (b) Error Counter cases.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 125
 (a) Karhunen-Loeve

(b) Direct Counting of Errors

Figure 1. Simulation setup schematics for this application note

Both of the project files model a 40 Gbps, NRZ, IM/DD system. The exact bit rate is 42.8 Gbps due to typical FEC
overheads.
The project file for K-L simulates 511 bits while the one for direct error counter simulates 300,000 bits. The ASE is
varied by scanning the OSNR. The range of OSNR is selected such that the BER is high enough to be directly counted
within practical timeframe over 300,000 transmitted bits. A direct error counter will require a large number of
transmitted bits and hence longer simulation time is the BER to be counted is expected to be very low.
After the parameter scan is carried out, the BER versus OSNR plots were super-imposed for better comparison and are
shown in figure 2.

126 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 2. BER vs OSNR for K-L (green color) and Error Counter (orange color)

As you can see, the semi-analytic error estimation using Karhunen-Loeve method matches very well with the direct
counting of errors using a BER counter. The deviation in BER at OSNR of 17.5 dB in above figure is due to less than
sufficient number of transmitted bits for direct counting of errors for counting BER that low. The user can increase the
number of simulated bits in the simulation parameters, to say, a million, and compare the results.

1.42 Comparison of Karhunen-Loeve (K-L) and Monte

Carlo (Chi^2) BER Estimations in 10- and 40-Gbps
Systems
The objective of this application note is to study: (1) how K-L semi-analytical and Monte Carlo BER estimation with
Chi^2 noise power spectral density (PSD) compare in 10- and 40-Gbps systems, (2) how amplified spontaneous
emission (ASE) PSD can be specified in terms of EDFA noise figure for single- and dual-polarization cases, and (3) how
the performance scales when one migrates from 10- to 40-Gbps systems.
The four project files corresponding to each of these three cases are available at:

RSoft/examples/optsim/sample_mode/BER/KL_MC/
Figure 1 shows the schematic layout common to all four project files.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 127
 Figure 1. Simulation schematic common to all four project files of this application note

The two project files for 10-Gbps NRZ deal with single and dual polarization, respectively, and the other two project
files deal with 40 Gbps (dual polarization) but simulate 511 and 2048 bits, respectively. The exact bit rates are 10.7 and
42.8 Gbps due to typical FEC overheads.
Each of these four layouts compare semi-analytic (K-L) and Monte Carlo with Chi^2 receiver noise PDF for BER
evaluation. Many prefer Chi^2 in ASE-dominant systems though Gaussian PDF is also found good enough for high
optical noise cases and gives BER similar to Chi^2 within half-a-dB or so deviation.
Each of these four layouts also shows two different ways of adding optical noise: (1) using EDFA noise figure and (2)
using a white noise generator noise model. These ways differ slightly in the way they add noise for single versus dual
polarization (to be discussed later).
Since the K-L estimator and white noise generator model require optical noise specification in terms of dual-sided ASE
power spectral density (PSD), we must correlate noise figure of the EDFA to the ASE PSD for an apple-to-apple
comparison.
The equation that relates the noise figure to the single-polarization dual-sided ASE PSD (ρASE) of an optical amplifier is:

ρASE = F * (G-1) * h * ν/2

where:
F is the noise figure (linear units), G is the gain (linear units), h is Planck’s constant (6.626068 x 10-34 m2kg/s), and ν is
the simulation frequency, which in our case is 192.37196 THz.
For 35 dB gain, the required noise figure is 9.85 dB to match K-L’s ASE setting of –27 dB [mW/GHz].
The user can also observe the single-polarized optical spectrum and calculate ASE PSD as follows:
P_ASE_dB_mW_GHz = N_dBm – 10*log10(BW_GHz), where BW_GHz is the bandwidth of the rectangular filter
used to view the spectrum and N_dBm is the noise floor. If you are observing the dual polarization spectrum, subtract 3
dB from the above relationship because the noise power is always specified for single polarization and for dual
polarization, the noise amount is doubled.
On the other hand, if you are using the noise generator model, it adds the same amount of noise power whether the
simulation is single- or dual polarization. As a result, if you want to match the noise PSD of the K-L and amplifier
models to that of the noise adder model, you will need to specify the noise adder’s PSD as 3 dB more than the ASE PSD

128 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
of K-L if your simulation is set for dual polarization (in order to match per-polarization noise amount of the K-L and
amplifier models, which add twice the noise power in case of dual polarization). Also, the noise adder model requires the
noise density in units of dB [mW/THz], so one needs to add 10*log10(1e3) = 30 dB to the ASE PSD of the K-L model.
With these values, the Q calculated at the K-L model, and using the Chi^2 probability density function after the optical
amplifier and optical white noise models are in good agreement:
Single-polarization:
Q for KL = 14.43633 dB
Q for Amplifier branch (Chi_2) = 14.56920 dB
Q for noise adder branch (Chi_2) = 14.81859 dB

Dual-polarization:
Q for KL = 13.89181 dB
Q for Amplifier branch (Chi_2) = 14.10296 dB
Q for noise adder branch (Chi_2) = 14.12553 dB

Migration from 10 Gbps to 40 Gbps

As far as the scaling and equivalence between the K-L model and Chi^2 Monte Carlo are concerned, the 40-Gbps system
behaves analogously to the 10-Gbps one. Since the bit rate is now quadrupled, optical and electrical filters have four
times larger bandwidths. As a result, the OSNR for 40 Gbps has to be higher by 10*log10(4) dB. Both of the 40 Gbps
project files for this application note reflect these changes. The Q-factor values for the dual polarization case are:
Number of simulated bits: 511
Q for KL = 13.89333 dB
Q for Amplifier branch (Chi_2) = 13.72141 dB
Q for noise adder branch (Chi_2) = 14.24472 dB
Number of simulated bits: 2048
Q for KL = 13.89333 dB
Q for Amplifier branch (Chi_2) = 13.96489 dB
Q for noise adder branch (Chi_2) = 13.75672 dB
As expected, the agreement between semi-analytical (K-L) and Monte Carlo (Chi^2) improves with increased number of
simulated bits.
It would be interesting to note that if there are many amplifiers in a system, and if the loss between each amplifier pair is
exactly compensated by amplifier gain, the next amplifier in the chain does not amplify the noise of the previous
amplifier but it simply restores its level, plus adds its own noise. In this case, the overall noise PSD due to the amplifier
chain can be given by:

ρASE = n * F * (G-1) * h * ν/2

where n is the number of amplifiers.

We hope that this application note illuminated a number of important topics with regards to correct ASE PSD settings for
single- and dual polarization cases, use of the K-L estimator, comparison with Monte Carlo methods, and scaling due to
increased bit rates.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 129
1.43 Comparison of OSNR sensitivities for Coherent PM-
QPSK, RZ-DQPSK and DPSK systems
The objective of this application note is to show that coherent reception for PM-QPSK offers significant OSNR
improvement as compared to RZ-DQPSK and DPSK systems. The three project files corresponding to each of these
three cases are available at:

RSoft/examples/optsim/sample_mode/PM-QPSK/Comparison/
Figures 1, 2 and 3 depict the schematic layouts for coherent PM-QPSK, RZ-DQPSK and DPSK systems.

Figure 1. Simulation setup schematic for Coherent PM-QPSK

Figure 2. Simulation setup schematic for RZ-DQPSK

130 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 3. Simulation setup schematic for DPSK

The line bit rates for each of these cases is 42.8 Gbps that includes the FEC overheads for 40 Gbps systems. The DQPSK
and DPSK use Karhunen-Loeve (K-L) semi-analytic BER estimation and the total number of simulated bits for these two
cases is 1024. The coherent receiver for the PM-QPSK uses a BER counter and in order to be able to count errors typical
to pre-FEC levels, we simulate 300,000 bits.
The ASE spectral density is defined in terms of OSNR over 0.1 nm resolution for all three cases. This enables us to do a
parameter scan over a range of OSNR and plot corresponding BER.
The figure 4 compares OSNR sensitivities of all three schemes at a typical pre-FEC BER value.

2 dB

1.3 dB
RZ-DQPSK

DPSK
PM-QPSK

Figure 4. OSNR Sensitivities of Coherent PM-QPSK, RZ-DQPSK, and DPSK

As can be seen, coherent PM-QPSK offers around 2-dB better sensitivity compared to RZ-DQPSK and around 1.3 dB
better sensitivity compared to DPSK systems [1] and hence PM-QPSK offers a viable alternative to the other two at high
bit rates.

Reference
1. J. Renaudier, et. al., “Linear Fiber Impairments Mitigation of 40-Gbit/s Polarization-Multiplexed QPSK by Digital
Processing in a Coherent Receiver”, Journal of Lightwave Technology, v.26, no.1, p.36-42, 2008’

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 131
1.44 Partial DPSK (PDPSK): Influence of MZI delay
mismatch in high bitrate dispersive channels
The objectives of this application note are to: 1. study a partial DPSK system and 2. study influence of MZI delay
mismatch in high bitrate dispersive channels. This application note is based on Reference [1].
The project file is available at:

RSoft/examples/optsim/sample_mode/PartialDPSK/RZpdpsk_DispBERvsOSNR.moml
The conventional DPSK receiver has delay between the two arms in the asymmetric Mach-Zehnder (AMZ)
interferometer filter set to the bit period. Any mismatch in the delay between the two arms due to receiver imperfection
[2] gives corresponding change in the free spectral range of the AMZ filter transfer function. When this relative delay is
less than the bit period, it results in what’s called “partial” DPSK [3].
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

A 40 Gbps DPSK signal passes through the RZ pulse carver [4] at the transmitter. The transmitted RZ DPSK spectrum is
shown in Figure 2.

132 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 2. Transmitted 40 Gbps RZ-DPSK Spectrum

The fiber dispersion is modeled by an ideal FBG. The delay imperfection in the receiver is specified by the Mach
Zehnder Delay mismatch parameter as percentage of the bit period in the Karhunen-Loeve BER estimator.
In presence of non-zero dispersion, the delay mismatch of less than one bit gives better performance than the delay
mismatch of more than one bit [1] as evident from the curve in Figure 3. It is interesting to observe that the optimum
performance in presence of dispersion does not correspond to zero mismatch in AMZ delay.

Figure 3. BER vs AMZ Delay Mismatch for dispersion of 80 ps/nm

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 133
This plot was obtained by setting a parameter scan of variable “mismatch” from –30% to 30% in steps of 5% for a
dispersion value of 80 ps/nm.
A target pre-FEC BER of 10-3 was chosen to obtain OSNR penalty plot of Figure 4. The main project file,
RZpdpsk_DispBERvsOSNR.moml was modified to create four cases with different dispersion values ranging from 0
ps/nm, 80 ps/nm, 100 ps/nm, and 120 ps/nm. For each of these cases, OSNR was varied and a family of plots was
obtained by plotting BER vs OSNR as a function of AMZ delay mismatch. Figure 4 shows one such plot with more
focus on the 10-3 BER range.

Figure 4. Screenshot of Excel data from the exported diagram for zero dispersion

134 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
The OSNR values at 10-3 BER for each mismatch were tabulated (say, in Excel) from different runs at different
dispersion values.

The difference between the OSNR at BER of 10-3 for each case and the OSNR at zero mismatch, zero dispersion for the
same BER gives OSNR penalty at BER of 10-3.
Figure 5 shows this plot from Excel.

Bit Delay Mismatch Penalty in Dispersive Channel

3.5 0 ps/nm
60 ps/nm
80 ps/nm
100 ps/nm
3
OSNR Penalty at 10-3 BER

2.5

1.5

0.5

0
-30 -20 -10 0 10 20 30
% Mismatch in AMZ Bit Delay

Figure 5. OSNR penalty plot from Excel for different dispersion values as function of % bit delay mismatch

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 135
This shows that in presence of increasing dispersion (chromatic and/or PMD), partial DPSK (with delay less than one bit
period) gives better performance than classical DPSK (where bit delay mismatch is zero).

References
1. Lize, Y. K., et al., “Free Spectral Range Optimization of Return-to-Zero Differential Shift Keyed Demodulation in the
Presence of Chromatic Dispersion,” Optics Express, pp. 6817-6822, vol 15, no. 11, 28th May 2007.
2. Bosco, G., and Poggiolini, P., “The Impact of Receiver Imperfections on the Performance of Optical Direct Detection
DPSK,” Journal of Lightwave Technology, vol. 23, pp. 842-848, 2005.
3. Mikkelsen, B., et al., “Partial DPSK with Excellent Filter Tolerance and OSNR Sensitivity,” Electronics Letters, vol.
42, pp. 1363-1384, 2006.
4. Winzer, P. J., et al., “Chirped Return-to-Zero Modulation by Imbalanced Pulse Carver Driving Signals,” IEEE
Photonics Technology Letters, vol. 16, no. 5, pp. 1379-1381, May 2004.

1.45 In-band Crosstalk in Partial DPSK Systems

The objective of this application note is to demonstrate modeling of in-band crosstalk in partial DPSK systems.
The project file is available at:

RSoft/examples/optsim/sample_mode/PartialDPSK/PDPSK_Xtalk.moml
In-band crosstalk is the crosstalk component having the same wavelength as the transmitted channel. One of the causes
of in-band crosstalk is when the channel passes through a number of ROADMs and wavelength select elements (filters)
[1-2]. In order to model this crosstalk, one approach is to split the arms and de-correlate one of the arms before
combining them. The polarization scrambler and the fiber models help de-correlation.
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

The 40 Gbps NRZ DPSK transmitter transmits 43 Gbps PRBS data including 7.5 % FEC overhead. The transmitter
output is split into two arms – the lower arm in above figure models the in-band crosstalk component. The length of the
single-mode fiber in the crosstalk arm is 5 km. An attenuator placed next to the fiber controls the crosstalk power level.
After combining the crosstalk arm to the main arm, the signal undergoes dispersion element and an amplifier before
reaching the receiver. The receiver has Mach-Zehnder delay line interferometer (DLI) mismatch parameter set to 65% of
the bit period (66 GHz free spectral range or FSR). A parameter scan is carried out for the received OSNR and the
attenuation value in the crosstalk arm thereby controlling the amount of in-band crosstalk. The optical power meter
model at the attenuator output measures the in-band crosstalk power level. The BER is estimated by the Karhunen-Loeve
(K-L) BER estimator model.
Figure 2 below shows a plot of BER versus in-band crosstalk power for a number of received OSNR values.

136 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 2. BER versus in-band crosstalk for various values of the received OSNR

The results are intuitive. As the in-band crosstalk increases, the BER worsens for a given OSNR. If the crosstalk-free,
baseline BER and corresponding OSNR are known, crosstalk induced penalties can be calculated as in Reference 2.

References
1. Tibulec, S., and Filer, M., “Transmission Impairments in DWDM Networks with Reconfigurable Optical Add-Drop
Multiplexers,” IEEE Journal of Lightwave Technology, vol. 28, no. 4, February 15, 2010, pp. 557-568.
2. Richards, D., Kota Pavan, S., Patel, J. and Ghillino, E., ”Improved Tolerance to the Combined Effect of In-Band
Crosstalk and Chromatic Dispersion in Partial DPSK Systems,” 15th IEEE International Workshop on Computer Aided
Modeling, Analysis and Design of Communication Links and Networks (CAMAD 2010), paper # 1569332939.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 137
1.46 All-optical Wavelength Conversion by Nonlinear
Polarization Rotation
The objective of this application note is to demonstrate non-linear polarization rotation and its application for all-optical
wavelength conversion.
The project file is available at:

RSoft/examples/optsim/sample_mode/Fiber_non-linear_effect/XPM/NonLinearPolRotation.moml
Strong non-linearities can induce polarization switching by way of nonlinear polarization rotation resulting into all-
optical wavelength conversion. This application note focuses on XPM-induced nonlinear polarization rotation of a CW
channel [1], called probe, at 10 Gbps. The exact bit rate is 10.7 Gbps due to typical FEC overheads.
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

A 10.7 Gbps signal (referred to as “control signal” in Ref .1) at 1550 nm and a CW signal (referred to as “probe” in Ref.
1) are coupled together and fed to a dispersion flattened highly nonlinear photonic crystal fiber (PCF) of 64-m length.
OptSim does not have a pre-built PCF model in library, so we used an SMF and set the PCF parameters as per Ref. 2.
While this will not make the SMF strictly a triangular-core PCF of Ref. 2, nonlinear polarization rotation can still be
observed. The dispersion and its slope are kept at –2 ps/nm/km and 10-3 ps/nm2/km. The nonlinear coefficient is set to
11.2 W-1km-1.
The control signal is vertically polarized and the probe signal is 450 linearly polarized. The control signal has average
power of 800 mW and the probe is relatively “weak” at 10 mW. The strong XPM effects will cause phase lag for the
CW [3], which becomes a change in power at the switched output at the polarizer. This non-linear rotation of
polarization gives an all-optical way of wavelength conversion. The NRZ data provides an average XPM effect on the
CW signal when it walks through. An optional polarization controller can be placed before the output polarizer such that
the probe signal is blocked in absence of the control signal, if needed.
The control signal (the user can add a probe before the receiver) and back-to-back received eye at the sensitivity are
shown in Fig. 2.

138 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 2. 1550-nm, 10 Gbps, NRZ Control Signal (left) and received eye at the receiver sensitivity (right)

The probe wavelength can be varied and the tunable filter at the switched output would filter out converted signal. The
1535 nm converted signal (the user can add a probe before the receiver) and eye diagram at receiver sensitivity are
shown in Fig. 3.

Figure 3. Converted 1535-nm signal (left) and eye at the receiver sensitivity (right)

Figure 4 shows BER versus Received Power for converted signal and back-to-back control signal.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 139
 Figure 4. BER vs. Received Power for back-to-back control signal (green) and converted output (orange)

Figure 5 shows BER versus Received Power for two different converted wavelengths and corresponding eye diagrams at
a received power. The user will need to modify scan parameters so as to have two sets (for two probe wavelengths) of
power scan values.

Figure 5. BER vs. Received Power for two different converted outputs

The power penalty due to difference in XPM-induced conversion efficiencies is within 0.5 dB. Thus, this scheme
potentially can provide relatively flat conversion over a range of probe wavelengths.

140 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
The nonlinear polarization rotation also finds applications in SOA-based wavelength conversion [4] and for NRZ to RZ
conversion [5].

References
1. Kwok, C. H., et al., “Nonlinear polarization rotation in a dispersion-flattened photonic-crystal fiber for ultrawideband
(>100 nm) all-optical wavelength conversion of 10 Gbit/s nonreturn-to-zero signals,” Optical Letters, vol. 31, no. 12,
June 15, 2006, pp. 1782-1784.
2. K. P. Hansen, et al., “Fully Dispersion Controlled Triangular-Core Nonlinear Photonic Crystal Fiber,” Post-deadline
paper PD2-1 to PD2-3, Proceedings of the OFC 2003.
3. Kwok, C. H., et al., “S/C/L-Band wavelength conversion by cross-polarization modulation in a dispersion flattened
photonic-crystal fiber,” Proceedings of the OFC 2006, Digital Identifier: 10.1109/OFC.2006.215680
4. Turkiewicz, J. P., et al., “1310-nm to 1550-nm wavelength conversion by utilizing nonlinear polarization rotation in a
semiconductor optical amplifier,” Proceedings of the OFC 2005, INSPEC Accession Number: 8687373.
5. Yang X., et al., “All-optical 40 Gbit/s NRZ to RZ conversion by nonlinear polarisation rotation in SOAs,” Electronics
Letters, vol. 43, no. 8, 12th April 2007.

1.47 ROADM Technology Selection and Deployment

Testing
The objective of this application note is to show how OptSim can help in technology selection and deployment testing of
Re-configurable Optical Add-Drop Multiplexers (ROADM) in order to meet dynamic network demands.
The project file is available at:

RSoft/examples/optsim/sample_mode/Networks/ROADM/ROADM_Test.moml
In a large, transparent, mesh optical networks, the lightpaths (wavelength channels) carrying information data potentially
with a variety of protocols, modulation formats and bit/line rates travel from source to destination through a path decided
by routing (and restoration) algorithms based on traffic congestion, priority assignments and other quality of service
(QoS) assurances. An end-to-end path comprises of a number of links and nodes where optical-electrical-optical (O-E-O)
conversions take place for switching and sometimes, supervisory purposes. These conversions potentially add to the
network costs, latencies, and often signal degradation.
A ROADM, on the other hand, eliminates O-E-O conversions there by eliminating need for expensive high-speed
switching electronics. Besides, all-optical switches are transparent to protocols, data-rates, modulation formats, etc. and
thus are more future-proof than their electronic counterparts. In long run, this provides savings on operating and
maintenance costs to the network operators and the service providers.
From network point of view, a ROADM includes [1] transponders, ROADM subsystem, optical service channel, optical
power monitoring, pre- and post-amplifiers, and dispersion compensating modules (DCM). The implementation of
ROADM subsystem depends upon whether it’s a fixed-point ROADM (which uses wavelength blockers (WB) and
integrated photonic Lightwave circuit (PLC)), or a small witch array (SSA) based ROADM, or a wavelength selective
ROADM that uses flexible filters, wavelength selective switches (WSS), and optical cross-connects (OXC). Each of
these sub-systems comprise of a number of photonic components. Designing (or choosing) these components with low
insertion loss, tunability (filters, lasers), etc. directly affect the network performance. Besides, since a ROADM is
expected to undergo fewer upgrade cycles, end-of-life modeling and statistical studies give valuable insights. In addition,
modeling also helps find optimum modulation format for the chosen technology. For example, partial DPSK (PDPSK) is
shown to perform better [2] with number of ROADM nodes along the path compared to classical DPSK.
The device modeling tools from RSoft can also be used to design, optimize device characteristics and select constituent
sub-system elements (like arrayed waveguide filters, PLC, etc.) of a ROADM before studying performance of the chosen
technology in OptSim. As a deployment test case, this application note evaluates performance of a WSS-based ROADM

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 141
based on its measured transfer function using custom optical filter option available in OptSim. The sample data file is
supplied with the project file. There are other choices of file formats as well, as described in the manual page for the
custom optical filter. The bitrate is 40 Gbps and the modulation format is RZ-DQPSK.
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

The baseline back-to-back case corresponds to an ideal WSS-based ROADM that behaves like a matched filter
(rectangular in time). When a signal is received with white Gaussian noise, the matched filter gives at its output the
maximum signal-to-noise ratio amongst all other filters [3].
The spectrum at the ROADM input is shown in Fig. 2 below.

Figure 2. Transmitted 40 Gbps RZ-DQPSK Spectrum

The ASE power spectral density is varied by scanning the OSNR. The plots of BER versus OSNR are compared for all
three (no filter, matched filter and ROADM filter) cases as shown in Fig. 3 below.

142 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
 Figure 3. BER versus OSNR plot for the ROADM under test as compared to matched filter and no filter at the receiver

This shows that the ROADM under test is suitable for 40 Gbps RZ-DQPSK systems and an OSNR of 12.5 dB or better
gives pre-FEC BER of 10-3 or better. This test can further be extended to study any given ROADM that is characterized
by its measured transfer function for different modulation formats and/or bit rates, presence of chromatic dispersion and
PMD, random fluctuations in ROADM transfer function bandwidth, crosstalk, etc.

References
1. Eldada, L., “ROADM Architectures and Technologies for Agile Optical Networks,” Proc. SPIE 6476, 2007.
2. Mikkelsen, B., et al., “Partial DPSK with Excellent Filter Tolerance and OSNR Sensitivity,” Electronics Letters, vol.
42, pp. 1363-1384, 2006.
3. Humblet, P. A., “Design of Optical Matched Filters,” LIDS-P-2029, GlobeCom 1991.

1.48 Unbalanced Mach-Zehnder Modulator with

Wavelength Dependent Optical Output
ProductInstDir/examples/optsim/sample_mode/Simple_components/Mach_Zehnder/UnBalancedMZM.moml

An Unbalanced Mach-Zehnder Modulator is basically a Mach-Zehnder dual-arm interferometer with an additional

phase-shift induced by an applied external electrical signal and by the unbalanced length of the arms. Figure 1 shows
schematic diagram of the Unbalanced MZM.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 143
 Figure 1. Schematic representation of an Unbalanced MZM

It consists of two waveguide arms, one longer and the other shorter. Incoming light from the Laser output splits and
traverses different distances as shown in the figure thus causing unbalanced phase-shifts between them and eventually
combines at the end of the device, resulting in the interference of the two beams. The extent of interference depends on
the external voltage signal applied to the electrodes surrounding to the two arms as shown above. Thus the resultant
superimposed output optical signal varies in intensity according to the modulating electrical signal applied externally to
the unbalanced MZM device.
Due to the unbalanced lengths of the two arms in the device, the output power also depends on the wavelength of the
optical beam traveling in the modulator due to the dependence of the phase-shift on the optical path, which varies with
the wavelength of the beam. This wavelength dependence of the output power in addition to the modulating voltage
makes the unbalanced MZM device very useful in many applications. For example, this additional feature is useful in
creating a high-speed Analog-to-Digital converter using Unbalanced MZM[1].
This example contains a simple setup illustrating the functionality of the unbalanced modulator model. Figure 2 shows
the schematic topology of the project.

Figure 2. Topology layout of the MZM based project example

144 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
The model is given a laser input that is to be modulated and at the other input, a modulating electrical voltage signal is
given. The intensity-modulated output signal from the block is captured and analyzed by an optical power meter. There
are some global variables defined in the ‘Symbols’ list of the project, which can be specified by the user. The center
frequency of the laser is set to 193.4 THz. The parameter V_in specifies the voltage value of the modulating electrical
signal in volts according to which the output power is changed. The TuningFreq_THz variable, which is set to 193.5,
specifies the central frequency, in THz, for the modulator corresponding to a zero shift. Similarly, the Bandwidth_GHz
variable is used to specify the dependence of the modulator response on the laser frequency. It is set to 250 GHz in this
example.
So, when a set of frequencies is transmitted through the unbalanced modulator model, the output genuinely follows the
modulating voltage only when the frequency of the transmitting beam equals that of the TuningFreq_THz parameter.
To show the functionality of the model as an intensity modulator and the wavelength dependence of its output power, a
scan has been setup by using the two parameters flas_THz and V_in. The flas_THz variable is scanned from 193.5 THz
to 193.625 THz in steps of 0.125 THz and the V_in is scanned from 0V to 5V in steps of 1V.
Figures 3 and 4 show the results of the simulation. Figure 3 illustrates the dependence of the output power on the
modulating voltage at various laser frequencies and Figure 4 represents the variation with laser frequency at different
modulating voltage values.

Figure 3. Output Optical Power Vs V_in for various values of flas_THz

Here, the output Optical power is plotted against the input voltage V_in for different values of laser frequency flas_THz.
We can easily see that the output power genuinely follows the modulating voltage when flas_THz equals 193.5 THz.
Also note that, when the laser frequency flas_THz exceeds its center value by half the Bandwidth_GHz value, the output
optical power completely becomes inverted.

In Figure 4, the output power is plotted against the laser frequency flas_THz which illustrates that the transfer function of
the modulator changes with the laser frequency making the model useful for various modern applications as mentioned
before.

OptSim Application Notes and Examples Chapter 1: Sample Mode Simulations • 145
 Figure 4. Output Optical Power Vs flas_THz for various values of V_in

References

[1] Chris Sarantos and Nadir Dagli, Fellow, IEEE, “A Photonic Analog-to-Digital Converter Based on an Unbalanced
Mach-Zehnder Quantizer”, IEEE, 2007

146 • Chapter 1: Sample Mode Simulations OptSim Application Notes and Examples
Chapter 2: Block Mode and
Transient Simulations

This chapter presents a selection of examples, tutorials and application notes for the block mode and transient
simulations. More examples of topologies that can be simulated in OptSim may be given in the Examples directory of
the distribution (examples/optsim/block_mode/).

2.1 Getting Started

2.1.1 10 Gbps Single Channel Link

RSoft/examples/optsim/block_mode/getting_started/10GbpsLink.moml
The purpose of this example is to demonstrate a simulation of a 10 Gbps direct modulated single channel optical link.
The example is found in the Examples directory of the OptSim installation in the file 10GbpsLink.moml. Several
models, component parameters, and options will be highlighted in this example.
Load the 10GbpsLink.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below. The topology contains a number of component models
represented by block icons which can be categorized into four categories: transmitter, channel, receiver, and control.
The transmitter category includes such models as the pseudorandom binary sequence generator (PRBS), electrical signal
generator, and direct modulated laser. The channel category includes models such as the fiber which carries the optical
signal generated in the transmitter. The receiver category includes such models as the compound receiver model and bit
error rate tester. Finally, the plot icons are included in the control category.

Figure 1. 10GbpsLink.moml

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 147
In this example, the PRBS block generates a binary sequence of length 27 (2^7) bits at the specified data rate of 10 Gbps
(10e9 bps) This pattern is a pseudorandom binary sequence, except that it has an extra zero added to it to make its length
a power of 2, and the first two bits and last three bits are zero. This signal is then passed on to the electrical signal
generator block and the BER tester block. The electrical signal generator block converts this binary sequence into an
electrical signal based on the specified parameters. In this example, the signal is a non-return-to-zero (NRZ) current
waveform with the binary value 0 represented as 0 amps and the binary value 1 represented as 36e-3 amps. The signal
waveform is created based on ramping the signal from the low to high values with the specified rise time and fall times.
A filter is used to add ringing to the electrical signal to model nonlinearities in the laser driver circuitry. Timing jitter
may also be added to the electrical signal if desired. The sampling rate of the signal is also specified in the electrical
signal generator by specifying the number of sampling points to be used to represent each bit in the sequence. In this
example, 25 (2^5) points per bit are selected. This gives a sampling rate of 3.2e11 samples/second, or a sample time
step of 3.125 ps. The electrical signal which is output from the electrical signal generator is passed to the input of the
direct modulated laser model. The direct modulated laser model models a semiconductor laser using laser rate equations;
parasitics are also accounted for. Nonlinearities in the laser, including relaxation oscillations, transients, and chirp are
modeled by the rate equations. The user can also use the Test button in the component parameter editing window to see
the L-I curve and the small signal frequency response which correspond to the specified component parameters. This is
useful in guiding the user’s choice of the parameters to model the desired system.
The output of the laser model is an optical signal which represents the transmitted bit sequence. The time-domain optical
signal magnitude can be viewed by double clicking on the signal plot icon which receives input from the laser model.
Likewise, the baseband RF signal spectra can be viewed with the spectra icon. The optical signal from the laser model is
passed on to the fiber model, which solves the nonlinear Schrödinger equation using the split-step Fourier method. The
fiber models the effects of attenuation, dispersion, and nonlinearities on the optical signal. The output of the fiber model
is an optical signal which is passed on to the optical power normalizer block.The power normalizer allows the user to
specify the desired average output power. The attenuation is determined by the model based on the average input power
to produce the desired average output power. This is useful for setting the average received optical power at the receiver.
The average output power of the power normalizer is set to a user variable named “averecpower”. This variable is
defined in the symbol table, or list of user variables. The utility of this arrangement is described below in the section on
simulating the link.
The optical signal output of the power normalizer is passed to the receiver model block. The receiver model incorporates
the photodetector, transimpedance amplifier, post amplifier and filter, and noise of the optical receiver. The receiver
model converts the optical input power to an electrical current, and then models the amplification and shaping of that
signal to produce the output electrical voltage signal. The electrical signal coming out of the receiver can be viewed
from the signal plot icon. In this example, the noise is not included in the signal plot. The eye diagram of the electrical
signal coming out of the receiver can be viewed from the eye diagram icon. The noise is included in the eye diagram in
this example. The baseband RF signal spectra of the electrical signal coming out of the receiver can be viewed with the
spectra plot icon. The electrical signal output of the receiver model is passed on to the BER tester. This block uses the
signal waveform and the time-dependent noise which accompanies it to determine the average bit error rate. The BER
block automatically determines the ideal sampling time and decision threshold based on the input signal waveform. For
each bit in the sequence, it determines the probability of error based on the signal level at the sampling time, the noise in
the signal, and the binary value which it represents (as supplied in the reference binary signal from the PRBS generator).
It then determines the average bit error rate by averaging together all the probabilities of error of each of the bits in the
sequence.
There are several options for performing the simulation. The quickest and easiest is to perform a single simulation run
using the nominal parameter values. This is accomplished by clicking on the green light button in the moml toolbar, or
choosing Go from the Run menu. During the course of the simulation, the component which is currently being simulated
is listed in the status line at the bottom of the OptSim window. At any point in the course of the simulation, the
simulation may be smomlped by pressing the red light button or choosing Smoml Simulation from the Run menu. At the
conclusion of the simulation, the simulation log file generated by the simulation can be viewed to see a record of the
simulation messages. If a warning is issued during the simulation, it is listed in more detail in the log file also. The log
file can be accessed from the user interface through the Utility->Open Simulation Log File menu item.
Using the scan variable simulation option, up to two user variables or symbols can be scanned across a range of values in
a nested fashion, with a simulation run being performed for each set of variable values. This simulation option is
optimized to minimize the computational requirements for the scan while maintaining its accuracy. For example,
components which are not affected by the variables being scanned are not resimulated at each iteration, but their

148 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
previous results are reused to speed up the simulation. The status of the scan simulation, showing how many iterations
are completed out of the total number of iterations, can be viewed in the lower right corner of the OptSim window during
the course of the simulation. To produce a plot of the BER vs. received optical power, choose the Scan Variable option
in the Run menu, and set the variable to be scanned to “averecpower”, the variable name used in the output power
parameter of the power normalizer block. Choose a start and end point for the scan, as well as a step value. For
example, the scan can start with –15, end with –21, and step by –2 for each scan. Scans may be performed with either
positive or negative step values. Also choose a filename prefix or Scan Meta Prefix which will be used to prefix the
filenames of the files generated by the simulation, including plot files. An iteration meta prefix can also be chosen for
each variable being scanned to identify which scan iteration each of the generated output files belongs to. Leaving the
iteration meta prefix empty will cause the plot icons to not generate plots at each iteration. Running this scan simulation
will produce a BER vs. received optical power curve.
Families of BER curves may be generated by scanning two variables simultaneously. For example, set the outer iteration
variable to be “Io”, the variable used in the bias current parameter of the laser. Choose a start and end point for the scan
of this variable, say 10e-3 and 60e-3 with a step of 10e-3. Then choose an outer iteration prefix and perform the
simulation. A family of BER vs. received optical power curves are generated, with each curve representing a different
laser bias current value.
Another simulation option available from the Scan Variable dialog is statistical simulations. If the number of statistical
simulations is set to 0, then only the nominal values for each parameter will be used in the simulation. However, if the
value is 1 or higher, then the specified number of simulation runs will be performed, with the parameters that have
specified distribution functions and nonzero standard deviations statistically varied according to their specifications. A
statistical iteration meta prefix should also be specified to allow simulation output files to be correlated to the statistical
run which generated them. Alternatively, if this meta prefix is left blank, the plot icons will not generate plots at each
iteration.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 149
2.2 Transmitters

2.2.1 NRZ, RZ, CRZ and CSRZ Modulation

RSoft/examples/optsim/block_mode/transmitters/ModulationFormats.moml
In this example we demonstrate two most used modulation formats in optical communications – nonreturn-to-zero
(NRZ) and return-to-zero (RZ) - as well as two additional variants of RZ format – chirped RZ (CRZ) and carrier-
suppressed RZ (CSRZ).

Figure 1. Schematic setup for different modulation formats.

150 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 NRZ Spectrum RZ Spectrum
0 0

-10 -10

-20 -20
Power (dBm)

Power (dBm)
-30 -30

-40 -40

-50 -50

-60 -60
15496 15498 15500 15502 15504 15496 15498 15500 15502 15504
x10-10 x10-10
Wavelength (m) Wavelength (m)

CRZ Spectrum CSRZ Spectrum

0 0

-10 -10

-20 -20
Power (dBm)

Power (dBm)
-30 -30

-40 -40

-50 -50

-60 -60
15496 15498 15500 15502 15504 15496 15498 15500 15502 15504
x10-10 x10-10
Wavelength (m) Wavelength (m)

Figure 2. Transmitter optical spectrum for different modulation formats

Figure 1 shows schematic setup with four transmission links with different modulation format. Each link consists of
PRBS generator, transmitter, optical filter, attenuator, receiver, and BER tester. Transmitters represented as compound
components blocks, i.e. combination of blocks. For example, NRZ transmitter combines CW Laser source, Electrical
signal generator (NRZ driver), external Mach-Zehnder modulator, and attenuator. The following parameters of
transmitter can be set: power, wavelength, extinction ration, rise/fall time, RIN, etc. In case of RZ transmitter the
electrical signal generator generate RZ signal with raised cosine shape and given duty cycle. In CRZ transmitter we add
a chirp to RZ optical by applying a phase modulation. Parameter PMcoeff specifies the amplitude of phase modulation
(zero-to-peak) in radians. And finally in case of CSRZ transmitter the RZ optical signal after Mach-Zehnder modulator
goes through phase modulator driven by analog sine wave generator at frequency equal to half of the bit rate. That will
introduce a π phase shift between any two adjacent bits and the spectrum will be modified such that the central peak at
the carrier frequency is suppressed.

NRZ waveform RZ waveformlot

0 3
Signal Magnitude (dBm)

Signal Magnitude (dBm)

-3 0

-6 -3

-9 -6

-12 -9

-15 -12

0 1 2 0 1 2
x10-9 x10-9
Time (s) Time (s)
x polarization x polarization

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 151
 CRZ waveform CSRZ waveform

3 3

Signal Magnitude (dBm)

Signal Magnitude (dBm)

0 0

-3 -3

-6 -6

-9 -9

-12 -12

0 1 2 0 1 2
x10-9 x10-9
Time (s) Time (s)
x polarization x polarization

Figure 3. Transmitter signal waveform for different modulation formats

Figure 2 shows transmitter optical spectrum for different modulation formats. One can observe the central peak
suppression in case of CSRZ. Figure 3 gives corresponding signal waveforms. In case of NRZ format, the optical pulse
representing each 1 bit occupies the entire bit slot and does not drop to zero between two or more successive 1 bits. In
the RZ format, each optical pulse representing 1 bit is chosen to be shorter than the bit slot, and its amplitude returns to
zero before the bit duration is over. The ratio of the pulse width to bit duration is referred to as the duty cycle of the RZ
bit stream.

For CRZ and CSRZ one can observe the phase modulation (Figs. 4 and 5) of the signal as well as chirp for CRZ case
(Fig. 4).

CRZ Transmitter Signal Phase Chirp at CRZ Transmitter

x1010
2

1
Frequency Chirp (Hz)
Phase (rad)

1
0

-1
0

0 1 2 0 1 2
x10-9 x10-9
Time (s) Time (s)

Figure 4. Phase and Chirp of CRZ Transmitter.

CSRZ Transmitter Signal Phase

-1
Phase (rad)

-2

-3

0 1 2
x10-9
Time (s)

Figure 5. Phase of CSRZ Transmitter.

152 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Finally, Figure 6 shows receiver eye diagrams for each of modulation formats.

Figure 6. Receiver eye diagrams for different modulation formats

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 153
2.2.2 Study of Duobinary Transmitter
RSoft/examples/optsim/block_mode/transmitters/duobinary.moml
In this example, we investigate generation and transmission of duobinary data. We simulate a single-channel (1550nm)
90-km long OC-192 link as shown below.

Figure 1. Topologies using single low-pass filter(left) and delay-and-add circuit (right)

It is known that a duo-binary filter can be approximated by a low-pass filter with half-power cut-off at approximately
one-fourth the data rate [1]. At this cut-off frequency, the spectral occupancy of the modulated optical field is restricted
to [f0 ± (Bit rate)/2], where f0 is the nominal continuous wave (CW) laser frequency. The receiver’s electrical bandwidth
requirement is identical for both the conventional non-return to zero (NRZ) and the amplitude-modulated phase-shift
keyed (AM-PSK) duo-binary system here. The frequency spectrum of an ideal duo-binary signal exhibits the first nulls at
[f0 ± (Bit rate)/2]. We can band-limit the signal at [f0 ± (Bit rate)/2] while preserving at the same time, enough
information for later reconstruction of the signal [2]. The duo-binary filter used for this example is a fifth order low-pass
Bessel filter. The topology is shown on the left in Fig. 1 above. The right hand side topology of Fig. 1 is an alternative
approach of generating duobinary signals where an ideal NRZ is passed through a delay-and-add circuit followed by an
optional bandlimiting filter of bandwidth (Bit rate)/2. These two implementations are different and accordingly will give
non-identical plots. For this example, we analyze the low-pass filter implementation of duobinary transmitter and leave
the delay-and-add circuit implementation as an exercise. Both of these topologies can be found at
/examples/duobinary.moml.
Figure 2 shows signal plots (left) and base-band spectra plots (right) for binary NRZ and duo-binary NRZ transmissions
respectively. The duo-binary filter compresses the spectral occupancy of the signal.

Figure 3 shows transmitted optical spectrum of duobinary data at the output of MZ modulator (left) and also shown on
the right is signal amplitude and 1800 phase transitions at the output of MZ modulator.

Figure 4 shows single scan eye diagrams at following points of interest: (1) at the output of duobinary filter (top left), at
the output of MZ modulator (top right) and (3) at the receive end of a 90-km standard single mode fiber (SMF) link with
17ps/nm.km dispersion.

154 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 2. Signals (right) and base-band spectra (left) plots of binary and duo-binary NRZ signals

Figure 3. Transmitted optical spectrum (right) and signal phase transitions at MZ modulator output (left)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 155
 Figure 4. Eye diagrams at the MZ modulator (top),at the duobinary filter (middle), and at the receiver.

References
1. Walkin, S., and Conradi, J., “On the relationship between chromatic dispersion and transmitter filter response in
duobinary optical communication systems,” IEEE Photonic Technology Letters, vol. 9, no. 7, July 1997, pp. 1005-
1007.
2. Lee, E. A., and Messerschmitt, D. G., Digital Communication, 2/e, Kluwer Academic Publishers, Norwell, MA,
USA, 1994.

156 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.2.3 Transmitter Band-limiting Filter Study
RSoft/examples/optsim/block_mode/transmitters/tx_bandlimit.moml
Here we study the influence of a transmitter band-limiting filter on the single channel link performance. It is not
necessary to employ any band-limiting filter at the transmitter. However, such a filter can restrict the spectral occupancy
of the electrical modulating signal before driving the modulator and we shall see that it can make an interesting impact
on the overall system performance.
Figure 1 shows the topology of a 90km, 1550nm single-channel optical link operating at OC-192 data rate.

Figure 1. tx_bandlimit.moml

The filter employed to restrict the spectral contents of the electrical modulating signal in this example is fifth order low-
pass Bessel filter. We define filter’s spectral efficiency as the ratio of input bit rate (bits/sec) to the filter’s 3-dB
bandwidth (in Hz). We run a parameter scan varying the spectral efficiency from 10% to 400%. The corresponding Q-
factor and BER plots are shown in Figure 2.

Figure 2. Q-factor (left) and BER (right) plots versus filter’s spectral efficiency

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 157
It would be equally interesting to see how such a filter can influence the performance as the length of the fiber varies.
We consider four different values of the filter’s spectral efficiency. The length of the fiber is varied between 80 to
95kms in uniform increments of half-a-kilometer each. Figure 3 depicts this behavior.

Figure 3. Effect of variation in fiber length on the BER for different cut-off frequencies of the transmit filter

158 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.2.4 DPSK Modulation
RSoft/examples/optsim/block_mode/transmitters/DPSK.moml
RSoft/examples/optsim/block_mode/transmitters/RZ_DPSK.moml
The purpose of this example is to demonstrate application of differential-phase-shift-keyed (DPSK) and RZ-DPSK signal
formats. DPSK format is a subset of PSK format which one of three modulation techniques used in digital
communications: ASK (amplitude-shift-keying, also known as on-off-keying – OOK), FSK (frequency-shift-keying),
and PSK.

1 3
2

(a)

(b)

Figure 1. Topology setting for DPSK modulation . Top topology (file DPSK.moml) and bottom topology (file RZ_DPSK.moml)

As it follows from PSK format definition, the optical bit stream is generated by modulating the phase while keeping the
amplitude and the frequency of the optical carrier constant [1]. In case of binary PSK (BPSK) the phase takes two values,
commonly chosen to be 0 and π. One of the consequences of PSK format is that optical intensity remains constants
during all bits and hence the direct detection receivers cannot be used to detect PSK signals. The additional
demodulation is required and some form of coherent detection technique needs to be applied.
The information carrying part for DPSK encoded data is the phase difference applied to the carrier corresponding to the
two consecutive data bits. If the previous bit was 0, no phase shift is applied to the encoding of the current bit. If the
previous bit was 1, the phase of the carrier for the current bit is applied a phase shift of 180o.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 159
In case of RZ-DPSK format the RZ pulse rather than CW signal is modulated, i.e. the optical pulse appears at each bit
slot, with a binary data decoded as either a 0 or π phase shift between adjacent bits. Unlike PSK, where the detection
methods dictate the carrier phase to be accurately recovered, the detection of DPSK does not impose too stringent phase
stability requirement. Since the phase difference of the received consecutive bits is all one needs to extract the
transmitted information, it would suffice if the phase of the carrier remains more or less stable for the time duration that
corresponds to two bits. Most optical communication systems employ conventional OOK signals. However there can be
situations when DPSK and RZ-DPSK format can improve system performance. For example, RZ-DPSK format
compared with standard amplitude modulated RZ format gives about 3dB optical SNR improvement because of optical
pulse being present in each bit slot.

Figure 2. Eye diagrams for DPSK (left column) and RZ-DPSK (right column) signals in transmission links.

The topology setup for transmission links with DPSK and RZ-DPSK modulation are shown in Fig. 1. The only
difference between two topologies is in DPSK Transmitter configuration - in DPSK case we used CW Laser as an optical
signal source, whereas for RZ-DPSK format we used for optical source a Mode-locked Laser, which generated a train of
Raised Cosine RZ pulses at repetition rate equal to bit rate. There is also another alternative way to create RZ-DPSK

160 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
modulated pulse – instead of Phase Modulator one can use Mach-Zehnder Modulator. MZM can provide the phase
modulation by driving at twice the switching voltage and by shifting bias to transmission null.
Figure 2 summarizes the transmission results by depicting the evolution of a signal eye diagram along the transmission
link for both DPSK (left) and RZ-DPSK (right) formats.
DPSK transmitter (Block 1 in Fig. 1) consists of Laser (optical source), Bit Pattern Generator, Electrical Signal
Generator, and Phase Modulator.
After transmission through 20 spans of optical fibers and amplifiers the DPSK modulated signal enters receiving section
of topology. The eye diagram of DPSK signal before demodulation is shown in the first row of Fig. 2. Here one can see
that optical signal has either constant intensity (for CW case) or only “1” bits (for RZ case), hence in the both cases, the
data cannot be detected by IM/DD receiver.
Next, Mach-Zehnder Delay Interferometer (MZDI, represented by Block 2 in Fig. 1) is used to demodulate DPSK signal.
The differential time delay for MZDI is set to the bit duration (i.e. 100 ps for 10 Gbps). Two outputs of MZDI
correspond to “constructive” and “destructive” ports. Maximum power appears at the “constructive port” when there is
no phase change between adjacent bits, and at the “destructive” port when the phase in adjacent bit differs by π . Then
two outputs of demodulator are input to a balanced receiver (see Block 3 in Fig. 1). Balanced receiver combines two
Optical Receivers for “constructive” and “destructive” parts of optical input signals. Eye diagrams corresponding to for
“constructive” and “destructive” ports are given in second and third row of Fig. 2. Next, the output electrical signal from
one of receivers is inverted and then both electrical signals are combined by Electrical Summer. Resulting eye diagram is
given in the last row of Fig. 2.

References
1. G. Agrawal , “Fiber-Optic Communicatiobn Systems” , Willey & Sons, 1997
2. A. H. Gnauck, and P. J. Winzer , “Optical Phase-Shift-Keyed Transmission”, J. Lightwave Technology, vol.23,
no.1, p.115

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 161
2.3 Fiber Dispersion

2.3.1 Dispersion Compensation

RSoft/examples/optsim/block_mode/fiber_dispersion/no_dispersion_comp_WDM.moml
RSoft/examples/optsim/block_mode/fiber_dispersion/post_dispersion_WDM.moml
RSoft/examples/optsim/block_mode/fiber_dispersion/pre_dispersion_WDM.moml
Different spectral components of the launched optical pulse travel within the fiber at slightly different group velocities.
This spreads the pulse in the time domain producing the effect known as chromatic dispersion (CD). The following
example illustrates the use of OptSim in studying dispersion compensation in a long-haul high-speed WDM system, and
demonstrates how OptSim can help in understanding, evaluating and optimizing the chromatic dispersion compensation
methods.
Dispersion management in single mode fiber links can be accomplished in many ways, though the most widely used
approach employs lengths of transport fiber of opposite dispersion characteristics to the principal fiber in the link,
usually standard singlemode fiber (SSMF). Typically a 10 to 20km length of dispersion compensating fiber (DCF) is
placed before the regenerators inducing negative dispersion to compensate for the positive dispersion accumulated over
the 60 to 80km length of the SMF. Although the total dispersion over the entire SMF-DCF span can be minimal, net
dispersion at any point along the span is non-zero, which keeps the nonlinear mixing effects at minimum levels.
Depending upon the placement of DCF in each span, the dispersion compensation is categorized into the two
implementations: dispersion post-compensation and dispersion pre-compensation. In the post-compensation scheme, the
DCF is placed after the SMF. In the pre-compensation scheme, the DCF is placed prior to the SMF.
The topology of Fig. 1 below has a total link-length of 600 km. Each 100-km span consists of 80 km of ITU-T G.652
SMF and 20 km of DCF. The total data rate of the 4-channel WDM link is 40 Gbps. The wavelength plan is a non-ITU-
T grid with widely placed channels in order to illustrate clearly the distinct dispersion slopes for each wavelength.

Figure 1. Topology of a 600-km, 40-Gbps WDM system used to illustrate dispersion compensation.

The Property Map module in OptSim can plot accumulated dispersion and power maps along the link [Ref. 1]. Figure 2
shows performance for an uncompensated (i.e., SMF span = 100km, and DCF span = 0km) link. The power map rises

162 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
with the link length because the amplifier over-compensates for the attenuation at each span. Since there is no dispersion
scheme employed, the accumulated dispersion for each wavelength produces a closed eye at the receiver even if the link
is not power-limited.

Figure 2. Performance with no dispersion compensation a) Dispersion map b) Power map, c) Eye diagram.

On the other hand, if we use DCF with a high figure of merit (FOM) to compensate for the accumulated dispersion, we
can see (Figure 3(d)) an impressive improvement in the performance. Figure 3(a) shows the dispersion maps for all four
channels. The unequal accumulated dispersion at the end of each SMF segment for each wavelength is due to the
wavelength-dependent dispersion in the fiber, also known as the dispersion slope. The power map in Figure 3(c) shows
that the power falls more rapidly in the DCF section than in the SMF section because of the larger attenuation typically
associated with the DCF. A closer look at the Span 1 dispersion map (Figure 3(b)) shows that the net dispersion at the
end of the span is non-zero, but minimal, and does not materially affect the simulation results in this example.
An alternate approach for dispersion compensation is known as “pre-compensation,” where we first introduce negative
dispersion in anticipation of subsequent SMF-induced positive dispersion.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 163
 Figure 3. Performance of a WDM link with dispersion post-compensation) Dispersion map, b) closer look at the Span 1 dispersion
map, c) Power map, d) Eye diagram

164 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 4. Performance of a WDM link with dispersion pre-compensation.a) Dispersion map, b) closer look at the Span 1 dispersion
map, c) Power map, d) Eye diagram

A careful comparison of the eye diagrams in Figure 3(d) and Figure 4(d) reveals that the pre-compensation scheme
produces a slight improvement in performance over the post-compensation scheme, as evidenced by the cleaner and
wider eye-opening in Figure 4(d). This is because pre-compensation decreases the signal power faster than post-
compensation due to the higher attenuation of the DCF, and the signal experiences normal dispersion while the signal
power is higher; whereas in post-compensation, the signal power falls more slowly in the SMF and experiences
anomalous dispersion while the signal power is higher. Pre-compensation has also been shown to result in pulse
compression due to self-phase modulation (SPM), rather than the more detrimental pulse broadening effect that occurs in
post-compensation [Refs. 2, 3]. Due to the interplay between dispersion, nonlinearities, and signal power, the dispersion
map strongly affects the pulse evolution in the link. For a more detailed analysis of these physical effects, the reader is
referred to the references.

References
1. OptSim Models Reference
2. Thiele, H. J., Killey, R. I., and Bayvel, P., “Influence of fibre dispersion and bit rate on cross-phase-modulation-
induced distortion in amplified fibre links,” Electronic Letters, vol. 34, 1998, pp. 2050-2051.
3. Rothnie, D. M., and Midwinter, J. E., “Improved standard fibre performance by positioning the dispersion
compensating fibre,” Electronics Letters, vol. 32, 1996, pp. 1907-1908.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 165
2.3.2 Chromatic Dispersion: Penalties and Compensation
In this example, we investigate effects of chromatic dispersion (Part I) and its compensation using the dispersion
compensating fiber (DCF) (Part II).
Part-I
RSoft/examples/optsim/block_mode/fiber_dispersion/no_dispersion_comp.moml

Fig.1 Topology for studying chromatic dispersion-induced penalties

The topology shown in Fig. 1 simulates a single-channel link. Four lengths of the single mode fiber (70km, 80km, 95km
and 115km) accumulate different amount of chromatic dispersion as shown in the dispersion map of Fig. 1. Since our
main focus here is to see the effect of chromatic dispersion-induced penalties, fiber-loss, non-linearities and PMD are
ignored. To run this example, click on the “GO” button.
Figure 2 shows that as the length of the fiber is increased, total accumulated dispersion increases resulting in dispersed
(inter-symbol interference) eye diagrams and deteriorated BER performance (Fig. 3). Fortunately, there are ways to
alleviate dispersion-induced penalties by appropriate choice of dispersion compensation techniques. One of these is
described below in Part-II.

166 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Dispersion Map

2000 Channels
λ=1.5500 µm

Dispersion [ps/nm]
1000

0 20 40 60 80 100 120
Distance [km]

Fig. 2 Dispersion map over 115km of single-mode fiber

BER (70-km, 10Gbps)

10-12

10-13

10-14
BER

10-15

10-16

10-17
-1 0 1
Single Result

(a) Eye (left) and BER (right) at 70km

BER (80-km, 10Gbps)

10-10

10-11
BER

10-12

10-13

10-14
-1 0 1
Single Result

(b) Eye (left) and BER (right) at 80km

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 167
 BER (95-km, 10Gbps)

BER
10-4

-1 0 1
Single Result

(c) Eye (left) and BER (right) at 95km

BER (115-km, 10Gbps)

10-2.2

10-2.3

10-2.4

10-2.5
BER

10-2.6

10-2.7

10-2.8

10-2.9

10-3.0
-1 0 1
Single Result
(d) Eye (left) and BER (right) at 115km
Fig.3 Received eye diagrams and corresponding BER values

Part-II

RSoft/examples/optsim/block_mode/fiber_dispersion/dispersion_comp.moml
The most common dispersion compensation technique used in long-haul links uses short lengths of DCFs followed by
relatively longer lengths of transmission fibers in each span. This is also known as post-compensation of chromatic
dispersion.
The 20-km of DCF above in each span has negative dispersion slope. The net accumulated dispersion in each of the 20
spans is non-zero in order to help control nonlinearity-induced performance penalties. The amplifier in each span
compensates for the fiber attenuation. The total length of the link is 2000km. Figure 5 below shows dispersion map for
the entire link as well as the map for one single span.
Based on the observations of Part I and Part II, one can conclude that the chromatic dispersion, unless properly
compensated, restricts transmission distances. The DCF helps compensating for chromatic dispersion thereby allowing
transmission over longer distances.

168 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Fig. 4 Topology using dispersion compensation

Dispersion Map Dispersion Map (Single Span)

1500 Channels 1400 Channels
λ=1.5500 µm λ=1.5500 µm
1200
1200

1000
Dispersion [ps/nm]

Dispersion [ps/nm]

900
800

600 600

400
300
200
0
0
0 1000 2000 800 810 820 830 840 850 860 870 880 890 900
Distance [km] Distance [km]

Fig. 5 Dispersion map for the entire link (left) and for a single span (right)

BER (2000-km, 10Gbps)

10-10

10-11
BER

10-12

10-13
-1 0 1
Single Result

Fig. 6 Eye diagram (left) and BER (right) after 2000km of dispersion compensated transmission

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 169
2.3.3 Chromatic Dispersion Compensation Study
RSoft/examples/optsim/block_mode/fiber_dispersion/disp_nodisp.moml
The purpose of this example is to study the influence of chromatic dispersion and its compensation on the performance
of a single-channel OC-192 link. This example simulates a 120km long 10Gbps point-to-point link deploying a standard
single mode fiber (SMF). We use a dispersion-compensating fiber (DCF) to provide dispersion post-compensation.
Figure 1 shows the topology.

Figure 1. disp_nodisp.moml

The topology shows two fiber blocks. The first block models a standard SMF and the second block models a DCF. The
length of the DCF is kept zero for the uncompensated transmission. The outer iteration in the parameter-scan window
shown in Figure 2 below takes care of absence or presence of the DCF. The total length of the link is maintained
identical in both of these cases. The inner iteration of the scan helps in understanding the impact of varying the
transmitted optical power.

Figure 2. Parameter scan window

170 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 3. Q-factor (left) and BER (right) plots for uncompensated and post-compensated links

Figure 3 shows performance plots (Q-factor and BER) for uncompensated and post-compensated cases.
Since high transmitter power presents a better SNR-floor, the performance of the link improves significantly as the
power increases. This improvement is seen in both the cases irrespective of presence or absence of the DCF. Also, for
the identical transmitter power, the post-compensated link exhibits marked improvement in bit-error-rates (BER) as
compared to those of an uncompensated link.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 171
2.3.4 Dispersion Shifted Fiber (DSF) Study
RSoft/examples/optsim/block_mode/fiber_dispersion/single_channel_smf_dsf.moml
RSoft/examples/optsim/block_mode/fiber_dispersion/wdm_smf_dsf.moml
The purpose of this example is to study the comparative performance of deploying a dispersion-shifted fiber (DSF) in
single-channel and WDM links. In this example, we first simulate a single-channel OC-192 link operating at 1550nm
wavelength using a standard single mode fiber (SMF). We observe its performance by replacing the SMF with a DSF of
identical length. Next, we simulate an 8-channel WDM link using the SMF with an aggregate bit-rate of 80Gbps. The
channels are spaced 100GHz apart. For the sake of simulation speed and simplicity, we ignore Raman and four-wave-
mixing (FWM) effects. We then replace the SMF with a DSF and repeat the simulation. We observe the performance
metrics (Q-factor and BER) of channel number 8 that corresponds to 1550nm wavelength in order to make a comparison
with its single-channel case counterpart. The length of the link is varied between 90km and 130km in both the cases.
Figure 1 shows the single-channel topology in file single_channel_smf_dsf.moml.

Figure 1. Topology schematic for the single-channel case (single_channel_smf_dsf.moml)

The outer iteration of the parameter-scan block (Figure 2) takes care of replacing the SMF with a DSF model. The inner
iteration is responsible for uniformly varying the length of the fiber from 90km to 130km. The continuous-wave (CW)
laser emits a zero line-width signal with nominal wavelength of 1550nm.

Figure 2. Parameter scan window

172 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
The Q-factor and BER plots are shown in Figure 3.

Figure 3. Q-factor (left) and BER (right) plots for varying fiber lengths

Because of better dispersion handling capabilities, a DSF shows marked improvement in performance as compared to
the single-channel link with an SMF.
Next, we simulate a similar study for a WDM link. Figure 4 shows the corresponding topology.

Figure 4. Topology for an 8-channel WDM system (wdm_smf_dsf.moml)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 173
The wavelength plan is shown in Figure 5.

Figure 5. WDM wavelength plan

We can see from Figure 5 that channel number 8 has nominal wavelength of 1550nm. This is also the wavelength used
in the single-channel case previously. The Q-factor and BER plots are shown in Figure 6.

Figure 6. Q-factor (left) and BER (right) plots for channel number 8

We can see that the qualitative performance of a WDM system shows improvement for DSF deployment in a fashion
analogous to that in the single-channel counterpart of Figure 3. However, for the WDM case, the fiber now supports
higher aggregate power and bit-rate, though the per-channel power and bit-rates are identical to those of the previous
single-channel scenario. The resultant non-linear effects and the far-from-ideal filters in the demultiplexer module are
responsible for further deterioration of the performance as compared to the case when fiber carried only one channel.

174 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.4 Fiber Linear Effects

2.4.1 Fiber-induced Loss: Penalties and Compensation

In this example, we investigate effects of fiber-induced loss (Part I) and ways to compensate it (Part II).
Part-I
RSoft/examples/optsim/block_mode/fiber_linear_effects/loss_penalties.moml

Fig.1 Topology for studying fiber-induced loss

The topology shown in Fig. 1 simulates a single-channel link. The transmitted power is kept constant while the bit-rate
and the length of the fiber are varied. Since our main focus here is to see the effect of fiber-induced loss, dispersion and
non-linearities are ignored. To run this example, click on the “Scan” button.
Figure 2 shows transmitted and received optical signals for the case of 10Gbps transmission over the distances of 80km
and 100km. The transmitted optical signal is attenuated at the rate of 0.25dB/km.

Transmitted Optical Signal (10Gbps) Received Optical Signal (10Gbps)

-12
6 Legend:
-13 80-km
5
-14
Signal Magnitude (dBm)

Signal Magnitude (dBm)

100-km
4 -15

3 -16
-17
2
-18
1
-19
0
-20
-1 -21
0 2 4 6 8 10 12 0 2 4 6 8 10 12
x10-9 x10-9
Time (s) Time (s)

Fig.2 Transmitted (left) and received (right) optical signals

Figure 3 shows corresponding received electrical eye diagrams at 80-km and 100-km distances. Notice the deterioration
in signal-to-noise ratio in the eye at 100-km distance due to the fiber attenuation as compared to the one at 80-km.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 175
 Fig. 3 Eye Diagrams at 80-km (left) and 100-km (right)

Figure 4 illustrates what impact the fiber attenuation can have over the supportable data rates and distances.

Q2
30 Legend:
bitrate = 1.000000e+010

bitrate = 2.000000e+010
20
bitrate = 3.000000e+010
Q2 (dB)

bitrate = 4.000000e+010

10

8 9 10
x104
Distance

176 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 BER

Legend:
bitrate = 1.000000e+010
10-1
bitrate = 2.000000e+010
-2
10
bitrate = 3.000000e+010
10-3
BER

10-5 bitrate = 4.000000e+010

10-9
10-16
10-27
10-47
10-81
10-138
8 9 10
x104
Distance

Fig. 4 Q (top) and BER (bottom) plots as functions of supportable distances and data rates

For a given receiver sensitivity, transmitted power, and the bit-rate, the fiber-loss can severely limit the transmission
distance as is evident from Fig. 4.
Part II

As we saw in Part I, fiber-induced signal loss puts limit on the transmission distance. The most common approaches for
loss compensation use either (a) discrete optical amplifier stages or (b) amplification scheme that makes use of
distributed Raman amplification.

RSoft/examples/optsim/block_mode/fiber_linear_effects/loss_compensation_lumped.moml
RSoft/examples/optsim/block_mode/fiber_linear_effects/loss_compensation_distributred.moml

(a) Lumped Amplification:

The topology for this scheme looks like:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 177
 Fig. 5 Topology for the fiber loss compensation scheme that uses discrete amplifier stages

The total length of the transmission distance is more than 1600km comprising of 20 spans each of which has 80-km of
single mode fiber followed by a 10-m length of erbium-doped fiber. The multiplexer combines data channels with the
pump signal. The erbium-doped fiber acts as an amplifier thereby compensating for the signal loss occurring in the 80-
km span of the single mode fiber preceding it. Fig. 6 shows eye diagram and Fig. 7 shows corresponding BER and Q-
factor values.

Fig.7 Received Eye Diagram

178 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Q2

21.2

21.0

20.8
Q2 (dB)

20.6

20.4

20.2

-1 0 1
Single Result

Fig. 8 Q-factor (left) and BER (right) of the received signal

As can be seen, compensation of fiber loss using lumped amplifier stages helps transmit over longer distances.
(b) Distributed Amplification:
Figure 9 shows topology layout of the loss compensation scheme that uses distributed Raman amplification over the
fiber link. Unlike lumped amplifier scheme, compensation of fiber loss is obtained in the same fiber by exploiting
distributed Raman amplification where high-power pump signals are launched (forward and/or backward) along with the
data signal.

Fig. 9 Topology layout of the loss compensation scheme using distributed Raman amplification

In above topology, we use three backward pumps and no forward pump. The distributed amplification takes place over
the length of 40-km of single-mode fiber in each of the total ten spans.
Figure 10 shows received eye after the transmission over 400-km. The corresponding Q-factor and BER are shown in
Fig. 11.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 179
 Fig. 10 Received Eye Diagram

Q2 BER
10-19
20.6
10-20
20.4
10-21
20.2
10-22
20.0
Q2 (dB)

BER

10-23
19.8
10-24
19.6
10-25
19.4
10-26
19.2
10-27
-1 0 1 -1 0 1
Single Result Single Result

Fig. 11 Q-factor (left) and BER (right) of the received signal

As one can see, distributed amplification help overcome signal attenuation thereby allowing larger transmission
distances. Like in most designs, the choice of appropriate loss compensation scheme (lumped, or distributed or both) will
depend on the trade-offs between the design objectives vis-à-vis cost, performance penalties, etc.

180 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.4.2 Fiber PMD Example
RSoft/examples/optsim/block_mode/fiber_linear_effects/pmd_fiber.moml
The purpose of this example is to demonstrate simulation of PMD in a fiber using the coarse step method. The full
polarization optical signal representation is also demonstrated. The example can be found in the pmd_fiber.moml
file in the Examples directory of the OptSim installation.
Load the pmd_fiber.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below.

Figure 1. pmd_fiber.moml

In this example, an electrical filter block is used after the electrical signal generator to model the electrical driving
circuitry. The optical signal of the CW laser and output from the modulator is fully polarized in the x direction. When
this is the case, the optical signal representation used is optimized for a single state of polarization for reduced memory
and computational requirements. A span of fibers is repeated a number of times after the modulator. The fiber models
in this example have their parameters set to include PMD in the simulation using the course step method. This results in
a randomization of the polarization state of the signal as it propagates down the fiber, and leads to polarization mode
dispersion. After the output of the repetition loop, signal plots are used to show the total optical signal including all
polarization states, and the signals in the x and y polarization states separately. The received signal shows distortions
due to a mixture of nonlinearity and PMD, and agrees well with results from the literature.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 181
2.4.3 Polarization Mode Dispersion (PMD) Induced Penalties in High Bit-
Rate Systems
RSoft/examples/optsim/block_mode/fiber_linear_effects/link_withPMD_40Gbps.moml
Previous example simulated PMD in fiber using coarse-step method. This example demonstrates the effect that
Polarization Mode Dispersion (PMD) has on signal propagation in a fiber and on system performance. The setup is
shown below:

Figure 1. Setup for PMD link, schematic link_withPMD40Gbps.moml

For this setup, a transmitter consists of a 40-Gbps PRBS generator, CW Laser source at 1550 nm, electrical driver,
external modulator, and optical power normalizer. A 40-Gbps RZ-modulated signal then is launched into a fiber span.
The output from the fiber span is inserted into a receiver.
The length of a fiber span is set to 100km. In the fiber model, the PMD effect is turned ON and the coarse-step PMD
method is selected. We simulate fiber with two different values for the PMD coefficient: 0.1 and 1.0 ps/km1/2,
corresponding to the cases for low-PMD and high-PMD fibers. PMD is a statistical effect caused by randomly varying
fiber birefringence, therefore the simulation results will be different for different settings of the random seed parameter
pmd_seed. PMD causes differential group delay (DGD) between x- and y- polarization components during propagation
in fiber, and, hence, eye distortion at the receiver. The mean DGD can be calculated according to the following formula:

DGDmean = PMDcoef x (Lfiber)1/2,

e.g. in our case it will be 1 and 10 ps, repectively. For 40-Gbps systems the bit duration is 25 ps, thus, we expect higher
PMD penalties for 10 ps of DGD compared to 1 ps.
One can run a parameter scan to obtain DGD and BER/Q for different values of the PMD coefficient and different
random seeds. For this example, the PMD coefficient takes the 2 values discussed above and pmd_seed parameter takes
values from 1 to 50 (to provide enough runs to capture the correct statistical behavior). After the simulation run is
finished one can double-click on various analysis blocks to view the signal plot, eye diagram, DGD, Stokes parameters
on Poincare Sphere, and BER/Q values.
With no PMD effect selected, the system will perform with BER = 10-10 and Q = 16 dB. Figure 2 shows Q-factor results
for a parameter scan of low- and high-PMD fibers cases.
For low-PMD fiber there are almost no system penalties and the Q is flat around 16 dB. For high-PMD fiber the
penalties are high, up to 7 dB in worst case. Figure 3 shows the DGD at the output of the fiber. For both low- and high-
PMD fibers the DGD fluctuates with the mean value close to the one predicted by theory. Due to the statistical nature of

182 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
the PMD effect, the principal state of polarization for each run is changing randomly as well. Figure 4 shows the
Poincare sphere plot for Stokes parameters for each seed – the points are distributed evenly on a sphere.

Figure 2. Scan results for Q-factor at 40 Gbps for low- and high-PMD fibers.

Figure 3. Scan results for DGD for low- and high-PMD fibers.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 183
 Figure 4. Poincare Sphere plot for Stokes parameters.

Figure 5. Correlation plot for Q-factor vs. DGD for low- and high-PMD fibers.

Let us take a look at two particular runs: (a) best case for low-PMD fiber; (b) worst case for high-PMD fiber. Figure 6
shows corresponding signal plots and eye diagrams. Corresponding Q-factors (and BER) are 16.0 dB (1x10-10) and 9.0
dB (2.5x10-3).

184 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 PMDlink40Gbxyseparseed1pmd1 Signal Plot
x10-6

Legend:
8 λ = 1550 nm (x)
7
Signal Magnitude (W)

λ = 1550 nm (y)
6
5
4
3
2
1

1 2 3 4 5
x10-10
Time (s)

(a) best case PMD

link withPMDxyseparPMD2seed13 Signal Plot

x10-6

Legend:
λ = 1550 nm (x)
10
Signal Magnitude (W)

λ = 1550 nm (y)
8

0
0 1 2 3 4
x10-10
Time (s)

(b) worst case PMD

Figure 6. Examples of signal plots and corresponding eye diagrams for best and worst case of PMD penalties at 40 Gbps.

In conclusion, we illustrated that PMD-induced differential group delay degrades system performance with penalties
more severe at higher bit rates and higher PMD coefficients in fibers.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 185
2.5 Fiber Non-linear Effects

2.5.1 Fiber Four Wave Mixing

RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/4chfwm.moml
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/4chnofwm.moml
The purpose of this example is to demonstrate a simulation of four wave mixing effects in the fiber model of a 4 channel
optical link. There are two files for this example which are found in the Examples directory of the OptSim installation.
These files are 4chfwm.moml which demonstrates simulation of four wave mixing, and 4chnofwm.moml which is
virtually identical except that four wave mixing is not included in the simulation. Several models, component
parameters, and options will be highlighted in this example.
Load the 4chfwm.moml file from the Examples directory. This will create a new window with the example topology
represented. It should appear as shown below.

Figure 1. 4chfwm.moml or 4chnofwm.moml

186 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
To allow simulation of four wave mixing between the WDM channels, the single frequency band signal representation
must be used. This representation samples the entire frequency band which includes all the optical channels in the
system as a single continuous frequency band. The signal representation used is controlled in the MUX block, where
SingleChannel indicates the single frequency band representation. When using the single frequency band representation,
the sampling rate (as set by the sample_rate_x user variable used by the points per bit parameter in the electrical
signal generator) must be set high enough that all the frequency components of all the channels are included. This
usually means that the sampling rate used in a single channel representation simulation must be greater than that used in
a multiple channel representation simulation.
By viewing the signal frequency spectra going into the fiber and comparing it with the signal frequency spectra coming
out of the fiber, the four wave mixing spectral peaks can be identified. The affects of the four wave mixing can also be
seen on the optical signal waveforms coming out of the DEMUX block. To compare the simulation results where four
wave mixing is accounted for and where it is not, load the 4chnofwm.moml file and simulate it. Note that the MUX
block is set to use the multiple frequency band (or MultiBand) optical signal representation. You may also notice that
the sampling rate is lower in the example file which does not include four wave mixing between the channels in the
simulation.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 187
2.5.2 FWM Resonance
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/32_ch_no_fwm_reson_smf.moml
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/32_ch_fwm_reson_smf.moml
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/32_ch_no_fwm_reson_smf_idf.moml
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/32_ch_fwm_reson_smf.moml
This example examines an important non-linearity in multi-channel systems, known as four-photon mixing or Four-
Wave Mixing (FWM) [1]. We simulate a 32-channel wavelength division multiplexed (WDM) system. The link is
1129km long and the inter-channel spacing is 100GHz. However, the wavelength plan is intentionally non-conventional:
we transmit non-return-to-zero (NRZ) data (16 channels) as well as continuous wave (CW) signals (16 channels) placed
alternatively in wavelength spectrum. Each data channel carries traffic at 12.3Gbps. The average power of data channels
is the same as that of CW channels. This arrangement ensures that the highest efficiency FWM product coincides with
the data channel [2]. We simulate two types of fiber plant scenario – one with dispersion compensation at the end of the
link (we observe FWM just before dispersion compensation); and the other with alternate 1:1 spans of ITU-T G.652
single-mode fiber (SMF) followed by inverse dispersion fiber (IDF). Figure 1 shows the basic topology and wavelength
plan used in both these cases.

(a) Topology

(b) Wavelength plan

Figure 1. Topology and wavelength plan for this example

In order to account for the random birefringence of the fiber along its length (and hence its random polarization mode
dispersion (PMD) contribution), the non-linear coefficient of fiber is multiplied by a (8/9) factor [3].

188 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Case I: In this case, the dispersion compensation is assumed at the receiving end only and we observe FWM effects just
before the dispersion compensation module (DCM). The multiplexer model in OptSim allows user the flexibility of
ignoring or including the FWM effects [4].
Figure 2 shows output optical spectra with and without FWM for this case and the crosstalk due to FWM effects on data
channels.

(a) CW and data channels (b) FWM crosstalk in data channels

Figure 2. Output spectra (CW and data) and crosstalk effects on data channels due to FWM

FWM resonance peaks are observed at 1537nm (3.1dB crosstalk) and 1541nm (-3dB crosstalk). The other lower peaks
are at 1535.4nm (2.5dB crosstalk) and 1545.8nm (2dB crosstalk). The frequency separation between these resonant
peaks can analytically be verified though beyond the scope of this example (for details, please refer to [2]). The
separation of resonant peaks can vary depending on the numbers of spans and channels, and the amount dispersion
compensation.
Case II: In this case, we consider alternate spans on SMF and IDF. This allows us to study FWM impairments in
presence of dispersion management. Figure 3 shows output spectra and crosstalk effects on data channels for the
dispersion managed link under consideration.

(a) CW and data channels (b) FWM crosstalk in data channels

Figure 3. Output spectra (CW and data) and crosstalk effects on data channels due to FWM

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 189
Since this configuration employs 1:1 alternating spans of SMF and IDF, the net dispersion at the end of each span is
zero. Zero dispersion does not augur well for nonlinear effects and hence much higher levels of crosstalk and more
number of resonant peaks are observed in Fig. 3 as compared to the link configuration in Case I earlier.

References
1. Tkach, R. W., et al., “Four-photon mixing and high-speed WDM systems,” Journal of Lightwave Technology, vol.
13, no. 5, May 1995, pp. 841-849.
2. Manna, M., and Golovchenko, E. A., “FWM resonances in dispersion slope-matched and nonzero-dispersion fiber
maps,” IEEE Photonic Technology Letters, vol.14, no. 7, July 2002, pp. 929-931.
3. Marcuse, D., Menyuk, C. R., and Wai, P. K. A., “Applications of the Manakov-PMD equation to studies of signal
propagation in optical fibers with randomly varying birefringence,” Journal of Lightwave Technology, vol. 15, no.
9, September 1997, pp. 1735-1746.
4. OptSim Models Reference.

190 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.5.3 Fiber Nonlinearity and Performance of NRZ- and RZ-formats in
High-Speed Links
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/NRZ.moml
RSoft/examples/optsim/block_mode/fiber_nonlinear_effects/RZ.moml
This example is based on Reference [1].
Topology layout for both NRZ and RZ cases is similar to the one shown in Fig. 1 below. In both cases, we consider link
with noise and without noise. In case of RZ, the number of spans simulated is double than that in case of the NRZ.

Fig.1 Topology layout for this example

Each span comprises of SMF (distance: 50km, dispersion: +16ps/nm.km, dispersion slope: +0.08 ps/nm.km2, loss:
0.2dB/km, and non-linear coefficient γ: 1.31W-1/km), DCF (distance: 10km, dispersion: -80ps/nm.km, dispersion slope:
+0.08 ps/nm.km2, loss: 0.5dB/km, and non-linear coefficient γ: 5.24W-1/km) and amplifiers (Noise Figure: 6dB). In each
span, the chromatic dispersion is fully compensated and the amplifiers fully compensate for the preceding fiber loss. The
settings in amplifier model allow inclusion or exclusion of noise. The non-linear coefficient γ can be controlled in
OptSim via the parameter “n2” (nonlinear refractive index of the fiber n(2)) according to the following relationship [7]:

2πf .n ( 2 )
γ = ,
c. Aeff
where the dimensionless parameter “aEff” of OptSim is related to Aeff as:

Aeff = a Eff .π .(d / 2) 2 ,

where d is the diameter of the fiber core. The Raman effects are disabled for the sake of simplicity.
Part I - NRZ
In this section, we consider the NRZ case. The NRZ.moml has two parts – the lower topology simulates a noiseless link.
Figure 2 shows Q-factor vs. average fiber input power plots at 240-km transmission for this topology with linear (γ=0)
and nonlinear DCF, with and without amplifier noise. As the launched power increases, the performance keeps on
improving until the launched power becomes high enough to cause nonlinearities adversely dominate the overall link
performance.
For our topology, if we examine the curves corresponding to the cases with and without amplifier noise, we see that until
the launched power is low enough, the link noise plays a dominant role. However, at higher launched powers, the
nonlinearities dominate the performance impairments as compared to the influence of link noise. Because of the smaller
core diameter of the DCF, optical intensities are enhanced thereby resulting in higher nonlinear effects in the DCF
section. The nonlinearities in the DCF, as seen in Fig. 2, can deteriorate the Q-factor by 6 to 9 dB depending upon the
launched power.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 191
 Q2 (dB) vs. Transmitted Power (Distance = 240km)

26

24
Without
noise
22
Linear
20 DCF
Q2 (dB)

18

16 Nonlinear
DCF
14

12
NF = 6dB
10
-10 -8 -6 -4 -2 0 2 4
Average Fiber Input Power (dBm)

Fig. 2 Receiver Q-factor as a function of launched power (240km)

Part II - RZ
This section examines the RZ case. The RZ.moml has two parts – the lower topology simulates a noiseless link.
Figure 3 shows Q-factor vs. average fiber input power plots at 480-km transmission for this topology with linear (γ=0)
and nonlinear DCF, with and without amplifier noise. As the launched power increases, the performance keeps on
improving until the launched power becomes high enough to cause nonlinearities adversely dictate the overall link
performance. Figures 3 and 2 qualitatively show resembling behavior except that the transmission distance is now
double.
Those with definitive license of OptSim, as an exercise, should run a parameter scan for transmission distance (number
of spans) for a given Q-factor and compare the performance in terms of supportable distance in cases of NRZ and RZ
modulation formats.
In general, there are various factors that affect performances of various modulation formats. These factors broadly
include whether the system is power limited or dispersion limited, whether it is a single channel system or a multi-
wavelength link, and whether the system operates in linear or non-linear region of the BER (or Q) curve. Other relevant
factors are the dispersion management scheme employed [2,3], average power per channel, inter-amplifier spacing [4],
dominant type of non-linearity [5], and polarization mode dispersion (PMD) characteristics of the link [6]. The user with
definitive OptSim license is encouraged to test various simulation scenarios based on these factors.

192 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Q2 vs. Transmitted Power (Distance = 480km)

30
Without
Noise
Q2 (dB)

20 Linear
DCF

Nonlinear
DCF

10
NF = 6dB

-10 -8 -6 -4 -2 0 2 4
Average Fiber Input Power (dBm)

Fig. 3 Receiver Q-factor as a function of launched power (480km)

References
1. Breuer D., and Petermann, K., “Comparison of NRZ- and RZ-Modulation format for 40-Gb/s TDM standard-fiber
systems,” IEEE Photonics Technology Letters, vol. 9, no. 3, March 1997, pp. 398-400.
2. Hayee, M. I., and Willner, A. E., “NRZ versus RZ in 10-40Gb/s dispersion-managed WDM transmission systems,”
IEEE Photonic Technology Letters, vol. 11, no. 8, August 1999, pp. 991-993.
3. Matsuda, T., Naka, A., and Saito, S., “Comparison between NRZ and RZ signal formats for in-line amplifier
transmission in the zero-dispersion regime,” Journal of Lightwave Technology, vol. 16, no. 3, March 1998, pp. 340-
348.
4. Casper, C., et al., “RZ versus NRZ modulation format for dispersion compensated SMF-based 10Gb/s transmission
with more than 100km amplifier spacing,” IEEE Photonic Technology Letters, vol. 11, no. 4, April 1999, pp. 481-
483.
5. Forghieri, F., Prucnal, P. R., Tkach, R. W., and Chraplyvy, A. R., “RZ versus NRZ in nonlinear WDM systems,”
IEEE Photonic Technology Letters, vol. 9, no. 7. July 1997, pp. 1035-1037.
6. Sunnerud, H., Karlsson, M., and Andrekson, A., “A comparison between NRZ and RZ data formats with respect to
PMD-induced system degradation,” IEEE Photonic Technology Letters, vol. 13, no. 5, May 2001, pp. 448-450.
7. OptSim Models Reference.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 193
2.6 Fiber Optical Parametric Amplifiers
The following examples illustrate different Fiber Optical Parametric Amplifier (OPA) designs.
The first two examples demonstrate Single- and Dual-Pump Fiber OPAs, with no SBS in the fiber, and fourth-order
dispersion neglected (if you choose to include SBS, you will need to add phase modulation to the pumps). These designs
are based on work described in [1] and [2]. We refer you to [1] in particular for an excellent discussion of phase-
matching conditions in single-pump OPA designs.
The final example demonstrates a Fiber-Based Phase-Sensitive Amplifier (PSA), and is based on the example presented
in [3]. Again, we neglect SBS and fourth-order dispersion.

2.6.1 Single-Pump Fiber OPA

RSoft/examples/optsim/block_mode/fiber_opa/singlepump_fopa.moml
First, open the topology for the Single-Pump Fiber OPA, singlepump_fopa.moml. In this design, a 1552-nm 2-W
pump is used. The fiber is 1 km in length with a zero-dispersion wavelength of 1550 nm and a dispersion slope of 0.050
ps/nm2/km. The time-step of the signals used in the simulation is small enough to ensure proper modeling of all the
important FWM products. As shown in Fig. 1, two scenarios are considered. In the top schematic, broadband noise over
1520 to 1580 nm is launched down the fiber along with the pump. Note that this noise is added directly to the pump
signal in order to ensure that the fiber nonlinearities operate on the noise. The fiber's optical output spectrum clearly
shows the shape of the gain profile near the pump frequency due to the amplified noise. In the bottom schematic, a 1541-
nm –40-dBm optical signal is launched down the fiber along with the pump. The gain measured by the Gain/NF
Analyzer reveals that the optical signal experiences a gain of approximately 30 dB.

Figure 1. Single-Pump Fiber OPA simulation topology.

194 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.6.2 Dual-Pump Fiber OPA
RSoft/examples/optsim/block_mode/fiber_opa/dualpump_fopa.moml
Next, load the topology for the Dual-Pump Fiber OPA, dualpump_fopa.moml. In this design a pair of 2-W pumps are
used at wavelengths of approximately 1511 and 1591 nm. These pumps are balanced (in frequency) around the zero-
dispersion wavelength, and help promote a wide-band gain profile. Again, we utilize a 1-km fiber with a zero-dispersion
wavelength of 1550 nm and a dispersion slope of 0.050 ps/nm2/km. As shown in Fig. 2, we again consider two separate
scenarios. In the top schematic, broadband noise over 1500 to 1600 nm is launched down the fiber along with the pumps.
The fiber's optical output spectrum clearly shows the shape of a broad gain profile due to amplification of the launched
noise. In the bottom schematic, a 1550-nm –40-dBm signal is launched down the fiber with the pumps. The gain
measured by the Gain/NF Analyzer reveals that the optical signal experiences a gain of approximately 62 dB.

Figure 2. Dual-Pump Fiber OPA simulation topology.

2.6.3 Fiber-Based PSA

RSoft/examples/optsim/block_mode/fiber_opa/fiber_psa.moml
In a PSA, the relative optical phase between pump, signal and an additional idler wave determines whether the fiber acts
as an amplifier or an attenuator. Following the treatment in [1] and considering two frequency-degenerate pumps, one
signal, and one idler wave, the relative phase difference θ between the various components is

θ( z ) = ∆β ⋅ z + 2φ p ( z ) − φs ( z ) − φi ( z )

where z is the position along the fiber, ∆β is the propagation mismatch between pump, signal, and idler, φp is the pump
phase, φs is the signal phase, and φi is the idler phase. By varying the value of θ at the fiber input, we can change whether
the fiber amplifies or attenuates the signal.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 195
Open fiber_psa.moml, whose schematic is illustrated in Fig. 3. This design, based on work presented in [3], models a
fiber-based PSA whose inputs are a single 175-mW cw pump at 1559.83 nm along with two -10-dBm cw signals at
1560.09 and 1559.57 nm, the latter of which acts as the idler wave. These are all launched down 1 km of highly
nonlinear fiber (γ = 9 W-1 ·km-1) with a zero-dispersion wavelength of 1558 nm and a dispersion slope of 0.018
ps/nm2/km. At the output of the fiber, we use a filter to select the 1560.09-nm signal and then calculate the gain at this
wavelength using a Gain/NF Analyzer.

To view the gain as a function of the relative phase difference θin at the fiber input, run the preconfigured Scan
simulation for this topology, which sweeps θin from –180° to 180°. At the conclusion of the simulation, you may view
the PSA gain as a function of θin via the Gain/NF Analyzer block. The results should match those shown in Fig. 4.
Taking into account the fact that, compared to the equation from [3], θin is calculated using an opposite sign, we see good
agreement between our simulation and the published results. As can be seen, as θin is varied, the fiber switches between
amplification and attenuation, as you would expect in a phase-sensitive fiber optical parametric amplifier.

Figure 3. Fiber-based PSA simulation topology.

Figure 4. PSA gain for the 1560.09-nm signal as a function of the relative phase difference at the input.

196 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
References
1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers
and their applications,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, no. 3, pp. 506-520, May/June
2002.
2. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE Journal
of Selected Topics in Quantum Electronics, vol. 8, no. 3, pp. 538-547, May/June 2002.
3. R. Tang, P. Devgan, P. L. Voss, V. S. Grigoryan, and P. Kumar, “In-line frequency-nondegenerate phase-sensitive
fiber-optical parametric amplifier,” IEEE Photonics Technology Letters, vol. 17, no. 9, pp. 1845-1847, September 2005.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 197
2.7 Soliton Transmission

2.7.1 Soliton in Optical Fiber

RSoft/examples/optsim/block_mode/soliton/soliton_lossless_fiber.moml
The purpose of this example is to demonstrate the propagation of soliton pulse in optical fiber. The existence of solitons
in optical fibers is the result of a balance between the chirps induced by fiber dispersion characterized by GVD (group-
velocity dispersion) coefficient β2 and fiber nonlinearity characterized by SPM (self-phase modulation) coefficient γ.
Analytically soliton is a solution of nonlinear Schrodinger equation describing pulse propagation in optical fiber and can
be derived as:

 t   π z
A( z , t ) = N Po sech   exp j  ,
 To   4 zo 
where Po - soliton peak power, To - pulse width, Zo - soliton period, and N - soliton order. Soliton period defined as

π To 2
Zo =
2 | β2 |
The optical pulse which corresponds to N=1 is called fundamental soliton. Pulses with N>1 are called higher-order
solitons. Soliton order parameter N depends on the balance between dispersion and nonlinearity and is defined as:
2
LD T
N2 = = γPo o
LNL | β2 |
The layout for generation of the solitons is shown in Figure 1. It consists of pulse generator (mode-locked laser), single-
mode lossless fiber, and waveform and spectrum analyzers. The fiber is assumed to be lossless to demonstrate ideal
soliton propagation. Fiber dispersion β2=-20 ps/km/nm and fiber nonlinear parameter g is calculated as
2πn2
γ =
λAeff
For given n2=2.6e-20 m2/W, Aeff =60 um2, and λ =1550 nm - γ =1.75e-3 1/m/W. The fiber length is set to one soliton
period, which for given parameters is Z0 = 27.525 km.
Initial pulse has a sech shape and FWHM pulsewidth is 33 ps, corresponding to To =18.7 ps. Pulse power for
fundamental soliton is 32.7 mW and for 3rd order soliton 293.4 mW.
By clicking on Scan button one can run simulation with sweep over the fiber length from zero to soliton period with a
step equal 0.1 of period. After simulation finishes one can click on signal and spectrum analyzers in schematics to see
resulting soliton waveforms and spectra.
Figures 2 and 3 show soliton pulse evolution (in time and frequency domains) in fiber along one soliton period for N=1
and N=3.
In case of fundamental soliton (Fig.2) the pulse waveform preserves its initial “sech” shape during the propagation in a
fiber. The same is true for optical spectrum of fundamental soliton. In case of third-order soliton the shape of waveform
and spectrum change along the fiber but returns to original shape at soliton period length.

198 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 1. Layout for soliton in optical fiber study.

Magnitude (a.u.)
1

0.5

0.0
0
0.0 0.5
Z/Zo
0.4
Time (ns) 1.0
0.8

Power (a.u.)
1

0.5

0.0
0
1544.9 0.5
Z/Zo
1550.0
Wavelength (nm) 1555.1 1.0

Figure 2. Fundamental soliton: propagation in time domain (top) and spectrum evolution (bottom).

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 199
 Magnitude (a.u.)
1

0.5

0.0
0
0.0 0.5
Z/Zo
0.4
Time (ns) 1.0
0.8

Power (a.u.)
1

0.5

0.0
0
1544.9 0.5
Z/Zo
1550.0
Wavelength (nm) 1.0
1555.1

Figure 3. Higher-order soliton: propagation in time domain (top) and spectrum evolution (bottom).

200 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.7.2 Loss-Managed Soliton Link
RSoft/examples/optsim/block_mode/soliton/soliton_loss_managed.moml
The purpose of this example is to demonstrate the path-averaged soliton regime in fiber link with loss and periodical
amplification. Figure 1 demonstrates the layout to study path-averaged soliton regime for a single pulse in amplifier
chain (the upper part of schematic) and loss-managed soliton link with 10-Gb/s modulated signal (the upper part of
schematic).

Figure 1. Layout for path-averaged soliton link.

The ideal soliton can exist in a lossless fiber with a balance between the chirps induced by fiber GVD and fiber
nonlinearity characterized by SPM (self-phase modulation). In a real fibers the fiber attenuation α ≠ 0 and would
produce the soliton broadening simply because a reduced peak power weakens the SPM effect necessary to counteract
the GVD. Solitons can maintain their shape in periodically amplified fiber link if amplifier spacing LA is kept smaller
than fiber dispersion length LD. The soliton peak power should be adjusted by factor defined by path-averaged power.
This is a concept of path-averaged soliton. If we introduce the amplifier gain as G = exp(αLA), then the enhancement
factor for loss-managed soliton can be derived as:
−1
 1 LA
 αL A G ln G
f LM = ∫0 exp( −α z ) dz  =
1 − exp( −αL A )
=
G −1
 LA 
In given example the fiber loss α = 0.2 dB/km and amplifier spacing LA is 50 km. Hence, gain G = 10 dB and
enhancement factor fLM = 2.56. Fiber dispersion and nonlinear parameters - β2 = - 20 ps2/km and γ = 1.75e-3 1/m/W 1.75
- for initial pulsewidth To = 14.18 ps and λ =1550 nm will provide dispersion length LD =100.57 km and soliton peak

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 201
power Po = 5.7 mW. The launched peak power will be (fLM x Po ) – thus soliton evolution in lossy fibers with periodic
lumped amplification is identical to that in lossless fibers with launch power Po providing LA < LD.

Width (FWHM) Map

25.8

25.5

Pulse Width (FWHM) [ps]

25.2

24.9

24.6

24.3

24.0

0 200 400 600 800 1000

Distance [km]

Figure 2. Soliton pulse width vs. fiber length.

Magnitude (a.u.)
1

0.5

0.0
0
0.0 0.5
L/Lmax
0.8
Time (ns) 1.0
1.6

Figure 3. Evolution of single soliton pulse.

The upper part of schematic in Fig.1 will demonstrate single soliton pulse evolution over 20 amplifier spans in a
circulated loop setup – each span consists of 50-km fiber and amplifier. The pulse source is a Mode-Locked Laser
generating a single pulse of “sech” shape with specified power and width. Total link length is 1000 km. After the
simulation run one can observe the evolution of soliton pulse FWHM along the link by clicking on Property Map
Analyzer block – see Figure 2. The pulse width stays within 24-26 ps range. Figure 3 shows 3D waterfall plot of soliton
wavefom evolution – one can produce this plot by opening individual Signal Plots after fiber in a loop, combining them
together and select WinPlot option for 3D Data Display -> 3D Slices. Property Map block will also produce plots for the
signal cumulative dispersion and power vs. fiber length – see Figure 4. The dispersion accumulates to –2000 ps2 but
SPM prevents the pulse broadening due to high dispersion.
The lower part of schematic in Fig.1 describes the soliton loss-managed link with the same transmission path – 1000 km
with 20 amplifiers inserted very 50-km. The transmitter is set up as a train of optical pulses generated by Mode-Locked

202 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Laser and constructed as solitons the same way as in the upper case, and then modulated by data at 10 Gb/s bit rate. The
output from fiber link is inserted into optical receiver followed by BER Tester and Eye Diagram Analyzer.

Dispersion Map Optical Power Map

0
-6
-7
-8
-9
Dispersion [ps2]

Power [dBm]
-10
-1000 -11
-12
-13
-14
-15
-2000 -16
0 200 400 600 800 1000 0 100 200 300 400 500 600 700 800 900 1000
Distance [km] Distance [km]

Figure 4. Signal dispersion (left) and power (right) vs. fiber length.

By clicking on Signal and Spectrum Analyzers after the simulation run one can see the resulting bit streams and
spectrums in the link. Figure 5 shows the optical bit stream at the fiber input and outputs. One can see a very little
distortion over 1000 km transmission – that demonstrates the robustness of path-averaged soliton pulse. It is supported as
well by receiver eye diagram depicted in Figure 6 – it is wide open and provides error-free communication.

Fiber Input Signal Plot Output Signal Plot

0.015 0.015

0.012 0.012
Signal Magnitude (W)
Signal Magnitude (W)

0.009 0.009

0.006 0.006

0.003 0.003

0.000 0.000
0 1 2 3 0 1 2 3
x10-9 x10-9
Time (s) Time (s)

Figure 5. Input and output bit stream in loss-managed soliton link.

Figure 6. Receiver eye diagram in loss-managed soliton link.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 203
2.7.3 Dispersion-Managed Soliton
RSoft/examples/optsim/block_mode/soliton/DMS.moml
The purpose of this example is to demonstrate the dispersion-managed soliton regime in a fiber link. with loss and
periodical amplification. Ideal lossless and loss-managed solitons require GVD parameter β2 to stay constant along the
fiber length. Modern WDM lightwave systems employ dispersion management to compensate for cumulative dispersion
and to suppress FWM penalties. It was demonstrated that solitons can form even when β2 varies along the fiber length
but their properties are quite different. This kind of solitons is called dispersion-managed solitons.

Figure 1. Layout for lightwave system schematic.

This example is based on Reference [1]. Figure 1 demonstrates the layout to study dispersion-managed soliton regime in
a long-haul fiber link corresponding to setup described in Ref.[1]. It represents the circulating loop setup, where each
loop is consist of six regular fiber spans, one dispersion-compensating fiber (DCF) span, optical filter and seven optical
amplifiers – EDFAs, wityh total loop length about 180 km. Pulse will travel total 100 loops or 18,000km. Fibers in a
loop are 30-km long with dispersion coefficient 0.2 ps/km/nm at 1550 nm and dispersion slope 0.07 ps/km/nm^2. For six
spans total accumulated dispersion is 36 ps/nm. DCF has dispersion –72 ps/km/nm and length 0.5 km, i.e. total
dispersion is –36 ps/nm and fully compensates the cumulative dispersion in the loop to zero. DCF is inserted after first
two 30-km spans. Fiber loss is 0.22 dB/km and EDFAs after fiber span set to 6.6 dB gain to compensate signal
attenuation. The optical filter is placed at the end of the loop and has a width of 2.7 nm.
The input pulse is generated by Mode-Locked Laser and has a “sech” shape with 7 ps pulse width. The pulse peak power
corresponds to N=1 soliton and is set to 11.56 mW. A number of signal and spectrum analyzers are attached to output
from laser, fiber, and amplifiers blocks. Property Map block tapped to outputs of elements in the loop will record pulse
dispersion, width, and optical power along the fiber length.

204 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Dispersion Map
Channels

10 λ=1.5500 µm

Dispersion [ps/nm]

-10

-20

0 3000 6000 9000 12000 15000 18000

Distance [km]

Figure 2. Dispersion evolution along the fiber length.

Width (FWHM) Map

Channels
30 λ=1.5500 µm
Pulse Width (FWHM) [ps]

20

10

0 3000 6000 9000 12000 15000 18000

Distance [km]

Figure 3. Pulse width evolution along the fiber length.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 205
 16 Legend:
10
FWHM
14
dispersion

Pulse Width (FWHM) [ps]

12

Dispersion [ps/nm]
0

10

8
-10

4
-20

17200 17400 17600 17800 18000

Distance [km]

Figure 4. Pulse width and dispersion map overlaid.

After running the simulation by clicking on Go button one can review the results by clicking on plotters. So, Figure 2
shows the dispersion map of a link – dispersion accumulation along the fiber length. In each loop the dispersion
compensated back to zero, but since DCF is inserted non-symmetrically, after second out of six fiber spans, the average
dispersion is small but non-zero, equal to –6 ps/nm. Non-zero local dispersion helps to reduce FWM penalties. Figure 3
shows the pulse width evolution – it starts at 7 ps, then oscillating with amplitude going up to 32 ps, and after about
10,000 km converges to steady-state with pulse width changing periodically between 6 and 13 ps within each loop.
Let us take a look at soliton evolution. Input soliton pulse first travels 60 km of anomalous dispersion fiber supporting
soliton propagation, but then DCF nonlinearity broadens the soliton pulse into a rectangular pulse with a linear chirp.
This up-chirped pulse is coupled into next 30-km long fibers with anomalous dispersion. Because the pulse after passing
through first 60-km is up-chirped and broadened, the pulse is linearly compressed by the anomalous dispersion and a
high-order soliton is excited in the next 180-km fiber. This results in large spectral broadening and soliton narrowing.
Figure 4 shows overlaid dispersion map plot with pulse width plot – one can see that pulse is narrowing in anomalous
dispersion fiber and broadening at DCF. When the pulse spectrum is broadening due to the high-order soliton effect and
third-order dispersion near the zero dispersion wavelength, the spectrum begin to be shaped by optical filter installed at
the end of the loop - it removes the unwanted spectral peak that gets created on the left hand side of the spectrum. Figure
5 shows the chirp of output signal. Figure 6 shows the pulse power evolution. After traveling a few first loops the pulse
converges to quasi-steady-state.
Figure 7 and 8 show pulse waveform and corresponding spectrum for input and output pulse after 100 loops,
respectively. Figure 9 gives 3D waterfall plot for waveform and spectrum as a function of transmission distance.
In conclusion, the pulse propagation in dispersion-managed soliton transmission link is similar to conventional
transform-limited soliton transmission link.

206 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 300

200

Frequency Chirp (GHz)

100

-100

-200

-300

-400
0 1 2 3 4 5 6 7 8
-10
x10
Time (s)

Figure 5. Frequency chirp of output pulse after 18,000 km.

Optical Power Map

Channels
-10 λ=1.5500 µm

-12
Power [dBm]

-14

-16

-18

-20
0 1 2
4
x10
Distance [km]

Figure 6. Pulse power evolution along the fiber length.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 207
 Optical Waveform

input
0.012
output

Signal Magnitude (W)

0.009

0.006

0.003

0.000
30 32 34 36 38 40 42 44
x10-11
Time (s)

Figure 7. Input and output (after 18,000 km) pulse waveform.

Optical Spectrum
-6
x10
3
Legend:
input

output
2
Power (W)

1548 1549 1550 1551 1552

x10-9
Wavelength (m)

Figure 8. Input and output (after 18,000 km) optical spectra.

208 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Power (a.u.)
1

0.5

0.0
0
1544.9 0.5
L/Lmax
1550.0
Wavelength (nm) 1.0
1555.1

Figure 9. Dispersion-managed soliton evolution in time (top plot) and frequency domain (bottom plot) along the fiber length.

References
[1]. M. Nakazawa, H. Kubota, and K. Tamura, “Nonlinear Pulse Transmission Through an Optical Fiber at Zero-
Averaged Group Velocity Dispersion,” IEEE Photonics Technology Letters, vol. 8, no. 3, pp. 452-454 (1996).

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 209
2.8 Raman Amplifier

2.8.1 Raman Amplification Tutorial

The Bi-directional Nonlinear Fiber model is the most complex model in OptSim, at least in terms of the number of
component parameters and modes of operation. In this tutorial we examine a range of increasingly complicated
problems using this model. The focus is on Raman amplification, since Raman effects are the only ones which have a
significant bidirectional aspect, but as discussed in the model documentation, the discussion has relevance for general
bidirectional signal propagation.
As the tutorial progresses we design an increasingly complicated and better-behaved amplifier for a WDM system with a
moderate number of channels. The example topologies may be found in the Examples/Raman directory of the OptSim
distribution.
The principal documentation for both the standard Nonlinear Fiber and the Bidirectional Nonlinear Fiber should be read
thoroughly before this chapter and referred to when necessary.

Single pump amplification

RSoft/examples/optsim/block_mode/Raman/singlepump.moml
Open the topology file “singlepump.moml” to obtain the layout pictured in Figure 1. The Raman amplifier configuration
is the lower of the two sets of components. A single pump laser is connected to the backward pump node of the
Bidirectional Nonlinear Fiber (BDNF) icon. The upper series of components generates a binary modulated signal and is
used later. Note that currently there is no signal input to the bidirectional fiber. Therefore there can also be no signal
output from the component. However, we have attached two analysis blocks to the output of the fiber to create a
complete topology. Without these blocks, the OptSim simulator would regard the amplifier as an incomplete link and
would not schedule the blocks for simulation. Indeed the upper signal-generating components are currently an
incomplete link and are not simulated.
Since there is no incoming signal to the BDNF the signal must be generated internally. Right click on the icon to
examine the parameter list and note the settings simulation_mode=PowerOnly and signal_spectrum=FixedRange.
These determine that the signal is a fixed spectral density across a specified wavelength range and that only the first
stage bidirectional solution will be performed. Since there is no coherent signal input, the simulation modes
CoherentOnly or Full are not appropriate and would generate errors.
Now change simulation_mode to InputOnly and hit the OptSim Go icon. (Accept the default value “lstmp” for the
output prefix by hitting OK.) The simulator finishes work almost immediately. Left click on the BDNF icon and observe
two plot filenames. Selecting either of these shows the input fields that have been specified. The
“lstmp_bdnf_raman_power_launch.pcs” plot shows the different signal and pump powers in frequency bins of
width nominal_channel_width=100GHz. As expected there is a single backward pump (green) and a broad flat signal
(red) of much lower power. Note that the simulation domain extends to longer wavelengths to allow for the generation
of spontaneous emission outside the signal band. This range can be adjusted if necessary with
sim_fixed_wavlength_range, sim_lambda_lo and sim_lambda_hi. The
lstmp_bdnf_raman_spectral_density_launch.pcs plot shows the actual spectral densities Sf(z=0) and Sb(z=L)
that combine the signal and pumps and are used in the model (see BDNF documentation).
In a moment we will perform the propagation. First, to examine the Raman gain spectrum that will be used, hit the Test
button at the bottom of the parameter dialog (opened by right-clicking on the BDNF icon). The current Raman spectrum
(in this case the default experimental profile) is shown assuming the pump wavelength pump_lam=1.45 µm which is
defined in the symbol table. Note that the gain spectrum peaks around 1.55 µm.

210 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 1. Layout for single pump.

PowerSolution
Now change simulation_mode back to PowerOnly, adjust power_density_units (located close to the bottom of the list)
to Watts/GigaHertz and hit the Go icon to run the simulation. The OptSim status line displays the current degree of
convergence as it iterates towards the current value bd_tol=1e-4 which should take a minute or so. At the conclusion,
left click on the BDNF icon. A large number of plot filenames are displayed. We examine some of these in turn.
• lstmp_bdnf_raman_channel_power.pcs
This shows the forward signal and noise powers at the exit of the fiber. For comparison, the launched
signal field is also shown. It is helpful to zoom in on different parts of the plot. Note that the final signal
power has a spectral form very similar to the Raman gain spectrum itself and that the largest gain occurs at
1.55 µm. The ASE noise (red) occurs in a broad band beyond the signal band. Discontinuities at long
wavelengths correspond to cascaded ASE. The spike at the pump wavelength is due to Rayleigh scattering
of the pump into the noise field. Try repeating the simulation with include_rayleigh=No. The spike
disappears. Remember to re-enable the Rayleigh scattering afterwards.
• lstmp_bdnf_raman_gain.pcs, lstmp_bdnf_raman_on_off_gain.pcs
These show the two standard gain measures. Typically the on-off gain is the most relevant in amplifier
design. Since we have only a single pump, the gain is highly uneven. This is not yet a good amplifier!
• lstmp_bdnf_raman_noise_figure.pcs
This shows the effective noise figure of the amplifier. Note that for some wavelengths, the noise figure is
negative. The interpretation is that the noise performance of the amplifier is better than any discrete
amplifier could be.
• lstmp_bdnf_raman_signal_power_evol.pcs, lstmp_bdnf_raman_pump_evol.pcs
These show the total power in the signal and noise, and in the pump channels as a function of distance. The
constant slope of the pump power curve shows that it is depleted largely by the loss. The depletion by the

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 211
 amplified signals is a minor effect. Increasing the signal strength to spec_dens=2e-14 (by opening the
symbol table) and repeating the simulation, the pump decays faster due to depletion by the signal.
• lstmp_bdnf_raman_solve_fwd.pcs
This is a contour plot of the forward spectral density as a function of distance and wavelength. Initially the
signal decays due to attenuation but as it nears the rear of the fiber, the pump is strong enough to produce
gain which occurs in a narrow band around 1.55 µm.
• lstmp_bdnf_raman_solve_back.pcs
This shows the corresponding contour plot for backward propagating energy, in this case a thin stripe
which is the pump. The contour plots are best-viewed with power_density_units set to a non-dB setting.
Since for large simulations, the multiple plots consume time in writing to the disk as well as disk storage space, they may
be controlled with the parameter generate_plots. All plots are produced for generate_plots=2. The contour plots are
disabled with generate_plots=1 while all plots are disabled with generate_plots=0.

Gain Tilt
Now turn off the pump by setting power_pump=0 in the symbol table. Recall that we can not simply disconnect the
pump since we would be left with an incomplete topology. Run the simulation, left click on the BDNF icon, and
examine the channel_power plot. The signal band has been attenuated by an average of 10dB, consistent with the loss
and length parameters, but zooming in on the final signal, we see a tilt in the signal power, with the longest wavelengths
stronger by around 1dB than the shortest. This is illustrative of the general long-wavelength drift of power in a Raman
system and indicates that with pumps connected, the model correctly accounts for gain tilt due to signal-signal coupling.
Inspect the …_solve_fwd .pcs contour plot for another nice illustration of this. If the plot appears featureless, check
that power_density_units is not set to a dBm unit.

Coherent input signals

We will now attach a real input signal and investigate the model’s treatment of coherent optical signals. Reload the
“singlepump.moml” topology file to regain all initial settings. Now use the wire connecting tool, to join the output of
the External Modulator to the Signal Plot icon and the first node of the BDNF. Your topology will look like Figure 2.
The OptSim interface will not smoml you from connecting the signal to one of the pump inputs to the BDNF, but an
error will be generated once the simulation commences. (Try it!)
Make the following adjustments: simulation_mode=InputOnly, signal_spectrum=Incoming and run the simulation.
The input spectrum now shows a narrow spike representing the single signal channel. Note however, by zooming in, that
unlike the CW pump it has a non-zero width due to the modulation bandwidth.
For reference, first run a standard simulation (no bidirectional or pumping effects) by setting
simulation_mode=CoherentOnly. Recall that this is identical to using the standard nonlinear fiber model. Hit the Go
icon and for the output prefix, enter “unpumped”. At the end of the simulation, click on the four plot icons to view the
input signal, and output signal and spectrum. Keeping these plots to the side, change simulation mode to Full, and
repeat the simulation, this time entering “pumped” for the output prefix.
First examine the powersolution plots by left-clicking on the BDNF as before. The gain plot
“pumped_bdnf_raman_gain.pcs” indicates that the gain across the signal ranges between 4.4 and 5.1 dB. Now click
on the two Spectrum Plots to see the input and output spectra from the fiber. The output Spectrum Plot icon is
configured to display a separate ASE plot as well, so pick the first of the offered plots pumpedspecout.pcf. Zoom in
on the peaks of the spectra and observe that the output peak is approximately 5 dB higher than the input peak. This
seems consistent with the gain range of 4.4-5.1 dB, but we are really interested in the overall gain of the signal, rather
than just at the peak of the spectrum and it is difficult to extract this information from a dB power spectrum. To make a
stronger confirmation of the consistency between the power and coherent solutions we proceed as follows. Examine the
signal evolution plot from the power solution (pumped_bdnf_raman_signal_power_evol.pcs). Recall that this
plot indicates the total signal energy integrated over the whole spectrum as a function of distance. Zoom in on the initial
signal power which should be –0.21 dBm. (Use the cross-hair cursor and the position coordinates in the lower right
portion of the plot to determine this number accurately). Now click exactly on the first input node of the BDNF to bring
up the signal input summary displayed in an edit program such as the Windows Notepad. (You may have to click 2 or 3

212 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
times to find the right spot.) You should see a table as in Figure 3 which summarizes properties of the optical signal
entering the BDNF at that node.

Figure 2. Layout for single pump and single coherent signal.

The field “Average” indicates that the total power in the signal is –0.2085 dBm, consistent with the start of the signal
evolution curve. The numbers are not identical due to the coarser numerical grid used in the power solution, but the
difference is negligible (and could be reduced by increasing frequency resolution in the power solution).

Figure 3. Signal summary for input to BDNF.

Now repeat this comparison for the end point of the signal evolution curve and the output node of the BDNF. We find
values 4.78 dBm and 4.76 dBm respectively, which are in excellent agreement considering the disparity in grids. Thus
we have demonstrated the consistency of the two-stage simulation process. The predicted output power from the power
solution, is also obtained at the conclusion of the coherent solution.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 213
ASE Noise
Open the BDNF plot “pumped_bdnf_raman_channel_power.pcs” and notice the spike in the ASE spectrum at the
pump wavelength 1.45 µm. Now examine the ASE spectrum in the output Spectrum Plot, (pick the lower of the plots
offered). The plots are similar, (though the latter is displayed on a frequency axis rather than wavelength). The spike at
the pump wavelength does not appear however. As the filter_noise parameter of the BDNF is enabled, the noise is
smoothed over at pump wavelengths to save the use of subsequent notch filters. Adjust filter_noise if this feature is not
desired.

Combination Signal Inputs

Finally, adjust signal_spectrum to FixedRange and repeat the simulation. In this case, the power solution is solved with
the broad band input spectrum, but the coherent solution still uses the actual binary signal input. Now the signal input
has an average power of approximately 0.001 W, while the broadband signal has a spectral density of 2e- 15W/Hz, so we
can think of the broadband signal as representing a WDM comb of copies of the original signal at a 50 GHz spacing.
Open the signal summary as before at the output of the BDNF. The signal power is now reduced to 3.79 dBm from the
previous value of 4.76 dBm due to saturation of the gain by the other channels.
In this way we can estimate the impact of a broad sequence of channels on the power behavior of a particular channel.
While this approach accounts for the gain saturation, it of course neglects signal-signal Raman couplings giving rise to
gain tilt and XPM or FWM effects during the coherent solution. It is a convenient way to initially optimize the amplifier
design. A full array of channels can subsequently be added for fine tuning gain tilt and channel coupling effects.
Multi Pump Amplification
Since we have only used a single pump so far, the gain spectrum obtained is far from flat and would be unsuitable for
broad-band amplification. The standard solution to this problem is to use a range of pump wavelengths and powers to
flatten the spectrum. This is an interesting design problem since the pumps are themselves coupled by the Raman gain.
Shorter wavelength pumps amplify longer wavelength pumps and hence we can not simply add the single pump gain
spectra to achieve the desired flat spectrum. Here we see how the BDNF model captures these effects.
Open the topology file “multiequalpump.moml”. An array of CW pumps is coupled by the Optical MUX model into
the backward port of the BDNF. For simplicity we use only PowerSolution mode in this section. Real signals can of
course be included as described above. As explained earlier, in order to create a complete link that will be scheduled, we
have attached a plot icon to the output port even though no signals leave the BDNF. Open the parameter dialog for the
BDNF, set test_output=loss and hit the Test button. The current loss profile, contained in the file smf28loss.dat is
displayed. Since we are using multiple pumps over a significant bandwidth it is important to have an accurate
description of the loss.
Now run the simulation, setting the output prefix to “equal”. The simulation will take a minute or two to complete.
First examine the launched fields in the plot “equal_bdnf_raman_power_launch.pcs” (by clicking the BDNF icon
and selecting the appropriate line). The seven pumps have equal powers of 20 dBm. Open the symbol table and notice
that these powers are entered using the “dBm” function, which converts a power in dBm to a power in Watts. Now
examine the signal on-off gain in “equal_bdnf_raman_power_launch.pcs”. The gain has a spread of over 15 dB
which is clearly totally unsatisfactory in a useful amplifier. The source of this problem is indicated by the pump
evolution plot in “equal_bdnf_raman_pump_evol.pcs”. Note that while the short wavelength pumps decay quickly,
the longer wavelength pumps actually increase in power initially due to Raman amplification by the shorter wavelengths.
This coupling complicates the task of designing a flat-gain amplifier.
Now open the topology file “multiunequalpump.moml” and run the simulation with an output prefix of “unequal”.
Open the launched power plot, and notice that this time we have chosen a range of unequal pump powers, with
decreasing powers towards the long wavelengths. The downward shift of power from the short wavelength pumps
should help to flatten the spectrum. Open the on-off gain plot to observe that this is true. Over the range 1530-1610
nm, the spread in gain is only 1 dB. With the addition of further pumps, or further experimentation with the pump
powers, the ripple could be reduced even further

214 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.8.2 Design of a 40-Channel OC-768 DWDM Link (50 GHz grid) with
Multiple Backward Pumped Raman Amplification
RSoft/examples/optsim/block_mode/Raman/DWDM_with_Raman.moml
This example simulates a realistic scenario of a 40Gbps DWDM link with inter-channel spacing of 50 GHz. Forty
individual channels carrying PRBS data are transmitted over a 50 km length of ITU-T G.652 single mode dispersive
fiber. The design objective is to utilize distributed Raman amplification to compensate for the link attenuation thereby
effectively increasing the inter-EDFA span in a longer-haul link.
Figure 1 below shows a snap-shot of the layout. The multi-line capability of OptSim’s CW laser model makes it very
convenient to generate the source-grid for simulating WDM channels.

Figure 1. Sectional snap-shot of a 40-channel DWDM link layout

Since backward pumping helps in averaging out power ripples at the receiver end, we choose a backward pumping
scheme that employs eight CW pump signals with carefully chosen nominal wavelengths and power values.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 215
Figure 2 depicts spectra of input and output channels in absence of Raman effects. The 50-km length of fiber induces ∼
13 dB of attenuation.

Figure 2. Transmitted and received (without Raman effects) optical spectra. a) 40-channel input, b) Output without Raman effects.

Raman amplification is a wide-band phenomenon having a highly irregular gain profile over wavelength. The highest
Raman gain is observed for a frequency differential range (range of difference between pump signal and data signal
nominal frequencies) of 8 to 12 THz. Outside this range, the gain profile exhibits a sharp decline [Ref. 1-2]. Therefore,
if the number of pumps, their wavelengths, and the power values are chosen carefully, we can achieve the desired gain
shape for the input DWDM channels.
Figure 3 (a) shows numerical values of eight pump-power and wavelengths selected after several simulation pre-runs,
and Figure 3 (b) shows the Raman amplified output. The attenuation is now reduced to ∼ 4 dB with a spread of ± 2 dB.

Figure 3. Using distributed Raman amplification in order to compensate for the fiber attenuation. a) Backward pumps chosen, b)
Raman amplification of DWDM channels

The output spectrum above takes in to account the pump-signal and the signal-signal interactions. Besides, the pumps
interact with each other, too. Shorter wavelength pumps provide power to longer wavelength pumps. As a result, we

216 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
can expect rise in longer wavelength pump powers and corresponding depletion of shorter wavelength pumps at the
launch end of the fiber before finally showing overall link attenuation as shown in Figure 4 below.

Figure 4. Backward pump power evolution over the entire DWDM link. a) Power evolution of backward pumps, b) Closer look at the
pump-pump interactions.

References
1. Ramaswamy, R., and Sivarajan, K. N., Optical Networks: A Practica Perspective, Morgan Kaufmann Publishers,
Inc., San Francisco, 1998, pp. 240-243.
2. OptSim User’s Manual, Bi-directional non-linear fiber model (Raman Amplifier), RSoft Design Group, Inc., NY,
2002.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 217
2.9 Effective Loss Due to Stimulated Brillouin Scattering
RSoft/examples/optsim/block_mode/fiber_sbs/SBS_Loss.moml
This example demonstrates the effect of stimulated Brillouin scattering (SBS) on a fiber’s transmission performance,
namely signal loss. The launch power of a fiber’s input signal is increased until SBS becomes important and begins
depleting the input signal.
Figure 1 depicts the topology used in this example. We launch an input signal into two versions of an SMF-28 fiber. In
the top branch of the topology, SBS is included in the model. In the bottom branch, it is not. All other fiber parameters
are identical, including the length of 20 km. This setup allows us to determine at what fiber launch power SBS begins to
have an effect.
Load the example topology and open the Parameter Scan Dialog. The dialog is preset to scan the fiber launch power
from 0 to 25 dBm in increments of 1 dB. Click Ok. When the simulation is complete, display the output power of each
fiber as a function of launch power using the monitor blocks OptMon_SBS (meta__OptMon_SBS_opt_pow.plc)
and OptMon_noSBS (meta__OptMon_noSBS_opt_pow.plc). These plots are shown in Fig. 2. By comparing the
results, we see that at a launch power of approximately 14 dBm, the output of the fiber begins to be depleted relative to
that of the non-SBS fiber. Beyond 14 dBm, the output is clearly reduced by the SBS effect.

Figure 1. OptSim topology for examining the effect of SBS in a fiber.

218 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 (a) (b)

Figure 2. Output power versus launch power for an SMF-28 fiber (a) with SBS and (b) without SBS.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 219
2.10 EDFA

2.10.1 EDFA Tutorial

Erbium-doped fiber amplifiers (EDFA’s) are an important component in the design of long-haul telecommunication
links, and OptSim’s Physical EDFA model is a useful tool for studying the impact of EDFA gain and noise
characteristics on a given link topology. In this tutorial, we introduce the main features of the Physical EDFA model by
presenting a simple topology that illustrates the primary model options. This topology may be found in the
“examples/edfa” directory of the OptSim distribution.
The model documentation for the Physical EDFA model should be read before beginning the tutorial activities. This
documentation is found in the OptSim Models Reference.

Main Features

RSoft/examples/optsim/block_mode/EDFA/edfa_tutorial.moml
Begin by opening the topology “edfa_tutorial.moml”, the schematic of which is illustrated in Figure 1. A
multiplexer combines a 1535-nm modulated input signal with a 980-nm cw pump for input at the EDFA’s forward input
node, while for the time being the EDFA’s backward input is empty. Various signal analysis blocks are also included to
assess the EDFA’s performance. The EDFA model parameters used in the following simulations are based largely on
data from [1].

Figure 1. Basic tutorial topology from "edfa_tutorial.moml".

To begin, we will first examine some of the EDFA-parameter characteristics. Right-click on the EDFA to open its
parameter editing window, and scroll to the bottom. Click on the Test button. A plot of the EDFA’s emission and
absorption cross-section spectra for the 1550-band should be displayed. To examine the corresponding 980-band
absorption cross section, change the model’s test_function parameter to 980_spectra(nm) and click the Test button again.
Next, close the parameter editing window, and run a simulation of the topology by clicking on OptSim’s Simulate Link
button and hitting OK. After the simulation has completed, begin studying the results by double-clicking on the two

220 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
time-domain Signal Analyzer blocks (the first is attached to the modulated input signal, the second to the EDFA output).
Notice how the signal has been dramatically amplified by the EDFA, its power levels increasing from µ range to the mW
range.
Next, double-click on the Spectrum Analyzer block at the EDFA output, and select the ASE output file,
“lstmpSpecPlt_1_ASE.pcs”. The displayed plot illustrates the spectral density of the amplified spontaneous
emission (ASE) exiting the EDFA. Notice how the shape is similar to that of the emission/absorption spectra, as one
would expect.
Finally, double-click on the EDFA block to select one of the following reference plots, which reveal in more detail the
operating characteristics of the EDFA:
• lstmp_EDFAPhys_1_signal_ase_evolution.pcs:
Shows the evolution of the total signal and ASE powers along the length of the EDFA. As can be seen,
both the total forward- and backward-propagating ASE powers grow significantly.
• lstmp_EDFAPhys_1_pump_evolution.pcs:
Displays the depletion of the co-propagating pump as it travels along the EDFA. Notice how the depletion
is most severe at the ends, where the total ASE power is strongest. Towards the middle of the device, the
pump power is reduced much more slowly [1].
• lstmp_EDFAPhys_1_1550_power_spectra.pcs:
Displays the 1550-band input and output power spectra, including both signals and ASE. The amplification
of the 1535-nm input signal is clearly displayed, as is the overall ASE spectra observed earlier. Notice how
in the vicinity of the output signal, the local ASE power is actually lower than the signal power. This
suggests that adequate spectral filtering of the ASE should significantly improve system performance.
• lstmp_EDFAPhys_1_ase_power_spectra.pcs:
Depicts the forward- and backward-propagating ASE power spectra at the output and input ends,
respectively, of the EDFA. While both curves have the same general shape, the backward-propagating
ASE actually has more power because of the co-propagating pumping scheme used in the topology.
Because the backward ASE experiences the most gain at the EDFA input end (where the pump and ASE
have the most power), it tends to more efficiently extract power from the pump, and therefore is better
amplified as compared to the forward ASE [1].
• lstmp_EDFAPhys_1_gain.pcs:
Plots the spectral gain at the discretized frequencies solved for by the EDFA model. As expected, the large
gain values reflect the significant signal amplification observed earlier, with the spectral dependence
generally conforming to the cross-section spectra at the displayed wavelengths.
• lstmp_EDFAPhys_1_noise_figure.pcs:
Displays the noise figure (NF) of the EDFA at the discretized frequencies solved for by the EDFA model.
Note that the NF is larger than the quantum limit of 3 dB [1].
• lstmp_EDFAPhys_1_average_densities.pcs:
Displays the average atomic-manifold population densities for atomic levels 1 and 2 along the length of the
EDFA. Notice how the inversion tends to peak in the middle of the EDFA, where the pump is most slowly
depleted. Furthermore, the combined effect of the co-propagating signal and forward ASE tends to deplete
the inversion most significantly at the output end of the EDFA.

Parameter Sweeps
Next, we will perform a number of parameter sweeps. In this topology, many of the key design parameters for the
signal, pump, and EDFA have been implemented using OptSim’s symbol table. These include the EDFA length
(edfa_length, units in m), pump power (pump_power, units in mW), pump wavelength (pump_wavelength, units in
m), signal power (signal_power, units in dBm), and signal wavelength (signal_wavelength, units in m). Thus, we
can readily vary these parameters to study their impact on EDFA performance.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 221
First, we will scan the EDFA’s length from 5 to 25 m, in 5-m steps. Click on OptSim’s Parameter Scan button. For the
Inner Iteration, set the Variable Name to “edfa_length”, the Starting Value to 5, the Ending Value to 25, the
Increment to 5, and the Iteration Meta Prefix to “i”. Click OK to run the simulation. When the simulation is complete,
double click on the EDFA and select the file “lstmp_EDFAPhys_1_gain_scan.pcs”. The resulting plot displays the
amplifier gain as a function of EDFA length. As can be seen, the gain is optimal at a length near 15 m. Note that this
type of simulation is ideal for designing an EDFA’s length in order to achieve a target gain.
Next, we will scan the signal wavelength from 1510 to 1580 nm, in 10-nm steps. Click on OptSim’s Parameter Scan
button and change the Inner Iteration Variable Name to signal_wavelength, the Starting Value to 1510e-9, the
Ending Value to 1580e-9, and the Increment to 10e-9. Click OK. At the conclusion of the simulation, double-click
on the EDFA block and again select “lstmp_EDFAPhys_1_gain_scan.pcs”, which now displays the variation of the
amplifier gain as a function of signal wavelength. As one would expect, the shape of this curve is similar to the shape of
the cross-section spectra, with a strong peak near 1530 nm.
Finally, we will scan the signal power from –40 to 0 dBm, in 4-dB steps. Open the Parameter Scan dialog, and change
the Inner Iteration Variable Name to signal_power, the Starting Value to –40, the Ending Value to 0, and the
Increment to 4. Click OK, and at the end of the simulation (the warning message may be safely ignored), double-click
on the Optical Monitor block and open “lstmp_OptMon_1_opt_pow.plc”. The displayed characteristic plots the
signal output power as a function of input power, clearly revealing the saturation of the EDFA at elevated signal powers.

Upconversion and Pair-Induced Quenching

Often upconversion and pair-induced quenching can limit the performance available from a given EDFA [1]. To
demonstrate this, we will next conduct two sets of scans to guage the impact of these effects on an EDFA’s gain.
First, open the Parameter Scan dialog and change the Inner Iteration Variable Name to pump_power, its Starting Value
to 10, its Ending Value to 80, and its Increment to 10. Then set the Outer Iteration Variable Name to C, its Starting
Value to 0, its Ending Value to 1.5e-22, and its Increment to 0.5e-22. Click OK, and at the end of the simulation,
double-click on the EDFA block and open “lstmp_EDFAPhys_1_gain_scan.pcs”. The displayed gain plots show the
effect of the upconversion parameter C on the amplifier gain. As expected, greater levels of upconversion make the
amplification process less efficient, thereby reducing the overall device gain.
Next, open the Parameter Scan dialog and change the Outer Iteration Variable Name to k, its Starting Value to 0, its
Ending Value to 0.2, and its Increment to 0.1. Click OK, and at the end of the simulation, double-click on the EDFA
block and open “lstmp_EDFAPhys_1_gain_scan.pcs”. This time, the displayed gain plots show the effect of the
pairing parameter on the amplifier gain. Since a greater proportion of pairs tends to reduce the amplifier’s efficiency, we
see that the overall amplifier gain is reduced as k increases.

Pump/Signal Recycling
In many cases, adding mirrors to an EDFA to recycle the pumps and/or signals is a powerful method for improving the
device’s gain characteristics. In the following simulations, we will study this design technique for a 9-m EDFA
amplifying a 1550-nm signal. We will be sweeping the pump power from 10 to 50 mW in 10-mW increments. Begin by
opening OptSim’s symbol table by clicking on the Edit Symbols button. Set edfa_length to 9 and signal_wavelength to
1550e-9.
First, we will provide a baseline simulation with no mirrors in the design. Double-click the Parameter Scan button and
for the Inner Iteration, set the Variable Name to pump_power, the Starting Value to 10, the Ending Value to 50, the
Increment to 10, the Scan Meta Prefix to norec, and the Iteration Meta Prefix to “i”. Delete, if it exists, the Outer
Iteration Variable Name setting. Run the simulation. We will review its results shortly.
Next, we will add a mirror at the EDFA output to recycle the 980-nm pump signal. Open the EDFA parameter entry
dialog, and set mirror_configuration to forward_mirror. This activates the mirror parameters, which are set for a
rectangular mirror centered at 980 nm. Double-click the Parameter Scan button, reset the Scan Meta Prefix to
pumprec, and run the simulation.
Finally, we will adopt a signal recycling scheme in which the signal input and output are actually at the same physical
end of the EDFA, with an optical circulator separating the two. Open the EDFA parameter entry dialog, set
mirror_configuration to signal_mirror, and change mirror_center to 1550. When the parameters have been set, open
the Parameter Scan dialog, reset the Scan Meta Prefix to sigrec, and run the simulation.

222 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
To compare the various designs, we have included a pre-formatted WinPLOT file. Click on the OptSim View Graphs
button, and open the file “recycling.pcs”. This compares the signal output powers (measured by the Optical Monitor
block) as a function of pump power for the three simulations we have just run. As can be seen, recycling of the pump
does improve the signal amplification, but not nearly as effectively as the signal recycling scheme, which allows the
signal to traverse the EDFA’s inversion twice. In either case, the advantages of adding mirrors for signal or pump
recycling are clear.

Pump Configurations
EDFA’s can be pumped in a number of configurations, with pumps co- or counter-propagating with the input signal. In
some cases, bidirectional pumping is used [1]. In the following simulations, we will compare the various approaches for
a 14-m EDFA with an input signal power of –20 dBm. Begin by clicking on OptSim’s Edit Symbols button, and setting
edfa_length to 14 and signal_power to –20. Also, reset the EDFA’s mirror_configuration parameter to no_mirror.
First, we will run a simulation on the current topology (where the pump co-propagates with the signal), sweeping the
pump power from 10 to 85 mW in 15-mW steps. Double-click the Parameter Scan button, and for the Inner Iteration set
the Variable Name to “pump_power”, the Starting Value to 10, the Ending Value to 85, the Increment to 15, the Scan
Meta Prefix to “co”, and the Iteration Meta Prefix to “i”. Run the simulation. We will review the results shortly.
Next, disconnect the cw pump from the multiplexer, and connect it to the backward input of the EDFA, as illustrated in
Figure 2. The pump will now counter-propagate with the input signal. Open the Parameter Scan dialog, set the Scan
Meta Prefix to “counter”, and run the simulation.

Figure 2. Basic EDFA topology with a counter-propagating pump.

Finally, disconnect the cw pump connected to the EDFA, and connect the two additional cw pumps situated below it in
the manner shown in Figure 3. In this case, we will be bidirectionally pumping the EDFA, with total pump power equal
to that used in the single pump cases simulated above. Open the Parameter Scan dialog, set the Scan Meta Prefix to
“bi”, and run the simulation.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 223
 Figure 3. Basic EDFA topology with bidirectional pumping.

To compare the performance of the different pumping schemes, we have prepared a pre-formatted WinPlot file. Click on
OptSim’s View Graphs button and open the file “pumps.pcs”. As can be seen, both the counter-propagating and
bidirectional pumping schemes provide better gain than the co-propagating case. For the counter-propagating scheme,
the advantage arises from the signal being amplified most heavily at the output end of the fiber, where the pump power is
largest and the signal power level has already been significantly amplified [1]. As for the bidirectional pumping scheme,
it is clear that it provides the best gain performance of the three approaches.

Reference
1. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology.
(San Diego, Academic Press, 1999).

224 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.10.2 EDFA-Based Optical Links
In the following simulations, we will study a number of more complicated link topologies that include EDFA’s for signal
amplification.

WDM Example

RSoft/examples/optsim/block_mode/EDFA/edfa_4ch_wdm.moml
Open the topology “edfa_4ch_wdm.moml”, which is shown in Figure 1. In this link, we have four signal channels at
wavelengths of approximately 1554, 1558, 1562, and 1566 nm, each with a signal power between 75 and 80 µm. The
signals are propagated down two spans of fiber, each pre-amplified by an EDFA counter-pumped with a 35-mW 980-nm
cw signal. With the topology loaded into OptSim, click the Simulate Link button and hit OK.

Figure 1. Four-channel WDM link with two EDFA-fiber spans.

Once the simulation has been completed, double-click the uppermost Spectrum Analyzer block attached to the output of
the EDFA-fiber spans. The power spectra of each signal channel is visible, superimposed on the local ASE power. As
can be seen, the signals at the shorter wavelengths (higher frequencies) have experienced the most gain, consistent with
the non-uniform gain/loss spectra for the EDFA’s.
This non-uniform gain can have a severe impact on the bit-error rate (BER) for each channel, as can be seen by
successively double-clicking the Eye Diagram Analyzers at the electrical output of each channel. As can be seen, the
longest-wavelength signal, with its relatively low amplification, is least able to overcome the effects of noise in the link’s
photoreceivers, resulting in a closed eye. The well amplified shorter wavelength channels, however, exhibit open eyes.
This discrepancy highlights the need to account for an EDFA’s non-uniform spectral gain when designing an optically
amplified link.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 225
Gain Compensation Example

RSoft/examples/optsim/block_mode/EDFA/edfa_gain_compensation.moml
In this example, we will demonstrate the use of EDFA’s in an optical link to minimize the degradation of an optical
signal’s average power. Open the topology “edfa_gain_compensation.moml”, depicted in Figure 2. In this design,
twelve spans of 81-km optical fiber are pre-amplified by 100-mW 980-nm pumped EDFA’s. The photoreceiver is also
preamplified by an EDFA. After loading the topology, run a simulation by clicking on OptSim’s Simulate Link button
and hitting OK.

Figure 2. Long-haul optical link using EDFA-based gain compensation.

At the conclusion of the simulation, double-click the Property Map block, which displays a plot of the signal power
along the link. As can be seen, at the end of the last EDFA-fiber span, the signal power is roughly equal to its value at
the start of the link. As an exercise, try adjusting the EDFA and fiber parameters to achieve uniform gain compensation
along the entire link (i.e., the power output of each fiber should be equal).

ASE Peaking

RSoft/examples/optsim/block_mode/EDFA/edfa_ase_peaking.moml
As a final example, open the topology “edfa_ase_peaking.moml”, depicted in Figure 3. We again have twelve
EDFA-fiber spans, with the fiber length in this case set to 35 km. With the topology loaded, click on OptSim’s Simulate
Link button, set the Output Prefix to “ase_peaking”, and click OK to run the simulation.

Figure 3. Optical link demonstrating the effect of ASE peaking.

An interesting effect in chains of EDFA’s is the peaking of the ASE output spectrum at longer wavelengths. Typically,
the ASE spectrum is most strongly peaked near 1530 nm, where an EDFA’s absorption/emission cross sections are the
largest. However, over a chain of amplifiers the gain tends to saturate, which shifts the gain peak, and hence the ASE

226 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
output spectra, to longer wavelengths [1]. To illustrate this behavior, we have prepared a pre-formatted WinPlot file.
Click on OptSim’s View Graphs button, and open the file “ase_peaking.pcs”, which depicts the ASE output spectra
after the chain’s first, fourth, and last stages. As can be seen, the spectral peak gradually shifts to shorter frequencies
(longer wavelengths), as expected.

References
1. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and
Technology. San Diego, Academic Press, 1999.
2. E. Desurvire, Erbium-Doped Fiber Amplifiers. New York, Wiley, 1994.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 227
2.10.3 EDFA Design for Dense WDM System
RSoft/examples/optsim/block_mode/EDFA/EDFA_WDM.moml
The purpose of this example is to demonstrate optical amplifier design for dense WDM system using EDFA Physical
Model. We consider a realistic case typical for long-haul systems when an optical amplifier has to support WDM link
providing, for example 10dB gain (i.e. about 50 km fiber span between amplifiers) and 13dBm total output power from
the amplifier for 64-channel 50GHz spacing system. The amplifier unit consists of EDFA, pump source (co-propagating
pump in our case), coupler, and optical filter. The purpose of optical filter here is to equalize gain and output power over
the bandwidth of amplifier, and conventionally is called gain flattening or gain equalizing filter. The snapshot of the
topology is given in Fig.1.

Figure 1. Topology for optical amplifier design EDFA_WDM.moml.

Gain Spectra

10.4

10.2

10.0
gain (dB)

9.8

9.6

9.4

1540 1550 1560

wavelength (nm)

Figure 2. EDFA gain shape over the 64-channel bandwidth of 25.2 nm.

228 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Input to EDFA is set up as 64 modulated channels with power per channel –15dBm (total power 3dBm) and wavelength
range 1537.4-1562.6 nm. CW pump source at 980 nm is co-propagating in EDFA through the coupler – Optical
Multiplexer. Insertion losses of coupler, optical filter, and fiber splices should be accounted for input and output losses.
Forward-input losses are set to 0.6dB and output losses are set to 3.4dB. For EDFA gain calculation we used Giles
parameters simulation mode with data files for gain and loss spectrum of commercially available OFS Er-doped fiber
HE980 [1] – given in files Gain_1550.dat and Loss_1550.dat, correspondingly.

Noise Figure

4.3
NF (dB)

4.2

4.1

1540 1550 1560

wavelength (nm)

Figure 3. Noise Figure of EDFA over the bandwidth with average about 4.2 dB.

Next we optimize the pump power and length of the Er-doped fiber to achieve required gain and at the same time to
minimize Noise Figure and peak-to-peak gain variation over the bandwidth. Pump power of 86 mW and EDFA length
of 14.5 m are chosen to provide 13 dBm total output power and 10 dB gain average across the bandwidth (see Fig. 2).
Noise figure has an average of 4.2 dB – see Fig. 3. Gain shape has about 1 dB peak-to-peak difference and so has the
channel power – see optical spectrum and signal shape after the EDFA in Fig. 4.

Spectrum After EDFA - Zoom In Signal After EDFA

-7.5 -1

-7.8
Signal Magnitude (dBm)

-8.1
Power (dBm)

-8.4
-2
-8.7

-9.0

-9.3
-3
154 155 156 0 2 4 6 8 10 12 14 16
x10-8 x10-9
Wavelength (m) Time (s)

Figure 4. Optical spectrum and signal in time domain after EDFA block.

To equalize all channels to the same power, we inserted a gain flattening optical filter (GFF) after EDFA block. The
shape of this filter is an inverse of EDFA gain shape – see Fig. 5. Here average loss of this filter across the bandwidth is
zero since filter’s insertion loss is included in the output loss of EDFA model. Filter data are given in file GFF.dat. Fig.
6 shows optical spectrum and signal shape after optical filter – now peak-to-peak difference for different wavelengths is
less than 0.1 dB and all 64 channels have practically the same power.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 229
 Optical Filter Wavelength Response
Power
0.8 0.4
Phase

0.6

Transmitted Phase (rad)

Transmitted Power (dB)
0.2
0.4

0.2 0.0

0.0
-0.2
-0.2

-0.4 -0.4

1540 1550 1560

Lambda (nm)

Figure 5. Shape of gain flattening optical filter.

Spectrum After GFF - Zoom In Signal After GFF

-7.5 -1

-7.8
Signal Magnitude (dBm)

-8.1
Power (dBm)

-8.4
-2
-8.7

-9.0

-9.3
-3
154 155 156 0 2 4 6 8 10 12 14 16
x10-8 x10-9
Wavelength (m) Time (s)

Figure 6. Optical spectrum and signal in time domain after gain flattening optical filter.

Reference
1. OFS Specialty Photonics Division, Erbium-Doped Fiber: High Performance Fiber for Superior Amplifier
Design, www.ofsoptics.com/product_info/documents/OFS_ED_broc.pdf

230 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.10.4 Cladding-Pumped EDFA
RSoft/examples/optsim/block_mode/EDFA/edfa_cladding_pumped.moml
Cladding-pumped EDFAs have been identified as a solution for L-band amplification. In [1], the noise performance of
these devices is studied for both co- and counter-propagating pump schemes. This example repeats some of the
numerical studies from [1], illustrating the advantages of large pump claddings for the minimization of ASE noise in the
amplifier, and therefore improved noise figure (NF).
Figure 1 depicts the topology used to study the noise performance of a cladding-pumped EDFA. In its initial
configuration, this topology implements a co-propagating pump scheme. The EDFA (model block EDFAPhys) is
configured for bi-directional operation in order to study the differences between forward and backward ASE (a cw signal
of insignificant power is launched at the EDFA’s backward input in order to facilitate the analysis). Based on data in [1],
the EDFA is 180 m and has a core radius of 4 µm, an index difference of 0.34%, an erbium concentration of 5.5·1024 m-3,
and a background loss of 5 dB/km. The absorption and emission cross sections are given in the files abs.dat and
em.dat, respectively, and are different from those used in [1]. To study the EDFA performance as a function of
cladding area, we launch a –16-dBm, 1590-nm cw signal (SigLaser) into the EDFA. Furthermore, we launch a 980-nm
cw pump (CoPumpLaser) into the EDFA as well. As we adjust the cladding area, the pump power is automatically
adjusted to achieve a 20-dB gain from the amplifier.

Figure 1. OptSim topology for simulation of the noise performance of a cladding-pumped EDFA.

As a first experiment, we will simulate this topology, sweeping the cladding area of the EDFA from 500 to 4500 µm2 in
increments of 1000 µm2. Load the topology into OptSim and open the Parameter Scan Dialog, which is already set up to
perform the desired sweep of the cladding area parameter Aclad. Click Ok. When the simulation is complete, open the
plot lstmp_OptMon_FwdOut_noise_pow.plc via the monitor block OptMon_FwdOut and the plot
lstmp_OptMon_BwdOut_noise_pow.plc via the block OptMon_BwdOut. These plots, reproduced in Fig. 2,
depict the ASE output powers of the EDFA in the forward and backward directions, respectively. As the results clearly
indicate, while the ASE power in the forward direction is very low (tens of µW) for all cladding areas, the backward
ASE output power is very high (hundreds of mW) for small claddings, but significantly lower as the area is increased.
These results are consistent with those presented in [1]. As explained there, large claddings help suppress the pump
efficiency, leading to a significantly more uniform longitudinal pump distribution.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 231
 (a) (b)

Figure 2. (a) Forward and (b) backward ASE output powers with a co-propagating pump scheme.

Next, we will simulate the amplifier using a counter-propagating pump scheme. Disconnect the cw laser CoPumpLaser
from the multiplexer OptMUXCo, and connect the cw laser CounterPumpLaser to the multiplexer OptMUXCounter. The
resulting schematic should look like that presented in Fig. 3. Next, open the Parameter Scan Dialog and click Ok. When
the simulation is complete, the plots for the forward and backward ASE outputs should match those in Fig. 4.
Essentially, the results are the reverse of those presented in Fig. 2, with the forward ASE now benefiting from large
cladding areas. However, the same essential reasoning behind this behavior holds, with large cladding areas leading to
more uniform pump distributions. To further demonstrate the benefits of large cladding areas, double click on
EDFAPhys and open the plot of NF versus cladding area (lstmp_EDFAPhys_noise_figure_scan.pcs). As can
be seen (Fig. 5), while the NF values are by no means low, they are significantly reduced for large cladding areas. These
results are again consistent with those presented in [1].

Figure 3. Topology modified to use a counter-propagating pump scheme.

232 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 (a) (b)

Figure 4. (a) Forward and (b) backward ASE output powers with a counter-propagating pump scheme.

Figure 5. NF as a function of cladding area for the counter-propagating pump scheme.

References
1. M. Söderlund, S. Tammela, P. Pöyhönen, M. Leppihalme, and N. Peyghambarian, “Amplified spontaneous emission
in cladding-pumped L-band erbium-doped fiber amplifiers,” IEEE Photonics Technology Letters, vol. 13, no. 1, pp.
22-24, January 2001.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 233
2.11 EYCDFA

2.11.1 Er-Yb-Based Master-Oscillator Power Amplifier (MOPA)

RSoft/examples/optsim/block_mode/eycdfa/eycdfa_mopa.moml
This example demonstrates a master-oscillator power amplifier using an EDFA and an Er-Yb co-doped fiber amplifier
(EYCDFA). The topology, shown in Fig. 1, is based on one presented in [1]. A 10-mW cw source is first pre-amplified
by an EDFA with 23-dB of gain. A 10-m EYCDFA, backward pumped at 975 nm, then boosts the signal to extremely
high output power. The EYCDFA is a cladding-pumped design configured with model parameters based on data from
[1]-[4]. The amplifier has a 30-µm diameter core and a 3.3×105-µm2 inner cladding. For simplicity, the core mode profile
is represented by an LP01 mode.

Figure 1. OptSim topology for simulating Er-Yb-based MOPA.

To demonstrate the capabilities of this configuration, we will first calculate the EYCDFA output power as a function of
source wavelength (ranging from 1550 to 1570 nm) and pump power (ranging from 50 to 350 W). Load the topology
into OptSim and open the Parameter Scan Dialog. The dialog should already be configured with source_wavelength as
the Inner Loop Variable, swept from 1550e-9 to 1570e-9 in increments of 5e-9, and with pump_power as the Outer
Loop Variable, swept from 50 to 350 in increments of 50. Click Ok. When the simulation is complete, open the plot
scan_OutputMonitor_opt_pow.plc via the block OutputMonitor. The resulting graph, shown in Fig. 2, depicts
the MOPA output versus source wavelength for different pump-power values. As can be seen, outputs on the order of
100 W can be achieved for sufficiently high pump powers. The output power can be further increased by raising the
pump power, though roll-over does eventually occur.
Next, we will plot the MOPA output power versus pump power at a source wavelength of 1550 nm. Open the Parameter
Scan Dialog and set the Inner Loop Variable to pump_power, swept from 50 to 350 in increments of 50, and the Outer
Loop Variable to (No_Scan). Click Ok. When the simulation is finished, again open the plot
scan_OutputMonitor_opt_pow.plc via OutputMonitor. The displayed graph, reproduced in Fig. 3, shows the

234 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
steady increase of MOPA output power as we increase the pump power, with the onset of roll-over manifest at higher
pump powers.

Figure 2. MOPA output power as a function of source wavelength (1550 to 1570 nm) and pump power (50 to 350 W).

Figure 3. MOPA output power at 1550 nm versus pump power.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 235
References
1. Y. Jeong, J. K. Sahu, D. B. S. Soh, C. A. Codemard, and J. Nilsson, “Tunable single-frequency ytterbium-sensitized
erbium-doped fiber MOPA source with 150 W (51.8 dBm) of output power at 1563 nm,” OFC 2005 Post-Deadline
Paper, 2005.
2. M. Achtenhagen, R. J. Beeson, F. Pan, B. Nyman, and A. Hardy, “Gain and noise in ytterbium-sensitized erbium-
doped fiber amplifiers: Measurements and simulations,” Journal of Lightwave Technology, vol. 19, no. 10, pp.
1521-1526, October 2001.
3. C. Lester, A. Bjarklev, T. Rasmussen, and P. G. Dinesen, “Modeling of Yb3+-sensitized Er3+-doped silica waveguide
amplifiers,” Journal of Lightwave Technology, vol. 13, no. 5, pp. 740-743, May 1995.
4. O. Lumholt, T. Rasmussen, and A. Bjarklev, “Modelling of extremely high concentration erbium-doped silica
waveguides,” Electronics Letters, vol. 29, no. 5, pp. 495-496, March 1993.

236 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.12 OptSim-LAD Interface

2.12.1 EDFA Gain Compensation via the LAD Interface

RSoft/examples/optsim/block_mode/LAD/lad_edfa_example.moml

The Liekki Application Designer (LAD) from Finnish company Liekki is a powerful simulation platform for the analysis
of fiber-amplifier and fiber-laser based systems. LAD includes support for Er- and Yb-doped fiber, cladding-pumped
designs, multimode effects, and other state-of-the-art features. The Liekki LAD Interface allows OptSim to interface with
the Liekki Application Designer (LAD), thereby permitting LAD designs to be easily deployed in an OptSim schematic.

The interface itself is simple to use, as shown in the following example. Figure 1 depicts an OptSim schematic that
implements gain compensation via the Liekki LAD Interface block. OptSim optical sources are used to generate a 1-mW
1550-nm signal and a 980-nm pump. These are launched into the LAD design shown in Figure 2, which includes input
ports for the signal and pump, 10-km of single-mode fiber, 3.5-m of Er-doped fiber, and an output port. The OptSim
Optical Monitors and XY Plotter are used to study the output signal power as a function of pump power.

LAD Interface Block

Measurement Blocks
for Output Plots
Figure 1. Topology for simulating EDFA gain compensation via the Liekki LAD Interface.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 237
 Input Ports

Output Port
Figure 2. LAD schematic implementing EDFA gain compensation of 10-km of single-mode fiber.

To run this example, load the OptSim schematic and open the Parameter Scan Dialog. The scan parameters should
already be configured to sweep the pump input power from 1 to 10 mW in 1-mW increments. Click Ok. At the
conclusion of the simulation, double-click on the XY Plotter block to display a plot of output signal power versus
launched pump power. As Figure 3 illustrates, increasing the pump power increases the output signal power as expected.
Furthermore, we see that in order to achieve full gain compensation and restore the signal power to 1 mW after its
propagation through 10 km of single-mode fiber, a pump power of approximately 6.4 mW is required.

Figure 3. Output signal power versus launched pump power.

238 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.13 SOA

2.13.1 Semiconductor Optical Amplifier (SOA)

RSoft/examples/optsim/block_mode/SOA/soa_singlechannelamp.moml
RSoft/examples/optsim/block_mode/SOA/soa_noise.moml
In this example, the SOA model is demonstrated in a number of topologies.

Figure 1. soa_singlechannelamp.moml

Figure 2. soa_noise.moml

Amplification in a single channel transmission system is demonstrated in topology file

“soa_singlechannelamp.moml”, depicted in Figure 1. In this example, the gain of the amplifier is around 25.9 dB.
Compared with this example, topology “soa_noise.moml” (Figure 2) added the NoiseAdder block in front of the SOA.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 239
The NoiseAdder introduced uniform noise with noisePeak of 1e-17 W/Hz, then the gain of the amplifier decreased to
24.2dB. Also, you can see the noise spectra before and after the SOA are different. After the SOA the noise spectrum is
no longer flat due to the gain tilt. Setting Curvature_SpectralGain = 0, the noise spectrum after the SOA would be flat
again, and the gain is also affected. By changing the noise power in the NoiseAdder, you will see the gain of the
amplifier will be affected due to the noise.

RSoft/examples/optsim/block_mode/SOA/soa_multichannelamp.moml

Figure 3. soa_multichannelamp.moml

Amplification of multiple channels is demonstrated in topology file “soa_multichannelamp.moml” (See Figure 3).
With the SOA, this link works fine. If you remove the SOA from this link, even without the attenuator the eyes and
BERs will be very poor. By looking at the spectra before and after the SOA, you can see some slight changes of the
relative amplitudes of different wavelengths. This implies that the SOA may apply different gains on different channels,
but it is not severe and the crosstalk is also not severe in this example where each channel power is well equalized.
However, if the power for different channels is significantly different, the crosstalk will be more severe. For example,
try 2mW, 0.5mW, 0.1mW and 1mW for these four channels respectively and observe the crosstalk effect in the channel
with 0.1mW. When no other channels are present the BER and eye for this channel will be much better than when all
the channels are there. When you try this, the Monte Carlo (MC) method is recommended. To use the MC method, you
need to set the “n_representation” as “MC” in both the receiver and the BERT blocks.

RSoft/examples/optsim/block_mode/SOA/soa_switch.moml
An example of using the SOA in switch applications is shown in topology “soa_switch.moml” (Figure 4). In this
example, the SOA in the upper arm is in the OFF state (pump current = 0), the degree of isolation is on the order of
70dB, and the switching time is on the order of ns, which can be observed by looking at the output signals of the SOA.
These results match well with the literature. The SOA in the lower arm is in the ON state and is used as an amplifier.

240 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 4. soa_switch.moml

RSoft/examples/optsim/block_mode/SOA/soa_wavelengthconverter_xgm.moml
RSoft/examples/optsim/block_mode/SOA/soa_wavelengthconverter_xpm.moml
The SOA model may also be used for wavelength conversion applications. As an example, let us consider conversion by
cross-gain modulation. This type of conversion makes use of the dependence of the gain of an SOA on its input power.
As the input power increases, the carriers in the gain region of the SOA get depleted, resulting in a reduction in the
amplifier gain. What makes this interesting is that the carrier dynamics within the SOA are very fast, happening on a
picosecond time scale. Thus the gain responds in tune with the fluctuations in input power on a bit-by-bit basis. The
device can handle bit rates as high as tens of Gb/s. If a low-power probe wave at a different wavelength is sent into the
SOA, it will experience a low gain when there is a 1 bit in the input signal and a higher gain when there is 0 bit. This
very same effect produces crosstalk when multiple signals at different wavelengths are amplified by a single SOA. One
of the drawbacks of this type of conversion is that the achievable extinction ratio is small (<10) since the gain does not
really drop to zero when there is an input 1 bit. The input signal power must be high so that the amplifier is saturated
enough to produce a good variation in gain. This high-powered signal must be eliminated at the amplifier output by
suitable filtering unless the signal and probe are counterpropagating. Moreover, as the carrier density within the SOA
varies, it changes the refractive index as well, which in turn affects the phase of the probe and created a large amount of
pulse distortion. This is also the mechanism of the conversion on the cross-phase modulation.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 241
 Figure 5. soa_wavelengthconverterxgm.moml

Look at topology file “soa_wavelengthconverterxgm.moml” shown in Figure 5. Since the added signal is out-of-
phase with the original signal, before the signal is sent to the BERT block it is sent to a 1×1 Expression operator, which
just takes the reverse of the signal (turn the signal over). By looking at the signals and spectra obtained one can observe
the physical phenomena described above.

Figure 6. soa_wavelengthconverterxpm.moml

Let us now consider conversion by cross-phase modulation. As mentioned above, the same phase-change effect that
creates pulse distortion in the cross-gain modulation can be used to create wavelength conversion. As the carrier density
in the amplifier varies with the input signal, it produces a change in refractive index, which in turn modulates the phase

242 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
of the probe. This phase modulation can be converted into intensity modulation by using an interferometer such as a
Mach-Zehnder interferometer (MZI). See topology file “soa_wavelengthconverterxpm.moml” (Figure 6). In this
example, two multi-port devices were used to set up the MZI, one SOA in each arm of the MZI. Here another purpose
to use the multi-port device is to demonstrate how to set the transfer matrix data file for the multi-port device model.
Actually the multi-port devices here can be easily replaced by optical couplers. The first multi-port device functions as
a coupler, its transfer matrix data file name is MultiportCoupler.txt. The second multi-port device functions as a
summer, its transfer matrix data file name is MultiportSummer.txt (these two files are included in the directory with
the topology files). If looking at the file MultiportCoupler.txt, one can find different coupling ratios in the two
arms were used, which will make the phase change in each amplifier different. Unlike in the cross-gain modulation
wavelength conversion, in the cross-phase modulation wavelength conversion the added signal is in-phase with the
original signal. In the two arms of the MZI, two optical phase shifters were used to monitor the influence of the phases
on the performance of the system though no phase shift was introduced in this example.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 243
2.13.2 RSOA-based PON with Upstream Remodulation
RSoft/examples/optsim/block_mode/soa/RSOA_PON.moml
Within the global fiber-optic infrastructure, passive optical networks (PONs) can play an important role in fiber-to-the-
home (FTTH) and fiber-to-the-premises (FTTP) solutions. In a typical PON, a central office (CO) distributes data over
passive optical fiber to various optical network terminations (ONTs), which in turn can send data back upstream to the
CO via the same fiber network. Researchers have proposed a number of low-cost solutions for the ONT upstream
transmitters, including the use of reflective SOAs (RSOAs) to remodulate the downstream signal from the CO in order to
produce the new upstream signal [1]-[3]. In this example, we demonstrate this concept via the simultaneous upstream
and downstream transmission of a single optical channel over a PON.
Figure 1 illustrates the schematic used in this example, which can be found in the file “RSOA_PON.moml”. This
schematic, based on the experiment described in [1], is a simplified representation of a PON, with a CO and ONT
connected via 20 km of optical fiber. For simplicity, we neglect scattering effects in the fiber and assume negligible
interaction between counterpropagating signals. Optical filters are used to model the filtering effects of AWGs in an
actual PON network. In the CO, a downstream transmitter generates a 1550-nm 2.5-Gbps NRZ signal whose extinction
ratio (in dB) can be approximately adjusted via the global symbol ER_dB. At the ONT, the downstream signal is routed
to both a receiver (whose input power can be set via the global symbol downRXpower_dBm) and an RSOA-based
upstream transmitter (whose input power can be set via the global symbol downRSOApower_dBm). The RSOA is
modulated with a 1.25-Gbps NRZ signal that effectively overwrites the downstream signal. This new upstream signal is
transmitted back over the same 20 km of fiber, where it is routed to a receiver at the CO (whose input power can be set
via the global symbol upRXpower_dBm).

Figure 1. Simplified PON for demonstrating RSOA-based upstream remodulation.

The effectiveness of this design depends on the ability of the RSOA to remodulate the received downstream signal with
the new upstream signal. Towards this end, the high-pass filtering effect of the RSOA, which becomes more pronounced
at higher input powers, can be used to suppress the downstream signal [4]. To demonstrate this, open the Simulation Run
Dialog and press OK. This simulates the bi-directional link in two passes, first taking into account the downstream
transmission in the fiber, and then simultaneously accounting for both the upstream and downstream signals. In this
simulation, we are using the initial settings of the schematic, which assume an approximate 4-dB extinction ratio in the
downstream signal, and –10 dBm of power at the RSOA input. The warning message at the conclusion of the simulation
can be safely ignored. If you now view the results of the BER Tester BERTest2, you can see that the BER is
approximately 7.3×10-10. This low value is due to the fact that we are operating the RSOA close to saturation, as can be
seen by plotting the gain versus input power of the RSOA at a bias current of 40 mA. The test-parameter settings of the
RSOA model have been preconfigured to display this plot; right-click on the RSOA and select Test Component to
display it (Fig. 2).

244 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 2. Plot of RSOA gain saturation at 1550 nm with a bias current of 40 mA.

To demonstrate what happens when the RSOA is operated in its linear regime, run two additional simulations with
different values for the RSOA input power (downRSOApower_dBm), –20 dBm and –30 dBm. The resulting BER
values are approximately 9×10-7 and 4.6×10-4, respectively. In other words, as the RSOA input power decreases and the
device’s operating regime becomes increasingly linear, the BER performance of the upstream signal deteriorates. Figure
3 depicts the eye diagram of the received signal in the upstream RX (which can be generated via the Multiplot Block
MultiPlot8 in the schematic) for each of the three RSOA input powers under consideration. As can be seen, as the RSOA
input power increases and the device becomes increasingly saturated, the downstream signal is increasingly suppressed,
which corresponds directly to the improved BER values.
The extinction ratio of the downstream signal also plays an important role in determining the effectiveness of the RSOA
remodulation. As you would expect, the greater this extinction ratio, the harder it is for the RSOA to overwrite the
downstream signal. To see this, set the RSOA input power back to –10 dBm and then run three simulations with
different values for the downstream signal’s extinction ratio (ER_db): 3, 4, and 5 dB. The respective upstream receiver
BER values are approximately 9.7×10-13, 7.3×10-10, and 5.2×10-8. As expected, as the extinction ratio increases, the
upstream link performance gets worse.

(a) (b)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 245
 (c)
Figure 3. Upstream received eye diagrams for RSOA input powers of (a) –10, (b) –20, and (c) –30 dBm.

References
[1] W. Lee, M. Y. Park, S. H. Cho, J. Lee, C. Kim, G. Jeong, and B. W. Kim, “Bidirectional WDM-PON based on gain-
saturated reflective semiconductor optical amplifiers,” IEEE Photonics Technology Letters, vol. 17, no. 11, pp.
2460-2462, November 2005.
[2] J.-M. Kang and S.-K. Han, “A novel hybrid WDM/SCM-PON sharing wavelength for up- and down-link using
reflective semiconductor optical amplifier,” IEEE Photonics Technology Letters, vol. 18, no. 3, pp. 502-504,
February 1, 2006.
[3] T.-Y. Kim and S.-K. Han, “Reflective SOA-based bidirectional WDM-PON sharing optical source for up/downlink
data and broadcasting transmission,” IEEE Photonics Technology Letters, vol. 18, no. 22, pp. 2350-2352, November
15, 2006.
[4] K. Sato and H. Toba, “Reduction of mode partition noise by using semiconductor optical amplifiers,” IEEE Journal
on Selected Topics in Quantum Electronics, vol. 7, no. 2, pp. 328-333, March/April 2001.

246 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.14 Receivers

2.14.1 Receiver Sensivity

RSoft/examples/optsim/block_mode/receivers/receiver_sensitivity.moml
The purpose of this example is to study the effect of optical receiver characteristics on a system performance.

Figure 1 depicts the layout of such a system consisting of: Bit Pattern Generator, NRZ Transmitter, Optical Power
Normalizer, Optical Receiver, BER Tester, Eye Diagram Analyzer, and XY-Plotter.

Figure 1. Layout for receiver sensitivity study.

First, run a single simulation by clicking Go button. The resulting BER at BER Tester will be 10-9. The receiver input
power is controlled by Optical Power Normalizer and is set to –25 dBm for a single run. Hence, the receiver sensitivity is
–25 dBm for 10-9 BER requirement.

This sensitivity was achieved by adjusting the receiver parameters. Let us describe in details the receiver setting. Optical
Receiver Model is a combination of a few components: PIN Photodiode, Electrical Filter, and electrical transimpedance
amplifier (TIA). Photodiode is characterized by Responsivity, which is defined by quantum efficiency. Current at
photodiode is derived as:

I(t) = R P(t) + N(t),

where R is Responsivity, P(t) -input optical signal, and N(t) noise generated at receiver. The current passed to TIA,
converted to voltage, and sent passes through electrical filter. For electrical filter we used low-pass 4-th order Bessel with
bandwidth 7.5 GHz.

Total noise is a combination of different noise contribution mechanisms: thermal noise from TIA, signal and dark current
shot noise, RIN noise (depends of RIN value of optical sources such as lasers), signal-spontaneous and spontaneous-
spontaneous beat noise. The receiver model allows to turn ON/OFF each of these noise contributions separately.

Figure 2 shows corresponding eye diagram at receiver for input power –25 dBm. Figure 3 shows for given power the
BER scan results vs. decision threshold level and sampling time.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 247
 Eye Diagram
0.005

0.004

0.003

Signal (V)
0.002

0.001

0.000

0 1 2
x10-10
Time (s)

Figure 2. Eye diagram for input power –25 dBm and BER = 10-9.

Decision level scan Decision time scan

10-1
10-1 10-2
10-2 10-3
10-3 10-4
10-4
10-5
BER
BER

10-5
10-6
10-6
10-7
10-7
10-8
10-8
10-9
10-9
10-10
8 10 12 14 16 18 20 22 24 26 -4 -3 -2 -1 0 1 2 3 4
x10-4 x10-11
Decision level (V) Decision level (s)

Figure 3. BER scan vs. decision threshold level (left) and sampling time (right).

BER
Q2
100 27

24
10-20
21
10-40
18
Q2 (dB)
BER

-60
10 15

12
10-80
9
-100
10
6
-29 -28 -27 -26 -25 -24 -23 -22 -21 -29 -28 -27 -26 -25 -24 -23 -22 -21
Average Receiver Power (dBm) Average Receiver Power (dBm)

Figure 4. BER (left) and Q-factor vs. receiver input power.

248 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 BER vs. Q-factor

100

10-10

BER

10-20

8 10 12 14 16 18 20
Q2 (dB)

Figure 5. BER vs. Q-factor.

Next we want to observe the effect of changing of receiver input power on BER. Click on Scan button and run parameter
sweep for input power specified by parameter averecpow from -29 to -21 dBm, i.e. within ±4 dB range from original
input power. After the simulation finished you can click on BER Tester models and see the plots for BER and Q-factor
vs. receiver input power – see Figure 4. By clicking on XY-Plotter block one can see the plot of BER vs. Q-factor – see
Figure 5.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 249
2.14.2 Forward Error Correction and Performance Budget Calculation in
Transmission Link
RSoft/examples/optsim/block_mode/receivers/FEC_PB_example.moml
The purpose of this example is to demonstrate how to use additional features of BER Tester model such as Forward
Error Correction (FEC) and performance budget calculation. Ability to include these features can be extremely important
in transmission link design. Here we give an example on the usage of these features - for detailed description of FEC
and performance budget calculation, see Models Reference Manual.

Figure 1. Topology setup for FEC and performance budget example.

The topology setup (see Fig. 1) consists of simple single-channel transmission link. RZ modulated channel at 10 Gbps
bitrate is launched into 500-km long transmission section. Output signal from transmission section passes through
Optical Filter and Attenuator before reaching Receiver. Depending on Transmit and Receive sections parameter setting
we may detect different values of BER in a system. First we study system performance with FEC encoding disabled.
Then we turn on Performance Budget Generation feature in BER Tester model with system performance BER
requirement set to 1e-13. Link simulation for given system parameters gives BER = 1.92e-7. Table 1 shows the
performance budget of the link without FEC – it shows that system Q is 3.2 dB short of performance requirement, i.e.
system will fail to meet the BER performance requirements.

Table 1. Performance Budget for topology with FEC off.

1. Simulation Q (dB) 14.11
2. Simulation BER 1.92e-007
3. BER Requirement 1.00e-013
4. Required Q (dB) 17.32
5. System Margin (dB) -3.21

In order to improve system margin (and hence, the system performance) FEC needs to be activated. All available
schemes for FEC in BER Tester model will be tried. We apply standard and enhanced FEC schemes: RS(255,239) and
RS Concatenated Code, correspondingly (see Models Reference for details), and also user-defined FEC scheme with
FEC conversion table given in a file FECtable.txt supplied with the example. For this particular example of user-
defined data, we used conversion table typical for standard RS(255,239), so we expect to get for UserDefined FEC
scheme results identical with RS(239,255) scheme.

250 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Important thing to remember while using FEC is that the system bit rate has to be modified according to the bit rate
overhead due to particular FEC scheme. So, standard FEC RS(255,239) scheme requires 6.7%, and enhanced RS
Concatenated code – 23% overhead. Table 2 summarizes simulations results with different selections of FEC codes. One
can see that using standard FEC, we improved our system margin to 2.6 dB, i.e. in this case FEC coding gain is about 5.8
dB. With enhanced FEC technique the system margin went up to 4.8 dB and coding gain for this FEC scheme is 8 dB.

Table 2. System margin without FEC and with FEC of different schemes.
No FEC FEC1: FEC2: FEC3:
RS(255,239) RS_Concat_Code UserDefined
Bitrate (Gbps) 10 10.67 12.3 10.67
Simulation Q (dB) 14.10 13.85 13.15 13.85
Simulation BER 1.9e-7 4.3e-7 2.8e-6 4.3e-7
Q after FEC (dB) - >17.30 >17.30 >17.30
BER after FEC - <1e-13 <1e-13 <1e-13
Required Q (dB) 17.30 11.20 8.35 11.25
Required BER 1e-13 1.4e-4 4.5e-3 1.3e-4
System margin (dB) -3.20 2.65 4.80 2.60

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 251
2.14.3 Electronic Dispersion Compensation using MMSE-based DFE and
FFE
RSoft/examples/optsim/block_mode/receivers/EDC_DFE.moml
This example demonstrates the application of electronic dispersion compensation (EDC) in a link. The equalization
cases shown are based on decision-feedback and feed-forward equalization with optimization based on the minimum
mean-square error (MMSE) method.

Figure 1. Link configuration under study

The OptSim example depicted in Figure 1 demonstrates an NRZ, 10 Gbps transmission over a standard single mode fiber
of length 100km. After the simulation is over, the eye diagram for the back-to-back received signal can be viewed by
double-clicking the b2b_Eye analyzer. Figure 2 shows the received eye diagram without any form of dispersion
compensation.

252 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 2. Received Eye with no EDC

Next, we use a decision-feedback equalizer (DFE) with 14 feed-forward and 5 feedback taps. The tap weights are
optimized using MMSE criterion. The corresponding eye diagram is shown in Figure 3.

(a)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 253
 (b)
Figure 3. Received eye diagram after DFE EDC (a) with receiver noise and (b) without receiver noise

By setting FeedBack_taps_number to 0, the equalization becomes feed-forward only. Figure 4 shows received eye
with FFE.

Figure 4. Received eye diagram after FFE

254 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.15 Relationship Between OSNR and ASE Power
Spectral Density in Block-Mode Models
RSoft/examples/optsim/block_mode/OSNR/BM_OSNR.moml
In block-mode, different models specify the ASE power spectral density (psd) in different ways. The two models we will
consider here are the Optical Noise Adder and the Black-Block EDFA.

Optical Noise Adder

In the Optical Noise Adder, the dual-sided ASE psd in units of W/Hz over both polarizations (ρASE,2-pol) is specified via
the parameter noisePeak. If the OSNR is calculated over a single polarization (OSNR1-pol), then

Psig ,1− pol [W ]

OSNR1− pol =
1
⋅ ρ ASE ,2 − pol [W/Hz] ⋅ ∆ν [Hz]
2
where Psig,1-pol is the signal power in one polarization, ∆ν is the optical bandwidth over which the noise is calculated, and
the factor of 1/2 converts the ASE psd in both polarizations to the value in a single polarization. Solving for ρASE,2-pol, we
obtain

Psig ,1− pol [W ]

ρ ASE ,2 − pol [W/Hz] = 2 ⋅ (1)
OSNR1− pol ⋅ ∆ν [Hz]

If the signal power is specified in dBm, the OSNR in dB, and the optical bandwidth in GHz, then the expression
becomes

2 [dBm]− OSNR1− pol [dB]−120) /10

ρ ASE ,2 − pol [W/Hz] =
(P
⋅10 sig ,1− pol (2)
∆ν [GHz]
If the OSNR is calculated over both polarizations, then

Psig ,2 − pol [W ]
OSNR2 − pol =
ρ ASE ,2 − pol [W/Hz] ⋅ ∆ν [Hz]

where Psig,2-pol is the signal power in both polarizations. Solving for ρASE,2-pol, we obtain

Psig ,2 − pol [W ]
ρ ASE ,2− pol [W/Hz] = (3)
OSNR2 − pol ⋅ ∆ν [Hz]

If the signal power is specified in dBm, the OSNR in dB, and the optical bandwidth ∆ν in GHz, then the expression
becomes

1 [dBm]−OSNR2− pol [dB]−120) /10

ρ ASE ,2 − pol [W/Hz] =
(P
⋅10 sig ,2− pol (4)
∆ν [GHz]

Black-Block EDFA
In the Black-Block EDFA, instead of specifying the ASE directly, we instead specify the amplifier’s noise figure F via
the parameter Fn. F can be related to the dual-sided ASE in both polarizations via the expression

ρ ASE ,2 − pol [W/Hz] = F ⋅ (G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 255
where G is the amplifier gain, h is Planck’s constant, and ν is the optical frequency which, since we are interested in the
ASE near the signal, we assume to be equal to the signal’s center frequency. Solving for F, we obtain

ρ ASE ,2 − pol [W/Hz]

F= (5)
(G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]
If the OSNR is calculated over a single polarization, then substituting (1) into (5), with Psig,1-pol in units of mW and ∆ν in
GHz, we obtain

Psig ,1− pol [mW] 10−12

F = 2⋅ ⋅
OSNR1− pol ⋅ ∆ν [GHz] (G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]

In units of dB, F can be expressed as

F [dB] = Psig ,1− pol [dBm ] − OSNR1− pol [dB ] − 10 ⋅ log10 ∆ν [GHz] −
  G [ dB ]   (6)
10 ⋅ log10   10 10 − 1 ⋅ h[J ⋅ s] ⋅ν [Hz]  + 10 ⋅ log10 2 − 120
 
  
If the OSNR is calculated over both polarizations, then substituting (3) into (5), with Psig,2-pol in units of mW and ∆ν in
GHz, we obtain

Psig ,2 − pol [mW] 10−12

F= ⋅
OSNR2 − pol ⋅ ∆ν [GHz] (G − 1) ⋅ h[J ⋅ s] ⋅ν [Hz]

In units of dB, F can be expressed as

F [dB] = Psig ,2− pol [dBm ] − OSNR2 − pol [dB ] − 10 ⋅ log10 ∆ν [GHz]
  G [ dB ]   (7)
−10 ⋅ log10   10 10 − 1 ⋅ h[J ⋅ s] ⋅ν [Hz]  − 120
 
  

Examples
For examples of these formulas, we have provided the topology BM_OSNR.moml, illustrated in Figure 1. Open the
topology and you will see two different transmitters, each followed by two different Optical Noise Adder configurations
and a Black-Box EDFA configuration. In the first case, the top transmitter generates a single-polarization 10.7-Gbps
signal, and Optical Noise Adder NoiseAdder1 adds ASE noise directly to the signal with a value specified using (2) (its
parameter noiseRepn is set to “InSignal”). The single-polarization OSNR in this case is specified as 16 dB using the
Global Symbol OSNR_1pol_dB. We assume an optical noise bandwidth of 12.5 GHz (which we do in all six cases
presented in this example), set via Global Symbol delv_GHz. Also, note that because the signal is in a single
polarization, only half the ASE noise is included in the output signal. The Optical Monitor OptMon1 then calculates the
OSNR using an optical noise bandwidth of 12.5 GHz (again, this bandwidth is used by all six Optical Monitors in this
example). It is critical to understand that the optical monitor always calculates a dual-polarized OSNR. However, in this
case, because the monitor’s input is only over a single polarization, the measured value of approximately 16.25 dB
agrees well with the value of OSNR_1pol_dB.
In the second case, Optical Noise Adder NoiseAdder2 adds ASE noise to the output of the top transmitter as a separate
optical power spectrum (its parameter noiseRepn is set to “InNoiseBins”). Again, the ASE is calculated using (2). In this
case, the output of the noise adder will contain noise in both polarizations. Thus, we would expect the OSNR calculated
by OptMon2 to be roughly half the value calculated by OptMon1 (remember that the Optical Monitor always includes
both polarizations), and, indeed, the measured value is approximately 12.99 dB, roughly 3 dB less than the single-
polarization OSNR calculated before.

256 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 1. Simulation schematic for different methods of including ASE as a function of OSNR in a block-mode simulation.

In the third case, Black-Box Amplifier EdfaBB1 introduces ASE noise as a separate optical spectrum; the noise figure of
the amplifier is specified via (6). As in the second case, the signal is single-polarized but the noise exists in both
polarizations, so we expect the OSNR calculated by OptMon3 to be roughly half the value calculated by OptMon1.
Indeed, the measured value is approximately 12.99 dB, roughly 3 dB less than the single-polarization OSNR calculated
by OptMon1.
In the fourth case, the bottom transmitter generates a dual-polarized 10.7-Gbps signal and Optical Noise Adder
NoiseAdder3 adds ASE noise directly to the signal with a value specified using (4) (its parameter noiseRepn is set to
“InSignal”). The dual-polarization OSNR in this case is specified as approximately 12.99 dB using the Global Symbol
OSNR_2pol_dB (set equal to OSNR_1pol_dB - 10·log102). This time, because the signal contains both polarizations, all
of the ASE noise is included in the output signal. The Optical Monitor OptMon4 then calculates the dual-polarized
OSNR. The measured value of 13.62 dB is close to the value specified by OSNR_2pol_dB.
In the fifth case, Optical Noise Adder NoiseAdder4 adds ASE noise to the output of the bottom transmitter as a separate
optical power spectrum (its parameter noiseRepn is set to “InNoiseBins”). Again, the output of the noise adder will
contain noise in both polarizations and the ASE is calculated using (4). In this case, we would expect the OSNR
measured by OptMon5 to be very close to the value specified by OSNR_2pol_dB, and in fact its measured value is
approximately 12.99 dB.
Finally, in the sixth and last case, Black-Box Amplifier EdfaBB2 introduces ASE noise as a separate optical spectrum;
the noise figure of the amplifier is specified via (7). In this case, both the signal and noise are dual-polarized and we
expect the OSNR measured by OptMon6 to be very close to the value specified by OSNR_2pol_dB. In fact, its
measured value is approximately 12.99 dB.
Finally, please note that in all of the Optical Monitors, the optical noise bandwidth is set to 12.5e9 Hz via the parameter
OSNR_DeltafNse. This bandwidth corresponds to ∆ν as used throughout this discussion. However, to properly calculate
the signal power, the signal is measured over a larger bandwidth of 50e9 Hz, as specified via the parameter
OSNR_DeltafSig.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 257
2.16 BER Estimation

2.16.1 Comparison of IMDD K-L and QA BER Calculations

RSoft/examples/optsim/block_mode/klber/imdd_klber_comparison.moml
This simple example demonstrates the validity of the Karhunen-Loeve (K-L) BER Estimator in the context of IMDD
transmission limited by thermal noise. The schematic, shown in Fig. 1, includes a 128-bit 10-Gbps PRBS Generator, a
basic Optical Signal Generator, and an Optical Power Normalizer to fix the transmitter power at –20 dBm. A simple
thermal noise limited Receiver and BER Tester are used to calculate the BER via the standard quasi-analytical (QA)
method, while a separate Karhunen-Loeve BER Estimator (KLBER1) is used to calculate the BER via the more advanced
K-L method. In a simple case such as this, we expect the two approaches to yield matching results. To observe this
agreement, run the preconfigured Scan simulation for this topology, which sweeps the receiver thermal noise density
from 10 to 150 pA2/Hz. When the simulation is finished, open up the WinPlot file imdd_klber_comparison.plc.
This preconfigured plot compares the results of the two BER calculations, as shown in Fig. 2. As can be seen, the K-L
results are within the error bars of the QA calculation.

Figure 1. OptSim topology for comparing IMDD K-L and QA BER calculations.

Figure 2. Comparison of IMDD K-L and QA BER calculations as a function of thermal noise

258 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.16.2 Monte Carlo BER Estimation in Long-Haul RZ-DPSK Transmission
RSoft/examples/optsim/block_mode/mcdpsk_ber/mc_dpsk_transmission.moml
This example demonstrates the use of the Monte Carlo (MC) DPSK BER Estimator in measuring the BER of a long-haul
RZ-DPSK link. The topology is based on a similar design used by the University of Central Florida to validate the
accuracy of the MC DPSK BER estimation algorithm [1].
As shown in Fig. 1, the design consists of an RZ-DPSK transmitter, a dispersion-managed fiber link (with a total
dispersion of 200 ps/nm), and a DPSK receiver followed by the BER Estimator. The transmitter uses a T Flip-Flop to
encode a 1024-bit 10-Gbps PRBS binary signal. This encoded signal is then used to generate the transmitted 1550-nm
33% RZ-DPSK optical signal. Note that while this signal is single-polarized, we include both polarizations in order to
properly account for all of the ASE later in the simulation. The signal then propagates over 40 fiber spans; each span
consists of 80 km of single-mode fiber (SMF) with a dispersion of 21.42 ps/nm/km, approximately 20.5 km of
dispersion-compensating fiber (DCF) with a dispersion of –83.3 ps/nm/km, and an EDFA for compensating the fiber
loss. A noise adder after the fiber spans merges the optical signal and ASE noise (in both polarizations), a necessary step
for the Monte Carlo based receiver and BER Estimator. The receiver itself corresponds to a typical design as described in
the MC DPSK BER documentation in the Block-Mode OptSim Models Reference. A 25-GHz first-order Gaussian optical
filter is used, along with a 7.5-GHz 3rd-order Bessel low-pass electrical filter. Note that we also include the additional
single-ended receiver required by the MC DPSK BER Estimator for determining the linear noise in the received DPSK
signal (as measured immediately after the optical filter). Finally, the MC DPSK BER Estimator is connected to the
original PRBS bitstream, the DPSK receiver, and the single-ended receiver in order to calculate the link BER. The
Estimator has been configured to assume that ASE appears in both polarizations.

Figure 1. OptSim topology for MC BER Estimation in a 4020-km RZ-DPSK dispersion-managed link.

The topology has been pre-configured to scan the launch power at the transmitter output and measure the BER at each
value. Click on Scan to open the Parameter Scan Dialog. The launch power will be swept from –10 to 15 dBm in 2.5-

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 259
dBm increments. Click OK to perform the simulation. At the conclusion of the simulation, double-click on the MC
DPSK BER Estimator to view the measured BER and Q values. Figure 2 depicts the BER versus launch power. As can
be seen, an optimal BER value is obtained for a launch power of approximately 7.5 dBm. Below this value, linear noise
is the main limiting factor, while above it nonlinear noise is dominant. The simulated BER values suggest that FEC
would work well in this design in order to further reduce the BER.

Figure 2. MC DPSK BER versus launch power.

References
[1] Y. Han (private communication), 2007.

260 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.17 WDM

2.17.1 10 Gbps 2 Channel WDM Example

RSoft/examples/optsim/block_mode/WDM/wdm_link.moml
The purpose of this example is to demonstrate a simulation of a 10 Gbps dual channel optical link. The example is found
in the Examples directory of the OptSim installation in the file wdm_link.moml. Several models, component
parameters, and options will be highlighted in this example.
Load the wdm_link.moml file from the Examples directory. This will create a new window with the example topology
represented. It should appear as shown below.

Figure 1. wdm_link.moml

This example represents a two channel WDM link with wide channel spacing. The two channels are specified at the
wavelengths 1300 nm and 1551 nm. The PRBS blocks are set to generate sequences which are offset from one another
so that each of the signals are not propagating the same bit value at all time points. The component parameter offset
determines the number of bits which the sequence should be rotated relative to the default before it is output. After the
signals are generated in the direct modulated laser models, they are multiplexed into a single optical signal by the MUX
model block. In this example, this model is set for ideal multiplexing. No filtering or losses are included in the ideal
mode. The optical signals at the output of the MUX are shown by the signal plot icon after the MUX. At the output of
the MUX, the optical signal passes through a length of fiber. The optical signals at the output of the fiber are shown by
the signal plot icon after the fiber. In this example, the demultiplexing operation is accounted for by the two optical
filters which receive the input from the fiber. Each of these two filters is modeled as a Fabry-Perot filter, with the center
wavelength set for the desired channel. The filtered optical signals are then passed into power normalizers to allow the
generation of BER vs. received optical power graphs. Then each of the filtered signals goes into a receiver model,
followed by a BER tester block, and signal plot and eye diagram plot blocks. The eye diagram plots here include the
receiver noise in their displays, while the signal plots are set to not include the receiver noise.
In this example, the multichannel optical signal representation is used. This option is controlled by the MUX model
block. This representation treats each logical optical signal as a separate sampled frequency band. The advantage is that
the unused frequency range between the two different signal bands is not sampled, which reduces the memory
requirements of the simulation. In this mode, four wave mixing between the channels in the fiber is not accounted for.
In another example, the Four Wave Mixing example, the single channel optical signal representation will be used to
demonstrate the simulation of four wave mixing with the fiber model.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 261
2.17.2 10 Gbps 4 Channel WDM Example
RSoft/examples/optsim/block_mode/WDM/em_wdm_link_4ch.moml
The purpose of this example is to demonstrate a simulation of an externally modulated 10 Gbps 4 channel Dense WDM
optical link. The example is found in the Examples directory of the OptSim installation in the file
em_wdm_link_4ch.moml. Several models, component parameters, and options will be highlighted in this example.
Load the em_wdm_link_4ch.moml file from the Examples directory. This will create a new window with the
example topology represented. It should appear as shown below.

Figure 1. em_wdm_link_4ch.moml

This example represents a 4 channel Dense WDM link with channels spaced at 100 GHz starting at an optical frequency
of 193.4 THz. Various system and component parameters such as the bit rate, frequency spacing, and starting frequency
are set by user variables. The PRBS block uses the bitrate user variable to set the simulation bit rate, and each of the CW
laser model blocks use a formula utilizing the user variables to set their wavelengths. This allows parameter scans to be
performed to view the BER vs. properties such as the bit rate and frequency spacing.
The PRBS block in this example generates four separate output binary sequences. The user can change the number of
input and output ports on various blocks which support a range of input and/or output ports by selecting the component’s
icon in the tool bar, then selecting Icon-Settings from the Options menu in the menu bar. In the case of the PRBS model,
the pseudo-random binary sequence is rotated between each of the output ports by a specified amount to decorrelate
them from one another. In this example, the shift parameter uses a formula based on the pattern length and the
number of output ports to set this value.

262 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
The MUX block takes the four separate optical signals and multiplexes them together into a single output optical signal
with four channels. In this example, the multichannel signal representation is used. Also in this example, the MUX
block is set to filter the input optical signals according to the specified user parameters. The filters are set to a
trapezoidal response shape, with equal frequency spacing between their centers. The initial frequency is set to the initial
frequency of the four optical channels, and the spacing is set to equal the spacing between the optical channels. An
optical loss is also included in this block. The WDM optical frequency spectrum can be viewed at the spectrum icon
connected to the output of the MUX.
Following the MUX in this example is the control block representing the beginning of a repetition loop. This marks the
start of a span which can be repeated in the simulation a specified number of times. The span includes all components
between the Repetition Loop Begin block and the Repetition Loop End block. This is particularly useful to represent
long distance optical links which utilize multiple spans of fiber and amplifiers. Utilizing this capability, parameter scans
can be performed to determine the optimal spacing between amplifiers and how the number of spans affects the system
performance. Also, changing the parameter of a component between the repetition loop begin and end blocks changes
the parameters for all the spans in a simulation represented by the repetition loop. In the simulation, the repetition loops
are intelligently coordinated with the scans to maximize performance and accuracy. For example, in the statistical
simulation mode (which will be highlighted in the parallel optical bus example), each of the spans or executions of the
repetition loop uses a different set of statistics to statistically vary the component parameters; however, each variable
scan uses the same statistics so that differences in performance between variable scans can be attributed purely to the
changes in the variable values, and not to any artificial differences in the statistically varied parameters used.
An attenuator with a specified attenuation is used instead of a power normalizer in this example, because the variable
scans will not be used to produce BER vs. received optical power plots. At the output of the attenuator is the
demultiplexer block. This component uses optical filters to demultiplex the channels in the input optical signal. Like in
the MUX block, the filters use the user specified type and parameters with an initial frequency center and an equal
frequency spacing. If the channels were spaced equally in wavelength instead, the DEMUX block could be set to use
values specified in terms of wavelength with equal spacing in wavelength. At the output of the DEMUX, the
demultiplexed signals go to receivers and BER Tester blocks. The signal waveforms and eye diagrams can be viewed at
the plot icons blocks attached to these components.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 263
2.17.3 Study of Polarization State Effect in WDM Channels
RSoft/examples/optsim/block_mode/WDM/WDM_orthogonal_polarization.moml
RSoft/examples/optsim/block_mode/WDM/WDM_random_polarization.moml
The purpose of this example is to demonstrate how polarization states of adjacent channels in WDM system affect the
channel performance. This effect is a manifestation of polarization dependence of nonlinear interactions (XPM, FWM,
Raman gain) between channels.

Figure 1. Topology setting for polarization dependence studies

The topology setup (see Fig. 1) consists of 8 channels launched into a single fiber span. Channel spacing is 50 GHz and
they are generated in groups by odd and even channels by two PRBS generators, Electrical Signal Generators, and CW
laser sources (each with 4 100 GHz-spaced wavelengths). Initially all channels have the same polarization state. All even
channels before being multiplexed with odd channels are passed through the Polarization Shifter, which rotates the
polarization state by angle “polAngle”. Fig. 2 shows parameter setting for Polarization Shifter. After multiplexing the
signal is launched into a fiber, and then is demultiplexed and sent to 8 receivers followed by BER Tester to measure
channel performance (BER and Q-factor) for given polarization state difference between adjacent channels.
Two topology files are included in this example. Both of them have the same settings (see Fig. 2) and the only difference
is in polarization angle treatment in parameter scan setting.
“WDM_orthogonal_polarization.moml” - here the polarization angle is scanned from 0 to 180 degrees
with 10 degrees step and Q-factor is measured versus polarization angle. Figure 3 shows results for one
odd (ch.3) and one even channel (ch.6). In both cases the Q-factor is minimal for polarization angles

264 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 equal to 0 or 180 degrees, i.e. when all channels have parallel polarization states; and Q has maximum
at 90 degrees, i.e. when adjacent channels polarization state is orthogonal to each other. Difference
between max and min Q’s is 0.4-0.6 dB for these cases.
“WDM_random_polarization.moml” - here the polarization angle is a randomly changing number with
distribution statistics defined as uniform distribution within a range from –180 to +180 degrees. Figure
4 shows the results of parameter scan simulations with 50 statistical runs for Q-factor for the case of
odd (ch.3) and even (ch.6) channels. Points represent Q’s of individual runs solid line - average Q over
50 statistical runs. For channel 3 case: min Q = 14.86dB and max Q = 15.48dB with average Q =
15.13dB and standard deviation = 0.21dB. For channel 6 case: min Q = 14.75dB and max Q = 15.20dB
with average Q = 14.90dB and standard deviation = 0.18dB.

Figure 2. Parameters setting for Polarization Shifter

Q2 for Ch 6 Q2 for Ch 3
16 16
Q2 (dB)

Q2 (dB)

15 15

14 14
0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180
Relative Polarization Angle Relative Polarization Angle

Figure 3. Channel performance versus polarization angle between adjacent channels: (left) Odd channel example (ch.3); (right) Even
channel example (ch.6)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 265
 Q2 for Ch 6 with random polarization Q2 for Ch 3 with random polarization
Legend Legend
15.4 Instant Q Instant Q
15.6
Average Q Average Q
15.2
15.4

15.0
15.2
Q2 (dB)

Q2 (dB)
14.8
15.0

14.6
14.8

14.4
14.6

0 10 20 30 40 50 0 10 20 30 40 50
runs runs

Figure 4. Channel performance statistics for randomly changing polarization angle between adjacent channels: (left) Odd channel
example (ch.3); (right) Even channel example (ch.6)

The results demonstrate that system penalties are polarization state dependent and the worst case corresponds to the all
channels being aligned to the same polarization state before being launched to fiber. Polarization scrambling (i.e. when
all channels polarization state is randomly changing over time) can improve system performance, in our example, case 2,
by a few tenths of dB. The best performance results (the lowest penalties) will be achieved if adjacent channels are
launched with orthogonal polarization relative to each other. In our example we observed 0.4-0.5 dB of improvement in
performance compared to the worst case.

266 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.17.4 CRZ Dispersion-Managed Link
RSoft/examples/optsim/block_mode/WDM/CRZ_DispManaged.moml
The purpose of this example is to demonstrate how optimization of dispersion map of transmission part can improve
management of nonlinear effects of in long-haul lightwave systems operating in quasi-linear regime.
When nonlinear effects in fiber are not negligible, even for perfect dispersion compensation (D=0) pulse parameters do
not restore to their input values. Eventually, the buildup of nonlinear distortion affect each pulse within the optical bit
stream so much that system cannot operate beyond a certain distance. For this reason, the management of nonlinear
effects is an important issue for long-haul lightwave systems. It turns out that the parameters associated with a dispersion
map (length and GVD of each section) can be controlled to manage the nonlinearity problem. Two main techniques have
evolved, and systems employing them are said to operate in the quasi-linear and soliton regimes. In the previous
examples we studies various soliton regimes, and here we will consider quasi-linear regime.
It was noted in several experiments that a nonlinear system performs best when GVD compensation is only 90–95% so
that some residual dispersion remains after each map period. In fact, if the input pulse is initially chirped such that β2C <
0, (C is chirp parameter) the pulse at the end of the fiber link may even be shorter than the input pulse. This behavior is
expected for a linear system and it also persists for weakly nonlinear systems. This observation has led to the adoption of
the CRZ (chirped RZ) format for dispersion-managed fiber links.
In this example we will consider a long-haul dispersion-managed system with CRZ-modulated transmitted signals at
different wavelengths. Depending on signal wavelength additional pre- and post-dispersion compensation will be applied
at the terminals (transmitter and receiver).
Figure 1 shows topology depicted in file CRZ_DispManaged.moml. The topology describes a long-haul system with
length of about 4600 km and 25.2 nm optical bandwidth. The system can support 64 channels with 50 GHz spacing. We
will study the effect of dispersion compensation on performance for three selected channels:
• channel 1 at the lowest wavelength in a bandwidth - 1537.4 nm;
• channel 2 at the middle of the bandwidth - 1550 nm;
• channel 3 at the highest wavelength in a bandwidth - 1562.6 nm.
Transmission part of the system consists of 10 loops, where each loop built up with 12 amplifiers, 20 fiber blocks, and
number of optical attenuators (to represent splice losses). Dispersion map of the loop is optimized to minimize system
penalties due to chromatic dispersion and nonlinear effects. Three types of optical fibers are used. Regular fiber span
consists of two fiber blocks, first with large effective area fiber (to reduce nonlinear penalties due to the high power high
after amplifier) and second with low dispersion slope fiber (to reduce cumulative dispersion). Both have small negative
dispersion at 1550 nm. To compensate the cumulative dispersion we put two fiber blocks with positive dispersion fiber
in a middle of a loop. Here channel 2 has near zero total dispersion while channels 1 and 3 accumulated almost –3500
and +4000 ps/nm, correspondingly (see Table 1).
On transmitter side each of three channels is CRZ-format modulated at 10 Gb/s and is passing through dispersion pre-
compensation fiber block. Since channel 2 is near zero dispersion no dispersion pre-compensation applied. For channel 1
we added a pre-compensation positive dispersion fiber with total dispersion of +1665 ps/nm, and for channel 3 - a pre-
compensation negative dispersion fiber with total dispersion of +1905 ps/nm. Chirp is applied to each channel, with sign
of chirp positive for channel 1 and negative for channel 3. Pulses have raised cosine shape with a pulse width 36 ps.
Power per channel is –15 dBm, i.e. a very low power corresponding to quasi-linear regime, and nonlinear length scale is
much larger than dispersion length scale - LNL > LD. After pre-compensation all three channels are multiplexed and
launched into transmission loop.
At the output from transmission loop optical signal goes through Demultiplexer, then each channel passes through post-
compensation block before entering Receiver. Again for channel 1 we added a pre-compensation positive dispersion
fiber with total dispersion of +2060 ps/nm, and for channel 3 - a pre-compensation negative dispersion fiber with total
dispersion of +1980 ps/nm. Total cumulative dispersion for 3 channels are 195, 295, and 135 ps/nm, i.e. some residual
non-zero dispersion remains.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 267
 Figure 1. Layout for CRZ dispersion-managed lightwave system.

After the simulation run one can click on Property Map blocks to see dispersion map in transmission loop and terminals.
Figure 2 shows dispersion map inside the transmission loop with taking into account pre-compensation. Figure 3 shows
total dispersion from terminals and transmission path.

Dispersion Map
Channels
λ=1.5374 µm
2000
λ=1.5500 µm
Dispersion [ps/nm]

1000 λ=1.5626 µm

-1000

-2000

0 1000 2000 3000 4000

Distance [km]

Figure 2. Dispersion Map on transmission path with pre-compenasation.

268 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Dispersion Map
3000 Channels
λ=1.5626 µm

2000 λ=1.5500 µm
Dispersion [ps/nm]

λ=1.5374 µm
1000

-1000

-2000
0 1000 2000 3000 4000 5000
Distance [km]

Figure 3. Dispersion accumulation at transmitter, transmission loops, and receiver.

Figure 4 shows input and output (after 4600km) optical spectrum. Figure 5 shows receiver eye diagrams for all three
channels. Resulting BER and Q-factor are given in Table 1.

Table 1. Channel dispersion and performance with dispersion compensation.

Ch λ (nm) Link Disp. Pre/Post Comp. Total Disp. BER Q (dB)

(ps/nm) (ps/nm) (ps/nm)
1 1537.4 -3530 +1665/+2060 +195 1.86e-12 16.8
2 1550.0 +295 0/0 +295 4.15e-15 17.8
3 1562.6 +4020 -1905/-1980 +135 1.85e-10 15.9

In conclusion we demonstrated that a system reach of long-haul lightwave link could be significantly improved by
optimizing dispersion map in transmission path and pre-chirping input pulses. Input powers were reduced to provide
quasi-linear regime. One also needs to optimize the length of compensation fiber on both terminal sides to maximize the
effect for channels away from zero-dispersion wavelength.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 269
 lnput Spectrum Output Spectrum

-20
- 20

- 40
Power (dBm)

Power (dBm)
-30
- 60

- 80

-40

-100
1530 1540 1550 1560 1570 1530 1540 1550 1560 1570
Wavelength (nm) Wavelength (nm)

Figure 4. Input and output (after 4600km) optical spectrum.

BER Tester Decision Eye - Ch 1 BER Tester Decision Eye - Ch 2

x10-5 x10-5

3
3
Decision Level (V)

Decision Level (V)

2
2

1 1

0 0
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
x10-11 x10-11
Decision Time (s) Decision Time (s)

BER Tester Decision Eye - Ch 3

x10-5

5
Decision Level (V)

0 1 2 3 4 5 6 7 8
x10-11
Decision Time (s)

Figure 5. Receiver Eye Diagrams for channels 1, 2, and 3.

270 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.17.5 DWDM Ring with OADM (Optical Add-Drop Multiplexer) Nodes
RSoft/examples/optsim/block_mode//WDM/DWDM_ring_example.moml
This example demonstrates an OptSim design for DWDM ring with Optical Add-Drop Multiplexers (OADM). The
configuration of DWDM ring is in Figure 1.
The DWDM ring consists of six nodes and six fiber spans. Total number of wavelengths used is eight, with 3 head-end
nodes adding/dropping five channels at the time and 3 serial OADM nodes adding/dropping two channels.
Figure 2 demonstrates an equivalent design of the OC-192 ring configuration in OptSim. Here for simplicity we used
only uni-directional fiber link with signals propagating in clock-wise direction. The example can be easily extended to
full fiber pair with signals propagating in both directions.

Figure 1. DWDM Ring configuration under study

The schematic consists of six OADM nodes connected by fiber spans of specified length and type of the fiber (Corning
LEAF fiber). For simplicity we assumed that all nodes are equidistant and all six fiber spans are 50-km long. To
compensate for the fiber attenuation in fiber spans we inserted fixed gain amplifiers after each fiber span. The power per
channel of -9 dBm was used at transmitters. We used 8 wavelengths at 50 GHz (0.4 nm) spacing starting at 1550 nm
wavelength. After each node we put also a plotter block MultiPlot to observe an optical spectrum evolution along the
ring.
To perform full ring simulation rather than conventional point-to-point link simulation we use TimeDelay block to
connect signal from the last node back to the first node and then use Multiple Iterations mode of simulations. This way
we can provide steady-state solution for ring simulation.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 271
 Figure 2. OptSim project for DWDM ring depicted in Fig.1.

Figure 3 shows more details of OADM node on the example of serial OADM with 2 wavelengths adding/dropping at λ3
and λ6. OADM block is modeled as a compound component (CC) or hierarchy block, i.e. is composed inside from other
OptSim library blocks. Each OADM node has one input and one output for line signal (in- and out-transport interfaces),
and also 8 inputs/outputs for added/dropped wavelengths (in- and out-clients interfaces). Here two single-channel NRZ-
modulated transmitters modulated at 10 Gbps bitrate (OC-192 rate) are connected to add-ports 3 and 6. Since the
OptSim requires that all input ports for CC models to be connected we use NullSignal model and connect it to the other 6
ports. At the output of CC we can connect only the ports of interest – in this case ports 3 and 6. Output from these ports
are connected to optical receiver blocks and then to plotter model MultiPlot which will provide plots for electrical signal
output waveform, spectrum, and eye diagram.

272 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 3. One of the OADM nodes with 2 wavelengths being added and dropped.

The OADM CC block can specify following parameters: crosstalk level, switching configuration, first channel
wavelength and channel spacing, optical filter bandwidth used in demultiplexing. The properties dialog window for
OADM CC block is shown at Figure 4. The switching configuration is given as an N-size array (N is a number of
channels in a link) where “1” stands for channel to be dropped at that port and “0” – for channel to go through. For
example, in the case of Node 2 where we are adding/dropping λ3 and λ6, the switch array is given as {0,0,1,0,0,1,0,0}.

Figure 4. Properties dialog window for OADM CC block.

To understand how the OADM CC block works let us look inside it – see Figure 5. The OADM CC block consists of
one 1x8 Demultiplexer, 8x1 Multiplxer, and 8 optical switches. The input from transport interface (Input1) is
demultiplexed into 8 wavelengths and each of them goes to a switch with corresponding input from client interface
(Input2-Input9). The switch can be in either bar or cross state (is set by the switching array value). One output from the
switch goes back to clients interface out ports (Output2-Output9) and the other output is being multiplexed with 7 other
outputs and then sent to transport interface output (Output1).

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 273
 Figure 5. Inside configuration of CC for OADM

Finally we can run simulations and review the results. Figures 5 and 6 demonstrate some of the results for DWDM ring
simulation. Figure 5 shows optical spectrum after two of nodes: (a) Node 1, and (b) Node 6. Figure 6 shows a few
examples of eye diagrams for dropped channels at (a) Node 1 λ3 and (b) Node 6 λ8. We expect that the difference in
eye diagrams comes from the difference in distance traveled before being dropped and from the difference in cumulative
dispersion experience by these channels. So, eye diagram for channel 3 at Node 1 is after 100-km (coming from Node 5),
and eye diagram for channel 8 at Node 6 is after 50-km (also coming from Node 5).

Optical Spectrum after Node 1 Optical Spectrum after Node 6

-10 -10

-20 -20
Power (dBm)

Power (dBm)

-30 -30

-40 -40

-50
-50

1550 1551 1552 1553 1550 1551 1552 1553

x10-9 x10-9
Wavelength (m) Wavelength (m)

(a) (b)

Figure 6. Optical spectrum at the node outputs.

274 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Eye Diagram - Channel 3 at Node 1 Eye Diagram - Channel 8 at Node 6
x10-4 x10-4

3
3

2
Signal (V)

Signal (V)
2

1
1

0 0
6 8 10 12 14 16 2 4 6 8 10 12
x10-11 x10-11
Time (s) Time (s)

(a) (b)

Figure 7. Receiver eye diagrams for dropped channels.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 275
2.18 TDM

2.18.1 TDM Link and Demultiplexing in Time Domain

RSoft/examples/optsim/block_mode/TDM/TDM_link_withDEMUX.moml
The purpose of this example is to demonstrate channel demultiplexing in optical time division multiplexed (OTDM)
network. Different configurations of fiber-based interferometric switches were proposed for demultiplexers in OTDM
systems. One of such configurations is so called TOAD device – Terahertz Optical Asymmetric Demultiplexer – first
proposed by P.Prucnal et al.[1], which employs semiconductor optical amplifier (SOA) as nonlinear switching element.

(a) original TOAD configuration based on Sagnac interferometer

(b) alternative TOAD configuration based on symmetric Mach-Zehnder interferometer

Figure 1. Setup for original and alternative TOAD configuration.

The TOAD device in its original configuration (see Fig.1, upper setup) is based on Sagnag interferometer (also referred
as nonlinear optical loop mirror - NOLM). In the absence of a control signal, incoming data signals enter the fiber loop,
pass through the SOA at different times as they counter-propagate around the loop, and recombine interferometrically at
the 50/50 coupler at the base of the loop. Since signals propagating around the loop in both directions see the same
medium, the data is reflected back toward the source. In the presence of the control signal, switching can occur. When
the control signal is injected into the loop and its power is high enough (it is chosen to be at least ten times the data pulse
energy), it saturates the SOA and changes its index of refraction. As a result, a differential phase shift can be achieved
between the two counterpropagating data pulses to switch the data pulses to the output port. SOA is offset from the
center position of the fiber loop and this offset will provide switching window duration.

Modeling of TOAD will require bi-directional signal propagation in a loop, and, hence, cannot be simulated by OptSim
directly. However, it was shown [2] that the same interferometric effect could be achieved using alternative
configuration of TOAD based on symmetric Mach-Zehnder (SMZ) interferometer (see Fig.1, lower setup) with SOA in
each arm of SMZ. In this configuration the data and control signals co-propagate and can be modeled in OptSim. Time

276 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
delay between two control pulses is equal to the switching window duration, i.e. width of TDM channel in DEMUX
applications. A polarization or wavelength filter is used at the output to reject the control signal and pass the switched
data signals.

The snapshot of the OptSim topology for OTDM link with TOAD modeled in SMZ configuration is given in Fig.2.

1
2

Figure 2. Topology setting for TDM_link_withDEMUX.moml

Block 1 in Fig.2 shows setup of 4x10 Gbps TDM transmitter. Four channels at wavelength 1550nm are RZ-modulated
with different PRBS pattern and RZ-format, have a 3-dB pulsewidth of 5 ps and the same power. Before being
multiplexed together each consequent channel is delayed by 25 ps (1/4 of the time window). Total power of all channels
is set to -12 dBm. The output from multiplexer is shown in Fig. 3.
Next, the control signal (block 2 in Fig.2) consists of pulse train generator with 10 GHz repetition rate, pulse splitter, and
two time delay blocks. The first time delay block will set the control signal to demultiplex the channel of interest (e.g.
time delay is zero if channel 1 to be multiplexed , time delay is 25 ps if channel 2 to be demultiplexed, and so on).
Control signal split in two parts before being coupled with data signal in two arms of SMZ is. The second time delay
block sets switching window duration and is set to data pulse duration, 5ps. Pulsewidth of control signal is set to 5 ps as
well, power per each control signal is set to 9dB higher than data signal, and the state of polarization is set to be
orthogonal to data signal.
Symmetrical Mach-Zehnder Interferometer (represented by Block 3 in Fig.2) consists of two 50/50 couplers, two
multiplexers, and two SOAs. Signal data are injected to SMZ through the upper input. Two outputs of SMZ correspond
to “switching” and “reflective” ports. Figure 4 shows the combined data and control signals at the inputs to SOA.
Output signals from both ports then go through the linear polarizer block to separate control pulses from data. Inputs to
the receiver blocks will have only data signals.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 277
 TDM link withDEMUXSigPlt 1 Signal Plot TDM link withDEMUXMultiPlot 2 Optical Frequency Spectrum
Legend: -10
0.10
λ = 1550 nm (x)
-20
0.08 λ = 1550 nm (x)
Signal Magnitude (W)

-30

Power (dBm)
λ = 1550 nm (x)
0.06
-40
λ = 1550 nm (x)

0.04 -50

0.02 -60

-70
0.00 1930 1931 1932 1933 1934 1935 1936 1937 1938
6 8 10 12 14 16 x1011
x10-10 Optical Frequency (Hz)
Time (s) x polarization

Figure 3. (Left) Sample of output signal of TDM transmitter from Multiplexer. Four different colors correspond to four TDM
channels; (Right) Output spectrum from Multiplexer. Sidebands are 40 GHz apart from the carrier frequency.

TDM link withDEMUXSigPlt 4 Signal Plot TDM link withDEMUXSigPlt 6 Signal Plot
Legend: Legend:
λ = 1550 nm (x) λ = 1550 nm (x)
0.006 0.006
λ = 1550 nm (y) λ = 1550 nm (x)
Signal Magnitude (W)

Signal Magnitude (W)

λ = 1550 nm (y)
0.004 0.004
λ = 1550 nm (y)

0.002 0.002

0.000
0.000
19 20 21 22 23 15 16 17 18
x10-10 x10-10
Time (s) Time (s)

Figure 4. Input signal to each SOA (left) and to both SOA combined (right). Higher power pulses correspond to control signals, the
lower power pulses – data. Notice time shift between two control signals on the right.

TDM link withDEMUXSigPlt 11 Signal Plot TDM link withDEMUX BERTest 1 signalpair 0 Signal Plot
0.005 x10-4

Legend:

0.004 << # 1
0.9
Signal Magnitude (W)

Signal Magnitude (V)

>> # 2
0.003
Binary Value

0.002

0.001

0
0.000 -0.1
0 2 4 6 8 10 12 1 2 3 4 5
x10-9 x10-9
Time (s) Time (s)

Figure 5 (left) SMZ-TOAD output pulses at switching port; (right) zoom-in of these pulses aligned with bit pattern for channel 1.

278 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 TDM link withDEMUXSigPlt 13 Signal Plot TDM link withDEMUX BERTest 2 signalpair 0 Signal Plot
0.05 Legend:
<< # 1
0.9
0.04
>> # 2
Signal Magnitude (W)

Signal Magnitude (V)

Binary Value
0.03

0.02

0.01

0.001
0.00 -0.1
0 2 4 6 8 10 12 1 2 3 4 5
x10-9 x10-9
Time (s) Time (s)

Figure 6. (left) SMZ-TOAD output pulses at reflective port; (right) zoom-in of these pulses aligned with bit pattern for channel 1.

TDM link withDEMUXEyeDiag 1 Eye Diagram TDM link withDEMUXEyeDiag 2 Eye Diagram
x10-4
5 0.008

4
0.006
Signal (V)

3
Signal (V)

0.004
2

0.002
1

0 0.000
0 1 2 0 1 2
x10-10 x10-10
Time (s) Time (s)

Figure 7. Eye diagrams corresponding to optical signal at Receiver. Left plot is for output from switching port.. Right plot is for
output from reflective port

Figures 5 and 6 show the signal output from switching and reflective ports respectively, after passing linear polarizer.
Right-side plots show zoom-in details of signal aligned with bit pattern of demultiplexed channel (channel 1). Finally,
Figure 7 shows corresponding eye diagrams at Receiver block for both ports. One can clearly see that output signal at
switching port carries data information of demultiplexed channel only and interference from other channels is negligible,
they are nicely suppressed. In conclusion, the simulation results for SMZ-TOAD model confirmed its functionality as
demultiplexer in TDM links.

References
1. J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “”A Terahertz Optical Asymmetric Demultiplexer (TOAD)”,
Photonics Technology Letters, 5, 787-790 (1993)
2. P. Toliver, R. J. Runser, I. Glesk, and P. R. Prucnal, “”Comparison of three nonlinear interferometric optical switch
geometries”, Optics Communications, 175, 365-373 (2000)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 279
2.19 OCDMA

2.19.1 Optical Code Division Multiple Access (OCDMA) Link with

Encoding/Decoding Based on Pseudo-Orthogonal Code.
RSoft/examples/optsim/block_mode/OCDMA/ocdma.moml
Data access security and ability to support asynchronous, bursty data transmission are two of the main driving forces
behind a lot of interest in the OCDMA techniques. On the other hand, the poor spectral efficiency of OCDMA systems
demand appropriate choice of coding techniques and multi-access interference (MAI) is often a limiting factor. This
example illustrates an OCDMA design [1] with a commonly used tree network topology [2] layout as shown in Fig. 1.

Figure 1. Topology layout for this example

Four mode-locked lasers are used to create a dense WDM multi-frequency light source. There are sixteen OC-48 users
requiring sixteen distinct signature codes. Pseudo-orthogonal (PSO) matrix codes [3] are popular for OCDMA
applications primarily because they retain the correlation advantages of PSO linear sequences while reducing the need
for bandwidth expansion. PSO matrix codes also generate a larger code set. An interesting variation is described in [1]
where some of the wavelength/time (W/T) matrix codes can permit extensive wavelength reuse and some can allow
extensive time-slot reuse. In this example, an extensive time-slot reuse sequence is used for User 1 (λ1λ3; 0; λ2λ4; 0).
There are four time slots used without any guard-band giving the chip period of 100 ps.
The Figure 2 shows modulated data and spectrum before encoding at User 1.

280 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 User 1: Signal Plot
-4
x10
16 Legend:

14 λ = 1550 nm (x+y)

Signal Magnitude (W)

12 λ = 1550.4 nm (x+y)

10 λ = 1550.8 nm (x+y)

8
λ = 1551.2 nm (x+y)
6

0 2 4 6 8 10 12 14
x10-9
Time (s)

(a)

User 1: Transmit Wavelength Spectrum

x10-7
9
8
7
6
Power (W)

5
4
3
2
1
0
1547 1548 1549 1550 1551 1552 1553 1554
x10-9
Wavelength (m)

(b)

Figure 2 (a) Modulated Data and (b) Spectrum before encoding (User 1)

Figure 3 shows several of the NRZ data bits and corresponding encoder output bits with User 1 signature.
In the given example schematic we placed encoders for only 3 users out of 16 for simplicity. The encoded data from all
users are multiplexed and then passed through a 60-km span of standard single mode fiber (SMF) followed by a loss
compensating optical amplifier. Amplifiers can also be used to compensate for the insertion losses due to encoders,
multiplexers, demultiplexers and decoders if needed. The output signal from a fiber span then passed through
splitter/demultiplexer and routed to the user’s decoder. The decoded signal finally arrives at optical receiver and BER
tester.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 281
Encoders and decoders respectively use delay and inverse delay line arrays [2] providing delays in terms of integer
multiples of chip times. The placement of the delay-line arrays and the amount of each delay are dictated by the specifics
of the user signatures.

NRZ ... 0 1 1 1 0 ...

1.0
0.9
0.8
0.7
Signal (Real) (V)

0.6
0.5
0.4
0.3
0.2
0.1
0.0

4 6 8 10 12 14 16 18 20 22 24
-10
x10
Time (s)

(a)

Output at the Encoder 1

0.08
Signal Magnitude (W)

0.06

0.04

0.02

0.00
8 10 12 14 16 18
x10-10
Time (s)

(b)

Figure 3 (a) NRZ signal and (b) W/T coded output at User 1

First in the example schematic we connected only encoder for User 1 to the multiplexer. In this case User 1 at the
decoder has no MAI. Figure 4 shows 1-user 4-slots eye diagram for the user 1 and corresponding electrical detected
signal. At the receiver side the detected signal Q-factor and BER are calculated as following: Q = 21.3 dB, BER = 2.2e-
31.

282 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Eye Diagram (User 1): 1 User, 4 Time Slots
x10-5

12

10

Signal (V)
6

0 1 2 3 4 5 6 7 8
x10-10
Time (s)

(a)

Detected Electical SIgnal: (User -1, no MAI)

x10-5

12

10
Signal (Real) (V)

0 1 2
x10-8
Time (s)

(b)

Figure 4. (a) Received eye diagram and (b) detected signal (User 1, no MAI)

Next, the reader can connect encoder for User 2 to the multiplexer and re-run simulation to observe at Decoder for User
1 the eye diagram degradation in the presence of MAI with 2 users - see Fig. 5 (a). The corresponding Q-factor and BER
are: Q=20.2 dB, BER=5.5e-25. Finally, the reader can connect encoder for User 16 to the multiplexer and re-run
simulation. Figure 5 (b) shows corresponding eye diagram for User 1 in the presence of MAI with 3 users. The
corresponding Q-factor and BER are: Q=18.3 dB, BER=3.5e-17.
One can clearly see both visually and quantitatively the performance degradation in the presence of multiple users due to
MAI. As a further exercise, the reader may add more Users at encoding/decoding sides and observe more eye diagrams
and their degradation in presence of MAI.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 283
 Eye Diagram (User 1): 2 Users, 4 Time Slots
x10-5
8
7
6
5

Signal (V)
4
3
2
1
0

0 1 2 3 4 5 6 7 8
x10-10
Time (s)

(a)

Eye Diagram (User 1): 3 Users, 4 Time Slots

x10-5
6

4
Signal (V)

0 1 2 3 4 5 6 7 8
x10-10
Time (s)

(b)

Figure 5. Received eye diagrams in presence of MAI with: (a) 2 users and (b) 3 users.

References
1. A. J. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, and W. J. Lennon, “Design and performance
analysis of wavelength/time (W/T) matrix codes for optical CDMA,” IEEE Journal of Lightwave Technology, vol.
21, pp. 2524-2533, Nov. 2003.
2. A. J. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennet and W. J. Lennon, “High-performance optical CDMA
system based on 2-D optical orthogonal codes,” IEEE Journal of Lightwave Technology, vol. 22, pp. 2409-2419,
Nov. 2004.
3. A. J. Mendez, R. M. Gagliardi, H. X. C. Feng, J. P. Heritage, and J. M. Morookian, “Strategies for realizing optical
CDMA for dense, high-speed, long span, optical network applications,” IEEE Journal of Lightwave Technology,
vol. 18, pp. 1685-1697, Dec. 2000.

284 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.20 Free-Space Optics (FSO)

2.20.1 Free-Space Optical Communication Link

RSoft/examples/optsim/block_mode/FSO/FSO_link.moml
The purpose of this example is to demonstrate a design in OptSim of Free-Space Optical Communication Link with a
free-space channel model based on weak-turbulence approximation.
Free-space optical (FSO) communications, also known as wireless optical communications, is a cost-effective and high
bandwidth access technique and has compelling economic advantages. With the potential high-data-rate capacity, low
cost and particularly wide bandwidth on unregulated spectrum, FSO communications is an attractive solution for the
“last mile” problem to bridge the gap between the end user and the fiber-optic infrastructure already in place.
In FSO communications, optical transceivers communicate directly through the air to form point-to-point line-of-sight
links. The transmitter converts the electrical signal to an optical one and sends it through the atmosphere (free space).
The receiver converts the optical signal back to an electrical signal. The quality of the transmission line is characterized
by the realized bit-error rate (BER).
Major impairments over FSO links are atmospheric attenuation and scatter phenomena that vary widely from one
micrometeorological area to another. Included here are scintillation, scattering, beam spread, and beam wander [1-2].
Scintillation is best defined as the temporal and spatial variations in light intensity caused by atmospheric turbulence.
Such turbulence is caused by wind and temperature gradients that create pockets of air with rapidly varying densities and
therefore fast-changing indices of optical refraction. The signal attenuation caused by scintillation effect depends on the
time of day and can vary orders of magnitude during a hot day. It drastically increases with distance and can impact the
BER performance (burst errors) on a milliseconds timescale. The scintillation is characterized by a scintillation index
parameter σI2 (or normalized variance of intensity) defined as
2
I2 − I
σ 2
I = 2
(1)
I
where I is signal intensity. In the weak-turbulence regime, scintillation index is less than unity, σI2 < 1.
The accurate statistical models for signal fading due to the atmospheric turbulence were developed based on lognormal
and gamma-gamma probability density functions [1-2]. It was shown that in the limit of weak turbulence the fade
statistics based on lognormal distribution provides an acceptable agreement with measurement data and can be applied to
estimate the link margin and availability.
This example employs OptSim compound component for FSO channel model developed under weak turbulence
approximation. The signal attenuation in this model is based on the FSO range equation that combines attenuation and
geometrical aspects to calculate the received optical power as function of range and receiver aperture size [3-4]. The
range equation can be given as:

 A RX  − ( α L / 10 )
PRX =   ⋅ T ⋅ 10 PTX + PBG (2)
 π [Θ / 2 ⋅ L ]
2

Here PRX is the received signal, PTX - transmitted signal, ARX - receiver aperture area, Θ - beam divergence angle, T -
combined transmitter receiver optical efficiency, PBG - optical power of background radiation, L – link range, and α –
environmental attenuation in dB/km. The first term in parenthesis is a geometrical attenuation due to beam spreading
and is calculated for given parameters ARX , Θ, and L as a ratio of aperture to signal beam cross-section . The
atmospheric attenuation α is a not a linear function of distance, it depends on many factors and changes randomly with
time. Combining together optical efficiency and attenuation, we can re-write Eq.(2) in the following form:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 285
 − ( α geom + α add ) / 10
PRX = 10 PTX + PBG (3)
where αadd represents total additional attenuation in dB for given distance and is specified with a mean value and
standard deviation. According to lognormal model the logarithm of signal intensity is a Gaussian random variable.
Hence, the signal attenuation in dB units, αadd , is a Gaussian random variable as well. If values for mean intensity 〈I〉
and scintillation index σI2 are known from either measurements or theoretical calculations then we can derive 〈αadd〉 and
σ through the following relationships:
α add = 4 . 34 (ln I − 1 / 2σ I2 )
(4)
σ = 4 . 34 σ I
The FSO compound component is shown in Figure 1. It consists of Optical Attenuator Block to model geometrical and
additional attenuation, and Optical Noise Adder Block to add the background radiation to received signal.

Figure 1. FSO compound component and it’s internal structure.

Now we can put together a FSO link consisting of transmitter, FSO channel, and receiver. Most current FSO systems
use in transmitters either LED or diode or semiconductor lasers (e.g. VCSEL) lasing at wavelength 800-850 nm or 1500-
1550 nm. Laser can be either CW with external modulation or directly modulated (for example with NRZ OOK or
DPSK). Receivers can feature detectors based on either PIN or APD.
Figure 2 shows a simple FSO link design under study with link parameters reported in [3]. Transmitter consists of PRBS
generator at bit rate 1.25 Gb/s, NRZ Driver, and directly modulated LED at 1550 nm. Optical power out of transmitter is
1.3 dBm. FSO link has a 500 meters range with beam divergence angle of 3 mrad. The environmental additional
attenuation is specified by its mean value of –4.92 dB and standard deviation (sigma) of 1.9 dB (that corresponds
according to Eq.(4) to σI2~0.19, i.e. less than one and weak-turbulence regime). Receiver is a PIN/TIA (with Bessel-
Thompson electrical filter with 1 GHz bandwidth) and is followed by BER Tester. There are also Optical Meter,
Spectrum, Eye Diagram, and Optical Waveform Analyzers.
Next, to study FSO link performance dependence on stochastic variations in additional attenuation αadd we can apply two
simulation techniques: 1) parameter scan over the range of values for additional attenuation; 2) statistical Monte-Carlo
runs where each time additional attenuation will take a random values according to specified values of mean and
standard deviation and a type of statistical distribution (Gaussian in this case).
First, we apply the parameter scan method. User has to click Scan button and in opened dialog window pick for Inner
Loop Variable atten_add, Starting value –10, End Value 0, and Increment 1 – see Figure 3 for the snapshot of Dialog
Window. Then click OK.

286 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 2. Schematic setup for FSO link example.

Figure 3. Dialog window for Parameter Scan

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 287
Results of parameter scan are shown in Figures 4 and 5. Fig.4 shows BER and Q-factor versus additional attenuation.
One can see the higher is attenuation the worse is performance. Assuming BER performance requirement is equal or less
than 10-12 we can see that additional attenuation should be less than –9 dB to satisfy the BER requirements. Total FSO
channel loss is a sum of geometrical and additional attenuations. The geometrical loss for given parameters here is about
-20 dB (-19.92 dB to be precise). Hence, this link can tolerate up to –29 dB losses in FSO channel. Fig.5 shows optical
power into receiver vs. attenuation. The threshold value of αadd (-9 dB) corresponds to received power of – 27.6 dBm.
The change in receiver input power due to variation in additional variation causes the change in BER.

BER Q2
40
10-2

10-4
10-6 30

-10

Q2 (dB)
10
BER

10-16
20
10-25
-38
10 Q=16.94 dB
10-58
10-90 10
10-138
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
atten_add atten_add (dB)

Figure 4. BER (left) and Q-factor (right) vs. additional attenuation of FSO channel. Red line corresponds to performance requirement
at BER = 1e-12.

Optical Power
-18

-20
Optical Power (dBm)

-22

-24

-26

-28

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
atten_add (dB)

Figure 5. Input power to the receiver vs. additional attenuation of FSO channel.

Second, we apply a statistical approach, which will be more representative taking into account the statistical nature of
signal fading in FSO systems. In order to run statistical scan (Monte-Carlo runs) user has to click on Scan button and set
in Dialog Window the number of Statistical Runs, e.g. 100, and disable the variable scan by setting (No_Scan) in
Variable Name – see Figure 6 for Dialog Window snapshot. Then click OK.

288 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 6. Dialog window for Statistical Scan

As a result of Monte-Carlo simulations for 100 trials many output files will be created by OptSim. The calculated values
of BER, Q, received power, etc. for each Monte-Carlo run will be stores in data files generated by BER Tester and
Optical Monitor blocks. To visualize these data and create typical statistical plots we did post-processing of data files
and applied some advanced features of OptSim plotting tool WinPlot. The results are given in Figures 7-10.
Figure 7 demonstrates the expected correlation between the receiver input power and BER (Q-factor) for 100 trials with
random values of αadd. Figure 8 shows the spread of receiver input power (for these 100 values for additional
attenuation αadd ) and corresponding histogram. As we mentioned above the signal fading fluctuations occur on
millisecond timescale, and thus one can look at this plot as a receiver power fluctuations with time where each run
correspond to 1 ms interval.
Figures 9 and 10 shows corresponding statistical properties of Q-factor and BER.

BER Q2
30
10-10
28
10-13

10-17 26

10-22
24
Q2 (dB)

10-28
BER

10-35 22
-44
10
20
10-56
10-71 18

10-90 16
10-113
-30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20
reciever power (dBm) reciever power (dBm)

Figure 7. Correlation plots for BER (left) and Q-factor (right) against receiver power for statistical study of FSO link performance.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 289
 Statistical Data Histogram
µ = -23.3208, σ =1.94425 25 bins, bin size =0.39008
-16 100

-18 12
80
-20 10
RX Power [dBm]

cumulative %
frequency
-22 8 60

-24 6
40
-26 4

-28 20
2

-30 0
0 10 20 30 40 50 60 70 80 90 100 -28 -26 -24 -22 -20 -18
run RX power [dBm]

Figure 8. Data fluctuation and histogram for Receiver input power

Statistical Data Histogram

µ = 24.1869, σ =2.96553 25 bins, bin size =0.56356

33
90
12
30 80
10
70
27

cumulative %
60
frequency

8
Q [dB]

24
50
6
21 40
4 30
18
20
2
15
10
0
0 10 20 30 40 50 60 70 80 90 100 14 16 18 20 22 24 26 28 30 32
run Q-factor [dB]

Figure 9. Data fluctuation and histogram for Q-factor

Statistical Data Histogram

µ = -71.7828, σ =45.6148 25 bins, bin size =9.3527
0
90
12
80
10 70
-100
cumulative %

60
frequency
log(BER)

8
50
6
40
-200
4 30
20
2
10
-300 0
0 10 20 30 40 50 60 70 80 90 100 -200 -100 0
run log(BER)

Figure 10. Data fluctuation and histogram for BER.

By analyzing statistical simulation data we can estimate the link availability by calculating the probability of additional
attenuation is not less than threshold value – 9 dB. Analytically, assuming normal distribution one can derive it as

290 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 1  x−µ 
1 − D (x) = 1 − erf   (5)
2   2σ 
Substituting here x = -9 dB, µ = -4.92 dB, σ = 1.9 dB, we can calculate availability of this link as 98.4%.
In conclusion, we demonstrated an example of system-level design of FSO link in the approximation of weak turbulence.
The demonstrated approach can be extended to system and engineering trade-off and optimization studies on FSO links
for different settings of parameters, such as link ranges, aperture size, laser types, modulation methods (e.g. DPSK) and
so on.
Further, for more advanced treatment of atmospheric attenuation readers can write their models e.g. for gamma-gamma
distribution models in MATALAB or C++ and use OptSim co-simulation feature. Or they can import for FSO channel
model the output from specialized atmospheric optics software packages, e.g. LOWTRAN, MODTRAN from ONTAR,
or WaveTrain from MZA [5].

References
1. L. Andrews, R.L. Phillips and C.Y. Hopen, Laser Beam Scintillation with Applications, SPIE Press, 2001
2. L. Andrews, Field Guide to Atmospheric Optics, SPIE Press, 2004
3. G. Hansel, E. Kube, J. Becker, J. Haase, P. Schwarz, “Simulation in the design process of free space optical
transmission systems,” Proc. 6th Workshop, Optics in Computing Technology, 2001.
4. S. Bloom, Physics of FSO, www.freespaceoptics.com/AirFiber-Physics-FSO.pdf
5. ONTAR Corp., www.ontar.com; MZA Associates Corp., www.mza.com

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 291
2.21 Fiber Optic Gyroscope (FOG)

2.21.1 Interferometric Fiber Optic Gyroscope (I-FOG)

RSoft/examples/optsim/block_mode/FOG/FOG_project.moml
The interferometric fiber-optic gyroscope (I-FOG) is today an important technology for many civilian and military
applications such as inertial navigation and guidance systems for automotive, aircraft, and space industries; satellite
antennas pointing and tracking; mining and tunneling operations; and helicopter attitude control. It brings the advantages
of solid-state technology (guided-wave optics and low-voltage low-power electronics) with a cost reduction that enlarges
the application domain.
The I-FOG is based on the Sagnac effect, which produces in a ring interferometer a phase difference proportional to the
dot product of the rotation rate vector by the area vector enclosed by the optical path, and takes advantage of single-
mode optical fiber as the propagation medium. Several critical system components and design characteristics affect the I-
FOG performance: the coil optical fiber; the active source; the passive and integrated-optics components; the optical
circuit configuration for reciprocity; and the detection schemes.
In this example we demonstrate the design of an open-loop FOG. Figure 1 illustrates the schematic that can be found in
the file “FOG_project.moml”. The system can be divided in three main sections: the broadband source, the I-FOG fiber
optic loop unrolled structure, and the signal detection. Figure 2 illustrates in details the broadband source layout. In
particular the signal spectrum is read from the file “BBSource_PS_dB.dat”, providing the user with great flexibility in
simulating various broadband sources just using different and possibly measured power spectra. A uniform noise
generator creates white noise with a flat spectrum constant in frequency. The following filter applies a given transfer
function to the white noise, obtaining the requested broadband source spectrum. Finally an optical normalizer ensures the
user-requested output power, amplifying or attenuating as needed.
The I-FOG fiber optic loop illustrated in Figure 1 is designed unrolling the coil structure. In particular the signal coming
from the broadband source is split in its clockwise and counter-clockwise components propagating inside the fiber optic
loop. The opposite-propagating components travel in two different optical paths. With this representation only the
interactions between clockwise and counter-clockwise signal components are neglected, and all the other effects
(polarization, Kerr, phase, etc.) are taken into account.
The polarizer, the splitter and the phase modulators are usually integrated on a single chip called Multi-component
Integrated Optic Chip (MIOC). The phase modulators are configured in a push-pull pair, four modulators are needed
because of the unrolled structure. They are driven with a clock signal having half of the period equal to the fiber loop
transit delay, the so-called proper (or eigen) frequency of the coil. At rest the biasing modulation is centered but in
rotation the signal becomes unbalanced. The modulated output can be demodulated in a signal that is a biased sine
response, thus increasing the device sensitivity around the zero rotation rate. In fact without biasing the I-FOG natural
intensity versus rotation curve has a cosine shape that is flat around the zero rotation rate.
Figure 3 illustrates the PM fiber model used in the fiber coil. In addition to the linear and nonlinear effects of the single-
mode fiber, the model can also take into account the PM polarization crosstalk and birefringence.
The Sagnac effect model captures the differential phase shift originating from the rotation of the fiber loop. The
following PhaseShift model can add an arbitrary phase shift. Finally the signal opposite-propagating components are
combined in the model OptCombiner thus originating the interferometry.
The I-FOG project enables the user to carry out various analyses on the device behaviour. Figure 4a illustrates the output
power versus rotation at different phase bias points. The phase modulation of the MIOC is turned on, for this reason the
output shape for phase bias equal to zero has a sine shape with maximum slope (and sensitivity) around the zero rate.
The power budget of the system is shown in Figure 4b. Finally the photodetector output signal over time for a rotation
rate of 1000 Deg/s is shown if Figure 4c.
The system of this example can represent a starting point to study more advanced systems including effects such as
noise, phase non-reciprocity and polarization non-reciprocity. Finally the layout can be modified to include different

292 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
optical sources such as super-luminosity diodes (SLD) and EDFA-based broadband sources, and to model various
detection schemes including open-loop, closed-loop, and digital closed-loop. Summarizing OptSim with its extensive
library of active and passive optical and electrical physical models represents an ideal platform to study next-generation
I-FOG.
For any question on advanced I-FOG design please contact Rsoftt OptSim technical support at:
support-optsim@rsoftdesign.com

Figure 1. I-FOG layout: Broadband source, I-FOG fiber optic loop unrolled structure, and signal detection sections

Figure 2. Broadband Source layout

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 293
 Figure 3. Polarization Maintaining Fiber layout

Figure 4: I-FOG Intensity vs. Rotation Rate at different phase bias points (a), Power Budget (b), Photodetector output signal over
time (c)

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2.22 CATV

2.22.1 Analog CATV Examples

RSoft/examples/optsim/block_mode/CATV/TwoToneDirectMod.moml
RSoft/examples/optsim/block_mode/CATV/TwoToneExtMod.moml
RSoft/examples/optsim/block_mode/CATV/ThreeTonesDM_CSO_CTB.moml
RSoft/examples/optsim/block_mode/CATV/analog20ch_dm.moml
This example demonstrates using OptSim in block mode to analyze analog CATV transmission systems. Here we
consider distortions such as composite second order, composite triple beat, and intermodulation distortion.
In fiber-based analog CATV transmission systems, there is usually one wavelength used for the signal transmission with
multiple analog RF channels modulated onto it. While BER is the most common performance metric in a digital
transmission system, measurements of distortions are the critical metrics in an analog transmission system. These results
can be produced through simulations in OptSim.
Let us first consider a two tone direct modulated analog transmission system shown below in Figure 1.
(RSoft/examples/optsim/block_mode/CATV/TwoToneDirectMod.moml)

Figure 1. TwoToneDirectMod.moml

In this example, there are two electrical sine-wave frequencies generated and summed. These two frequencies are at 500
MHz and 525 MHz. These are then modulated onto a direct modulated DFB laser at a wavelength of 1550 nm. This is
then propagated over 40 km of singlemode optical fiber to a PIN-based optical receiver. The RF spectra can be viewed in
the spectrum analyzer to measure the distortions such as composite second order (CSO) distortion, which are due to new

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 295
frequencies generated at f1 + f2 and f2 – f1. Figure 2 shows the RF spectra with power at frequencies 1025 MHz and 25
MHz as well as the original frequencies of 500 MHz and 525 MHz. Also shown are the modulation distortions at 2*f1
and 2*f2 at 1000 MHz and 1050 MHz respectively.

Figure 2. RF Spectra for Directly Modulated Two Tone System

Let us next consider a two tone externally modulated analog transmission system shown below in Figure 3.
(RSoft/examples/optsim/block_mode/CATV/TwoToneExtMod.moml)

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 Figure 3. TwoToneExtMod.moml

As in the previous example, there are two electrical sine-wave frequencies generated and summed. These two
frequencies are at 500 MHz and 525 MHz. These are then modulated onto a CW DFB laser output at a wavelength of
1550 nm using a Mach-Zehnder modulator. This is then propagated over 40 km of singlemode optical fiber to a PIN-
based optical receiver. The RF spectra can be viewed in the spectrum analyzer to measure the distortions such as
composite second order (CSO) distortion, which are due to new frequencies generated at f1 + f2 and f2 – f1. Figure 4
shows the RF spectra with power at frequencies 1025 MHz and 25 MHz as well as the original frequencies of 500 MHz
and 525 MHz. Also shown are the modulation distortions at 2*f1 and 2*f2 at 1000 MHz and 1050 MHz respectively.
The most striking difference between this and the direct modulated example are the additional distortions at a number of
additional frequencies.

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 Figure 4. RF Spectra for Externally Modulated Two Tone System

Let us now consider the third example, ThreeTonesDM_CSO_CTB_latest.moml which is shown in Figure 5. In this
example, a single sine wave generator model block is used in frequency comb generator mode to generate a frequency
comb of three frequencies at 62.5 MHz, 125 MHz, and 187.5 MHz. These three frequencies are then modulated together
onto a DFB laser with wavelength 1550 nm and propagated over 40 km of standard singlemode fiber (SMF-28) to a PIN-
based receiver. The RF spectrum at the receiver can be viewed to analyze the composite second order, composite triple
beat, and other distortions in the system. As shown in Figure 6, the CSO = -36 dBc (at f = f1 + f2 = 250 MHz and f = f2
+ f3 = 312.5 MHz), and the CTB = - 41 dBc (at f = f1 + f2 + f3 = 375 MHz).

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 Figure 5. Three Tone Analog CATV Example

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 Figure 6. RF Spectra of Three Tone CATV Example

Let us now consider the fourth example, analog20ch_dm.moml, as shown in Figure 7. This example demonstrates a
simulation of a 20-channel analog CATV system. In this example as in the above, we focus our attention on the
distortions. In this example, a system with twenty channels starting at 500 MHz with a frequency step of 6 MHz is
simulated. To view the distortions that are modulated onto adjacent channels, we drop the tenth channel so that we may
view the distortions at this frequency generated by the other channels. In Figure 8, we see the modulated frequencies for
the twenty channels minus the dropped channel at 554 MHz, and the distortions present at that frequency. You may also
observe the distortions at other frequencies by zooming the RF Spectra result into other frequency ranges in this
example.

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 Figure 7. Twenty Tone Directly Modulated Analog CATV Example

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 Figure 8. RF Spectra of Twenty Tone CATV Example

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2.23 FTTH

2.23.1 FTTH System with GEPON Access Architecture

RSoft/examples/optsim/block_mode/FTTH/FTTH_GEPON_1_user.moml
RSoft/examples/optsim/block_mode/FTTH/FTTH_GEPON_16_users.moml
This example demonstrates an OptSim design for FTTH GEPON link. Here we consider typical GEPON FTTH design
for downlink with 16 subscribers and 20-km reach.
Passive optical network (PON) access architecture is the accepted choice of triple-play (voice, video, and data) service
delivery from service providers to the end users in FTTH (fiber-to-the-home) access networks. Three major PON
technologies are currently accepted as the basis for FTTH deployments: Broadband PON (BPON), Gigabit PON
(GPON), and Ethernet PON (EPON or GEPON). GEPON architecture is specified by IEEE 802.3ah standard and
supports Gigabit Ethernet 1.25 Gbps transmission rate for data component in both down- and up-link configuration.

Figure 1. FTTH GEPON layout with 1 end user as in the project file FTTH_GEPON_1_user.moml

In a PON, the active optoelectronics are situated on either ends of the passive network. An optical line termination
(OLT) device is installed in the central office (CO), and an optical network termination (ONT) device is installed on the
other end, in or near each home or business site. Fiber distribution is done using a tree-and-branch architecture.

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First, we describe in details the configurations for Central Office OLT and single end-user ONT and then will generalize
the treatment to all 16 uses. In this example we consider downstream configuration of GEPON with bitrate 1.25 Gb/s
and support for triple-play. FTTH layout with single end-user is shown in Figure 1.
The triple-play service is realized as a combination of data, voice, and video signals. The high-speed internet component
is represented by a data link with 1.25 Gb/s downstream bandwidth. The voice component can be represented as VOIP
service (voice over IP, packet-switched protocol) and can be combined with data component in physical layer
simulations. Finally, the video component can be represented as a RF video signal (traditional CATV) or as IPTV signal
that also can be combined with data. In our case we consider the former case with RF video link. To optimize the
bandwidth in PON the transmission through the optical fiber path employs the CWDM technique with data/voice
component transmitted at wavelengths in the range of 1480-1500 nm, and video within the 1550-1560 nm range.

Figure 2. FTTH GEPON layout with 16 users as in the project file FTTH_GEPON_16_users.moml

CO OLT block (Transmitter block) consists of Data/VOIP and Video components. The Data/VOIP transmitter modeled
with pseudo-random data generator (PRBS), NRZ modulator driver, direct-modulated laser, and booster amplifier. The
video component modeled as RF SCM (sub-currier multiplexed) link with only two tones (channels) for simplicity. The
two channels we used are from standard NTSC analog CATV frequency plan - channel 2 and channel 78 at frequencies
55.25 MHz and 547.25 MHz, respectively. RF video transmitter consists of two Electrical Signal Generators, summer,
direct-modulated laser, and pre-amplifier. Next, Data/Voice and Video signals are multiplexed at Multiplexer and
launched into 20-km fiber span. Output from the fiber trunk goes through the 1:16 splitter and then to individual users.
User’s ONT consists of splitter and data and video receivers. Data receiver configured with optical filter, PIN/TIA
receiver, and BER Tester. The video signal receiver consists of optical filter, PIN/TIA receiver and electrical filters.
Yellow-colored blocks on schematic correspond to measurement instruments – to visualize to link’s optical spectrum,
waveforms, eye diagrams, etc.
Next, after we specified the detailed single-user layout we can generalize the setup to all 16 users by adding another 15
users ONTs. In order to simplify the schematic we can apply the hierarchy model feature in OptSim – i.e. we can group a
set of components into a sub-system called compound component (can be also referred to as hierarchy or superblock)

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represented by a single icon on a project. Figure 2 shows full 16-users GEPON configuration – here each ONT block is a
compound component with inside configuration equivalent to ONT setup in Fig.1 (all blocks inside a blue box).
Similarly, CO OLT is represented as compound component with inside configuration given in Fig.1 for OLT.
The parameters of all components are set according to typical values and are optimized to provide the required link
performance. Next, we can run simulation for this layout and look at the results.
Figure 3 shows the OLT output optical waveforms for data and video signal, and Figure 4 shows OLT output optical
spectra for data and video signals. Next two figures depict results at the received side for ONT_1. Figure 5 shows
received eye diagram for data signal and the corresponding BER. On can see that a BER computed value of 2.14x10-16 is
better than the link BER requirement of 10-12. Figure 6 shows the received RF spectrum of video signal with two tones
(channels) recovered, and for comparison the RF video spectrum at the transmitter.
In summary, we described a simple example for typical layout of FTTH GEPON system in OptSim. This layout can be
further modified to study links with more specific details and provided components specifications. For example, a fiber
trunk can consist of few fiber spans and splices, the drop-off cables from splitter to users ONTs can be added. The
upstream configuration can be studied as well.

OLT Output Signal

Legend:
11 λ = 1490 nm (x)

10
Signal Magnitude (dBm)

λ = 1550 nm (x)
9

3
7 8 9 10 11 12
x10-8
Time (s)

Figure 3. OLT output for data and video signals.

Video Signal Optical Spectrum Data Signal Optical Spectrum

-10 0

-20 -10

-30 -20
Power (dBm)

Power (dBm)

-40 -30

-50 -40

-60 -50

-70 -60

-80 -70
-90
1549.4 1549.6 1549.8 1550.0 1550.2 1550.4 1489.6 1489.8 1490.0 1490.2 1490.4
Wavelength (nm) Wavelength (nm)

Figure 4. OLT output optical spectrum – video signal (left) and data signal (right)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 305
 Eye Diagram for Data Signal BER

0.024
10-15
Signal (V)

0.022

BER
10-16
0.020

0.018
2 4 6 8 10 12 14 10-17
-10
x10 -1 0 1
Time (s) Single Result

Figure 5. Data Signal – received eye diagram (left) and corresponding BER (right).

Video Signal Transmitter Spectrum Video Signal Receiver Spectrum

-10 0

-20 -10

-20
-30
Power (dBmV)

Power (dBmV)

-30
-40
-40
-50
-50
-60
-60

-70 -70

-80 -80
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
Baseband Frequency (MHz) Baseband Frequency (MHz)

Figure 6. Video Signal’s RF spectrum – at transmitter (left) and at receiver (right).

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2.24 Transients

2.24.1 Fast Power Transients in EDFA Chains

RSoft/examples/optsim/block_mode/transients/Fast_Power_Transients_in_EDFA_Chains.moml
This example is intended to show the phenomena of fast power transients in EDFA chains. The schematic shown in
Figure 1 (examples/block_mode/transients/Fast_Power_Transients_in_EDFA_Chains) demonstrates the
accumulation of fast power transients in a chain of three EDFAs. Two CW laser sources at wavelengths 1550 nm and
1556 nm are transmitted along the EDFA chain. The 1550 nm signal is connected to an instance of the Transient Optical
Switch model. The switch simulates adding and dropping of the signal at wavelength 1550 nm. The signal at 1556 nm is
the surviving channel. The attenuators simulate loss of the fibers. The optical multiplexers combine the signals, including
the EDFA pump signals at 980 nm. The example demonstrates the effect of cross saturation in EDFA chains. As seen in
Figure 2, the plot obtained at TPlotter1 in the schematic, the surviving signal power levels experience power excursions
when some channels are dropped or added. The figure also shows that the power excursions experience faster rise times
as the number of EDFAs in the chain increases. This is the phenomena of fast power transients shown experimentally in
[1].

Figure 1. Chain of 3 EDFAs: Cross-saturation in EDFAs.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 307
 Figure 2. Optical signals after all 3 EDFAs.

Reference
1. J. L. Zyskind, Y. Sun, A. K. Srivastava, J. W. Sulhoff, A. J. Lucero, C. Wolf, and R. W. Tkach, “Fast Power
Transients in Optically Amplified Optical Networks,” Optical Fiber Communication Conference (Optical Society of
America) post deadline paper PD31.

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2.24.2 An All-Optical Gain Control Scheme
RSoft/examples/optsim/block_mode/transients/All_Optical_Gain_Control.moml
This is a simple example that demonstrates an all-optical gain control scheme. The schematic shown in Figure 1
(examples/optsim/block_mode/transients/All_Optical_Gain_Control) uses a feedback loop to create a
ring laser configuration. The EDFA provides the necessary gain. The signal at wavelength 1550 nm is turned on and off
by the switch model shown in the schematic. The signal at wavelength 1557 nm is the surviving signal. The lasing signal
at 1537 nm clamps the gain of the surviving channel when the signal at 1550 is dropped. As shown in Figure 2, the
relaxation oscillations of the lasing signal at 1537 nm causing some relatively minor oscillations to be transformed to the
surviving channel. However, these small power excursions are much smaller than those that would be realized without
the gain control mechanism. The lasing signal evolves from the ASE noise of the EDFA. The lasing wavelength is
selected by the filter in the feedback path. By controlling the amount of loss in the feedback path, we can trade gain
stability for EDFA gain. Lowering the loss in the loop leads to a stronger lasing signal and consequently greater stability
of the surviving signal. However, this is achieved at the expense of the overall gain of the EDFA. The Delay Block must
be part of all feedback loops in OptSim. It provides an initial signal for the multiplexer to satisfy the requirements of the
simulation scheduler. It does not affect the physical properties of the signals passing through it.

Figure 1. An All-Optical Gain Control Scheme.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 309
 Figure 2. Signals at the Output of the EDFA

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2.24.3 Compact Transient EDFA Model Comparisons
RSoft/examples/optsim/block_mode/compact_trans_edfa/ctedfa_dc_comparison.moml
RSoft/examples/optsim/block_mode/compact_trans_edfa/ctedfa_tran_comparison.moml
The Compact Transient EDFA model is a numerically efficient alternative to both the Transient and Physical EDFA
models. The model’s accuracy is also very good in comparison with these models, as long as the assumption of uniform
inversion is not excessively violated in cases where ASE noise generation, background loss, and homogeneous
upconversion are considered. Below, we evaluate the dc and transient accuracy of the model for some illustrative cases.

DC Comparisons
First, open the topology “ctedfa_dc_comparison.moml”, the schematic of which is illustrated in Figure 1. This
example compares the dc performance of the Compact Transient EDFA and Physical EDFA models. Gain/NF Analyzers
are used to measure the gain and noise figure results for each model. In the simulation, an EDFA amplifies a 1535-nm
–40-dBm signal via a 40-mW 980-nm co-propagating pump, both with and without upconversion.

Figure 1. OptSim topology for evaluation of dc performance of Compact Transient EDFA model.

Click on OptSim’s Parameter Scan button. The dialog is pre-configured to scan the EDFA device length from 1 to 20 m
in increments of 1 m for two different upconversion coefficients (0 and 1.5e-22 m3/s). Click OK to run the simulation.
When it is complete, open the WinPlot files “dc_gain_comparison.plc” and “dc_nf_comparison.plc” to
see comparisons of the gain and noise figure values resulting from each model. These results are shown in Figure 2. As
can be seen, agreement between the Compact and Physical models is good up to roughly 10 m, with the non-
upconversion case showing the best results for longer devices. However, clearly for moderate device lengths
upconversion can be accurately accounted for.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 311
 Figure 2. Comparison of Gain and Noise Figure calculations using the Compact and Physical EDFA models.

Transient Comparison
Next, open the topology “ctedfa_tran_comparison.moml”, the schematic of which is illustrated in Figure 3.
This example compares the transient performance of the Compact EDFA and Transient EDFA models. Transient plotters
are used to measure the output signals from the two amplifiers. In the simulation, a 10-m EDFA is used to amplify a pair
of optical signals. A 1550-nm signal is dropped and then added in the presence of a constant 1556-nm signal. Uniform
upconversion is included in the simulation.

Figure 3. OptSim topology for evaluation of transient performance of Compact Transient EDFA model.

312 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Click on OptSim’s Go button, and click OK to run a transient simulation lasting 500 µs. When the simulation is
complete, double-click on the Transient Plotters at the outputs of the two EDFA models. Figure 4 shows the results. As
can be seen, the agreement between the two models is very good.

Figure 4. Comparison of transient responses using the Compact and Transient EDFA models.

In cases such as those presented here, the model performs best when the assumption of uniform inversion is valid. When
dealing with larger device lengths, higher signal powers, and counter-propagating pumping schemes, the accuracy of a
full model implementation may be required. Feel free to experiment with both topologies to gain a better understanding
of these limitations.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 313
2.25 General Purpose

2.25.1 How to Create a Block Mode Compound Component (CC)

Follow these steps:

1. Open a new schematic, set type to compound component (CC) and name the CC:

2. After step 1, a blank topology layout area will open up where you will place your models and make
connections. Say, you want to make a simple single channel transmitter that you will use in several topologies.
Also, let’s assume that your project will use this transmitter several times but with different PRBS. So place all
necessary component except the PRBS in the drawing area and make connections:

314 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 3. Now we need to add input and output ports to above layout so that we can make connections when we use this
CC in a bigger project. Here are these ports to choose from:
Single-port Input Multi-port Input

Single-port Output Multi-port Output

Single-port terminals are for block-mode compound components and multi-port terminals are for sample mode
compound components. If one needs multiple ports for input or output in case of block mode, use fork in the main
topology like we shall do for output port in this example (Step 7). These forks are here:

4. In our case, we need input port before ElecGen1 (electrical signal generator) model and one output port after the
ExtMod1 (modulator) model. So we place these ports (right click the mouse, select ports and drop by right-
clicking mouse again in the drawing area), make connections and save and close the completed CC:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 315
 5. In order to make this CC available for use in various projects from within the models tree of the left-hand pane,
follow these steps:

(a) Open User Libraries Organizer from the Utilities:

(b) Import your CC:

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 (c) Add CC to User Directory:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 317
 If you expand User Directory, you will see your transmitter CC there:

318 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 (d) Close User Libraries Organizer

(6) Your CC is now ready to be used in your main project. Open a new (or existing) project where you want this CC to
be placed, drag and drop your CC from models tree:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 319
(7) Connect a PRBS at the input, connect a fiber and a back-to-back receiver at the output. Since the output port needs
two connections (one for fiber and one for the receiver), use a fork as below:

(8) It’s possible to look inside the CC (but not change it) from the main topology file like shown below. The CC
schematic will be in color to differentiate it from the main CC.

You can also set an icon for a CC if you have an image file.

You are also encouraged to read User Guide, Chapter 1 for another kind of CC (local, not re-useable) called “In Line
CC.”

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2.25.2 Compound Component Example
RSoft/examples/optsim/block_mode/general_purpose/hier4chfwm.moml
The purpose of this example is to demonstrate a hierarchical topology representation. This example is virtually identical
to the 4chfwm.moml example, except that it uses hierarchy to represent the topology. The example can be found in the
hier4chfwm.moml file in the Examples directory of the OptSim installation.
Load the hier4chfwm.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below.

Figure 1. hier4chfwm.moml

Rather than including the CW laser, the electrical signal generator, and the modulator models four times each in the top
level of the topology, they are included only once each in the second level of hierarchy. Each level of the hierarchy
below the top level is referred to as a compound component (CC). It is essentially a block like any other, with an icon
which may either be unique or use the default CC icon. Double click on one of the icons which receive input from the
PRBS block. This is a custom icon which the user is easily able to create upon the creation of a CC. Double clicking on
it opens the CC in a separate topology editing window. It looks like any normal topology in this representation, except
that it includes two symbols which are not normally found in a single-level topology representation. These are the
hierarchical input signal port and the hierarchical output signal port icons. They are used to specify the input and output
ports of the CC, and indicate where the signals from the input ports go in the topology and which component output
ports in the topology are attached to the CC’s output ports. The parameters of the CC at the top level are the user
variables specified in the CC’s own topology representation. In this example, there are five user variables specified in
the CC’s topology. These become the five parameters of the CC in the top level of the hierarchy.
There are several advantages to using CCs in a topology. For example, in a single level topology, any changes to a
component’s parameters which are common to all instances of the component in the topology must be made to each
instance independently. In a multi-level topology, if that component is included in a CC which has multiple instances in
the top level, the changes can be made just once to the component in the CC, and propagated automatically to all the
instances of the CC in the top level topology

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2.25.3 How to Co-simulate with BeamPROP
Follow these steps:

1. Invoke BeamPROPTM from OptSimTM’s block mode examples directory:

2. Select “WDM Router Layout” from the “Utility” menu of BeamPROPTM:

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3. Insert parameter values as: Input Port 1; Output Port 4; Wavelength Channels 4; #Arrayed Waveguide 16; Center
Wavelength 1.55 µm; Channel Spacing: 0.0016; …, Layout File Meta Prefix: jkp and click on “OK.”

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4. Open “Utility” menu in BeamPROPTM and select input file (jkpin.ind) in “WDM Router Simulation:”

And

324 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
5. A parameter window will open up. Give the script file meta prefix:

6. Run OptSimTM and open CallBeamPROP.moml example:

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 325
7. A topology window will open up. Open the parameter window of Multiport icon and type/select these parameter
values: Signalbandwidth Narrow; ComandLine “bsimw32 @jkpscanall.scr” ; FileName jkpscanall.dat (or select the
transfer matrix data file generated by WDM Router Simulation utility due to Step 6 above); and click on “OK.”

326 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
And,

8. Run simulation by clicking on the “Go” button and you observe results. OptSimTM will invoke BeamPROPTM as soon
as simulation engine of OptSimTM encounters “Multiport” icon. Once the AWG is co-simulated in BeamPROPTM, the
simulation results are available to OptSimTM for futher link level simulation:

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And, the channel 1 output from OptSimTM looks like:

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2.25.4 BeamPROP Interface Example
RSoft/examples/optsim/block_mode/general_purpose/callbeamprop.moml
The purpose of this example is to demonstrate the simulation of a link utilizing a component modeled in RSoft Design
Group’s BeamPROP tool. The procedure was illustrated above. The example can be found in the
callbeamprop.moml file in the Examples directory of the OptSim installation.
Load the callbeamprop.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below.

Figure 1. callbeamprop.moml

In this example, a four channel WDM system is modeled. The N×M multiport optical device model block is used to
represent a WDM router designed and modeled at the device level in BeamPROP. When the OptSim simulation reaches
the N×M multiport optical device model, the command specified in its CommandLine parameter is executed. For the
purposes of this example, the simulation results which BeamPROP would produce when being called from OptSim have
already been computed and provided in a data file with the filename specified in the N×M multiport optical device model
block. In essence, this file specifies a set of wavelength-dependent transfer functions for each of the input/output port
pairs. When a BeamPROP script is called from OptSim, device-level simulations are performed over the specified
wavelength range to compute the transfer functions for each of the input/output port pairs. A data file is then generated
to provide OptSim with these results for its system-level simulation of the link.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 329
2.26 Miscellaneous

2.26.1 10 Gbps Externally Modulated Single Channel Link

RSoft/examples/optsim/block_mode/miscellaneous/extmodlink.moml
The purpose of this example is to demonstrate a simulation of a 10 Gbps externally modulated single channel optical
link. The example is found in the Examples directory of the OptSim installation in the file extmodlink.moml.
Several models, component parameters, and options will be highlighted in this example.
Load the extmodlink.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below.

Figure 1. extmodlink.moml

This example is similar to the 10GpsLink.moml example in most respects. Therefore, the differences between this
and the previous example will be concentrated on in this description. The most significant difference is that rather than
modulating a laser directly with the electrical signal, a CW laser model is used and an external modulator is used to
modulate the optical signal with the electrical signal. The optical power output of the CW laser model is set to the user
variable “power” so that it can be used in the Scan Variable simulation. The modulator block models the function of a
Mach-Zehnder modulator, with a specified chirpfactor. The modulated waveform and the frequency chirp of the
modulated optical signal can be viewed using the signal plot and chirp plot icons attached to the output of the modulator.
Following the fiber in this example is an optical amplifier model. In this example, a parametric model for an erbium
doped fiber amplifier (Black Box EDFAwith gain saturation is used. The Black Box EDFA adds amplified spontaneous
emission (ASE) noiseto the optical signal. At the output of the EDFA, the optical signal waveform and the wavelength
spectra can be viewed. In this example, the wavelength spectra of the signal and of the ASE noiseare shown in separate
graphs. Following the EDFA in this simulation example is a Fabry-Perot optical filter. The effect of the filter on the
optical signal and noise spectra can be seen by viewing the spectra at the output of the filter. Following the optical filter,
the signal goes through the power normalizer, followed by the receiver model and the BER tester block.
As in the single channel 10 Gbps link example, a single simulation run can be executed with the Go button.
Alternatively, a Variable Scan simulation can be executed by using the Perform Parameter Scan button or the Scan
Variable option in the Run menu.

330 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.26.2 Light–Emitting Diode (LED)
RSoft/examples/optsim/block_mode/miscellaneous/LED_modulation.moml
The purpose of this example is to demonstrate spectral bandwidth and modulation response typical for Light-Emitting
Diodes (LED). The snapshot of the schematic is given below in Figure 1:

Figure 1. Setup for LED, schematic LED_modulationt.moml

In this schematic, NRZ data modulate a 1300-nm LED and output from the LED goes to the optical receiver (after
passing through an attenuator). The BER Tester analyzes the electrical output signal from the receiver.
For LED model parameters we use values typical for 1300-nm LEDs:
• Responsivity R = 0.01 W/A
• Spectral linewidth = 10 THz (or 56 nm at 1300-nm wavelength)
• Rise-fall time (carrier lifetime τc) = 2 ns

The spectral linewidth defines spectral distribution of a light source. The spectral distribution is governed by the
spectrum of spontaneous emission and typically follows a Gaussian shape. Figure 2 shows the output spectrum of the
LED in our example with 56 nm of spectral width.
Intrinsic LED rise/fall time is equivalent to carrier lifetime if circuit parasitics are negligible and parasitic response time
is much shorter than τc – that is the case in our example.
For given LED parameters we can calculate the LI-curve (see Figure 3a) and small signal transfer function (see Figure
3b). The latter one characterizes the LED modulation response.
The modulation response of LEDs depends on carrier dynamics and is limited by the carrier lifetime. The LED 3-dB
modulation bandwidth is defined as the modulation frequency at which the LED transfer function is reduced by 3 dB and
can be derived as
f3dB =√3 (2π τc)-1

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 331
 Figure 2. Optical Spectrum from LED at resolution 1-nm.

(a) (b)
Figure 3. LED characteristics: (b) LI (or PI) curve; (b) Small-Signal transfer function

332 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
In our example f3dB is about 138 MHz. Thus, at modulation frequencies (bit rates) higher than 138 MHz (138 Mb/s) the
BER for received signal will rapidly degrade. To demonstrate that the modulation bit rate in our schematic is varied
through parametric runs from 100 Mb/s to 1 Gb/s.
Figure 4 shows resulting Q-factor and BER vs. modulation bit rate. The Q-factor decreases from ~ 23 dB at 100 Mb/s to
~ 8 dB at 1 Gb/s. Figure 5 demonstrates eye diagrams for modulation bit rates of 100 Mb/s and 500 Mb/s – one can
clearly see the eye opening penalties at higher bit rates.

Figure 4. Q-factor and BER vs. modulation bit rate.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 333
 Figure 5. Eye diagram at the receiver at modulation rates 100 Mb/s (left) and 500 Mb/s (right).

In conclusion, we illustrated a spectral distribution and modulation response for a typical 1300-nm LED.

334 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.26.3 Parallel Optical Bus Example
RSoft/examples/optsim/block_mode/miscellaneous/parallel_8.moml
The purpose of this example is to demonstrate the simulation of a synchronous parallel optical bus. The use of the
statistical simulation functionality is also demonstrated in this example. The example can be found in the
parallel_8.moml file in the Examples directory of the OptSim installation.
Load the parallel_8.moml file from the Examples directory. This will create a new window with the example
topology represented. It should appear as shown below.

Figure 1. parallel_8.moml

Aspects of a synchronous optical bus which differ from a typical WDM optical link are accounted for in this simulation.
The most significant of these is the statistical variation in component parameters between the channels. In parallel
optical bus systems, these variations can be the limiting factors in the system performance rather than noise. To simulate
these variations, OptSim includes a statistical simulation option. Each of the numerical component parameters in the link
can have a standard deviation and statistical distribution specified in addition to the nominal value. In the parameter scan
simulation dialog, the number of statistical simulation runs to execute is set by the value for number of statistical runs.
When this value is zero, a single run at each of the scanned variable iterations is performed with the nominal parameter
values only. If this value is set to one or more, the specified number of simulations are performed at each of the scanned
variable iterations with each run using a different set of statistically varied parameters. However, the statistics used to
vary the parameters are the same in all of the scanned variable iterations. This ensures that any differences in the
simulation results between the scanned variable iterations can be attributed purely to the changes in the scanned variable,
and not to any artificial differences in the statistics used to vary the statistically varied component parameters.
The PRBS block is used to generate a pseudorandom binary sequence to drive the simulation of each of the parallel
channels. As in the previous WDM examples, the offset is used to decorrelate each of the output bit streams from one
another. The nominal parameter values of the component models in each of the channels are the same; however, in a
real system, variations in the parameters will occur from one channel to the next. To account for this in the simulation,
particular component parameters are set to have nonzero standard deviations and statistical distributions. In this
example, only selected parameters are varied to see the effect of variations on these particular parameters on the overall

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 335
link performance. These include the rise and fall time of the electrical signal generator, the wavelength and bias current
of the laser, and the attenuation and skew in the fiber. The skew parameter of the fiber is designed specifically to
phenomenologically include the timing skew between different fibers in the link simulation. After the signals propagate
through the parallel fibers, the optical power normalizer block is used to attenuate all the channels by the same amount
such that the channel with the maximum average optical power determines the attenuation value for all the channels.
This ensures that the performance of the channels relative to one another is maintained during sweeps of the received
optical power for generation of BER curves. At the output of the receiver blocks, an electrical crosstalk block is used to
add a specified amount of crosstalk between the channels. This may model the electrical crosstalk present in a
monolithic receiver array, for example. For example, the effect of a specified amount of crosstalk on the link
performance can be studied to determine the maximum acceptable crosstalk level through simulations. At the output of
the crosstalk block, the eye diagram of each of the channels can be viewed independently. A combined eye diagram plot
is also shown to directly view the effects of the statistical variations on the overall link performance by the amount of
vertical eye closure from variations in power levels and horizontal eye closure from timing skew between the channels.
The BER Tester block actually computes the byte error rate, as it computes the BER of each of the channels at the
identical threshold level and sample times. An error in any of the channels at a given bit time equals an error in the
received byte. Therefore, the byte probability of error is the maximum bit probability of error of each of the channels at
a given sample time.

336 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
2.26.4 Chirp-Managed Laser (CML)
The objective of this application note is to demonstrate simulation example reproducing dispersion tolerance effect in
transmission link by using Chirp-Managed Laser (CML).

RSoft/examples/optsim/block_mode/fiber_dispersion/ChirpManagedLaser.moml
The parameters used for CML and transmission link setup were taken from publications by AZNA [1-4]. Since not all
parameters necessary for simulations for the laser and optical filter were available in AZNA publications, the goal of this
simulation example was to show the qualitative agreement, i.e., to demonstrate the concept of dispersion tolerance
improvement by chirp-managed laser at the transmitter. The user will adapt and incorporate this concept to meet his/her
design objectives.
The principle for CML is described in Ref. [1]. We also created a simple test setup similar to the one proposed by a
group of authors and described in Ref. [2-3]. Figure 1 depicts this schematic.

Figure 1. Simulation setup schematic for link setup with CML

The Chirp-Managed Laser transmitter consists of 10 Gb/s PRBS data source, NRZ driver with 20 ps rise/fall time,
Directly Modulated Laser, and Gaussian Optical Filter to provide optical spectrum reshaping (OSR). The optical
normalized is added after the filter to control the launch power into a fiber span.

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 337
 Figure 2. Signal spectrum before the OSR

Laser has a threshold current 15 mA and is driven well above the threshold with 50 mA bias and 50 mA modulation
current. As a result of high bias current the laser output spectrum will show a “blue” frequency shift for “1” bits
compared to “0” bits – see Figure 2. Such a laser shows low transient chirp but low extinction ratio (ER is only 2.6 dB).
OSR is set with 3-dB bandwidth 7.1 GHz and the center of OSR is set to the “1” bits carrier frequency (lasing frequency
+ blue shift corresponding to “1” bits). Figure 3 shows waveform intensity and frequency chirp before OSR. Figure 4
shows optical waveform and spectrum after OSR. One can see OSR cuts optical spectrum in half and extinction ratio
goes up to ~16 dB. The output signal from OSR is launched to the transmission link and then to optical receiver.

Figure 3. Signal waveform (left) and frequency chirp (right) before the OSR

338 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
 Figure 4. Signal waveform and spectrum after OSR

The transmission link consists of 160-km SMF-28 fiber compiled out of four spans of 40 km and 4 amplifiers to
compensate for fiber attenuation. Total accumulated fiber is dispersion is ~2700 ps/nm. The optical receiver is calibrated
to have back-to-back BER of 10-13 at –25 dBm input power. Figure 5 (a) shows back-to-back eye diagram without OSR.
Figure 5 (b) shows the received eye diagram for link with OSR and 160-km fiber – resulting BER is 5x10-6. Finally,
figure 5(c) shows eye diagram for the same link with no OSR – the BER in this case is only 9x10-3
If the forward-error-correction (FEC) is required, the BER tester model has options for pre-defined FEC and super-FEC
as well as for the custom FEC schemes.

(a)

OptSim Application Notes and Examples Chapter 2: Block Mode and Transient Simulations • 339
 (b)

(c)
Figure 5. Receiver eye-diagrams: (a) back-to-back, (b) with OSR, and (c) without OSR

In conclusion, this example does demonstrate that Chirp-Managed Laser with OSR does provide better tolerance to
dispersion penalties and improved the eye opening and BER significantly. So, the improvement in BER from 1e-2 to 1e-
5 and better allows bringing BER to the level at which standard FEC can decode BER to error-free transmission.

References
1. Y. Matsui, D. Mahgerefteh, X. Zheng., C.Liao, Z. F. Fan, K. McCallion, and P. Tayebati, “Chirp-Managed Directly
Modulated Laser (CML)”, Journal of Lightwave Technology, v.18, no.2, p.385, 2006’
2. S. Chandrasekhar, C. R. Doerr, et al., “Flexible Transport at 10-Gb/s from 0 to 675km (11,500ps/nm) using a Chirp-
Managed Laser, no DCF, and a Dynamically Adjustable Dispersion-Compensating receiver,” OFC 2005, Paper #
PDP30.
3. D. Mahgerefteh, and Z. F. Fan, “Chirp-Managed Laser Technology Delivers > 250 km Reach”, Lightwave,
September 2005
4. www.aznacorp.com, AZNA, LLC.

340 • Chapter 2: Block Mode and Transient Simulations OptSim Application Notes and Examples
Chapter 3: Multimode
Simulations

This chapter presents a selection of multimode examples including optical coupling and multimode fiber simulations.
More examples of topologies which can be simulated in OptSim may be given in the multimode folder within
examples directory of the distribution (examples/optsim/block_mode/multimode). You will be able to run
these examples only if you have a license of ModeSYS.

3.1 Laser-Fiber Coupling

RSoft/examples/optsim/block_mode/multimode/laser_fiber_coupling.moml
This example is intended to demonstrate the coupling of the optical spatial field of a laser into the spatial configuration
of the multimode fiber model. The use of lenses and couplers will also be demonstrated.
Consider the topology of Figure 1(examples/optsim/block_mode/multimode/laser_fiber_coupling.moml)
which is a simple simulation that consists of the spatial VCSEL model driven by a PRBS electrical signal connected to a
coupler and the multimode fiber model. The VCSEL has been configured to emit all of its power in the Ex polarization.
The model’s spatial attributes have been activated and the VCSEL has been configured to emit a Laguerre-Gaussian
beam with azimuthal index 2, radial index 0 and a beam waist of 5 microns. The transverse output field of the VCSEL is
shown in Figure 2.

Figure 1: Sample topology.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 341

 Figure 2: VCSEL output beam.

The spatial parameters that describe this configuration are listed below:

VCSEL Spatial Parameters

Spatial_Modes : spatial_effects on
Spatial_Modes : mode_default_grid_spacing no
Spatial_Modes : mode_dx 0.5
Spatial_Modes : mode_dy 0.5
Spatial_Modes : mode_default_domain yes
X_Spatial : x_single_mode_type LG
X_Spatial : x_l 2
X_Spatial : x_m 0
X_Spatial : x_wo 5

As seen in Figure 2, the VCSEL output is centered about the fiber axis (x=0, y=0). In this example, the VCSEL is to be
shifted by 5 microns in the x-direction and 5 microns in the y-direction. Additionally, it is to be rotated by 5 degrees
about the x-axis. The spacing between the VCSEL and the fiber is to be 25 microns. These attributes can be set through
the following parameters:

Spatial Coupler Parameters

xoffset 5
yoffset 5
distance 25
phi_x 5

The multimode fiber model is set to run in its parabolic configuration with the following settings:

Multimode Fiber Parameters

General : spatial_effects on
General : operational_mode parabolic
General : core_radius 25
Index: peak_index 1.414
Index: delta 1
Spatial: mode_default_grid_spacing no
Spatial: mode_dx 0.5

342 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Spatial: mode_dy 0.5

To make this example run quickly, the fiber and laser grid spacing has been manually set to 0.5 micron and all spatial
analyzers are configured to plot in accuracy=low mode. The user can obviously adjust these settings as needed. The
output of the coupler is shown in Figure 3.

Figure 3: Spatial coupler output.

The center of the optical beam has clearly been shifted. The effect of the tilt is not visibly discernable due to the short
propagation distance, but rest assured that is properly accounted for in the complex field representation. The spatial
analyzer connected to the coupler output delivers the following report:

OpSig Spatial Field Summary

---------------------------
Input consists of one OpSig

OpSig #1 has an Ex time-domain field and a spatial field in the X direction.

Average power in the x-polarization is 0.00208988
wavelength=820 nm
startTime=0 s

Despite the tilt about the x-axis, the coupler produces only one OpSig as an output. (Recall from the coupler
documentation that in general, a single optical field can produce two OpSigs as an output.) This is
( )
because φ x , φ y = 0, φ z = 0 is one of a few special cases and because the field is restricted to the x-polarization (i.e.,
E y (t ) = 0 ). A counter-example will be shown shortly. The spatial analyzer report also indicates that indeed, a spatial
field exists in the x direction. This is important because at least one spatial field is required to couple into the multimode
fiber. The average power is calculated by summing the powers of each element in the E x (t ) array and dividing by the
number of points. Finally, the startTime is indicated to be 0. Since the signal has not yet encountered any delay
elements, this is the expected result. To produce these results, the spatial coupler model first applies the specified
rotations and translations to the input spatial field, then it propagates this field the specified distance through free-space.
Figure 3 is the field that is presented to the fiber input.
The multimode fiber model calculates the coupling coefficient between the field of Figure 3 and each of the fiber’s
transverse modes. In this case, the transverse modes Ei (r , φ) are analytically calculated.
n
E in (r , φ, t ) = E in (r , φ)E in (t ) =
∑ [c E
i =1
i in (t )]Ei (r , φ)

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 343

 2π ∞
ci =
∫ ∫E
0 0
in (r , φ)Ei* (r , φ)rdrdφ

As described in the multimode fiber documentation, the fiber model produces one OpSig at its output for each fiber
mode. The time-varying part of each output OpSig is a copy of the time-varying part of the input OpSig scaled by the
coupling coefficient for the fiber mode under consideration and delayed by the propagation time of that mode. The
spatial part of each output OpSig is obviously the fiber mode itself. Mathematically, this is described by:
E out ,i (r , φ, t ) = [c i E in (t − τ i )]E i (r , φ)

Here, E in (t − τ i ) is the single input signal after being shifted by the modal delay τi , E i (r , φ) is the ith fiber spatial mode,
c i is the ith coupling coefficient between E i (r , φ) and the spatial field shown in Figure 3 and E out ,i (r , φ, t ) is the ith output
signal. Dispersive effects are omitted from this example for simplicity. The fiber output is a linked list of these signals:
n
E out (r , φ, t ) =
∑ [c E
i =1
i in (t − τ i )]Ei (r , φ)

This simulation was run at 820 nm; for the parameters previously specified, the fiber supports 190 spatial modes. If
plot_type=individual in the spatial analyzer that is at the fiber output, each of the fiber modes will be plotted. As there
are, in this case, 190 individual modes, this can be extremely time consuming. If the user wishes to view a specific fiber
mode, it is more efficient to use the mode plotting features of the multimode fiber test function. A few representative
ones are shown below:

Figure 4: Representative individual fiber modes using the multimode fiber test function.

The other two plotting modes are plot_type=total and plot_type=weighted. The first mode simply superimposes the
spatial portion of all of its input signals:
n
E total ( x, y ) =
∑ ψ i ( x, y )
i =1
The second plotting mode weights the spatial portion of the signal by its time-domain field value. See the spatial
analyzer documentation for a full explanation.
n
E total ( x, y ) =
∑ E i ψ i ( x, y )
i =1

344 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 5: Spatial analyzer output using plot_type=total (left) and plot_type=weighted (right).

While Figure 5 plots the magnitude of the transverse electric field, it is instructive to examine the field directly. The
VCSEL output beam in Figure 2 is purely real as evidenced by Figure 6 which plots all of the relevant fields with the
plot_mode=real_imag setting.

Figure 6: Real/imaginary field plots for VCSEL output (left), coupler output (center), multimode fiber output (right). Top is a plot of
the real part of the field, bottom is a plot of the imaginary part.

The free-space propagation over 25 µm and the x-axis tilt cause the VCSEL field to become complex, as evidenced by
the coupler output in Figure 6. Recall that when the spatial analyzer is run in plot_type=Weighted mode, the total field
is constructed by weighting each transverse mode by its time-domain field value. Recall also that in the multimode fiber
model, the time-domain field is scaled by the coupling coefficient of each fiber mode with the spatial input. Since each
fiber mode is real (Figure 4) and since the fiber input is complex (Figure 6, center), each coupling coefficient should be
complex. This is reflected in the real/imaginary fiber output shown at the right of Figure 6.
As mentioned previously, the coupler in this simulation produced only one optical signal at its output due to the way the
simulation was configured. Consider the same simulation as Figure 1 except that the VCSEL now emits in both the x
and y polarizations; further, allow the coupler to tilt about both the x and y axes: (φ x = 5 o , φ y = 3 o , φ z = 0) . As
explained in the coupler documentation, this configuration will cause the coupler to produce two output signals (OpSigs)
in response to the single OpSig input. The new configuration requires the following changes:

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 345

VCSEL Parameters
Optical : azimuth 30
Optical : ellipticity 0
Spatial_Modes : mode_polarization xy_ unique
Y_Spatial : y_single_mode_type LG
Y_Spatial : y_l 0
Y_Spatial : y_m 0
Y_Spatial : y_wo 5

Spatial Coupler Parameters

xoffset 5
yoffset 5
distance 25
phi_x 5
phi_y 3

The VCSEL azimuth and ellipticity parameters are set so that 70% of the VCSEL power is coupled into the x
polarization and 30% into the y polarization. See the VCSEL documentation for more details. A zero-order, 5-µm-waist
Laguerre-Gaussian beam is chosen for the VCSEL transverse mode in the y direction. Finally, the phi_y parameter in
the coupler is set to three degrees of tilt about the y-axis. The optical summary produced by the spatial analyzer at the
coupler input is shown below. Clearly, there is one OpSig with both x and y components.

OpSig Spatial Field Summary

---------------------------
Input consists of one OpSig

OpSig #1 has both Ex and Ey time-domain fields and both X and Y spatial fields.
Average power in the x-polarization is 0.00156741
Average power in the y-polarization is 0.000522469
wavelength=820 nm
startTime=0 s

The summary at the coupler output is:

OpSig Spatial Field Summary

---------------------------
Input is a linked list of 2 OpSigs.

OpSig #1 has both Ex and Ey time-domain fields and both X and Y spatial fields.
Average power in the x-polarization is 0.00156311
Average power in the y-polarization is 3.26118e-008
wavelength=820 nm
startTime=0 s
OpSig #2 has both Ex and Ey time-domain fields and both X and Y spatial fields.
Average power in the x-polarization is 0
Average power in the y-polarization is 0.0005185
wavelength=820 nm
i

As expected, the presence of both Ex and Ey at the coupler input together with the rotational offsets has forced the
coupler to produce two output signals.

346 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Both of these signals are passed to the multimode fiber model. Because both signals have both polarizations, a total of
four sets of coupling coefficients are calculated. The spatial analyzer at the fiber output is configured to plot the
weighted fields in both polarizations:

Figure 7: Fiber output in response to VCSEL field with Ex and Ey polarizations and φ x and φ y tilts. Weighted field in the x
direction is on the left, y direction on the right.

Finally, we introduce a new laser/fiber coupling topology to facilitate discussion of the lens model
(examples/optsim/block_mode/multimode/laser_fiber_lens.moml):

Figure 8: Laser/fiber coupling using lens.

The link at the top of Figure 8 shows a system with no lens. The link at the bottom shows the same system with a lens
and coupler inserted between the laser and the fiber. The lens model in Figure 8 has been configured as follows:

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 347

Lens Parameters
focal_length 0.5
aperturing yes
lens_diameter 5
lens_reflectance 0
outer_reflectance 0

In this example, it is assumed that the laser and the lens are packaged together in close proximity with minimal offset and
tilt. The VCSEL output has been purposely sized quite large (40 µm, fundamental mode beam) to illustrate the effect of
the lens. The coupler is intended to model free-space propagation between the VCSEL/lens transceiver and the
multimode fiber input by setting distance = 500 µm. As seen in Figure 9, the beam that emerges from the VCSEL is
quite large. After passing through the lens, however, it is reduced significantly. If no lens is used (top of Figure 8),
since the VCSEL beam is much larger than the multimode fiber, a significant portion of it is truncated (i.e., it misses the
fiber entirely). The average receiver output power in this case is 5.58e-007 V^2 (determined by double-clicking on the
receiver output node). As seen in Figure 9, once the lens/coupler pair is inserted into the link (bottom of Figure 8), the
lens focuses the VCSEL beam down to a size that falls entirely within the fiber face. In this, case, the average receiver
output power increases to 1.17e-006 V^2. Thus, by focusing the VCSEL beam, we have more than doubled the received
power.

Figure 9: Output of VCSEL (left), output of coupler (center), receiver output (right).

348 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.2 Spatial Photodetector Coupling
RSoft/examples/optsim/block_mode/multimode/spatial_photodetector.moml
This is a simple example that demonstrates the spatial attributes of the photodetector and the photoreceiver. Both of
these models are supersets of their standard OptSim counterparts. The main enhancement is the spatial modeling of a
finite detector active area. Consider the topology of Figure 1 (examples/optsim/block_mode/multimode/
spatial_photodetector.moml):

Figure 1: Spatial photodetector topology.

This topology demonstrates the effects of a spatial offset between the multimode fiber output and the photodetector. The
relevant spatial model parameters are listed below:

VCSEL Spatial Parameters

Spatial_Modes : spatial_effects on
X_Spatial : x_single_mode_type LG
X_Spatial : x_l 7
X_Spatial : x_m 2
X_Spatial : x_wo 5

Multimode Fiber Parameters

General : spatial_effects on
General : operational_mode parabolic
General : core_radius 62.5/2

Spatial Photoreceiver Parameters

Spatial : pd_spatial_effects on
Spatial : pd_aperture_type round
Spatial : pd_aperture_dimension 75

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 349

First, we run a simulation with no offset between the fiber and the detector. The output of the coupler and the output of
the receiver are depicted in Figure 2. The VCSEL is driven with a 10 mA constant current source. All noise sources
have been deactivated in the receiver, the transimpedance and filter gain have been set to 1.0, and the bandwidth of the
preamplifier and filter have been set high enough that they do not affect the signal. The quantum efficiency has been set
to 0.8 so that the detector responsivity is approximately 0.53 A/W at the simulation wavelength of 820 nm.
The output of the coupler is an approximately 2.09 mW CW optical signal, while the output of the receiver is a 1.10
mV continuous voltage. The receiver output is the expected value in view of the relation:
Vout = G f Z T ℜPin

where Vout is the receiver output voltage, G f is the filter gain, Z T is the preamplifier transimpedance, ℜ is the detector
responsivity, and Pin is the incident optical power.

Figure 2: Simulation with no fiber/detector offset. Coupler output (left), receiver output (right).

The fiber’s and the coupler’s spatial distributions are shown in Figure 3; as expected, the coupler does not perturb the
signal.

Figure 3: Simulation with no fiber/detector offset: Fiber output (left), coupler output (right).

Now, the spatial coupler is set to shift the fiber output by 25 microns in both the x and y directions:

Spatial Coupler Parameters

General : xoffset 25

350 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

General : yoffset 25

Essentially, we are trying to create a situation similar to that of Figure 4:

Figure 4: Schematic illustration of fiber/detector misalignment.

The coupler output after the shift has been activated is shown in Figure 5. Additionally, Figure 5 depicts the receiver
output waveform after the shift. The output voltage level is now 0.55 mV, a reduction of about 50%.

Figure 5: Coupler output after shift (left), receiver output after shift (right).

The detector portion of the receiver has effected this reduction by scaling the time-domain signal by the percentage of
optical power that falls within the detector’s active area (75 µm diameter).
We can achieve the same effect by using the spatial aperture model and turning off spatial effects in the photoreceiver
(pd_spatial_effects=off), though this is not recommended since there is additional overhead associated with the aperture
model that is neither necessary nor useful for this simulation
(examples/optsim/block_mode/multimode/photodetector_aperture.moml):

Spatial Aperture Parameters

General : aperture_type round
General : dimension 75

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 351

 Figure 6: Fiber/detector offset simulation using spatial aperture model instead of using photoreceiver spatial effects.

Figure 7: Apertured beam (left), receiver output voltage (right).

As seen in Figure 7, in this scenario, the beam is first apertured then photodetected. This is in contrast to the previous
simulation in which the aperturing took place automatically internal to the spatial photoreceiver model.

352 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.3 Connector Simulation
RSoft/examples/optsim/block_mode/multimode/connector_two_fiber.moml
This example shows how the coupler model can be used to simulate an optical connector. A two-fiber simulation is
highlighted in this section. Figure 1 depicts a topology in which a VCSEL is connected to the coupler model.

Figure 1: Simple connector topology.

Attenuation in the connector can be modeled through the insertion_loss parameter in the coupler model. Here, we set
insertion_loss=1 dB. Figure 2 below shows both the VCSEL and connector output power.

Figure 2: VCSEL output (left), coupler output (right).

The steady-state power in the high state is 2.09 mW at the VCSEL output and 1.66 mW at the coupler output, an
attenuation of 1 dB.
Next, we consider a more involved example (examples/optsim/block_mode/multimode/connector_two_
fiber.moml) in which two 300-m-long fibers are concatenated using the coupler model.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 353

 Figure 3: Two-fiber simulation.

Notice the use of the signal-band converter model in Figure 3. Recall that the multimode fiber model produces a linked
list of signals, one for each guided fiber mode. The signal-band converter collapses the linked list into one field so that
its aggregate time-domain power properties can be viewed. Without the converter, the signal analyzer tool will produce
hundreds of separate plots, one for each signal in the linked list (see signal-band converter documentation). For this
simulation, the coupler and the fibers (identical properties for both) have been configured as follows:

Spatial Coupler Parameters

General : xoffset 3
General : yoffset -2
General : distance 5
General : insertion_loss 1

Multimode Fiber Parameters

General : spatial_effects on
General : operational_mode parabolic
General : dispersion 0
General : length 300
General : core_radius 25

The fibers are offset from each other by 3 µm in the x direction and -2 µm in the y direction. The fibers are spaced 5 µm
apart. Finally, the connector imposes 1 dB of insertion loss. The VCSEL produces 2.09 mW of CW power in response
to a steady-state current of 10 mA.
The simulation flow is as follows. The VCSEL output (one spatial mode) is coupled into the first multimode fiber. At
820 nm, this fiber supports 190 guided modes; consequently, the fiber output is a linked list of 190 OpSigs. Each of
these 190 OpSigs is propagated through the coupler model. When the longitudinal distance is nonzero, a beam-
propagation algorithm is employed to model propagation; this can sometimes be quite time consuming. The 190 signals

354 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

emerge from the coupler and arrive at the input to the second multimode fiber. Since the two fibers are identical, the
second fiber also supports 190 guided modes. Multimode inputs (e.g., linked lists of OpSigs) are treated one at a time;
consequently, coupling coefficients are calculated between each of the multimode inputs and each of the guided fiber
modes. For example, 190 coupling coefficients are calculated for the first signal in the linked list, 190 for the second,
and so on. In this case, a total of 190x190=36,100 coupling coefficient calculations are required. This can be extremely
time consuming. The computational overhead can be adjusted somewhat by tailoring the spatial description of the fields
(e.g., the grid spacing, the field domain, the number of points) in many of the models: VCSEL : Spatial_Modes :
mode_default_domain, VCSEL : Spatial_Modes : mode_default_grid_spacing, MultimodeFiber : Parabolic :
mode_default_grid_spacing, MultimodeFiber : Parabolic : mode_default_radius. Turning on SpatialCoupler :
reduce_field can also help matters by eliminating peripheral nulls in the field profiles; however, the reduction process
itself is time consuming and should be used carefully. Figures 4 and 5 show some simulation results:

Figure 4: Single transverse output of VCSEL (left). Weighted spatial field at the first fiber output (right).

Figure 5: Connector output (left). Weighted output of second fiber (right).

Now, the same simulation is run again with a larger offset between the two fibers:

Spatial Coupler Parameters

General : xoffset 13
General : yoffset -12
General : distance 5

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 355

General : insertion_loss 1

The output of the coupler and the second multimode fiber are shown in Figure 6.

Figure 6: Coupler output with larger offset (left), second multimode fiber (right).

The connector output appears as expected; the weighted output of the second multimode fiber, on the other hand, is more
distorted than in the previous case. If one would open the signal plots after the connector and after the second fiber span
she/he can see that the total output power for the second fiber is lower than the input power by approximately 1.26 dB,
whereas in the previous case of smaller offset it is approximately the same as the input power. Both fibers in this
example were assumed to be loss-less (attenuation = 0). As explained in the multimode fiber model documentation, the
fiber modes only form a complete basis well inside the fiber core. This is because OptSim does not model unguided
modes such as lossy or radiation modes. Thus, while significant power does in fact get coupled into the fiber’s guided
modes (Figure 6, right), the large connector offset of this simulation also results in a non-negligible amount of loss (i.e.,
power coupled into unguided modes).

356 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.4 Multimode Inputs to Multimode Fiber
RSoft/examples/optsim/block_mode/multimode/multimode_mux.moml
RSoft/examples/optsim/block_mode/multimode/multimode_compact.moml
RSoft/examples/optsim/block_mode/multimode/multimode_wdm.moml
In OptSim, multimode signals are represented as a linked list of OpSigs. Basically, there is one signal in the linked list
for each unique spatial field object. In this example, we will demonstrate how to construct multimode signals and how
the multimode fiber deals with such signals. Figure 1 (examples/optsim/block_mode/multimode/multimode_
mux.moml) shows one method for constructing a multimode signal.

Figure 1: Topology illustrating construction of multimode signal.

In Figure 1, each VCSEL is identical except for the transverse mode that it emits. For this example, the VCSELs are
configured to emit 5-µm Laguerre-Gaussian beams with azimuthal numbers of 0 and radial numbers of 0-4 (Figure 2).

Figure 2: Five different VCSEL output mode profiles.

Each VCSEL is followed by an attenuator that allows only 20% of the power to pass. Basically, we are using this
topology to emulate a single VCSEL that emits an equal amount of power (one-fifth of the total) into each of five distinct
transverse modes. The five VCSEL signals are combined using the optical multiplexer model in

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 357

Representation=MultiBand mode which concatenates the five independent signals into a linked list. This approach
demonstrates the use of the multiplexer model to generate multimode signals; a short-hand method to accomplish this
will be illustrated later in this section. In this simulation, all of the VCSELs emit light at 820 nm. The fiber is run with
the setting operational_mode=parabolic. At 820 nm, the analytical parabolic fiber model calculates 190 different
guided modes. The aggregate, multiplexed VCSEL spatial signal is depicted in Figure 3.

Figure 3: Five spatial VCSEL signals multiplexed together.

As described in the documentation, the multimode fiber model will produce one signal at its output for each of its guided
modes. The spatial portion of each signal will be the fiber mode itself, while the temporal portion of each signal will be
a copy of the time-domain part of the input signal modified to reflect the effects of delay, dispersion, attenuation, and
coupling. In this case, the multimode fiber model will produce a linked list of 190 spatio-temporal signals.
When the fiber input is multimode, as in Figure 1, the coupling coefficients and delay/dispersion/attenuation
characteristics are calculated between each of the inputs and each of the fiber modes. Thus, in this example, 5 x 190
= 950 sets of calculations are required. Note that while there are five distinct inputs, because they are all at the same
wavelength, the fiber modes themselves are the same for all five sets of calculations. Because the same set of 190 fiber
modes is applied to all five inputs, it would be an inefficient use of memory to replicate these spatial profiles five times
at the output. To circumvent this wasteful situation, the fiber model still produces 190 spatio-temporal signals at its
output. The spatial portion of each signal still consists of a single fiber mode profile; however, the temporal portion of
each output signal reflects the effects of coupling, delay, dispersion, and attenuation between the fiber mode in question
and all five of the input signals. In essence, the multimode fiber model internally multiplexes the time-domain portion
of the five sets of signals. The fact that only 190 signals are produced is seen in Figure 4, which is the first part of the
summary report prepared by the spatial analyzer at the fiber output:

OpSig Spatial Field Summary

---------------------------
Input is a linked list of 190 OpSigs.

OpSig #1 has an Ex time-domain field and a spatial field in the X direction.

Average power in the x-polarization is 0.000319986
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=820 nm
startTime=1.415179223321e-006 s
OpSig #2 has an Ex time-domain field and a spatial field in the X direction.
Average power in the x-polarization is 0.000318985
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=820 nm
startTime=1.415180771222e-006 s
•
•

Figure 4: Spatial analyzer report at fiber output.

358 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Figure 5 depicts the fiber output. Since the aggregate spatial field of Figure 3 is well confined to the core, the fiber
modes form an approximately complete basis. The weighted field profile that emerges from the fiber is different from
Figure 3, however, due to differences between how different modes propagate in the fiber.

Figure 5: Weighted multimode fiber output.

When a multimode input consists of signals at different wavelengths, this procedure cannot be applied because the fiber
modes and their delay characteristics are functions of wavelength. For example, consider a simulation in which two
VCSELs, each lasing at a different wavelength (e.g., 820 nm and 850 nm), are coupled into the multimode fiber in a
manner similar to that depicted in Figure 1 (set the second VCSEL’s wavelength to 850 nm, and disconnect the outputs
of the third, fourth, and fifth VCSELs from their subsequent attenuators). In order to calculate the coupling coefficients
and delay/dispersion relationships between the fiber and the first input, the fiber model first has to determine the fiber
modes and delays at 820 nm. We know from before that there are 190 modes at 820 nm. Because the fiber modes and
delays at 850 nm are different from those at 820 nm, to treat the second VCSEL signal, it is now necessary to calculate
the fiber properties at 850 nm. At this wavelength, there are 171 modes. Thus, the fiber output consists of 190+171=361
different output signals. Figure 6 depicts the summary report produced by the analyzer at the fiber output.

OpSig Spatial Field Summary

---------------------------
Input is a linked list of 361 OpSigs.

OpSig #1 has an Ex time-domain field and a spatial field in the X direction.

Average power in the x-polarization is 0.000410704
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=820 nm
startTime=1.415179223321e-006 s
•
•
•
OpSig #190 has an Ex time-domain field and a spatial field in the X direction.
Average power in the x-polarization is 0
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=820 nm
startTime=1.415250049489e-006 s
OpSig #191 has an Ex time-domain field and a spatial field in the X direction.
Average power in the x-polarization is 9.20443e-006
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=850 nm
startTime=1.415179237711e-006 s
•
•
•
OpSig #361 has an Ex time-domain field and a spatial field in the X direction.
Average power in the x-polarization is 0
X spatial field grid spacing: dx=0.1 um, dy=0.1 um
X spatial field domain: xmin=-50 um, xmax=50 um, ymin=-50 um, ymax=50 um
wavelength=850 nm
startTime=1.415247494907e-006 s

Figure 6: Spatial analyzer output for multiwavelength multimode input.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 359

The topology of Figure 1 can be simplified by using the multimode aspects of the Spatial VCSEL model as seen in
Figure 7. In this figure, the VCSEL is set to run in multimode mode through the parameter Spatial_Modes :
mode_mapping. When this flag is set to multi_from_single, multiple VCSEL output modes are produced by splitting
up the VCSEL output power (refer to the Spatial VCSEL documentation for more detail). The parameter
multi_mode_powers enables the user to set the number of output modes as well as their relative power weightings. To
replicate the previous example (Figure 1), multi_mode_powers=0.2 0.2 0.2 0.2 0.2. (Note the space between each 0.2
entry.) The fact that there are five values means that five output modes should be created. The fact that all five values
are 20% means that the output power should be divided equally among the five modes. The same five modes are chosen
for this example, namely 5-µm Laguerre-Gaussian beams with azimuthal numbers of 0 and radial numbers of 0-4. These
are achieved by setting the following VCSEL parameters under the X_Spatial menu: x_l_lo=0, x_l_hi=0, x_m_lo=0,
x_m_hi=4. The simulation results as generated by
examples/optsim/block_mode/multimode/multimode_compact.moml are shown in Fig. 8.

Figure 7: Compact topology illustrating a multimode input to the fiber model.

Figure 8: Laser output (left), fiber output (right).

As an example of the OptSim multimode fiber model’s ability to handle very large multimode input signals, consider a
coarse WDM simulation in which four VCSELs at 820 nm, 840 nm, 860 nm, and 880 nm each emit power into five
different transverse modes (Figure 9: examples/optsim/block_mode/multimode/multimode_wdm.moml). This
results in a fiber input that consists of 20 modes (Figure 10).

360 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 9: 20-mode simulation.

Figure 10a: Five spatial modes for the VCSEL at 820 nm.

Figure 10b: Five spatial modes for the VCSEL at 840 nm.

Figure 10c: Five spatial modes for the VCSEL at 860 nm.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 361

 Figure 10d: Five spatial modes for the VCSEL at 880 nm.

Figure 10e: Left to right -- Total output of the 820 nm, 840 nm, 860 nm, and 880 nm VCSELs.

Figure 11 shows the total fields at the fiber input and at the output.

Figure 11: Multimode fiber input (left), output (right).

Figure 12 shows the total fields at the demultiplexer outputs.

Figure 12: Spatial fields at demultiplexer output.

At 820 nm, the fiber supports 190 guided modes; at 840 nm there are 171 modes, at 860 nm there are also 171 modes,
and at 880 nm there are 153 modes. Thus, the fiber output in Figure 11 consists of 685 spatial fields. As this example
shows, OptSim is capable of simulating even large multimode systems.

362 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.5 Linear Multimode Fiber Configuration
RSoft/examples/optsim/block_mode/multimode/linear.moml
RSoft/examples/optsim/block_mode/multimode/linear_wdm.moml
The multimode fiber models represents the spatial modes and propagation constants of an optical fiber through various
configurations (e.g., library, parabolic). These configurations operate directly on the optical field, applying various
transforms and operations to model the effects of delay, dispersion, coupling, and attenuation. As explained in the
multimode fiber documentation, it is sometimes advantageous to consider the multimode fiber from a higher-level,
simplified perspective. The linear configuration of the multimode fiber operates on the total optical power incident to
the fiber rather than on the field. The optical phase in the signal is not considered nor are the individual fiber modes nor
their propagation properties. Rather, the linear configuration models the optical fiber as an optical filter with various
parameters to simulate dispersion, delay, and the like. As a reminder, to use the linear configuration, the user must set
spatial_effects=off under the General menu. Figure 1
(examples/optsim/block_mode/multimode/linear.moml) depicts a simple topology.

Figure 1: Topology illustrating linear configuration of the multimode fiber model.

Notice that a linewidth adder is placed directly after the modulator output. In general, the linewidth is an artificial
measurement construct used to quantify the effects of phase noise on the optical field. Linewidth is often characterized
by the rms spread of the optical spectrum. As explained in the documentation for the linewidth adder model, the effects
of linewidth can be specified either by explicitly adding random noise into the optical phase or by setting the linewidth
value in the OptSim optical signal structure to a given value. The multimode fiber model requires the latter (“add by
value”). The linewidth σ src is required by the linear fiber model when computing the power transfer function:

[
E out ( f ) = H ( f ) E in ( f )E in
*
]
(f )
[
H ( f ) = exp − ln(2)(σf ) 2 − j 2πft d ]
σ 2 = σ 2mat + σ 2mod

σ mat = σ src LD
1
σ mod =
γ
 1  cutback
Bim ⋅  
L
If the user erroneously uses linewidth_mode=phase_noise or if the linewidth_mode=value but linewidth=0 (or
equivalently if no linewidth adder model is present), the fiber model will assume σ src is zero and will proceed with the
simulation, but will produce a simulation warning. The required linewidth adder model settings are depicted below.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 363

Here, 5 nm of linewidth is used as an example. The multimode fiber model settings for this simulation are also below.
The intermodal bandwidth Bim was set unrealistically high so that the modal dispersion σ mod would be negligible.

Linewidth Adder
linewidth_model value
linewidth_units wavelength
linewidth 5e-9

Multimode Fiber
General : spatial_effects off
General : dispersion_mode calculate
Linear : Bim 1e32

Figure 2 demonstrates the impact of linewidth by comparing two simulations: one with a 0.001 nm linewidth and one
with a 5 nm linewidth. Clearly, the effect of dispersion on the signal with the larger linewidth is more pronounced.

Figure 2: Fiber input (left), fiber output with 0.001 nm input linewidth (center), fiber output with 5 nm input linewidth (right).

Finally, Figure 3 (examples/optsim/block_mode/multimode/linear_wdm.moml) depicts a more involved four-

channel WDM example. In this simulation, there are four transmitters emitting at 820 nm, 840 nm, 860 nm, and 880 nm.
The optical power in each of the signals is 1 mW, 0.8 mW, 0.6 mW, and 0.4 mW, respectively.

364 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 3: Coarse WDM topology.

Figure 4 shows the fiber input and the output. The multiplexer is run in single-band mode so the four optical channels
are concatenated as a linked list. All four channels are clearly visible at both the fiber input and the fiber output. The
right side of Figure 4 shows the receiver outputs all plotted on one graph.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 365

 Figure 4: Fiber input (left), fiber output (center), four receiver channels superimposed onto one graph (right).

366 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.6 Mode Coupling in Multimode Fiber
RSoft/examples/optsim/block_mode/multimode/mode_coupling/modedist_modecoupling.moml
RSoft/examples/optsim/block_mode/multimode/mode_coupling/pulse_modecoupling.moml
These two examples demonstrate how mode coupling can significantly affect the spatial and transient performance of
multimode fiber. First, load the example modedist_modecoupling.moml, whose topology is shown in Fig. 1. In
this example we consider 8 km of 50-µm diameter multimode fiber with a parabolic index profile. A 1-mW cw signal
with a 2.5-µm Gaussian mode profile is launched into two separate versions of the fiber. In fiber mmf1, mode coupling is
neglected. In fiber mmf2, mode coupling is included, with the highest mode group being dropped during simulation to
represent the effect of differential mode attenuation [1]. By adjusting the offset in spatial_coupler_1, we can
preferentially excite different modes in each fiber and observe how mode coupling affects the redistribution of modes
after propagation.
Open the Parameter Scan Dialog, which should be configured to simulate two different laser-fiber offsets: 0 and 10 µm.
Click Ok. When the simulation is complete, view the normalized radial intensity profiles at the outputs of each fiber via
spatial_analyzer1 (no coupling) and spatial_analyzer2 (coupling). Fig. 2 compares the output profiles for both the center
and offset launches. In the center-launch case (Fig. 2a), we see that mode coupling tends to redistribute power to higher
order modes, thereby resulting in a broadening of the intensity profile as compared to the coupling-free case. In contrast,
for an offset launch (Fig. 2b), in which higher-order modes are preferentially excited at the fiber input, coupling tends to
redistribute power back to the lower order modes, resulting in a smoother and more Gaussian intensity profile. In both
cases, we see that coupling tends to produce outputs that are very similar, indicating that over sufficient distances we
would expect to observe convergence to a single mode distribution [2].
Next, open the example pulse_modecoupling.moml, which is depicted in Fig. 3. In this topology we consider 4
km of 50-µm diameter multimode fiber with a parabolic index profile. A 50-ps pulse with a 2.5-µm Gaussian mode
profile is launched into the fiber. In this case, we will observe how mode coupling redistributes power between different
mode groups, thereby smoothing out the response of the fiber.
Open the Parameter Scan Dialog, which is configured to simulate two different coupling factors, 106 and 108. Click Ok.
When the simulation is finished, you can view the fiber response via SigPlt1. Figure 4 depicts the response in both cases.
In the case of very low coupling (106), we see that intermodal dispersion results in secondary pulsations in the tail of the
output pulse. This result is essentially the same as that observed without any coupling at all. However, with the coupling
coefficient increased to 108, we see that mode coupling tends to smooth out these pulsations as power is exchanged
between higher- and lower-order modes [1],[3].

Figure 1. OptSim topology for comparing mode redistribution at a multimode fiber’s output both with and without mode coupling.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 367

 (a) (b)

Figure 2. Comparison of the normalized radial output intensity profiles for a multimode fiber, both with and without
mode coupling, under (a) center and (b) offset launch conditions.

Figure 3. OptSim topology for comparing a multimode fiber’s pulse response under different mode-coupling conditions.

Figure 4. Comparison of the multimode fiber pulse responses under different mode-coupling conditions.

368 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

References
[1] K. Balemarthy, A. Polley, and S. E. Ralph, “Electronic equalization of multikilometer 10-Gb/s multimode fiber
links: Mode-coupling effects”, Journal of Lightwave Technology, vol. 24, no. 12, pp. 4885-4894, December 2006.
[2] S. Savović and A. Djordjevich, “Optical power flow in plastic-clad silica fibers,” Applied Optics, vol. 41, no. 36, pp.
7588-7591, December 20, 2002.
[3] S. E. Ralph, A. Polley, K. D. Pedrotti, R. P. Dahlgren, and J. A. Wysocki, “New methods for investigating mode
coupling in multimode fiber: Impact on high-speed links and channel equalization,” Technical Digest: SOFM 2006,
pp. 133-138, September 19-20, 2006.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 369

3.7 Encircled Flux Simulation
RSoft/examples/optsim/block_mode/multimode/encircled_flux.moml
As detailed in the documentation for the Encircled Flux Analysis Tool, the encircled flux is a measure of the amount of
optical power that falls within a given radial distance from the fiber axis. In this section, we depict a simple encircled
flux simulation. Consider Figure 1 which illustrates a topology with a multimode fiber and the encircled flux analysis
tool (examples/optsim/block_mode/multimode/encircled_flux.moml).

Figure 1: Topology for encircled flux simulation

The VCSEL has been configured as follows:

VCSEL Spatial Parameters

Spatial_Modes : spatial_effects on
X_Spatial : x_single_mode_type LG
X_Spatial : x_l 0
X_Spatial : x_m 0
X_Spatial : x_wo 5

For this first simulation, the spatial coupler provides no offset. The fiber and the EF analyzer are configured as:

Multimode Fiber Parameters

General : spatial_effects on
General : operational_mode parabolic
General : dispersion 0
General : length 300
General : core_radius radius

Encircled Flux Analyzer Parameters

radius radius
plot_EF Yes
plot_radial_intensity Yes

370 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

accuracy medium

Note that the fiber and the EF analyzer use the symbol table variable radius as seen in Figure 2. As discussed in the
documentation, setting the accuracy to low enables a quick, cursory analysis of the encircled flux. For a more detailed
analysis, the accuracy parameter can be set as needed.

Figure 2: Symbol-table definition of radius variable.

The simulation output is depicted in Figure 3:

Figure 3: Fiber output (left), encircled flux (center), average radial intensity (right).

As a review, the encircled flux and radial intensity are computed as:

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 371

 r

∫
1
EF (r ) = ⋅ 2π r ′I (r ′)dr ′
EFmax
0
d
2πrI (r ) = EFmax ⋅ EF (r )
dr
The encircled flux plot in Figure 3 correctly shows that the integrated power at the fiber axis (r = 0) is zero and that it
rises quickly, peaking at about 8 microns. Because the encircled flux is normalized by its maximum value, it ranges
from 0 to 1.
The same simulation is run with a 10 micron offset in both the x and y directions:

Spatial Coupler Parameters

General : xoffset 10
General : yoffset 10
General : distance 0
General : insertion_loss 0

Figure 4 shows the simulation output that results:

Figure 4: Fiber output (left), encircled flux (center), average radial intensity (right).

As expected, the integrated power begins to increase at the radial position where the fiber field first becomes
nonnegligible.
Consider now an example of a multimode input signal to the fiber. The VCSEL model has been configured to emit four
spatial modes, each with one-fourth of the total power. The modes are described in the file mode_types.txt (Figure
5): Lagurerre-Gaussian beam (azimuthal number 4, radial number 7, beam waist of 5 microns, inverse radius of
curvature of 0), LG(0,0,3,0), LG(1,3,6,0), and LG(11,5,5,0).

4
lg 4 7 5 0
lg 0 0 3 0
lg 1 3 6 0
lg 11 5 5 0

Figure 5: File contents of mode_types.txt.

372 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

VCSEL Spatial Parameters
Spatial_Modes : mode_mapping multi_from_single
Spatial_Modes : multi_mode_powers 0.25 0.25 0.25 0.25
X_Spatial : x_multi_mode_type file
X_Spatial : x_multi_mode_file mode_types.txt

Figure 6: The four output modes of the VCSEL.

The combined VCSEL output, the superposition of the modes shown in Figure 6, is depicted in Figure 7. As seen in this
figure, the encircled flux and radial intensity can be calculated even for highly irregular spatial fields. In this simulation,
xoffset and yoffset are returned to 0.

Figure 7: Total VCSEL output (left), encircled flux (center), average radial intensity (right).

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 373

3.8 Differential Mode Delay
RSoft/examples/optsim/block_mode/multimode/dmd_sweep.moml
In this section, we expand upon the discussion contained in the documentation for the Differential Mode Delay Analysis
Tool. Figure 1 shows a simple topology used to measure the DMD of a multimode fiber
(examples/optsim/block_mode/multimode/dmd_sweep.moml).

Figure 1: DMD simulation topology.

Since DMD is a measure of the fiber’s spatio-temporal impulse reponse, it is important to use an input pulse that
approximates a delta function in both space and time. To this end, we use the mode-locked laser model to produce a 50-
ps-wide Gaussian pulse that has as its spatial content a zero-order Gaussian beam with a 2.5 micron beam waist (Figure
2). We can consider this to be a spatio-temporal point source.

Figure 2: Source characteristics: time (left), space (right).

Mode-Locked Laser Parameters

Optical : pattern Single
Optical : type Gaussian
Optical : peakPower 1e-3
Optical : width 50e-12
Spatial_Modes : spatial_effects on
X_Spatial : x_single_mode_type LG
X_Spatial : x_l 0
X_Spatial : x_m 0
X_Spatial : x_wo 2.5

Recall that the DMD measurement is performed by scanning the optical source across the face of the fiber (Figure 3)

374 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 3: DMD measurement process.

To accomplish this, the xoffset parameter in the spatial coupler is varied from 0 to the fiber’s core radius. (Note that
since the fiber is circularly symmetric, we could just as easily vary yoffset instead). The DMD analyzer requires access
to certain properties of the multimode fiber. To facilitate this process, three symbol-table variables are defined:
length=600 m, radius=15 microns, and shift (initial value of 0). Here, we use an artificially low value for radius
to make the example run more quickly; typical multimode fiber usually has a radius of at least 25 microns. (At 850 nm, a
multimode fiber with a radius of 25 microns supports 171 modes versus 66 modes for a 15-micron-radius fiber).

Figure 4: Symbol table for DMD simulation.

The relevant coupler, fiber, and DMD analyzer parameters are shown below:

Spatial Coupler Parameters

xoffset shift
yoffset 0
distance 0
phi_x 0

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 375

phi_y 0
phi_z 0

Multimode Fiber Parameters

General : spatial_effects on
General : operational_mode parabolic
General : length length
General : core_radius radius

DMD Analyzer Parameters

length length
radius radius
scale_plot yes
power_tolerance 100e-6

The DMD topology makes use of OptSim’s parameter scanning feature. By clicking on the parameter scan icon,

a dialog box is opened (Figure 5):

Figure 5: Parameter scan dialog box.

Basically, the DMD is simulated by using the spatial coupler to shift the laser input by a distance specified by the
variable shift (defined in the symbol table). OptSim’s parameter scanning feature is used to step the shift from 0 to 15

376 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

microns in 2 micron increments (Figure 5). (Typically, the parameter scan is done in 1 micron increments to satisfy the
10 Gb Ethernet standard, but for the sake of time, this example uses 2 micron increments). The parameter scanner runs
one complete simulation for each value of the sweep variable (shift=0, shift=2, …). The DMD analyzer tool has
been designed to store the temporal simulation results after each parameter scanning run, then to plot the aggregate
results after the last scan. Figure 6 shows the results of this simulation:

DMD plot, length=600 m

16

14
Offset from fiber axis (microns)

12

10

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6
Time (ps/m)

Delay vs. Radial Offset

0.4
Pulse Width

Delay Spread

0.3
Time (ps/m)

0.2

0.1
0 10 20
Offset from fiber axis (microns)

Figure 6: DMD simulation results.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 377

3.9 Spreadsheet Model Comparison
RSoft/examples/optsim/block_mode/multimode/spreadsheet_comparison.moml
The most popular design approach in the multimode community is to use the so-called Gigabit Ethernet Spreadsheet
Model. This model, which was created by researchers at Agilent Technologies during the development of the Gigabit
Ethernet standard, is implemented in the Microsoft Excel spreadsheet tool and is distributed without cost. The model
attempts to calculate multimode optical system performance through the use of broad assumptions and simplifications.
Here, we do not use the term simulation since the spreadsheet model is based solely on static algebraic calculations.
The Gigabit Ethernet specification is based on the worst-case performance of all components in the optical link; since it
is extremely unlikely that all components will perform at their worst-case values simultaneously, the standard has been
criticized as being overly conservative. The worst-case performance for a given component is fairly easy to predict; of
significantly more difficulty is the prediction of component performance as a function of multiple external factors. For
example, it is straightforward to state that a multimode fiber will, in the worst case, support 500 MHz-km of bandwidth.
It is well known, however, that the fiber bandwidth can increase or decrease as functions of factors such as the laser/fiber
positioning and the laser field profile. When the goal is to optimize multimode system performance, rather than to
merely accept its lowest grade of performance, a more comprehensive analysis is clearly necessary.
The reasons for the widespread acceptance of the spreadsheet model are obvious. First, it is simple to use; the user
merely inputs several performance parameters and the model outputs the system power margin. As long as the final
result conforms to the standard, engineers feel assured that their designs are in compliance. The simplicity of the model
enables engineers to design links without an understanding of the underlying issues. Second, the model is free; there is
no need to elaborate on this issue. Third, the model has gained widespread acceptance. Despite its shortcomings, the
spreadsheet model continues to be used because there is no compelling alternative.
Since the Gigabit Ethernet standard was based on the spreadsheet model, engineers designing Gigabit Ethernet systems
merely have to comply with the model. In general, these developers have no need for a more comprehensive, accurate
analysis. In this regard, the spreadsheet model is adequate. On the other hand, when engineers wish to analyze the
performance of generic multimode optical links, a more comprehensive modeling capability is required. For example,
the spreadsheet cannot capture such phenomena as the thermal dependence of the laser threshold current nor its nonideal
transient characteristic due to spatial effects. It cannot model the fiber bandwidth reduction due to laser offset, the
effects of misalignment between the fiber and the detector, and the like. Development of the 10 Gigabit Ethernet
standard attempted to resolve these issues with massive amounts of laboratory measurement. Thousands of
representative fibers and transceivers were characterized and empirical figures of merit were developed. Simulation can
clearly alleviate the investment in manpower required for such an undertaking. Unfortunately, these empirical quantities
are neither scalable nor generic. For example, can links designed to these requirements be extended by another 100 m?
Can they be operated not at 10 Gb/s but at 40 Gb/s? If so, what length reduction will be necessary?
One of the deficiencies of the spreadsheet model is that it assumes that all signals are ideal. For example, it assumes that
optical signals will have well-behaved on-off behavior with a specific 20%-80% rise time. It further attempts to model
most of the components with ideal Gaussian transfer functions. Another shortcoming is that many of the input
parameters to the model are actually system output parameters. For example, while the fiber bandwidth is an input
parameter, in reality it is an output function of several variables. The eye opening is a model input; in reality, a model
should produce an output eye as a function of all of the inputs. Similar arguments hold for intersymbol interference; this
is a system performance metric, not an input quantity. The inaccuracies of the assumptions made in the spreadsheet
model are largely compensated for by the Gigabit Ethernet worst-case design philosophy via overly restrictive
performance margins.
By using detailed physical device models and by simulating the actual time-domain waveforms, the OptSim multimode
platform can be used to analyze generic multimode systems. The inputs to the system are the component attributes and
the waveform at the start of the link. The system output is the received power, the output eye diagram and the bit error
rate. Many intermediate quantities can be analyzed along the way. In this example, we will illustrate a comparison
between the OptSim multimode platform and the spreadsheet model.

378 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

For the optical source, the spreadsheet model inputs are the center wavelength (Uc=850 nm), the linewidth (Uw=0.85
nm), the output optical power (Min Launch Power=-9.5dBm), the extinction ratio (Spec ER=9dB), the signal rise time
(Ts 20-80=260ps), the RIN (RIN=-117dB/Hz), the mode partition noise coefficient (MPN k), and the bit rate (Effective
Rate=1389 Mbaud). We used the topology below to model the optical source:

We set the following parameters in OptSim to mimic these requirements:

Model Parameter Value

PRBSGenerator : patternType PRBS
PRBSGenerator : bitRate 1389e6
ElectricalSignalGenerator : driveType on_off_ramp
ElectricalSignalGenerator : Vmin 3.775e-3 A
ElectricalSignalGenerator : Vmax 0.88e-3 A
ElectricalSignalGenerator : tr 260 ps
ElectricalSignalGenerator : tf 260 ps
SpatialVCSEL : wavelength 850 nm
SpatialVCSEL : kf 4.06e-9 W
SpatialVCSEL : tn 2.25e-9 s
SpatialVCSEL : beta 1e-6
SpatialVCSEL : parasitics off
SpatialVCSEL : RIN -117 dB/Hz
LinewidthAdder : linewidth_model phase_noise
LinewidthAdder : linewidth_units wavelength
LinewidthAdder : linewidth 0.85 nm

The OptSim multimode laser model currently does not support mode partition noise; thus, MPN will be set to 0 in the
spreadsheet comparison. The figure below shows a portion of the VCSEL output.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 379

The high value of the VCSEL output is 199.8 µW and the low value is 25.1 µW; this is an extinction ratio of 9 dB. The
average power level that emerges is 0.1122 mW or –9.5 dBm.

Optical Signal Summary

Set = 56
Wavelength = 8.5000000000000001e-007 m
Frequency = 352697009411764.69 Hz
Average = 0.00011216629104260809 W / -9.5013764052872229 dBm
Peak noise density = 0 W/Hz / -Infinity dBm/Hz
Bitrate = 1389000000 bps
Pattern length = 256 bits
Start time = 0 s
Duration = 1.8430525557955363e-007 s
Time step = 5.6245500359971202e-012 s

The connector is modeled by using OptSim’s spatial coupler model. The spreadsheet models connectors by their
insertion loss (Connections=1.5dB); accordingly, we set

Model Parameter Value

SpatialCoupler : insertion_loss 1.5 dB

The multimode fiber is specified by several parameters in the spreadsheet model: the modal bandwidth (BWm=1689
MHz-km), the dispersion slope (So=0.11 ps/nm/nm/km), the zero-dispersion wavelength (Uo=1310 nm), the fiber
attenuation (Atten=3.5 dB/km @ 850 nm), and the fiber length (L=0.8 km). We used the OptSim multimode fiber model
and modeled the delays using the WKB approximation to treat the modes as groups:

Model Parameter Value

MultimodeFiber : spatial_effects on
MultimodeFiber : operational_mode library
MultimodeFiber : length 800 m
MultimodeFiber : dispersion_mode calculate
MultimodeFiber : S0 0.11 ps/nm/nm/km
MultimodeFiber : lambda0 1310 nm
MultimodeFiber : delay method WKB

We depict the fiber simulation below:

380 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

We ran a simulation and measured both the input and the output spectra. The frequency response is plotted below:

The fiber in the above topology was 300 m long and the 3-dB bandwidth was 5.63 GHz; thus, the modal bandwidth is
1689 MHz-km.
The spreadsheet models the receiver with a sensitivity of –17 dBm with a BER of roughly 10-12 (Q=7). The bandwidth
is Rec_BW=1000MHz.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 381

Model Parameter Value
SpatialReceiver : n_thermal YES
SpatialReceiver : pd_quantumEff 0.8
SpatialReceiver : fe_tz 1 V/A
SpatialReceiver : fe_pole 1e9 Hz
SpatialReceiver : n_a0 8.188e-22 A*A/Hz
SpatialReceiver : n_a2 – n_a6 0

For the simulation above, the average optical power at the receiver input is - 17 dBm; the resulting Monte Carlo BER is
1.0005x10-12. This demonstrates that the receiver is properly calibrated. A CW modulated laser is used to ensure that
any ISI effects caused by the VCSEL are not included in the simulation.
We assembled a typical Gigabit Ethernet link in OptSim and simulated it using the parameters described above:

The topology is contained in (examples/optsim/block_mode/multimode/spreadsheet_comparison.moml).

At this point, OptSim does not model mode partition noise in the laser. Similarly, microbends, material nonuniformities,
and other fiber mode-mixing effects are not yet incorporated. Consequently, OptSim cannot currently predict the modal
noise penalty of the link through a physical analysis. Instead, we place an attenuator in front of the multimode fiber and
set its attenuation value to the modal noise penalty of 0.15 dB used in the spreadsheet.
The average launched optical power is –9.5 dBm and the receiver sensitivity is - 17 dBm. By definition, the Gigabit
Ethernet link budget is then 7.5 dB. The simulation shows that the average power at the receiver input is –13.95 dBm,
well above the receiver’s –17 dBm sensitivity. Thus, it would appear that there is a power margin of 3.05 dB. To test
this hypothesis, we put a –2.0 dB attenuator just in front of the receiver which lowers the average received power to –
15.95 dBm -- again well above the sensitivity limit. However, the BER is 4.03x10-11, which is worse than the system
requirement. Since the average received power accounts for all losses in the system, the degradation in BER must be due
to a factor other than attenuation. Judging from the system eye diagram below, intersymbol interference is a likely
cause.

382 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

After some experimentation, we set the attenuator to –1.612 dB. In this case, the average power at the receiver was –
15.57 dBm, which is again well above the receiver sensitivity limit; however, in this case, the BER is equal to the target
1.02x10-12. (It should be noted that to account for ISI in the BER calculation, ISI bits were set to 2 in the BER tester
parameter dialog box.)
Thus, it is clear that the power margin must be determined not from the difference between the average received power
and the receiver sensitivity. Rather, it is the amount of power in excess of the power that is required to produce a BER of
10-12. In this example, then, the true power margin is not 3.05 dB; rather, it is 1.62 dB.
OptSim was able to deduce the power margin implicitly through detailed waveform simulation. On the other hand, the
Gigabit Ethernet spreadsheet model contains explicit quantities called power penalties. One can interpret the power
penalty as the amount of extra power that must be added to the system to maintain the same BER in the presence of a
particular degrading factor. When performing waveform simulation, each model is configured, then the system is
simulated. The simulation output (eye, BER, etc.) accounts for all of the link factors together; thus, it is not always clear
from waveform simulation what the degrading factor is. In the Gigabit Ethernet spreadsheet model, however, power
penalties are explicitly calculated then subtracted from the average received optical power before the margin is
determined. For example, there is an ISI power penalty, a RIN power penalty, a power penalty due to optical eye
closure, etc. Each of these power penalties is determined analytically after making various simplifying assumptions.
While the spreadsheet model provides insight into the individual performance impairments, the price to be paid for this is
a reduction in accuracy due to the necessary assumptions.
While OptSim calculated a power margin of 1.61 dB, the Gigabit Ethernet spreadsheet model calculated a margin of 1.36
dB. Thus, the spreadsheet model was overly pessimistic by 0.25 dB.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 383

The OptSim multimode platform is obviously not limited to the simplistic topologies that we just discussed. It can
address a wide range of simulation scenarios such as analyzing shifts in the laser/fiber offset/tilt, the effect of lenses in
the optical path, thermal and spatial effects in the optical source, differential mode delay, encircled flux, and the like.

References
1. D. G. Cunningham and W. G. Lane, Gigabit Ethernet Networking. Indianapolis, IN: Macmillan Technical
Publishing, 1999.
2. M. C. Nowell, D. G. Cunningham, D. C. Hanson, and L. G. Kazovsky, “Evaluation of Gb/s laser based fibre LAN
links: Review of the Gigabit Ethernet model,” Optical and Quantum Electronics, vol. 32, pp. 169-192, 2000.
3. Gigabit Ethernet Spreadsheet Model: www.ieee802.org/3/10G_study/public/email_attach/All_1250.xls

384 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.10 Arbitrary Refractive Index Profiles
RSoft/examples/optsim/block_mode/multimode/arbitrary_index.moml
The documentation for the multimode fiber model describes the mode solver that is built into OptSim to enable the
simulation of fibers with arbitrary refractive index profiles. In this section, we will show some examples of its usage.
The first mode of operation that we will discuss is the file-based method to specify the refractive index profile. The
figure below (examples/optsim/block_mode/multimode/arbitrary_index.moml) is a simple multimode link
that we will use to demonstrate the use of the mode solver. Note that for this portion of the example, the coupler
parameters are all set to zero (no offset, no tilt, no free-space propagation).

Figure 1: Simple multimode topology.

To enable the file-based mode, the user should set operational_mode=file in the General menu. The example is
currently set up to read in the refractive index from the file parabolic.ipf as specified by the field index_file in the
Index menu. This file is located in the examples/optsim/block_mode/multimode directory. As a reminder,
OptSim will first check for the index file in the present working directory; if it is not located there, it will look in the
directory C:\RSoft\products\optsim\block_mode\data_files. This file describes a parabolic index profile
with a peak index of 1.4142, an index step of 1% and a core radius of 25 microns. The first few lines of this file are:

501 0 50 0 OUTPUT_REAL
1.4141999999999999000000000e+000
1.4141997737279819000000000e+000
1.4141990949117103000000000e+000
1.4141979635505335000000000e+000
As described in the multimode fiber documentation, this corresponds to an index profile that is real, has 501 points
starting at r=0 and ending at r=50 microns.
For this example, the parameters l_max, m_max, lambda_step, and mode_set are left at their default values. By
choosing output_type=index_file in the Test menu, we plot the refractive index profile represented by parabolic.ipf
in Figure 2.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 385

 Figure 2: Refractive index profile represented by the index file parabolic.ipf.

Setting output_type=report in the Test menu, we see that the fiber described by parabolic.ipf has 190 modes at
820 nm. This is the expected result based on the parabolic index simulations conducted in the previous examples (note
that we are simulating a 1 km link in this example).

Multimode Fiber Test Report

===========================
mmf_1 is described via a numerical solution of the scalar radial
Helmholtz equation based on the index profile in the file:
c:/RSoft/examples/optsim/block_mode/multimode/parabolic.ipf

There were a total of 190 modes found at a wavelength of 8.2e-007 m.

(azimuthal #, radial #) delay (s)

----------------------- ---------------------
(0,0) 4.71726427e-006
(0,1) 4.71727018e-006
(0,2) 4.71728204e-006
(0,3) 4.71729988e-006
.
.
.

Using the topology of Figure 1, we examine the spectrum of the signal entering the fiber and the spectrum of the signal
exiting the fiber (Figure 3). Considering only the positive frequencies, we can subtract the output spectrum from the
input spectrum (using a spreadsheet tool, for example) since PowerUnits=dBm in the spectrum analyzer, normalize to 0
dB at DC, and plot the resulting transfer function (Figure 4). Note that to determine the names of the files used to
generate the plots in Figure 3, the user should select Edit->View from the WinPlot menu.

386 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 3: Fiber input spectrum (left), output spectrum (right).

Figure 4: Fiber frequency response.

We see that for this set of conditions, the fiber throughput is slightly higher than 10 GHz. The interested user can
compare these results with those obtained by running this simulation in operational_mode=library mode with the
parabolic_multimode_fiber_library. Since this library was generated with the same index profile, the results
should be comparable.
Another sample index file is contained in the examples/optsim/blockmode/multimode directory. This file,
dip.ipf, contains a profile used to mimic the central-line defect often found in multimode fibers. We repeat the steps
detailed previously to generate Figure 5:

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 387

 Figure 5: File-based refractive index profile used to simulate central dip defect (left), frequency response (right).

The next method to specify the refractive index profile is operational_mode=function. As described in the multimode
fiber documentation, this operational mode follows the general OptSim function evaluation syntax. To enable proper
simulation, the following symbol table entries are generated:

Figure 6: Symbol table entries.

388 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

The actual index function is entered as shown in Figure 7:

Figure 7: Specifying the index function.

Note that r is automatically understood by OptSim in the function definition; note also that core_index_profile and
cladding_index_profile must be equal at the core-cladding interface.
The final index-specification method is operational_mode=alpha. From the perspective of the numerical mode solver,
there is nothing particularly special about the alpha profile. However, because the alpha profile (see multimode fiber
documentation) is so widely studied, users can simulate it in OptSim by specifying only the core_radius, the
peak_index, delta, and alpha. OptSim automatically generates the index function internally. Note that the user could
just as easily generate the profile manually as shown in Figure 8. The result would be the same.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 389

 Figure 8: Alpha profile simulated using operational_mode=function.

We close this example with a discussion of some of the numerical tolerance parameters under the Index menu. As stated
in the multimode fiber documentation, for the most part, users should leave lambda_step and mode_set at their default
values. If the user feels that certain modes that should exist are instead cut-off, he can increase mode_set in an attempt
to force the mode solver to find them. If the user feels that nonphysical delay values are being calculated, he can reduce
lambda_step.
The azimuthal and radial number maxima l_max and m_max must be adjusted through experimentation. For the
parabolic index simulation, we knew a priori that these parameters should be 18 and 9, respectively. Note, however, that
we set l_max=20 and m_max=10; since no modes exist with l = 19, l =20, or m = 10, OptSim simply attempts to solve
for them but determines that the modes do not exist.
As an example, let us set operational_mode=file and use the parabolic.ipf index profile. Set l_max and m_max to
10 and 5 respectively and run a test using output_type=report. In this case, OptSim only finds 122 modes because we
instructed it to stop at the specified maximum values (recall that there are 190 modes total at 820 nm).

Multimode Fiber Test Report

===========================
mmf_1 is described via a numerical solution of the scalar radial
Helmholtz equation based on the index profile in the file:
c:/RSoft/examples/optsim/block_mode/multimode/parabolic.ipf

There were a total of 122 modes found at a wavelength of 8.2e-007 m.

(azimuthal #, radial #) delay (s)

----------------------- ---------------------
(0,0) 4.71726427e-006
(0,1) 4.71727018e-006
(0,2) 4.71728204e-006
(0,3) 4.71729988e-006

390 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 (0,4) 4.71732373e-006
(0,5) 4.71735345e-006
(1,0) 4.71726620e-006
(-1,0) 4.71726620e-006
.
.
.

Now repeat with l_max and m_max set to 3 and 2. This time only 21 modes were found.

Multimode Fiber Test Report

===========================
mmf_1 is described via a numerical solution of the scalar radial
Helmholtz equation based on the index profile in the file:
c:/RSoft/examples/optsim/block_mode/multimode/parabolic.ipf

There were a total of 21 modes found at a wavelength of 8.2e-007 m.

(azimuthal #, radial #) delay (s)

----------------------- ---------------------
(0,0) 4.71726427e-006
(0,1) 4.71727018e-006
(0,2) 4.71728204e-006
(1,0) 4.71726620e-006
(-1,0) 4.71726620e-006
(1,1) 4.71727471e-006
(-1,1) 4.71727471e-006
(1,2) 4.71728917e-006
(-1,2) 4.71728917e-006
(2,0) 4.71726943e-006 .
.
.
.

Unfortunately, there is, in general, no way to know the optimal l_max and m_max settings in advance. One approach is
to set these parameters to extremely large values and to run a simulation. If the located modes have azimuthal and radial
numbers less than these values, the user can easily deduce what l_max and m_max should be for subsequent runs.
However, beware that setting l_max and m_max to large values can result in extremely long simulation times. If, on the
other hand, the located modes have azimuthal and radial numbers equal to l_max and m_max, there is a high probability
that modes exist beyond these values. In this case, the user can increase l_max and m_max and resimulate. This is what
could be referred to as a brute-force technique.

It is quite possible that for some index profiles there are so many modes that in the process of increasing l_max and
m_max, the user’s computer will run out of memory and thus be unable to locate all of the guided modes. When the
brute-force method fails, the strategy no longer becomes one of attempting to find all guided modes. Rather, the focus
shifts to intelligent techniques to determine which guided modes are important and to solve only for those. One
recommended approach is to adjust l_max and m_max, simulate, then observe a measurable parameter. Next, increase
l_max and m_max, and observe the parameter again. This process should be continued iteratively until the measurable
parameter fails to change appreciably.

Using the previous example, simulate each of the following: (l_max, m_max) = (3, 2), (10,5), (15,6), (20,10), and
(25,15). For each simulation, observe the receiver’s temporal output to determine the impact of (l_max, m_max) on
modal dispersion (Figure 9). For these simulations, set xoffset=20 in the spatial coupler model to accentuate the effects
of modal dispersion. Furthermore, set patternLength=2 and pointsPerBit=8 in the mode locked laser model to reduce
the bounds of the simulated data. First note that for these five sets of (l_max, m_max), the number of modes found was
21, 122, 167, 190, and 190. The fact that increasing (l_max, m_max) beyond (20, 10) does not increase the number of
modes is a good indication of the proper upper limit values. The pulse broadening also does not change appreciably
beyond (20, 10).

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 391

 (l_max, m_max) = (3, 2), 21 total modes (l_max, m_max) = (10, 5), 122 total modes

(l_max, m_max) = (15, 6), 167 total modes (l_max, m_max) = (20, 10), 190 total modes

(l_max, m_max) = (25, 15), 190 total modes

Figure 9: Receiver output for various values of (l_max, m_max).

392 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.11 Gigabit Ethernet Link Design Based on 1000BASE-
SX, -LX Standards
RSoft/examples/optsim/block_mode/multimode/gigabit_Ethernet/
A few example topologies were developed for Gigabit Ethernet Physical Medium Dependent (PMD) sublayer according
to IEEE 802.3 Standard [1]. Total eight examples were created for all eight scenarios described in Ref. [1], “Clause 38,
Physical Medium Dependent (PMD) sublayer and baseband medium, type 1000BASE-LX (Long Wavelength Laser) and
1000BASE-SX (Short Wavelength Laser)”. The schematics files for these examples are accessible in examples folder
examples/optsim/block_mode/multimode/gigabit_ethernet/:

1000BASE_SX_625MMF_220m_160M.moml
1000BASE_SX_625MMF_275m_200M.moml
1000BASE_SX_50MMF_500m_400M.moml
1000BASE_SX_50MMF_550m_500M.moml
1000BASE_LX_625MMF_550m_500M.moml
1000BASE_LX_50MMF_550m_400M.moml
1000BASE_LX_50MMF_550m_500M.moml
1000BASE_LX_SMF_5000m.moml
The first four topologies (_SX) cover short-wavelength laser examples at 850 nm operational wavelength, and the next
four (_LX) topologies cover long-wavelength laser examples at 1300 nm. Next, suffix _625MMF or _50MMF refers to
multimode fiber with 62.5- or 50-micron diameter. Suffix _SMF stands for single-mode fiber case. Suffix _XXXm
refers to maximum operational distance of the topology, and last suffix, _XXXM, specifies in case of multimode fiber
the modal bandwidth in units of (MHz x km). For example, 1000BASE_SX_625MMF_220m_160M.moml describes
the Gigabit Ethernet link operating at wavelength 850-nm, having maximum reach of 220 m, using multimode fiber with
62.5-um core diameter and 160 MHz x km modal bandwidth. Figure 1 shows the topology snapshot for this example. It
also corresponds to other seven example layouts of 1000BASE-X PMD block diagram given in Fig.38-1 of Ref. [1].
Next we describe in details the set up for one particular example mentioned above. The other examples were constructed
following the same approach. First, we discuss the link layout, and then deal with the settings for transmitter, receiver,
and the transmission medium (fiber and patch cords).

Figure 1. Topology snapshot of 1000Base-SX example with 62.5-um MMF of 220-m.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 393

Layout
The standard topology is depicted in Figure 1. It consists of a transmitter block, a transmission medium block and a
receiver block. The transmitter block is comprised of PRBS data generator, NRZ Driver (electrical signal generator),
externally modulated laser (VCSEL), linewidth adder, and optical power normalizer. Output signal from the transmitter
is connected to a patch cord (Connector1) represented as coupler model. Output from the transmitter is also connected to
the PIN photodetector and eye diagram analyzer to see the transmitter eye diagram. Output from the first connector is
sent to Multiplot Analyzer block and is set as TP2 (test point #2). Further the signal is launched to the fiber and then to
the second connector (patch cord). Output from the Connector2 is then sent to another Multiplot Analyzer and set as
TP3. Also, the output from the Connector2 is connected to the Receiver and then to the BER Tester blocks. The Eye
Diagram Analyzer after the receiver gives the received eye.

Transmitter
The parameters of components in transmitter block were adjusted to satisfy optical specifications given in Table 38-3 of
[1]:
Bitrate signaling speed - bitrate: 1.25 Gbps
Wavelength - lambda: 850 nm (range 770-860 nm)
RMS spectral width (max) - linewidth: 0.85 nm
Average launch power (min) - TXPower: -9.5 dBm
Rise/fall time (max) – tr_time: 260 ps at λ > 830nm or 210 ps at λ < 830nm
Extinction Ration (min) - ExtRatio: 9 dB
RIN (max) - RIN: -117 dB/Hz
The parameter names in bold fonts correspond to the respective entries in the Global Symbols table. Figure 2 shows
simulated transmitter eye diagram along with transmitter eye mask specified in Figure 38-3 in Ref.[1]. Figure 3 shows
the signal plot for the first few bits at the output from transmitter (TP2). Also, the laser output spatial filed satisfies
radial overfilled (ROFL) launch condition.

Figure 2. Simulated transmitter eye diagram along with transmitter eye mask

394 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 TP2 Signal Plot

-8
-9

Signal Magnitude (dBm)

-10
-11
-12
-13
-14
-15
-16
-17
0 1 2 3 4
x10-8
Time (s)

Figure 3. Signal plot for transmitter output

Receiver
The parameters of components in the receiver block were adjusted to satisfy optical specifications given in Table 38-3 of
[1]:
Receiver Sensitivity at BER=10^-12: -17 dBm
Receive electrical filter 3-dB upper
cutoff frequency (max) – RX_BW: 1500 MHz
The receiver sensitivity is not a direct input parameter in receiver block and one has to adjust receiver noise contribution
to achieve a desirable BER at the given input power. In order to calibrate the receiver sensitivity we have connected the
transmitter directly to the receiver at given input power (-17 dBm) and adjusted the thermal noise contribution from the
transimpedance amplifier of the receiver (parameter n_a0) until the simulated BER of 10^-12 is achieved.

Fiber and Connectors

The topology’s transmission medium consists of a fiber span and patch cords (or connectors). Connectors specifications
are given by offset and total loss: ConnectorsOffset = 4.5 um, ConnectorsLoss = 1.5 dB.
Fiber optical characteristics are given in Table 38-12 [1]:
Operating distanse – MMF_Length: 2-220 m
Fiber core diameter – MM_Diameter: 62.5 um
Fiber attenuation – MMF_Loss: 3.75 dB/km
Modal bandwidth (min, overfilled launch): 160 MHz x km
Zero dispersion wavelength - ZDW: 1340 nm (range 1320-1365-nm)
Dispersion slope (max) - DispSlope: 0.11 ps/nm^2 km
All of the parameters except the modal bandwidth can be set directly in the multimode fiber model. The modal
bandwidth of the fiber is defined by its refractive index profile. The index profile of graded-index multimode fiber is
modeled by power-law formula:
  r 
α 1/ 2
n1 ⋅ 1 − 2∆    , r≤a
   a  
n( r ) =  

 n ⋅ (1 − 2∆ )1/ 2 = n , r>a
 1 2

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 395

Here n1 is a peak index, ∆ – index step, and a - core radius. We used for peak index and index step the values typical for
62.5-um MMF, i.e. peak_index =1.5, indexStep = 2 %. The power-law parameter α (alpha) is the one to be
optimized to provide required modal bandwidth of the fiber. At α = 2 we have an ideal parabolic profile which maximum
modal bandwidth.
To find out what is the value of parameter alpha required a simple topology for modal bandwidth measurement can be
used – see Figure 4 for the layout. It consists of a short pulse source (mode-locked laser), a fiber, a receiver, and
spectrum and transfer function analyzers. A single short pulse (50 ps) launched into the fiber will provide its impulse
response, and the Fourier transform will give us corresponding frequency response.
Since the target modal bandwidth is 160 MHz x km at a distance of 220 meters, the 3-dB bandwidth of the frequency
response should be 727 MHz. By optimizing the parameter alpha and maintaining the laser output field satisfying fiber
overfilled launch condition we found out that at alpha = 2.112, we achieve the target bandwidth. Figure 5 shows a plot
of frequency response out of Transfer Function Analyzer.

Figure 4. Simple schematic layout for modal bandwidth calculation

Transfer Function (Frequency Response)

0
Transfer Function [dB]

-1

-2

-3

-4

-5

-6
0 2 4 6 8 10 12 14 16
x108
Frequency [Hz]

Figure 5. Frequency response of multimode fiber after 220 m

Link Performance
After the topology setting is complete, we can run the simulation. For the given example, the computed BER is
9.94x10^-14 which is better than the BER requirement of 10^-12. According to Ref. [1], the current 1000Base-SX link
should have an unallocated margin of 0.84 dB. Figure 6 shows the receiver eye diagram and the Fig. 7 show signal plot
and spectrum at TP3.

396 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 BER Tester Decision Eye
x10-5

Decision Level Offset (V)

2

-1

-2

-4 -2 0 2 4 6 8 10
x10-10
Decision Time Offset (s)

Figure 6. Receiver Eye Diagram

TP3 Signal Plot TP3 Wavelength Spectrum

-10

-10 -20
Signal Magnitude (dBm)

-30
-12 Power (dBm)
-40
-14
-50

-16 -60

-70
-18
-80
-20
-90
0 1 2 3 4 5 6 8499 8500 8501
x10-8 x10-10
Time (s) Wavelength (m)

Figure 7. Signal plot and spectrum at TP3 (before receiver)

BER vs Length

10-12

10-13
BER

10-14

10-15

10-16

10-17
100 120 140 160 180 200 220
FIber Length (m)

Figure 8. Link BER versus fiber length

The link performance can then be recalculated at different operating points, such as distance, laser wavelength, launch
power, etc. For example, if one wants to re-calculate system performance at different operational distances, he/she can

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 397

perform a parameter scan over the length of the fiber. For demonstration, here we run a parameter scan over the fiber
length ranging from 100 m to 220 m with 20-m steps. Figure 8 shows resulting BER dependence on the fiber length.

Reference
1. IEEE Std 802.3™-2002 (Revision of IEEE Std 802.3, 2000 Edition): http://standards.ieee.org/getieee802/802.3.html

398 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.12 1000BASE-BX (IEEE 802.3ah) Bi-directional EFM
System
The objective of this application note is to demonstrate simulation example based on IEEE 802.3ah specifications for a
1000BASE-BX Bi-directional Ethernet in the First Mile (EFM) system using standard single mode fiber.

RSoft/examples/optsim/block_mode/multimode/gigabit_ethernet/1000BASE_BX.moml
In June 2004, IEEE approved the IEEE 802.3ah EFM. The specifications used for this application note are based on
public domain information from Reference 1. The PHY in IEEE 802.3ah has three sub-layers:
1. Physical Coding Sub-layer (PCS): The forward error correction (FEC) is optional.
2. Physical Media Attachment (PMA): Takes care of the synchronization of burst signals.
3. Physical Medium Dependent (PMD): Specifies power, wavelengths, on/off times of laser diode and eye
patterns.
The PMD is newly defined for GE-PON but PMA and PCS come from other gigabit Ethernet specifications.
Figure 1 depicts this schematic.

Figure 1. Simulation setup schematic for the 1000BASE-BX EFM

The system consists of a 10-km standard single mode fiber for bi-directional transmission. The bitrate is 1.25 Gbps. The
upstream and downstream wavelengths are 1310nm and 1490nm respectively. The transmitted power is –8.2 dBm and
the minimum extinction ratio is better than 6 dB. The RIN at the laser is –117.5 dB/Hz. The 10% - 90% rise/fall times
for the downstream and upstream transmitters are 405 ps and 331 ps respectively. The fiber attenuation is 0.4 db/km. The

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 399

fiber model provides coherent solution and behaves like the standard single mode fiber model with additional support for
backward propagating signal and noise because of the upstream transmission over the same fiber.
Figure 2 shows transmitted optical signals for downstream and upstream.

Figure 2. Transmitted Signals: 1410-nm Downstream (top) and 1310-nm Upstream (bottom)

Figure 3 shows received eye diagram and corresponding BER for the downstream receiver and the figure 4 shows eye
diagram and BER for the upstream receiver.

400 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 3. Downstream Eye Diagram and BER

Figure 4. Upstream Eye Diagram and BER

If the forward-error-correction (FEC) is required, the BER tester model has options for pre-defined FEC and super-FEC
as well as for the custom FEC schemes.
In conclusion, this example demonstrates modeling bi-directional GE-PON based on IEEE 802.3ah EFM standard.

Reference
1. IEEE P802.3ah EFM Task Force, http://grouper.ieee.org/groups/802/3/efm/index.html, June 2004.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 401

3.13 10 Gigabit Ethernet Link Design Based on 10GBase
Standards.
RSoft/examples/optsim/block_mode/multimode/10_gigabit_Ethernet/
Here we demonstrate 10 Gigabit Ethernet standard links design according to specifications given in IEEE 802.3ae
Standard [1], in particular Clause 52, “Physical Medium Dependent (PMD) sublayer and baseband medium, type
10GBASE-S (Short Wavelength Serial), 10GBASE-L (Long Wavelength Serial), and 10GBASE-E (Extra Long
Wavelength Serial)” and Clause 53,” Physical Medium Dependent (PMD) sublayer and baseband medium, type
10GBASE-LX4”.
10 Gigabit Ethernet links can be divided into two categories: serial - 1 channel at 10 Gbps, (Clause 52), and parallel
(CWDM), e.g., LX4 – 4 channels at 2.5 Gbps, (Clause 53).
We have created one example for 10GBASE-LX4 link with long-wavelength laser source at 1300-nm and multimode
fiber link of 50-um core diameter and 500 MHz km bandwidth, and one example for 10GBASE-SR link with short-
wavelength laser source at 850-nm and multimode fiber link of 50-um core diameter and 500 MHz km bandwidth.
The corresponding schematics files 10GBASE_SR.moml and 10GBASE_LX4.moml are given in examples directory
examples/optsim/block_mode/multimode/10_gigabit_ethernet/.

Figure 1. Snapshot of topology for 10GBASE-SR example with 50-um MMF of 82-m – file 10GBASE_SR.moml

10GBASE-SR Link
The standard topology for 10GBASE-SR similar to the one for Gigabit Ethernet and is show in Figure 1. Here PMD
transmitter combines PRBS data generator, NRZ Driver (electrical signal generator), laser source, external modulator
laser, linewidth adder, and optical power normalizer. Output signal from transmitter is connected to patch cord

402 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

(Connector1) represented as coupler model. Output from transmitter is connected as well to PIN receiver and eye
diagram analyzer to show transmitter eye diagram and receiver sensitivity. Output from first connector is sent to
Multiplot Analyzer block and set as TP2 (test point #2). Also the same output is connected to Encircled Flux Analyzer
to monitor the encircled flux requirement. Further the signal is launched to fiber and then to second connector. Output
from Connector2 is sent to another Multiplot Analyzer and set as TP3. Then output from Connector2 is inserted into
Receivers and to BER Tester block. Eye Diagram Analyzer after receiver is available as well.
The parameters of components in transmitter block were adjusted to satisfy optical specifications given in Table 52-7 of
[1]:
Bitrate signaling speed - bitrate: 10.3125 Gbps
Wavelength - lambda: 850 nm
RMS spectral width (max) - linewidth: 0.85 nm
Average launch power (min) -TXPower: -7.5 dBm
Extinction Ration (min) - ExtRatio: 3 dB
RIN (max) - RIN: -128 dB/Hz

In addition the transmitter output should satisfy the encircled flux requirements - the encircled flux at 19 µm shall be
greater than or equal to 86% and the encircled flux at 4.5 µm shall be less than or equal to 30% when measured into
Type A1a (50/125 µm multimode) fiber per ANSI/TIA/EIA-455-203-2001.
The parameters of components in receiver block were adjusted to satisfy optical specifications given in Table 38-3 of [1]:
Receiver Sensitivity at BER=10-12: -7.5 dBm
Receive electrical filter 3-dB upper
cutoff frequency (max) – RX_BW: 12.3 GHz
The receiver sensitivity is a not a direct input parameter in receiver block and one has to adjust receiver noise
contribution to achieve a desirable BER at given input power. In order to calibrate the receiver sensitivity we have
connected the transmitter directly to the receiver at given input power (-7.5 dBm) and adjusted the thermal noise
contribution from transimpedance amplifier in receiver (parameter n_a0) till simulated BER arrived at 10^-12.
The topology’s transmission medium consists of fiber span and patch cords (or connectors). Connectors specifications
are given by offset and total loss: ConnectorsOffset = 5 um, ConnectorsLoss = 1.5 dB.
Fiber optical characteristics are given as:
Operating distanse – MMF_Length: 82 m
Fiber core diameter – MM_Diameter: 50 um
Fiber attenuation – MMF_Loss: 3.5 dB/km
Modal bandwidth (min, overfilled launch): 500 MHz x km
Zero dispersion wavelength - ZDW: 1310 nm (range 1320-1365-nm)
Dispersion slope (max) - DispSlope: 0.11 ps/nm^2 km

As in the case for Gigabit Ethernet the fiber index profile here is adjusted to provide given modal bandwidth.
After the topology setting is complete we can run the simulation. For given example the computed BER is 6.53e-05 i.e.
(Q = 17.75 dB) better that BER requirement of 1e-12 (and equivalent Q = 16.95 dB). According to Ref.[1] current
10GBase-SR link at operational distance 82 meter should have 5 dB allocation for penalties and additional 0.5 dB
insertion loss is allowed.
Figure 2 shows the transmitter eye diagram and TP2 signal waveform plot. Figure 3 shows the encircled flux plot for the
fiber input signal. The encircled flux musk is applied to demonstrate that optical signal satisfy the encircled flux
requirement - 4.5-um < 30% and at 19-um > 86%. Finally, Figure 4 shows the received eye diagram.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 403

 Transmitter Eye Diagram TP2 Signal Plot
-6

0.14

Signal Magnitude (dBm)

-7
0.12
Signal (V)

-8
0.10

0.08 -9

0.06
-10
2 4 6 8 10 12 0 2 4 6 8 10 12
x10-11 x10-9
Time (s) Time (s)

Figure 2. Transmitter eye diagram (left) and signal plot (right) at TP2 .

Encircled Flux vs. r

1.0
0.9

0.8
0.7
Encircled Flux

0.6
0.5

0.4

0.3
0.2

0.1
0.0
0 10 20 30
r

Figure 3. Encircled flux plot with the flux mask at 4.5-um < 30% and 19-um > 86%.

Receiver Eye Diagram

0.10

0.09

0.08
Signal (V)

0.07

0.06

0.05

0.04

3 4 5 6 7 8 9 10 11 12 13
x10-11
Time (s)

Figure 4. Receiver Eye Diagram.

404 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

10GBASE-LX4 Link
The standard topology for 10GBASE-LX4 is shown at Figure 5 and is similar to the one for Gigabit Ethernet, except the
case that PMD transmitter consists of four transmitter blocks at different wavelengths and a multimplexer, and receiver
block consist of demultiplexer and four receivers. Each transmitter block is represented as a Compound Component,
which combines PRBS data generator, NRZ Driver (electrical signal generator), laser, modulator, linewidth adder, and
optical power normalizer. Multiplexed output signal from transmitter is connected to patch cord (Connector1)
represented as coupler model. Output from individual transmitter is connected as well to PIN receiver and eye diagram
analyzer to show transmitter eye diagram. Output from first connector is sent to Multiplot Analyzer block and set as TP2
(test point #2). Further the signal is launched to fiber and then to second connector. Output from Connector2 is sent to
another Multiplot Analyzer and set as TP3. Then output from Connector2 is inserted into Demultiplexer and then to four
Receivers and to BER Tester blocks. Eye Diagram Analyzer after receiver is available as well.

Figure 5. Snapshot of topology for 10GBASE-LX4 example with 50-um MMF of 300-m – file 10GBASE_LX4.moml.

The parameters of components in transmitter block were adjusted to satisfy optical specifications given in Table 53-7 of
[1]:
Bitrate signaling speed - bitrate: 3.125 Gbps
Wavelength – lambda_ch1: 1275.6 nm
lambda_ch2: 1300.2 nm
lambda_ch3: 1324.7 nm
lambda_ch4: 1349.2 nm
RMS spectral width (max) - linewidth: 0.62 nm
Rise/fall time (max) – tr_time: 120 ps

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 405

 Average launch power (min) -TXPower: -0.5 dBm per channel
Extinction Ration (min) - ExtRatio: 3.5 dB
RIN (max) - RIN: -120 dB/Hz
Here four wavelengths are equidistant at 24.5 nm channel spacing and occupy total bandwidth ~ 75 nm in the range 1269
– 1356 nm.
The parameters of components in receiver block were adjusted to satisfy optical specifications given in Table 53-8 of [1]:
Receiver Sensitivity at BER=10-12: -10.5 dBm
Receive electrical filter 3-dB upper
cutoff frequency (max) – RX_BW: 3.75 GHz
The receiver sensitivity is a not a direct input parameter in receiver block and one has to adjust receiver noise
contribution to achieve a desirable BER at given input power. In order to calibrate the receiver sensitivity we have
connected the transmitter directly to the receiver at given input power (-10.5 dBm) and adjusted the thermal noise
contribution from transimpedance amplifier in receiver (parameter n_a0) till simulated BER arrived at 1e-12.
The topology’s transmission medium consists of fiber span and patch cords (or connectors). Connectors specifications
are given by offset and total loss: ConnectorsOffset = 3.6 um, ConnectorsLoss = 1.5 dB.
Fiber optical characteristics are given as:
Operating distanse – MMF_Length: 300 m
Fiber core diameter – MM_Diameter: 50 um
Fiber attenuation – MMF_Loss: 1.5 dB/km
Modal bandwidth (min, overfilled launch): 500 MHz x km
Zero dispersion wavelength - ZDW: 1310 nm (range 1320-1365-nm)
Dispersion slope (max) - DispSlope: 0.11 ps/nm^2 km
As in the case for Gigabit Ethernet the fiber index profile here is adjusted to provide given modal bandwidth.
After the topology setting is complete we can run the simulation. For given example the computed BER for all four
channels is better that BER requirement of 1e-12.
Figure 6 shows the transmitter and receiver eye diagrams for channel 1 and Figure 7 - TP2 signal waveform plot. Figure
8 shows received eye diagrams for other three channels and Figure 8 shows calculated BER for all four channels.

Transmitter Eye Diagram - Channel 1 Receiver Eye Diagram - Channel 1

0.12 0.21

0.10 0.18
Signal (V)

Signal (V)

0.15
0.08

0.12
0.06

0.09
0.04

1 2 3 4 1 2 3 4
x10-10 x10-10
Time (s) Time (s)

Figure 6. Eye diagrams at transmitter (left) and receiver (right) for channel 1.

406 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 TP2 Signal Plot

Signal Magnitude (dBm)

-1

-2

-3

0 1 2
x10-8
Time (s)

Figure 7. Optical waveform plot at TP2.

Channel 2 RX Eye Diagram Channel 3 RX Eye Diagram Channel 4 RX Eye Diagram

0.16 0.16 0.16

0.14 0.14 0.14

0.12 0.12 0.12

Signal (V)

Signal (V)

Signal (V)
0.10 0.10 0.10

0.08 0.08
0.08

0.06
0.06 0.06

1 2 3 4 1 2 3 4 1 2 3 4
x10-10 x10-10 x10-10
Time (s) Time (s) Time (s)

Figure 8. Receiver eye diagrams for channels 2, 3, and 4.

10-12

10-13

10-14
BER

10-15

10-16

10-17

1 2 3 4
Channel number

Figure 9. BER for four channels.

Reference
1. IEEE Std 802.3ae™-2002 (Amendment to IEEE Std 802.3, 2002 Edition).
http://standards.ieee.org/getieee802/802.3.html

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 407

3.14 Refractive Index Profile Distortions and Multimode
Fiber Links Performance - Cambridge 81-Fibers
Statistical Model.
RSoft/examples/optsim/block_mode/multimode/CambridgeModel/CambridgeModel_case2.moml
RSoft/examples/optsim/block_mode/multimode/CambridgeModel/CambridgeModel_case2.moml
The goal of multimode graded-index fiber manufactures is to get a fiber refractive index profile as close as possible to
ideal parabolic profile that theoretically provides the highest bandwidth. However, various index profile defects of fiber
preform (center defects as tips and dips, deviation of power-law parameter α from 2, core/cladding interface defects,
bulges, etc.) can significantly reduce the modal bandwidth and, hence, degrade its performance. The characteristics of
multimode fiber links may vary greatly from one link to another.
The upgrade of MMF links bit rates from 1 Gb/s to 10 Gb/s and beyond requires a change in launch condition - the
overfilled launch (OFL) based on LED light sources has been replaced with restricted mode launch (RML) by using
lasers, like VCSELs. This can be explained that gigabit LED sources when focused for injection into MMF often only
illuminate a small area at the core center of the fiber. Hence, only a small number of low order modes are excited. If
there exists in the fiber refractive index profile a localized distinct peak or dip at the core center (or other defect), the
lowest order modes may have largely different propagation times when compared with higher order modes. The
increased mode dispersion that results can thus cause link failures, the observed effective link bandwidth being
substantially below the OFL specification. In order to overcome this problem, restricted launch schemes have been
developed. Center launch schemes, which only excite the fundamental propagating mode, can achieve high bandwidths
but these require tight alignment tolerances and are very sensitive to mode coupling effects that occur due to
perturbations in the refractive index profile. Alternatively, offset launch schemes, in which a large number of higher
order modes propagate, have been shown to offer a more reliable technique for maintaining stable, high bandwidth
operation.
Upgrade of existing Ethernet links from 1 to 10 Gb/s should satisfy the performance requirement for 300-m transmission
reach for the great majority of fibers that are currently installed. The approach to study of upgrade feasibility at 10
Gigabit Ethernet IEEE 802.3aq Standard development task force [1-3] is to apply statistical analysis of a large number of
worst-case multimode fiber channels for launch condition and link reach.
In this example we demonstrate how ModeSYS can be applied to use this statistical approach based on so-called
Cambridge 81-fibers model [1-3].
The approach of Cambridge model is to consider a set of pre-determined index defects that are believed to be
representative for installed base of multimode FDDI-grade fibers, and to calculate fiber characteristics for those different
distorted index profiles. The fiber unperturbed power-law index profile is given as:
  α 1/2

 r 
 n1 ⋅  1 − 2 ∆    , r ≤ a
   a   (1)
n(r) =   α = 2 - parabolic profile

 n ⋅ (1 − 2 ∆ ) 1 / 2 = n , r > a
 1 2

where n1, ∆, and a are the peak index in the core, the index step, and the core radius, respectively.
The following types of distortions are being considered and each takes three different values:
Mixed power-law distortion
- alpha inner (for r < a/2) α 1 = {1.89, 1.97, 2.05};
- alpha outer (for a > r ≥ a/2) α 2 = {1.89, 1.97, 2.05};
Center distortion

408 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

- none, tip, dip. Center defect is modeled as a Gaussian shape with 3-dB width of 3 microns and amplitudes +0.002 (tip)
or –0.004 (dip)
Core-cladding interface distortion
- none, sudden, exponential. Width of the defect is set to 3 microns.
All possible combinations of these 4 defects with 3 different values for each give us 3^4 = 81 fiber index profiles. Figure
1 demonstrates the index profile with these different distortions.

Figure 1. Refractive index profile with deviations from ideal parabolic profile.

A ModeSYS user can input the fiber index profile n(r) into a fiber model using one of three available methods: alpha,
function, and file. The first method implement power-law representation of index profile (see Eq.(1)) where user
specifies power-law parameter alpha.
The second method allows users to specify the refractive index profile as an analytical function. Two fields are provided
for this purpose: core_index_profile and cladding_index_profile. Then, for example, refractive index given by Eq.(1)
can be specified numerically through the following settings:
core_index_profile = n1*sqrt(1-2*delta*(r/radius)^alpha)
cladding_index_profile = n1*sqrt(1-2*delta)
Here, n1, delta, and radius represent the peak value of the index in the core, the index step, and the core radius,
respectively. Radial position is given by r. Using this method we can in principle recreate an index profile for each of 81
models of Cambridge model with the help of some special functions available in simulator (e.g. step function u(x)). For
example, in the case of different alpha parameters for inner and outer region and peak center defect (with given peak
amplitude Cpeak and 3-dB width Cwidth) the functional representation of index profile can be given as:
core_index_profile = n1*sqrt(1-2*delta*(r/radius)^alpha_inner)*u(radius/2-r) +
+ n1*sqrt(1-2*delta*(r/radius)^alpha_outer)*u(r-radius/2) +
+ Cpeak*exp(-4*ln2*r^2/Cwidth^2)
The last method, file configuration, enables user to specify the refractive index profile in a text file. This is the most
flexible method and works for any arbitrary index profile and we use this method in this example. 81 fiber index profiles

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 409

are created according to Cambridge model for FDDI-graded fiber with fiber diameter a=62.5 microns, peak index n1=1.5
and index step ∆=0.0172. These index profiles are stored in files with names sequentially from index1.ipf to index81.ipf,
and have a format specified in multimode fiber model description. Below you may see the structure of index1.ipf :

1500 0 62.500 0 OUTPUT_REAL

1.496000000
1.496001277
1.496005120
1.496011528
1.496020493
...
In addition to these 81 fibers models we added an ideal parabolic index profile in file index0.ipf, which can be useful for
comparison studies of unperturbed fiber. The file CambridgeModel_info.txt provides information on each index profile
and what kinds of distortions/defects were included.
In this example we demonstrate the effect of index distortion on link performance only on two sample index profiles: (1)
a sample of distorted profile with tip at the center and sudden distortion at the edge, index16.ipf; (2) a sample of
distorted profile with dip at the center and exponential decay at the edge, index75.ipf. These two index profiles are given
in the example directory. All of 81 fibers index profiles are provided and given in zipped file
81fibers_index_profile.zip. Reader can use any of other index profiles for additional studies.

Figure 2. Schematic CambridgeModel_case1.moml for studying multimode link bandwidth with fiber index distortions.

Now we are ready to start investigation of the effect of index distortions on fiber performance. First we study a simple
schematic given at Figure 2, which allows us to find fiber characteristics such as impulse and frequency responses,
modal delays, and modal bandwidth for given index profile and offset. The schematic consists of laser source (pulse
generator), coupler (laser-fiber connector), multimode fiber, receivers, and plotting tools such as spectrum, signal, and
transfer function analyzers. To open this schematic please go to RSoft examples directory and open the file
examples\optsim\block_mode\multimode\CambridgeModel\CambridgeModel_case1.moml. Laser model
generates a single pulse and allows users to specify pulse duration, beam width, beam spatial composition, and many
other parameters. The coupler model allows to specify radial, angular, and longitudinal offsets.
We specified the launched signal out of laser as 50-ps temporal pulse (corresponding to 10 Gb/s bitrate) with spatial
mode profile taken as fundamental Laguerre-Gaussian mode LG(l=0,m=0) with 4.2 um of beam width (corresponds to
FWHM=7 um), i.e. to provide single-mode restricted mode launch (RML). The laser wavelength is 1300 nm.
Multimode fiber is set to file operational mode and in parameter index_file we specify the name of file with refractive
index – either index16.ipf, or index75.ipf. Fiber length is set to 300 m. Output of the simulation will be fiber delay and
bandwidth, frequency and impulse responses.

410 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Refractive Index - Fiber #16

1.50

Refractive Index
1.49

1.48

0 10 20 30 40 50 60 70
Radial Coordinate (um)

Figure 3. Refractive index profile for fiber #16 with tip in the center and sudden drop at core-cladding interface.

First we run the example for fiber #16. Its index profile is shown at Figure 3. We will be modifying the launching
condition by changing parameter offset in a coupler model. The following offset values are used: zero, 5, 10, 15, 20, and
25 microns. Figure 4 shows relative group delay of fiber at different offset positions. Figure 5 shows frequency
responses and Figure 6 shows impulse responses at different offsets.

Figure 4. Relative group delays for fiber #16 at different launch offsets.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 411

 Figure 5. Frequency responses for fiber #16 at different launch offsets.

lnput Pulse
x10-4
10
9
8
7
Signal (Real) (V)

6
5
4
3
2
1
0
6 7 8 9 10
x10-9
Time (s)

Offset 0-um Offset 5-um Offset 10-um

x10-4 x10-4 x10-4
10 5 3
9
8 4
7
Signal (Real) (V)

Signal (Real) (V)

Signal (Real) (V)

2
6 3
5
4 2
1
3
2 1
1
0 0 0
6 7 8 9 10 6 7 8 9 10 6 7 8 9 10
x10-9 x10-9 x10-9
Time (s) Time (s) Time (s)
Offset 15-um Offset 20-um Offset 25-um
x10-4 x10-4 x10-4
3 3 4

3
Signal (Real) (V)

Signal (Real) (V)

Signal (Real) (V)

2 2

1 1
1

0 0 0
6 7 8 9 10 6 7 8 9 10 6 7 8 9 10
x10-9 x10-9 x10-9
Time (s) Time (s) Time (s)

Figure 6. The impulse responses of multimode fiber #16. The top plot is for input signal and the next six plots are impulse responses
at different launch offsets: 0,5,10,15,20, and 25 microns.

412 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Next, we run the example for fiber #75. Its index profile is shown at Figure 7. Figure 8 shows relative group delay of
fiber at different offset positions. Figure 9 shows frequency responses and Figure 10 shows impulse responses at
different offsets.

Refractive Index - Fiber #75

1.50

Refractive Index
1.49

1.48

0 10 20 30 40 50 60
Radial Coordinate (um)

Figure 7. Refractive index profile for fiber #75 with dip in the center and exponential drop at core-cladding interface.

Figure 8. Relative group delays for fiber #75 at different launch offsets.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 413

 Figure 9. Frequency responses for fiber #75 at different launch offsets.

Offset 0-um Offset 5-um Offset 10-um

x10-4 x10-4 x10-4
5 3 3

4
Signal (Real) (V)

Signal (Real) (V)

Signal (Real) (V)

2 2
3

2
1 1

0 0 0
6 7 8 9 10 6 7 8 9 10 6 7 8 9 10
x10-9 x10-9 x10-9
Time (s) Time (s) Time (s)
Offset 15-um Offset 20-um Offset 25-um
x10-4 x10-4 x10-4
3 3 3
Signal (Real) (V)

Signal (Real) (V)

Signal (Real) (V)

2 2 2

1 1 1

0 0 0
6 7 8 9 10 6 7 8 9 10 6 7 8 9 10
x10-9 x10-9 x10-9
Time (s) Time (s) Time (s)

Figure 10. The impulse responses of multimode fiber #75 at different launch offsets: 0,5,10,15,20, and 25 microns.

After that we study the effect of index distortions on eye diagrams in data-modulated multimode link. For this task we
use the second schematic given in example directory - it is shown in Figure 11. To open this schematic, please go to the
file examples\optsim\block_mode\multimode\CambridgeModel\CambridgeModel_case2.moml. The
schematic consists of data generator, direct modulated laser source, coupler (laser-fiber connector), multimode fiber,
receivers, and plotting tools. The transmitter is set to 1.25 Gb/s and fiber length is 500 meters.
By running this schematic with two fiber profiles – index16.ipf and index75.ipf - and different launch offsets the
following results can be produced. Figures 12 and 14 show eye opening of this link versus offset for fibers #16 and #75,
respectively. In both cases the eye opening degrades at small offset of 5 microns and then starts to improve at higher
offsets. This is in agreement with fiber frequency responses given in Figures 5 and 9. Figures 13 and 15 show
corresponding eye diagrams.

414 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 11. Schematic CambridgeModel_case2.moml for studying multimode link eye diagrams with fiber index distortions.

Eye Opening for fiber #16

x10-5
6

4
Eye Height (V)

0
0 10 20 30
offset

Figure 12. Eye opening for link with fiber #16 at different launch offsets.

offset=0 um offset=5 um offset=10 um

x10-5 x10-5 x10-5
11
10 10 10
9 9 9
8 8
8
7 7
Signal (V)

Signal (V)

Signal (V)

7
6 6
6
5 5
5
4 4
3 4
3
2 3
2
1 2
1
1
2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
x10-10 x10-10 x10-10
Time (s) Time (s) Time (s)

offset=15 um offset=20 um offset=25 um

x10-5 x10-5 x10-5
11
10 10 10
9 9 9
8 8 8
7 7 7
Signal (V)

Signal (V)

Signal (V)

6 6 6
5 5 5
4 4 4
3 3 3
2 2 2
1 1
1

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
x10-10 x10-10 x10-10
Time (s) Time (s) Time (s)

Figure 13. Eye diagrams for link with fiber #16 at different launch offsets: 0,5,10,15,20.and 25 microns.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 415

 Eye Opening for fiber #75
x10-5
6

Eye Height (V)

4

1
0 10 20 30
offset

Figure 14. Eye opening for link with fiber #75 at different launch offsets.

offset=0 um offset=5 um offset=10 um

x10-5 x10-5 x10-5
11
10 10 10
9 9 9
8 8
8
7 7
Signal (V)

Signal (V)

Signal (V)
7
6 6
6
5 5
5
4 4
3 4
3
2 3
2
1 2
1
1
2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
x10-10 x10-10 x10-10
Time (s) Time (s) Time (s)

offset=15 um offset=20 um offset=25 um

x10-5 x10-5 x10-5

11
10 10 10
9 9 9
8 8 8
7 7 7
Signal (V)
Signal (V)

Signal (V)

6 6 6
5 5 5
4 4 4
3 3 3
2 2
2
1 1
1

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
x10-10 x10-10 x10-10
Time (s) Time (s) Time (s)

Figure 15. Eye diagrams for link with fiber #75 at different launch offsets: 0,5,10,15,20.and 25 microns.

Finally we want to demonstrate that more complete statistical studies can be performed using the simulator. Reader can
use all 81–fibers index profiles and run the parameter scan simulation with input file name as a scanning variable. In
order to do it one has to define in the Symbol Table two variables: count parameter k = 1 and string parameter
index_file = sprintf("index%d.ipf",intRound(k)). Then in a fiber model, in the field for parameter
index_file, instead of the file name put this string variable index_file. Now one can perform the parameter scan
over parameter k with values from 1 to 81. For each run multimode fiber will use different index profile file:
index1.ipf, index2.ipf, and so on.
Figures 16 and 17 show the results of such a parameter scan for all 81 fibers at zero offset. Figure 16 demonstrates modal
delays for all fibers. Values for relative delays spread from –3.5 ps/m to 2.5 ps/m. Figure 17 shows the frequency
responses for all 81 fibers. The spread of frequency responses is from 810 MHz (fiber #16) to 19.3 GHz (fiber #32).
From a frequency response one can derive a modal bandwidth (in units MHz×km ) by scaling the calculated frequency
response from 300 meters to 1 km. Then modal bandwidth will range from 243 MHz×km to 5790 MHz×km.

416 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 16. Fiber delays at zero offset for all 81-fibers index profiles.

Frequency Response for 81-Fibers at Zero Offset

0
Transfer Function [dB]

-1

-2

-3

0 1 2
x1010
Frequency [Hz]

Figure 17. Frequency responses at zero offset for all 81-fibers index profiles.

References
1. M. Webster, L. Raddatz, I. H. White, and D. G. Cunningham, “A Statistical Analysis of Conditioned Launch for
Gigabit Ethernet Links Using Multimode Fiber”, J. of Lightwave Technology, vol.17, p.1532, 1999.
2. D.G.Cunningham and W. G. Lane, Gigabit Ethernet Networking. Indianapolis, IN: Macmillan Technical Publishing,
1999.
3. IEEE P802.3aq 10GBASE-LRM Task Force, http://www.ieee802.org/3/aq/public/index.html

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 417

3.15 Vortex Launch to Multimode Fiber Link
RSoft/examples/optsim/block_mode/multimode/vortex_launch_example.moml
In multimode fiber links the launch condition of the optical input signal can have a significant effect on link performance
[1-2]. Depending on the fiber refractive index profile and link bitrate the different types of launch - e.g., overfilled,
restricted-mode center or offset, vortex launches – can be found to be most efficient.

Figure 1. Picture of different launch conditions: overfilled, restricted-mode center, restricted-mode offset, and vortex launches. Black
circle - fiber cross-section, red - fiber input launch.

In case of overfilled launch, the laser (LED) beam spot size is about equal to or larger than fiber radius. In case of
restricted mode launch, the beam spot is less than MMF radius and usually is of the order of SMF radius. The vortex
launch provides maximum radial intensity away from the fiber center, similar to donut launch but with smoother change
of intensity.
The multimode fiber manufacturing process can have variances in the fiber profiles that present themselves as various
defects, e.g., peak or dip defect near the center of the fiber. If then the input signal is focused to the center of the fiber, a
small number of low order modes are excited and these modes may have largely different propagation times when
compared with higher order modes. As a result the increased mode dispersion can cause link failures. In order to
overcome this problem, different launch schemes have been developed [1-3]. Center launch schemes, which only excite
the fundamental propagating mode, can achieve high bandwidths but these require tight alignment tolerances and are
very sensitive to mode coupling effects that occur due to perturbations in the refractive index profile. Alternatively,
offset launch schemes, in which a large number of higher order modes propagate, have been shown to offer a more
reliable technique for maintaining stable, high bandwidth operation. Other methods for exciting higher order modes
include an angular tilt to the launch fiber, an overfilled launch, and vortex launch. Most of these methods are similar in
that they all strive to excite the skew rays in the fiber without exciting the low order axial modes where the imperfections
are dominant.

Figure 2. Schematic for vortex launch.

Overfilled and restricted mode launch conditions are being studied in other examples. Here we demonstrate the example
of vortex launch into multimode fiber.

418 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Figure 1 shows a simple schematic setup to create a vortex launch. This schematic is given in a file
c:\Rsoft\examples\optsim\block_mode\multimode\vortex_launch_example.moml. It consists
of a laser source and vortex lens. Spatial Analyzers are added to plot optical field magnitude and phase. The schematic
also has a block for multimode fiber that is not connected to lens initially. We discuss the purpose of this fiber later.
The laser source has a spatial component constructed as fundamental Gaussian mode (Laguerre-Gaussian mode LG00)
with beam spot size of 25 microns. That represents a (radial) overfilled launch condition. Output from laser is connected
to vortex lens model, which applies vortex transformation of phase front and focusing (defocusing) of incoming signal.
The focal length is set to 2 mm. One can run simulations for specified vortex order m, or run a simulation parameter scan
for multiple values of m. Figures 3 and 4 show results of simulation of parameter scan for m= 0, 2, 4, 6, 8.
Figure 3 shows radial intensity of optical signal output from vortex lens for different values of m. One can see that for
non-zero vortex orders the peak of intensity shifts away from center. So, for example, at m = 2, the peak shifts to ~ 3
microns, and for m = 6 to ~5.5 microns. Figure 4 shows phase of output signal for different values of vortex order.
In contour plots for phase we used for clarity black-and-white color scale instead of default spectrum color scale. To
change a color scale user can either enter command /cscl”bw” in Winplot script, or go to Winplot menu Options ->
3D Data Display -> Color Scale. It will open a file chooser; go to the folder PLOTDIR and choose file bw.scl. For
more information on color maps and scales for contour plots see User Guide Ch.10, Appendix 10.9.

Radial Intensity
vortex
1.0
order
0.9 m=0
0.8
m=2
0.7
m=4
0.6
P (a.u.)

0.5 m=6

0.4
m=8
0.3
0.2
0.1
0.0
0 10 20 30
r (microns)

Figure 3. Radial intensity of optical field output from vortex lens for different values of vortex order.

If we launch here the output from vortex lens directly to multimode fiber then the modes not at the center but away from
the center by 3-6 microns (i.e. higher-order modes) will be more excited.
If higher values of intensity peak shift are needed then one can try further to optimize the vortex launch condition by
adjusting beam spot size of laser, focal length, and vortex order.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 419

 Figure 4. Optical signal phase for vortex order m=2,4,6,8.

An alternative and an efficient way to increase the radial peak shift is to add a MMF jumper – a short piece of multimode
fiber with graded-index profile. Optical signal propagating in graded-index fiber will further shift its peak from a center
due to the vortex nature of its phase front.
Figure 5 shows modified schematic for launch setup where we now connect the vortex lens to a short multimode fiber
jumper. Fiber’s length is only 0.5 meter and its radius is 25 microns. Next we can repeat the simulations with a fiber for
different values of vortex order.

Figure 5. Schematic for vortex launch with multimode fiber jumper connected.

420 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Radial Intensity
vortex
1.0
order
0.9 m=0
0.8
m=2
0.7
m=4
0.6

P (a.u.) 0.5 m=6

0.4
m=8
0.3
0.2
0.1
0.0
0 10 20 30
r (microns)

Figure 6. Radial intensity of optical field output from fiber for different values of vortex order.

Figure 7. Output signal from fiber - spatial optical field magnitude and phase for vortex order m=0.

Figures 6, 7, and 8 show the results of simulations parameter scan for m = 0, 2, 4, 6, 8 for schematic with MMF jumper.
Figure 6 shows radial intensity of optical signal output from fiber. One can see that these radial shifts are significantly

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 421

higher now. So, at m = 2, the peak shifts to ~ 7 microns, and for m = 6 to ~13.5 microns. Figure 7 shows spatial field
intensity and phase of fiber output signal for m = 0 and Figure 8 for m = 2, 4, 6, 8.
The vortex launch from MMF jumper then can be inserted into multimode fiber link.

Figure 8.Output signal from fiber - spatial optical field magnitude and phase for vortex order m=2,4,6,8.

422 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

References
1. D. G. Cunningham and W. G. Lane, Gigabit Ethernet Networking. Indianapolis, IN: Macmillan Technical
Publishing, 1999.
2. M. Webster, L. Raddatz, I. H. White, and D. G. Cunningham, “A Statistical Analysis of Conditioned Launch for
Gigabit Ethernet Links Using Multimode Fiber”, J. of Lightwave Technology, vol.17, p.1532, 1999.
3. E. G. Johnson, J. Stack, and C. Koehler, “Light Coupling by a Vortex Lens into Graded Index Fiber”, J. of
Lightwave Technology, vol.19, no.5, p.753 (2001)

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 423

3.16 MATLAB Cosimulation: Vortex Lens Example
RSoft/examples/optsim/block_mode/multimode/matlab/MatCosim_VortexLens.moml
RSoft/examples/optsim/block_mode/multimode/matlab/VortexLens.m
MATLAB cosimulation within the context of a ModeSYS design can be a powerful means for implementing custom
components that operate upon the transverse modes of optical signals within a multimode simulation. This example
demonstrates the use of a MATLAB model for a vortex lens and compares the results to those generated by OptSim’s
built-in vortex lens block.
Within OptSim, load the file MatCoSim_VortexLens.moml, which contains the schematic shown in Fig. 1. This
example is based on the design and settings described in the “Vortex Launch to Multimode Fiber Link” application note
(please refer there for any applicable references). A cw laser (SpCWLaser1) produces an optical signal with a Gaussian
mode whose spot size is 25 µm. This signal is connected to two vortex lens models: MatlabVortexLens1 is a CCM that
invokes the vortex lens model contained within VortexLens.m, and Vortex1 is OptSim’s built-in Vortex Lens block.
VortexLens.m implements the vortex-lens transfer function as described in [1], which is the same model implemented
within the built-in block. Unlike the built-in model, however, VortexLens.m does not account for power loss due to
aperturing or reflectance. By opening the parameter dialog for MatlabVortexLens1, you may adjust the MATLAB lens
vortex order (vortex_order), focal length (focal_length in mm), and index (lens_index). Also, note that under the
Spatial tab, spatial_handling is set to matrix in order to ensure that spatial fields at the lens input are passed to MATLAB
as matrices. Finally, the remainder of the schematic is comprised of Spatial Analyzers for plotting the magnitude and
phase of transverse modes both before and after the lenses.

Figure 1. OptSim topology for comparison of the MATLAB and built-in vortex lens models.

In this example, both lenses are configured to have a focal length of 2 mm, an index of 1.4, and a vortex order
configurable via the Global Symbol m. In addition, Vortex1 is configured with zero reflectance and no aperturing, in
order to allow an apples-to-apples comparison between the two models. By default, the schematic is configured with m =
4. Run a single simulation and then compare the lens outputs, shown in Fig. 2, via Spatial Analyzers spatial_analyzer2
(the MATLAB lens output) and spatial_analyzer3 (the Vortex1 lens output). As you can see, the outputs of the two

424 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

models are in agreement. You may also run a scan simulation which sweeps m from 0 to 8 in increments of 2. The
results in this case are also in agreement.

(a) (b)

Figure 2. Comparison of vortex lens model outputs for m = 4: (a) MATLAB model, (b) built-in model.

References
1. E. G. Johnson, J. Stack, and C. Koehler, “Light coupling by a vortex lens into graded index fiber”, J. of
Lightwave Technology, vol. 19, no. 5, p. 753-758, May 2001.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 425

3.17 Spatial BeamPROP Interface: Waveguide Example
RSoft/examples/optsim/block_mode/multimode/beamprop_interface/soi_ribwaveguide.moml
RSoft/examples/optsim/block_mode/multimode/beamprop_interface/soi_rib.ind
In this example, we use the Spatial BeamPROP Interface to simulate the use of a silicon-on-insulator (SOI) rib
waveguide for coupling of an externally modulated laser to multimode fiber. The waveguide in question is based on the
design presented in [1], and can be found in the index file soi_rib.ind. Figure 1 depicts a top view of the waveguide.
The waveguide has an input/output width of 14 µm, which tapers to 8 µm in the central region. The total waveguide
length is 6 mm, with 4 mm devoted to the central region. The transverse index profile of the waveguide in this central
region is depicted in Fig. 2. The substrate is silicon (with an index of 3.5), on top of which is a 1-µm layer of SiO2 (1.5
index). The waveguide core is also silicon, separated from the surrounding air by a 0.5-µm layer of SiO2.
To view the multimode link in which this waveguide is used, open the OptSim file soi_ribwaveguide.moml. The link
topology is shown in Fig. 3. The link consists of the following sub-components: a transmitter consisting of a 1310-nm
externally modulated laser driven by a PRBS-modulated electrical signal, a Spatial Coupler (Coupler1) that simulates
misalignment of the transmitter and rib waveguide, the rib waveguide, simulated via a call to BeamPROP using the
Spatial BeamPROP Interface and the file soi_rib.ind, another Coupler (Coupler2) to simulate any misalignment
between the waveguide and multimode fiber, 300 meters of 50-µm multimode fiber, and a receiver, coupled to the
multimode fiber via another Coupler (Coupler3).

Figure 1. BeamPROP layout of an SOI rib waveguide.

426 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 2. Waveguide index profile at z = 3 mm. Material indices are: purple (air) – 1.0; blue (SiO2) – 1.5; red (Si) – 3.5.

Figure 3. OptSim topology for the simulation of a multimode link using an SOI rib waveguide for transmitter-fiber coupling.

To illustrate the operation of the waveguide, run a single simulation of this topology. Figure 4 shows the optical signal’s
spatial profile at the input and output of the waveguide. In this example, the input is a Gaussian beam with a spot-size
parameter of 4 µm. As can be seen, the resulting output signal’s transverse mode shape is defined by the modal
properties of the waveguide, and is no longer Gaussian.
Of particular interest in this topology is the impact of the waveguide on the overall link performance. For example, how
does the link BER vary as a function of transmitter-waveguide alignment or the transmitter output beam’s spot-size
parameter? To answer these questions, we will make use of OptSim’s Scan capabilities. First, open OptSim’s Scan dialog
and set the Inner Loop Variable to wgoffset. wgoffset controls the vertical misalignment of the transmitter and
waveguide (set within the component Coupler1). An offset of 6 µm roughly corresponds to alignment of the transmitter
output beam with the center of the waveguide. Make sure the Starting Value for this variable is 2, the End Value is 10,
and the Increment is 2. Click Ok to run the simulation. When the simulation is complete, the BER Tester block BERT
should produce as one of its outputs the plot of Fig. 5(a), which shows the link BER as a function of wgoffset. As can be
seen, at a value of 6 µm, the BER is a minimum, and gets progressively worse as the transmitter output is misaligned up
or down relative to the waveguide.
Finally, open the Scan dialog again, this time setting the Inner Loop variable to wo. This variable determines the spot-
size parameter of the laser output (set within the component CWLaser). Leave the remaining dialog values the same and

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 427

click Ok to run the simulation. The new BER plot from BERT should correspond to Fig. 5(b). As can be seen, the plot
suggests optimum link operation for a spot-size parameter no larger than 4 µm.

(a) (b)

Figure 4. (a) 4-um Gaussian spot at waveguide input. (b) Waveguide output after 6 mm.

(a) (b)

Figure 5. Simulated link BERs as a function of (a) transmitter-waveguide vertical offset and (b) laser output spot size.

428 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

As this example again demonstrates, the Spatial BeamPROP Interface makes it possible to simulate complex device
geometries in the context of a link simulation. Feel free to further experiment with the topology to study the effects of
variations in other design parameters, such as waveguide-fiber alignment, receiver sensitivity, etc.

References
1. U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib
waveguides,” Photonics Technology Letters, vol. 8, no. 5, pp. 647-648, May 1996.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 429

3.18 Spatial BeamPROP Interface: Lens Example
RSoft/examples/optsim/block_mode/multimode/beamprop_interface/lens_comparison.moml
RSoft/examples/optsim/block_mode/multimode/beamprop_interface/thin_lens.ind
The Spatial BeamPROP interface is a powerful block for modeling a wide range of optical components in the context of
a multimode link simulation. The interface lets a multimode simulation in OptSim call RSoft’s BeamPROP for the BPM
simulation of devices with arbitrary three-dimensional index profiles. This example illustrates the use of the interface for
the accurate simulation of a double-convex lens.
Consider a lens with a 220-µm focal length and a diameter of 20.8 µm. For an input Gaussian beam with a 5-µm spot
size parameter and flat phase front, the thin-lens approximation [1],[2] (neglecting aperturing effects) predicts a
minimum output spot-size parameter of 4.61 µm at a distance of 32.99 µm beyond the central plane of the lens. To
demonstrate the limits of this approximation, we have implemented a spherical double-convex lens in BeamPROP with
the geometry shown in Fig. 1. This lens can be viewed in the file thin_lens.ind. The front and back lens radii are
10.34 and –11.374 µm, respectively, the lens diameter is approximately 20.8 µm, the lens thickness is roughly 16.95 µm,
and the lens material index is 1.517. The resulting focal length in the thin-lens approximation would be 220 µm. In
BeamPROP, the lens resides between z = 0 and z = 16.95 µm, and we will simulate propagation from z = 0 to z = 20 µm.
As we will see, the thin-lens approximation does not apply in this case.

Figure 1. BeamPROP layout of double-convex lens.

To compare the thin-lens and BPM approaches side-by-side, open the OptSim example lens_comparison.moml, the
topology of which is shown in Fig. 2. In the top branch of the topology, the built-in Thin Lens and Spatial Coupler
models are used to simulate the propagation of a VCSEL output Gaussian beam through a thin lens with a 220-µm focal
length and a diameter of 20.8 µm, followed by free-space propagation. In the bottom branch, the Spatial BeamPROP
Interface is used instead to simulate this combination in BeamPROP using the file thin_lens.ind. First, we will see
how the lens-coupler combination performs. Open the Parameter dialog for the Spatial Coupler block and set the
distance parameter equal to 32.99 µm. Next, run a single simulation. Figure 3(a) depicts the VCSEL output spatial
profile (via SpatialAnalyzer1), while Fig. 3(b) depicts the resulting output profile (via SpatialAnalyzer2) after the lens
and free-space propagation. The thin lens model predicts a final spot-size parameter of 4.6 µm, consistent with the value
predicted by theory. Next, set the distance parameter of the coupler to 9.68 µm, which corresponds to the distance from
the lens central plane to the output plane in our BeamPROP simulation. Re-run the simulation. Figure 4(a) depicts the
output of the lens-coupler combination, while Fig. 4(b) shows the corresponding output from the Spatial BeamPROP

430 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

Interface (via SpatialAnalyzer3). As can be seen, the BPM calculations predict a smaller spot size at this distance, in
contrast to the thin-lens results.

Figure 2. OptSim topology for comparison of thin-lens and BeamPROP-lens models.

(a) (b)

Figure 3. (a) 5-um Gaussian VCSEL output. (b) Focused spot at a distance of 32.99 µm from the thin lens.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 431

 (a) (b)

Figure 4. Comparison of simulated output beam at 9.68 µm from the (a) thin-lens and (b) BeamPROP-lens models.

In this example, the spot size of the input beam is of a size comparable to the BeamPROP-simulated lens’s diameter and
thickness. Under such conditions, it is not surprising that the thin-lens approximation would break down. Cases such as
these reveal the importance of using a more detailed BPM simulation, such as that available via the Spatial BeamPROP
Interface, when simulating certain components in a multimode link.

References
1. J. W. Goodman, Introduction to Fourier Optics, 2ndEd. New York, McGraw-Hill, 1996.
2. J. T. Verdeyen, Laser Electronics, 3rd Ed. New Jersey, Prentice Hall, 1995.

432 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.19 Spatial CODE V Interface: Lens Example
RSoft/examples/optsim/block_mode/multimode/codev_interface/codev_lens.moml
RSoft/examples/optsim/block_mode/multimode/codev_interface/lens_design.seq
RSoft/examples/optsim/block_mode/multimode/codev_interface/bsp_commands.seq
RSoft/examples/optsim/block_mode/multimode/codev_interface/lens_fullsim.seq
The Spatial CODE V interface is a powerful block for modeling a wide range of optical components in the context of a
multimode link simulation. The interface lets a multimode simulation in OptSim call CODE V for an analysis of an
optical device via either Beam Synthesis Propagation (BSP) or FFT Beam Propagation (BPR). This example illustrates
the use of the interface for the BSP simulation of a double-convex lens. Specific details on CODE V, including
descriptions of BSP and BPR, can be found in the CODE V Reference Manuals.
In this example, we will perform a ModeSYS simulation which includes a spherical double-convex lens designed in
CODE V. The front and back lens surface radii are 10.34 and –11.374 µm, respectively, the lens thickness is 16.95 µm,
and the lens material index is 1.517. We will simulate this lens in response to an input Gaussian beam with a 5-µm spot
size and a flat phase front incident directly on the front lens surface. We will take the output at 3.05 µm after the back
lens surface. Given that the lens resides between z = 0 and z = 16.95 µm, we will essentially be simulating propagation
from z = 0 to z = 20 µm.
Within OptSim, load the file codev_lens.moml, which implements the schematic shown in Fig. 1. In this design, the
VCSEL produces an output Gaussian beam with a spot size of 5 µm. This signal is passed to the Spatial CODE V
Interface block SpCodeV1, which will be used to simulate our CODE V lens design. Spatial Analyzers SpatialAnalyzer1
and SpatialAnalyzer2 can be used to view the transverse mode profiles before and after the lens.
To see how SpCodeV1 is configured, open its parameter dialog. As you can see, we have configured the interface to
automatically (codev_sequence set to auto) configure and perform a BSP simulation (propagation set to BSP) using
the specified lens and user sequence files, as well as default BSP settings (as specified under the BSP tab). Parameter
lens_file specifies that the model should use the lens defined in the sequence file lens_design.seq, while parameter
user_seq_file is set equal to bsp_commands.seq. The lens design uses the parameters discussed above, while the user
sequence file includes additional commands for configuring the BSP simulation in order to more accurately simulate the
lens.
Next, run a single simulation and compare the optical signal’s transverse mode profiles before and after the lens via
Spatial Analyzers SpatialAnalyzer1 and SpatialAnalyzer2, respectively. As shown in Fig. 2, the lens focuses the input
beam considerably even after only 3.05 µm of propagation beyond the back lens surface. If you would like to review the
simulation sequence and data files automatically generated by the Spatial CODE V Interface, set SpCodeV1’s
cleanup_files parameter to no and re-run the simulation.
We have also provided a single CODE V sequence file, lens_fullsim.seq, which can be used with the Spatial CODE
V interface when the parameter codev_sequence is set to custom. In this case, lens_fullsim.seq fully specifies the
entire CODE V lens design and BSP simulation, and does not require additional lens and user-sequence files. Change
SpCodeV1’s parameter codev_sequence to custom, and re-run the simulation. You will find the same results are
generated as before.
Finally, if it appears that CODE V is not being invoked by the simulation, it is possible that OptSim cannot find the
CODE V executable. In this case, as described in the documentation for the Spatial CODE V Interface, make sure to
either include the CODE V executable in your system path, or define the environment variable CODEV_DIR to point to
the directory containing this executable.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 433

 Figure 1. OptSim topology for demonstrating a lens simulation within CODE V.

(a) (b)

Figure 2. (a) 5-µm Gaussian VCSEL output. (b) Focused spot after lens.

434 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.20 Electronic Dispersion Compensation in multimode
link by applying the Forward-Feedback Equalization
Filter
RSoft/examples/optsim/block_mode/multimode/EDC_example.moml
This example demonstrates the application of electronic dispersion compensation (EDC) in a multimode link. Upgrade
of existing Ethernet links from 1 to 10 Gb/s with keeping the 300-m transmission reach faces the challenge of
overcoming performance degradation due to the higher modal dispersion penalties. One of the solutions for this problem
is being implemented in IEEE standard for 10 Gigabit Ethernet 10GBASE-LRM [1] and is based on applying electronic
dispersion compensation to the signal at the receiver.

Figure 1. Link configuration under study

The OptSim example depicted in Figure 1 demonstrates a 10 Gigabit multimode link. The multimode fiber is a 300-m
graded-index fiber with a 50-micron core diameter. The fiber refractive index profile has a dip defect in the center of the
core – one of the typical profile distortions due to manufacturing imperfections. See Figure 2 for the fiber index profile.
The deviations of index profile from an ideal graded-index may cause increase in differential modal delay, and as a result
the performance degradation.
The output signal from the transmitter has a single-mode Gaussian pulse profile with 7 micron FWHM. The connector
between transmitter and fiber adds 10 micron offset from the fiber core center. As a result, the received eye diagram at
the PIN/TIA receiver is distorted – see Figure 3 – and the computed link BER for this eye diagram is as high as 3.1x10-3.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 435

 Refractive Index Test Plot

1.500

1.497

Refractive Index
1.494

1.491

1.488

1.485

0 10 20 30
Radial Coordinate (um)

Figure 2. Fiber index profile

Eye Diagram - Before EDC

0.10

0.08
Signal (V)

0.06

0.04

0.02

0.00
0 1 2
-10
x10
Time (s)

Figure 3. Received eye diagram before EDC

To improve the eye diagram and BER of the link, we apply EDC to electrical signal after the first receiver in the form of
equalization filter implemented as an electrical finite-impulse response (FIR) filter. This equalization scheme is also
known as linear or forward-feedback equalization (LE or FFE). The FIR filter model used applies the following
transformation to the electrical signal:
N
y (t ) = ∑ C ⋅ x(t − i∆T )
i =− N
i

where x(t) is incoming signal, y(t) - outgoing signal, (2N+1) – number of taps, Ci- weight coefficients or taps, and ∆T –
taps delay.

436 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Eye Diagram - after EDC
0.05

0.04

0.03

Signal (V) 0.02

0.01

0.00
0 1 2
-10
x10
Time (s)

Figure 4. Received eye diagram before EDC

For the eye diagram shown in Figure 3, we found that a FFE parameters setting with 3 taps, tap delay of ½TB, and taps
coefficients {-0.3, 1.0, -0.3} is sufficient to improve the eye diagram quality, and hence, the BER. Figure 4 shows the
received eye diagram after applying EDC, which shows a significant improvement. The corresponding computed BER is
equal to 3.7x10-13, i.e. satisfies the link BER requirement of 1x10-12 or better.
Figure 5 shows the electrical signal waveforms before and after the EDC and Figure 6 shows the transfer function for the
applied FIR filter.

Electrical Signal before and after EDC

0.10

0.08
Signal (Real) (V)

0.06

0.04

0.02

0.00
0 1 2 3 4 5 6 7 8 9 10
x10-9
Time (s)

Figure 5. Electrical signal waveforms before (dashed line) and after (solid line) equalization

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 437

 Transfer Function (Frequency Response)

Transfer Function [dB]

0

-2

-4

-6

-8

-5 -4 -3 -2 -1 0 1 2 3 4 5
x1010
Frequency [Hz]

Figure 6. Transfer function of FFE filter with given parameter settings.

In this example the parameters of equalization filter are optimized for the given offset of laser-fiber alignment. To
demonstrate that we can perform the parameters scan simulation for different values of offsets. Figure 7 shows simulated
link BER and Q-factor before and after EDC for different values of offset, ranging from 0 to 20 microns. One can see
that the biggest gain from EDC is observed at the 10-micron offset – i.e. the one we use in the example. Thus, if one
wants to use different offset values, then the FFE parameters have to be modified (optimized) for the best performance.

BER Q2
100 20
Q before EDC

-2
10 Q after EDC

-4
10

10-6
Q2 (dB)
BER

10
10-8

10-10
BER before EDC
10-12
BER after EDC

10-14 0
0 10 20 0 10 20
offset (microns) offset (microns)

Figure 7. The link BER and Q-factor before and after EDC for different values of connector offset.

References
1. IEEE P802.3aq 10GBASE-LRM Task Force, http://www.ieee802.org/3/aq/public/index.html

438 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.21 25 Gbps Directly Modulated VCSEL
The objective of this application note is to show high-speed direct modulation of the VCSEL.
The project file is available at:

RSoft/examples/optsim/block_mode/multimode/VCSEL_25Gbps.moml
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

With the focus on high-speed data links using multimode fiber, user is often interested in modulating VCSEL at 10 Gbps
or higher. This example uses a directly modulated VCSEL at 25 Gbps. The VCSEL model in OptSim/ModeSYS is very
flexible and if the physical parameters are available to the user either from datasheets or from measurements, user can
insert them via the parameter window of the VCSEL model. However, often in practice, more emphasis is on the
behavior modeling as far as the VCSEL modulation speed is concerned or not all physical parameters are accessible to
the user. The rate equations described in the manual pages for VCSEL can help in determining which parameter to
change for desired behavior. For example, the gain constant was set to a much higher value than the default one for this
application note. Please note that some changes may lead to a non-realistic VCSEL.
The length of the multimode fiber is 100m. The linewidth adder model helps specify transmitter’s linewidth. The optical
signal launched into the fiber is shown in Fig. 2.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 439

 Figure 2. Output of the VCSEL driven at 25 Gbps

The modal dispersion in the fiber results in a distorted eye as shown in Fig. 3.

Figure 3. Received Eye Diagram without an EDC

440 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

An electronic dispersion compensation (EDC) can optionally be applied to compensate for the dispersion. Figure 4
below shows an eye diagram after the EDC.

Figure 4. Received Eye Diagram after an EDC

Four such VCSELs can be used for VCSEL-based 100GBASE system designs.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 441

3.22 IEC 60793-1-41: Bandwidth Measurement
The objective of this application note is to show how OptSim/ModeSYS can help in compliance testing for international
standards. In this specific scenario, a multimode fiber’s bandwidth measurement as per Method A of the IEC 60793-1-41
standard is studied as a test case.
The project file is available at:

RSoft/examples/optsim/block_mode/multimode/IEC60793_1_41.moml
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

Method A, Section 6.1 of the IEC Standard 60793-1-41 describes time-domain (pulse-distortion) method of multimode
fiber’s bandwidth measurement testing. For this case study, the mode-coupling is set to ON, and an arbitrary refractive
index data file is used for describing the refractive index profile of the fiber. The data file is supplied at the same location
as the project file for this example. This enables users to modify it, say, to account for various manufacturing defects of
interest. The “Test” tab of the fiber’s parameter window, amongst various other plots, can give user the refractive index
profile plot to make sure it looks as the user wanted, prior to running the actual simulation.
The mode-locked laser is attached to an SMF pigtail and emits an extremely narrow Gaussian pulse at 850 nm (change to
1300 nm if that’s your region of interest). The length of the multimode fiber is 1 km and its core diameter is 62.5 µm.
The time-domain pulse at the coupler output is shown in Fig. 2.

442 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Figure 2. Pulse at the coupler output

The Section B.1.1 of Annex B of the standard describes transfer function calculation for the pulse distortion
measurement method (Method A). The transfer function measured from ModeSYS is shown in Fig. 3.

Figure 3. Transfer function of the fiber under test

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 443

The 3-dB bandwidth, as defined in Section 3.1 of the standard, and as seen in the above plot for the multimode fiber
under test is 4.5 MHz. Thus, ModeSYS can help user see if the fiber meets specifications as described in relevant
standards.
In the next example, we shall study compliance test case for another IEC standard, namely, IEC 60793-1-49.

444 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

3.23 IEC 60793-1-49: DMD Test and Measurement
The objective of this application note is to show how OptSim/ModeSYS can help in compliance testing for international
standards. In this specific scenario, a multimode fiber’s differential mode delay (DMD) measurement as per the IEC
60793-1-49 standard is studied as a test case.
The project file is available at:

RSoft/examples/optsim/block_mode/multimode/IEC60793_1_49/DMD.moml
Figure 1 shows the schematic layout.

Figure 1. Simulation setup schematics for this application note

The scope of the standard IEC 60793-1-49 is to describe modal structure of the multimode fiber. The standard specifies
how to calculate DMD. The DMD data is then compared to the supplied DMD data based on the standards committee’s
measurement and modeling on a number of transmitters and subsequently to calculate the effective modal bandwidth.
We restrict the scope of this application note to DMD measurement and omit the other parts due to potentially
proprietary nature of the data supplied in the standard.
For this case study, the mode-coupling is set to ON, and an arbitrary refractive index data file is used for describing the
refractive index profile of the fiber. The data file is supplied at the same location as the project file for this example. This
enables users to modify it, say, to account for various manufacturing defects of interest. The “Test” tab of the fiber’s
parameter window, amongst various other plots, can give user the refractive index profile plot to make sure it looks as
the user wanted, prior to running the actual simulation.
The mode-locked laser is attached to an SMF pigtail and emits an extremely narrow Gaussian pulse at 850 nm (change to
1300 nm if that’s your region of interest). The length of the multimode fiber is 600 m and its core diameter is 30 µm. The
coupler at the fiber input scans the launce of the pulse from the center of the core to the edge of the core. This is
accomplished by a parameter scan in steps of 2 µm. The rest of the setup follows guidelines from Section 4 Apparatus of
the standard.
The differential mode delay (DMD), as defined in Section 3.1 of the standard is plotted via the DMD Analyzer model of
ModeSYS and is shown in Fig.2.

OptSim Application Notes and Examples Chapter 3: Multimode Simulations • 445

 Figure 2. DMD plot for the multimode fiber under test

The delay versus the radial offset plot is shown in Fig. 3.

Figure 3. Delay versus radial offset plot for the multimode fiber under test

Thus, ModeSYS can help user see if the fiber meets specifications as described in relevant standards.

446 • Chapter 3: Multimode Simulations OptSim Application Notes and Examples

 Chirp Analysis 41
Chirp Measurement 41
Chirped RZ (CRZ) 152, 269
Chirp-Managed Laser (CML) 339
Chromatic Dispersion Compensation 172

Index Chromatic Dispersion: Penalties and Compensation 168

Cladding-Pumped EDFA 233
CODE V Interface 435
Coherent and Non-coherent Systems Comparison 131
Coherent PM-QPSK 131
Compact Transient EDFA Model 313
Comparison of IMDD K-L and QA BER Calculations
260
Compound Component (CC) 316, 323
Connector Simulation 355
Coupler 3
1 Cross Gain Modulation for Wavelength Conversion 244
Cross Phase Modulation (XPM) 16
10 Gbps 2 Channel WDM 263
Cross-Phase Modulation for Wavelength Conversion
10 Gbps 4 Channel WDM 264
244
10 Gbps Externally Modulated Single Channel Link
CRZ Dispersion-Managed Link 269
332
CSRZ-DPSK 65
10 Gbps Single Channel Link 65, 69, 81, 111, 149, 152
CSRZ-DQPSK Modulation 70
10 Gigabit Ethernet Link Design 404
Custom Component Executable (CCE) 54
1000BASE-BX (IEEE 802.3ah) Bi-directional EFM
Custom Component for MATLAB (CCM) 57
401

2 D
Decision Feedback Equalizer (DFE) 254
25 Gbps Directly Modulated VCSEL 441
Demultiplexing in Time Domain 278
Differential Mode Delay 376
A Direct Counting of Errors 126
All-Optical Gain Control 311 Direct Modulation Laser 6
All-optical Wavelength Conversion 139 Dispersion Compensation 7, 164
All-Order PMD 13 Dispersion Measurement 12
Analog CATV Examples 297 Dispersion Shifted Fiber (DSF) 174
Arbitrary Refractive Index Profiles 387 Dispersion-Managed Soliton 206
ASE Peaking 228 Distributed Amplification 181
DPSK 131
DPSK BER Estimator 50
B DPSK Modulation 65, 161
BeamPROP Interface 62, 331 DQPSK Modulated Radio-over-Fiber (ROF) 117
BER Estimation 50 DQPSK Modulation 69
Bitrate Discrimination Circuit (BDC) 111 Dual-Carrier PM-QPSK 87
Black-Block EDFA 257 Dual-Pump Fiber OPA 197
Block Mode and Transient Simulations 149 Duobinary 65
Burst Mode PON using TDMA 107 Duobinary Modulation 40
Burst Mode Transmission 107 Duobinary Transmitter 156
Burst-Mode Receiver 111 DWDM 217, 230
DWDM Ring with OADM 273
C
E
Cambridge 81-Fibers Statistical Model 410
Carrier-Suppressed RZ (CSRZ) 152 EDFA 29, 222
CATV 35, 297 EDFA Amplifier 5
Chirp 41 EDFA Design for Dense WDM System 230

OptSim Application Notes and Examples Index • 447

EDFA Gain Compensation via the LAD Interface 239 Iterations 63
EDFA Tutorial 222
EDFA-Based Optical Links 227 K
Electrical Jitter 5
Electronic Dispersion Compensation (EDC) 254, 437 Karhunen-Loeve (K-L) and BER Counter Comparison
Encircled Flux 372 126
Er-Yb-Based Master-Oscillator Power Amplifier Karhunen-Loeve (K-L) and Monte Carlo Comparison
(MOPA) 236 128
External Modulation 332 Karhunen-Loeve (K-L) BER Estimation 128
EYCDFA 236 Karhunen-Loeve (KL) Semi-analytical BER Estimation
126
Karhunen-Loeve BER Estimator 260
F
Feed-Forward Equalizer (FFE) 254 L
Fiber Dispersion 7, 164
Fiber Linear Effects 177 Laser 3
Fiber Linearities 12 Laser-Fiber Coupling 343
Fiber Nonlinear Effects 188 Lens Example using BeamPROP Interface 432
Fiber Non-linearities 13 Liekki Application Designer (LAD) 239
Fiber Nonlinearity and Performance of NRZ- and RZ- Light–Emitting Diode (LED) 333
formats 193 Linear Multimode Fiber 365
Fiber Optic Gyroscope (FOG) 294 Loss-Managed Soliton Link 203
Fiber Optical Parametric Amplifier (OPA) 196 Lumped Amplification 179
Fiber-Based Phase Sensitive Amplifier 21
Fiber-Based PSA 197 M
Fiber-induced Loss: Penalties and Compensation 177
Fixed-Gain Optical Amplifier 51 Mach-Zehnder Modulator 4
Forward Error Correction (FEC) 252 Matched Filter 4
Forward-Feedback Equalization (FFE) 437 MATLAB cosimulation in ModeSYS 426
Four Wave Mixing (FWM) 18, 188 MATLAB Cosimulation: Vortex Lens Example 426
Free-Space Optics (FSO) 287 Maximum Likelihood Sequence Estimation (MLSE)
FTTH 305 Receiver for Uncompensated Transmission
FTTH GEPON 305 System 74
FTTH System with Broadband PON Access Microwave Photonic Links with Balanced Detection
Architecture 36 122
FWM Resonance 190 Microwaves on Fiber Optics (MFO) 42
Migration from 10 Gbps to 40 Gbps 130
Minimum Mean-Square Error (MMSE) 254
G
Miscellaneous Examples 332
Gain Compensation 228 Mode Coupling in Multimode Fiber 369
Getting Started with Sample Mode 1 Monte Carlo BER Estimation 128
Gigabit Ethernet Link Design 395 Monte Carlo BER Estimation in Long-Haul RZ-DPSK
Transmission 261
Multimode Fiber 62
H
Multimode Inputs to Multimode Fiber 359
Histogram 33 Multimode Simulations 343
How to Co-simulate with BeamPROP 324 Multiple Backward Pumped Raman Amplification 217
How to Create a Block Mode Compound Component
(CC) 316 N
Network Components 31
I
Nonlinear Polarization Rotation 139
IEC 60793-1-41 Bandwidth Measurement 444 Non-Return to Zero (NRZ) 65, 152, 193
IEC 60793-1-49 Differential Mode Delay 447 NRZ, RZ, CRZ and CSRZ Modulation 65, 69, 81, 111,
In-band Crosstalk in Partial DPSK Systems 137 152
Interferometric Fiber Optic Gyroscope (I-FOG) 294

448 • Index OptSim Application Notes and Examples

O Refractive Index Profile Distortions 410
Relationship Between OSNR and ASE Power Spectral
OC-768 DWDM Link with Raman Amplification 217 Density in Block-Mode Models 257
Optical Add-Drop Multiplexing (OADM) 31 Relationship Between OSNR and ASE Power Spectral
Optical Circulator 33 Density in Sample-Mode Models 50
Optical Code Division Multiple Access (OCDMA) 282 Return to Zero (RZ) 152, 194
Optical Cross Connector 34 Ring Configuration 35
Optical Cross-connect (OXC) 142 ROADM Technology Selection and Deployment
Optical Mu-Demultiplexing 34 Testing 142
Optical Noise Adder 257 RSOA-based PON with Upstream Remodulation 246
Optical White Noise Generator 51 RZ-DPSK 65
Optimization of the Dispersion Map 65 RZ-DQPSK 131
Optimum Dispersion Value 12 RZ-DQPSK Modulation 70
OptSim-LAD Interface 239
Orthogonal Frequency Division Multiplexing (OFDM)
101 S
Sallen-Key Low-pass Filter 58
P Sample Mode Simulations 1
Saturation Model 6
Parallel Optical Bus 337 Self Phase Modulation (SPM) 13
Parametric Gain (PG) 20 Semiconductor Optical Amplifier (SOA) 241
Parametric Runs 63 Sensitivity Receiver 4
Partial DPSK (PDPSK) 133 Signal Regeneration 49
Performance Budget Calculation 252 Simple Components 3
PM-16QAM Receiver 93 Single-Pump Fiber OPA 196
PM-64QAM Receiver 97 SOA 30
PM-BPSK Receiver Sensitivity 90 SOA as Wavelength Converter 243
PMD 13, 183, 184 SOA in Switch Applications 242
PM-QPSK modulation and the LMS dynamic receiver Soliton Transmission 40, 200
81 Spatial BeamPROP Interface 428, 432
PM-QPSK with External Local Oscillator 85 Spatial CODE V Interface: Lens Example 435
PM-QPSK with Training Sequence-based LMS Spatial Photodetector Coupling 351
Receiver 77 SPICE Cosimulation 111
Polarization Mode Dispersion (PMD) Induced Penalties SPICE Co-simulation (CCS) 58
184 SPICE Co-simulation: Non-linear Laser 60
Polarization Multiplexed QAM (PM-QAM) 93 SPICE Co-simulation: Sallen-Key Low-pass Filter 58
Polarization Multiplexed QPSK 76 Spreadsheet Model for Gigabit Ethernet 380
Polarization State Effect on WDM Channels 266 SRS-induced Cross-talk 24
Power Transients in EDFA Chains 309 Standard OC 64
Pseudo-Orthogonal Code-based Encoding/Decoding Stimulated Brillouin Scattering (SBS) 220
282

T
R
TDM 278
Radio over Fiber (ROF) 117 TOAD 278
Raman 212 Transients 309
Raman Amplification 212, 217 Transmitter Band-limiting Filter 159
Raman Amplifier (RA) 25 Transmitters 152
Raman Cross-talk 23
Raman Effect 23
Raman Gain Coefficient 25 U
Receiver Sensivity 249 Unbalanced Mach-Zehnder Modulator 144
Receivers 249
Re-configurable Optical Add-Drop Multiplexers
(ROADM) 142 V
Recorder & Playback 63 VCSEL 62

OptSim Application Notes and Examples Index • 449

Vortex Launch to Multimode Fiber Link 420, 426

W
Waveguide Example using BeamPROP Interface 428
Wavelength Converter 34
Wavelength Selective Switche (WSS) 142
WDM 227, 263, 264, 266
WDM Systems 27

450 • Index OptSim Application Notes and Examples