FOUR WAVE MIXING NONLINEARITY EFFECT IN WAVELENGTH

DIVISION MULTIPLEXING RADIO OVER FIBER SYSTEM

HAFIZ ABD EL LATIF AHMED HABIB
UNIVERSITI TEKNOLOGI MALAYSIA
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ABSTRACT
The integration of wireless and optical networks is a potential solution for the
increasing capacity and mobility as well as decreasing costs in the access networks.
Optical networks are fast, robust and error free, however, there are nonlinearity
obstacles preventing them from being perfect media. The performance of wavelength
division multiplexing (WDM) in radio over fiber (RoF) systems is found to be
strongly influenced by nonlinearity characteristics in side the fiber. The effect of four
wave mixing (FWM) as one of the influential factors in the WDM for RoF has been
studied here using Optisystem and Matlab. From the results obtained, it is found that
the FWM effects have become significant at high optical power levels and have
become even more significant when the capacity of the optical transmission line is
increased, which has been done by either increasing the channel bit rate, and
decreasing the channel spacing, or by the combination of both process. It is found
that when the channel spacing is 0.1 nm, 0.2 nm and 0.5 nm the FWM power is
respectively, becomes about -59 dBm, -61 dBm and -79 dBm. This result confirms
that the fiber nonlinearities play decisive role in the WDM for RoF system. The
simulation results obtained here are in reasonable agreement as compared with other
numerical simulation results obtained, elsewhere, using different simulation tools.
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TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION iii
DEDICATION iv
ACKNOWLEGEMENT v
ABSTRACT vi
ABSTRAK vii
TABLE OF CONTENTS viii
LIST OF TABLES xi
LIST OF FIGURES xii
LIST OF ABBREVIATION xv
LIST OF SYMBOLS xvii
LIST OF APPENDICES xix
1 INTRODUCTION 1
1.1 Introduction 1
1.2 Problem Background 2
1.3 Problem Statement 3
1.4 Objective of the Project 4
1.5 Scope of the Project 5
1.6 Organization of the Thesis 5
2 RADIO OVER FIBER TECHNOLOGY 7
2.1 Introduction 7
2.2 What is Radio over Fiber? 8
2.3 Benefits of RoF Technology 9
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2.3.1 Low Attenuation Loss 9
2.3.2 Large Bandwidth 10
2.3.3 Immunity to Radio Frequency Interference 11
2.3.4 Easy Installation and Maintenance 11
2.3.5 Reduced Power Consumption 12
2.3.6 Multi-operator and Multi-service Operation 12
2.3.7 Dynamic Resource Allocation 13
2.4 The Application of Radio over Fiber Technology 13
2.4.1 Cellular Networks 13
2.4.2 Satellite Communications 14
2.5 RoF Multiplexing Techniques 15
2.5.1 Sub-Carrier Multiplexing in RoF System 15
2.5.2 Wavelength Division Multiplexing in RoF System 17
3 NON-LINEAR EFFECTS 19
3.1 Introduction 19
3.2 Types of Fibers 20
3.3 Fiber Losses 20
3.4 Fiber Nonlinearities 21
3.4.1 Self Phase Modulation 22
3.4.2 Cross Phase Modulation 23
3.4.3 Four Wave Mixing 25
3.4.3 Stimulated Brillouin Scattering 29
3.4.5 Stimulated Raman Scattering 30
4 METHODOLOGY 32
4.1 Introduction 32
4.2 Simulation using Optisystem Software 32
4.3 The Simulation Model 33
4.4 Simulation of the Four Wave Mixing effect 35
4.5 Simulation of FWMfor Higher Number of Channels 40
4.6 Effect of Different Power Level of the Signal Sources 41
4.7 Effect of Increase Dispersion of the Fiber Optic 41
4.8 Effect of Increase Effective Area f the Fiber Optic 42
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4.9 Modelling the Effect of FWM 42
5 RESULTS AND DISCUSSIONS 47
5.1 Introduction 47
5.2 Simulation of the Four Wave Mixing Effect 47
5.3 Simulation Results without the External Modulated Signal 48
5.3.1 Effect of Channel Spacing 48
5.3.2 Effect of Different Power Level of the Signals Sources 51
5.3.3 Effect of Increase Dispersion of the Fiber Optic 53
5.4 Simulation Results with the External Modulated Signal 54
5.4.1 Effect of Channel Spacing 55
5.4.2 Effect of Different Power Level of the Signals Sources 58
5.4.3 Effect of Increase Dispersion of the Fiber Optic 61
5.4.4 Effect of Increase Effective Area of the Fiber Optic 61
5.5 Simulation of FWM for Higher Number of Channels 62
5.5.1 Simulation Results for Four Signal Source without External
Modulated Signal 63
5.5.2 Simulation Results for Four Signal Source without External
Modulated Signal 65
5.6 Discussion 67
5.7 Analytical Modelling 68
5.8 FWM reduction 70
5.8.1 Effect of Unequal Channel Spacing 70
5.8.1 Effect of Increase Effective Area of the Fiber Optic 72
6 CONCLUSIONS AND RECOMMENDATIONS 73
6.1 Conclusion 73
6.2 Recommendations for Future Work 74
REFERENCE 75
Appendix 77
xi
LIST OF TABLES
TABLE NO. TITLE PAGE
3.1 Comparison between SBS and SRS 31
4.1 Global parameters 37
4.2 CW Laser sources parameters 38
4.3 DM 2x1 multiplexer parameters 38
4.4 Main tab and dispersion tab parameters for optical fiber 38
4.5 Nonlinear tab parameters for optical fiber 39
4.6 Numerical tab and PMD tab parameters for optical fiber 39
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LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 The Radio over Fiber System Concept 8
2.2 Operating regions of optical fiber 10
2.3 These robust RAPs are connected to the central base
station via the ROF 14
2.4 SubCarrier Multiplexing of Mixed Digital and Analogue
Signals 16
2.5 WDM system using multiple wavelength channels and
optical amplifiers 17
3.1 Frequency chirping effect 23
3.2 Four wave mixing products 26
3.3 The arising new frequency components due to FWM 27
3.4 FWM products versus channel count 28
3.5 FWM mixing efficiency in single-mode fibers 29
4.1 Direct Modulation 33
4.2 External modulation 33
4.3 Simulation model with external modulated signal 34
4.4 Simulation model without external modulated signal 35
4.5 Simulation model with three channels 40
4.6 flowchart illustrate the modeling steps 40
4.7 The phase matching condition of two different
wavelengths 45
5.1 Optical spectrumat the input of the fiber when channel
spacing is set to 0.1 nm 48
5.2 Optical spectrumat the onput of the fiber when channel
spacing is set to 0.1 nm 49
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5.3 Optical spectrumat the input of the fiber when channel
spacing is set to 0.2 nm 49
5.4 Optical spectrumat the input of the fiber when channel
spacing is set to 0.2 nm 50
5.5 Optical spectrumat the input of the fiber when channel
spacing is set to 0.5 nm 50
5.6 Optical spectrumat the onput of the fiber when channel
spacing is set to 0.5 nm 51
5.7 Optical spectrumat the output of the fiber when input
power is set to 20 dBm 52
5.8 Optical spectrumat the output of the fiber when input
power is set to 20 dBm 52
5.9 Optical spectrumat the output of the fiber when input
power is set to -10 dBm 53
5.10 Output optical spectrum when the dispersion of fiber
optic is set to 16.75 ps/nm/km 54
5.11 Optical spectrum at the input of the fiber when the
channel spacing is set at 0.1 nm 55
5.12 Optical spectrum at the output of the fiber when the
channel spacing is set at 0.1 nm 56
5.13 Optical spectrum at the input of the fiber when the
channel spacing is set at 0.2 nm 56
5.14 Optical spectrum at the output of the fiber when the
channel spacing is set at 0.2 nm 57
5.15 Optical spectrum at the input of the fiber when the
channel spacing is set at 0.5 nm 57
5.16 Optical spectrum at the output of the fiber when the
channel spacing is set at 0.5 nm 58
5.17 Optical spectrum at the output of the fiber when input
power is set at 20 dBm
59
5.18 Optical spectrum at the output of the fiber when input
power is set at 10 dBm 59
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5.19 Optical spectrum at the output of the fiber when input
power is set at -10 dBm 60
5.20 Optical spectrum at the output of the fiber when input
power is set at 0 dBm 61
5.21 Optical spectrum at the output of the fiber when the
effective area of the fiber optic is set at 76.5 m
2
62
5.22 Four optical spectrum at the input of the fiber when the
channel spacing is set at 0.1 nm 63
5.23 Four output optical spectrum channels when the channel
spacing is set at 0.1 nm 64
5.24 Four output optical spectrum channels when the channel
spacing is set at 0.5 nm 64
5.25 Four input optical spectrum channels when the channel
spacing is set at 0.1 nm 65
5.26 Four output optical spectrum channels when the channel
spacing is set at 0.1 nm 66
5.27 Four output optical spectrum channels when the channel
spacing is set at 0.5 nm 66
5.28 Power per channel vs. FWM power 69
5.29
Channel spacing versus FWM power
69
5.30 Optical spectrumat the input of the fiber when the
channel spacing is unequal 71
5.31 Optical spectrum at the output of the fiber with unequal
channel spacing 71
5.32 Optical spectrum at the output of the fiber when the
effective area of the fiber optic is set at 76.5 m
2
72
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LIST OF ABBREVIATIONS
RoF - Radio over Fiber
SPM - Self Phase Modulation
XPM - Cross Phase Modulation
FWM - Four Wave Mixing
SRS - Stimulated Raman Scattering
SBS - Stimulated Brillouin Scattering
WDM - Wavelength Division Multiplexing
DWDM - Dense Wavelength Division Multiplexing
SMF - Single Mode Fiber
nm - nanometer
E/O - Electrical-To-Optical Converter
O/E - Optical - To Electrical- Converter
RF - Radio Frequency
IF - Intermediate Frequency
CW - Continuous Wave
RAU - Radio Antenna Unit
THz - Teri hertz
OTDM - Optical Time Division Multiplexing
SCM - Sub-Carrier Multiplexing
EMI - ElectroMagnetic Interference
IM-DD - Intensity Modulation and Direct Detection
OFM - Optical Frequency Multiplication
GSM - Global System for Mobile communication
MVDS - Multipoint Video Distribution Service
MBS - Mobile Broadband System
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GHz - Gigahertz
RHD - Remote Heterodyne Detection
TDM - Time Division Multiplexing
OADM - Optical Add-Drop Multiplexer
LED - Light Emitting Diode
GVD - Group velocity dispersion
ITU - International Telecommunication Union
MUX - Multiplexer
NDSF - Non Dispersion Shifted Fiber
PMD - Polarization Mode Dispersion
NRZ - Non-Return to zero
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LIST OF SYMBOLS
A - Pulse amplitude
A
eff
- Effective area of optical fiber
c - Speed of light
c
o
- Speed of light in vacuum
D - Dispersion parameter
d
ijk
- Degeneracy factor
E - Electric field, vector
E - Electric field, scalar
f - Frequency
I - Intensity
L - Length
L
eff
- Effective length
n - Refractive index
n
o
- Wavelength dependent refractive index
n
2
- Nonlinear refractive index
n
2
/A
eff
- Nonlinear coefficient
P - Total polarization, vector
P - Power
p
i
- Input power
r - Radius
t - Time
z - Distance
- Attenuation constant [1/m]

dB
- Attenuation constant [db/km]

i
- Propagation constant of the mode i
- Nonlinear parameter
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o
- Vacuum permittivity
- Wavelength

o
- Center wavelength
- Normalized time constant

i
- Angular frequency

(j)
- j
th
order susceptibility
xix
LIST OF APPENDICES
APPENDIX TITLE PAGE
A AMatlab Program for FWM power and channel
spacing 78
1
CHAPTER 1
INTRODUCTION
1. 1 Int roduct ion
In the past, dating back to the beginning of the human civilization,
communication was done through signals, voice or primitive forms of writing and
gradually developed to use signaling lamps, flags, and other semaphore tools.
As time passed by, the need for communication through distances, to pass
information from one place to another, became necessary and the invention of
telegraphy brought the world into the electrical-communication. The major
revolution that affected the world however was the invention of the telephone in
1876. This event has drastically transformed the development of communication
technology. Todays long distance communication has the ability to transmit and
receive a large amount of information in a short period of time.
Since the development of the first-generation of optical fiber communication
systems in the early 80s [4], the optical fiber communication technology has
developed fast to achieve larger transmission capacity and longer transmission
distance, to satisfy the increased demand of computer network. Since the demand on
the increasing system and network capacity is expected, more bandwidth is needed
because of the high data rates application, such as video conference and real-time
image transmission, and also to achieve affordable communication for everyone, at
2
anytime and place [1]. The communication capabilities allow not only human to
human communication and contact, but also human to machine and machine to
machine interaction. The communication will allow our visual, audio, and touch
sense, to be contacted as a virtual 3-D presence [3].
To keep up with the capacity increasing requirement, new devices and
technologies with high bandwidth are greatly needed by using both electronic and
optical technologies together to produce a new term Radio over Fiber (RoF). The
progress made so far has been impressive, where information rate at 1 terabits/s can
be handled by a single fiber [5].
RoF is a technology used to distribute RF signals over analog optical links. In
such RoF systems, broadband microwave data signals are modulated onto an optical
carrier at a central location, and then transported to remote sites using optical fiber.
The base-stations then transmit the RF signals over small areas using microwave
antennas and. Such a technology is expected to play an important role in present and
future wireless networks since it provides an end user with a truly broadband access
to the network while guaranteeing the increasing requirement for mobility. In
addition, since it enables the generation of millimeter-wave signals with excellent
properties, and makes effective use of the broad bandwidth and low transmission loss
characteristics of optical fibers, it is a very attractive, cost-effective and flexible
system configuration.
1.2 Problem Background
Normally light waves or photons transmitted through RoF have little
interaction with each other, and are not changed by their passage through the fiber
(except for absorption and scattering). However, there are exceptions arising from
the interactions between light waves and the material transmitting them, which can
affect optical signals in RoF. These processes generally are called nonlinear effects
because their strength typically depends on the square (or some higher power) of
intensity rather than simply on the amount of light present. This means that nonlinear
3
such as self phase modulation (SPM), cross phase modulation (XPM), four wave
mixing (FWM), stimulated raman scattering (SRS), and stimulated brillouin
scattering effects (SBS) are weak at low powers, but can become much stronger
when light reaches high intensities [7]. This can occur either when the power is
increased, or when it is concentrated in a small area-such as the core of an optical
fiber. Nonlinear optical devices have become common in RoF applications, such as
to convert the output of lasers to shorter wavelengths by doubling the frequency. The
nonlinearities in RoF are small, but they accumulate as light passes through many
kilometers of fiber. Nonlinear effects are comparatively small in optical fibers
transmitting a single optical channel. They become much larger when wavelength-
division multiplexing (WDM) packs many channels into a single fiber [9].
WDM puts many closely spaced wavelengths into the same fiber where they
can interact with one another. It also multiplies the total power in the fiber. A single-
channel system may carry powers of 3 milliwatts near the transmitter. DWDM
multiplies the total power by the number of channels, so a 40-channel system carries
120 mW. That's a total of 2 mW per square micrometer-or 200,000 watts per square
centimeter [11]. Several nonlinear effects are potentially important in RoF, although
some have produce more troublesome than others. Some occur in systems carrying
only a single optical channel, but others can occur only in multichannel systems.
1. 3 Problem Statement
The rapid development of the wireless communication networks has
increased the need of the optical signal processing. The link lengths have grown to
thousands of kilometers without need to convert optical signals back and forth to
electric form, and the transmission speeds of terabits per second are feasible today
[5]. This ever-growing demand for the high speed communication has forced to use
higher bit rates as well as transmission powers.
Nonlinear effects on communication have become significant at high optical
power levels and have become even more important since the development of
4
erbium-doped fiber amplifier (EFDA) and DWDM systems. By increasing the capacity
of the optical transmission line, which can be done by increasing channel bit rate,
decreasing channel spacing or the combination of both, the fiber nonlinearities come
to play even more decisive role.
The origin of the nonlinearities is the refractive index of the optical fiber,
which is varies with the intensity of the optical signal. This intensity-dependent
component of the refractive index includes several nonlinear effects, such as SPM,
XPM, FWM, SRS, and SBS, and becomes significant when high powers are used.
Although the individual power in each channel may be below the level needed to
produce nonlinearities, the total power summed over all channels can quickly
become significant. The combination of high total optical power and large number of
channels at closely spaced wavelengths is a source for many kinds of nonlinear
interactions.
Form the above-mentioned reasons, this study is aimed to gain insight into
nonlinear effect caused specifically by FWM in the WDM for RoF system and
measure the coefficient behind these nonlinear effects. Nonlinear coefficient of the
RoF may become an important parameter, when new optical long-haul transmission
lines and networks are being deployed.
1. 4 Obj ect ive of the Project
The main objective of this project is to evaluate the FWM in WDM for RoF
technology, in order to calculate the impairments associated with long-distance high-
bit rate optical fiber communication systems. In order to achieve the objective,
optisystem and matlab programming software will be used respectively in the
numerical simulation and the analytical modelling will be verified through
comparison with optisystem simulation.
5
1. 5 Scope of the Proj ect
To study the efficiency of the FWM in WDM for RoF optical network, two
approaches were followed in this project. The first approach is the numerical
simulation using Optisystem software which almost replicates a real system. The
second aproach is the analytical modeling, which is simple and faster to analyze its
performance. MATLAB programming is used to implement the analytical model. To
verify the analytical system, a comparison is made with the Optisystem software.
Since Routing and wavelength assignment algorithm (RWA) needs to set up the path
immediately to reduce network delays, the analytical model developed in this project
can be used to calculate the impairments fast enough so that the routing decisions can
be made efficiently, to achieve optimal systems.
1. 6 Organi zat ion of the Project
Chapter 1 provides the introduction to this project where brief background of
the study problem and to the statement of the problem. Followed by the objective,
and the scope of the study. Chapter 2 reviews the literature, which includes
introduction to the RoF, the benefits, and applications of the Radio over Fiber
Technology in both satellite and mobile radio communications. In addition various
types of RoF Multiplexing Techniques, such as Sub carrier multiplexing and
wavelength division multiplexing, have also bee covered. Chapter 3 provides
information about the fiber characteristics, and the non linear effects such as SPM,
FWM, SBS, SRS, and XPM.
Chapter 4 describes the methodological processes by showing detailed diagram of
the methods implemented as well as highlighting briefly the steps those have been
followed to achieve the objective of this project. Chapter 5 presents the results
derived from the methods explained where some analyses and simulations were done
based on the FWM effects. Finally the conclusions of the study, as well as some
suggestions for future work were summed up in Chapter 6.
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CHAPTER2
RADIO-OVER-FIBER TECHNOLOGY
2.1 Introduction
The integration of wireless and optical networks is a potential solution for
increasing capacity and mobility as well as decreasing costs in the access network,
by RoF. The concept of RoF means to transport information over optical fiber by
modulating the light with the radio signal. This modulation can be done directly with
the radio signal or at an intermediate frequency. RoF technique has the potentiality to
the backbone of the wireless access network. Such architecture can give several
advantages, such as reduced complexity at the antenna site, radio carriers can be
allocated dynamically to the different antenna sites, and Transparency and scalability
[10].
RoF technology is now ubiquitous in the telecommunications infrastructure.
Fiber optics and WDM technology have increased significantly the transmission
capacity of today's transport networks, and they are playing important roles in
supporting the rapidly increasing data traffic.
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2.2 What is Radio over Fiber?
RoF technology entails the use of optical fiber links to distribute RF signals
from a central location (headend) to Remote Antenna Units (RAUs). In narrowband
communication systems and Wireless Local Area Network (WLANs), most of signal
processing (including coding, multiplexing, RF generation, modulation, etc) are
made in central stations (CS-s) rather than in the base station (BS-s) [1]. The signal
between CS and BS is transmitted in the optical band via a RoF network. This
architecture makes design of BS-s quite simple. In the simplest case, the BS consists
mainly from optical-to-electrical (O/E) and electrical-to-optical (E/O) converters, an
antenna and some microwave circuitry (two amplifiers and a diplexer).
The centralization of Radio Frequency (RF) signal processing functions
enables equipment sharing, dynamic allocation of resources, and simplifies system
operation and maintenance. These advantages could be translated into major system
installation and operational savings, especially in wide-coverage broadband wireless
communication systems, where a high density is necessary. Figure 2.1 shows that the
concept of RoF system.
Figure 2.1 The Radio over Fiber System Concept [5]
8
2.3 Benefits of RoF Technology
The RoF technology holds many advantages compared to the electronic
signal distribution. Some of these advantages will be given in the following sections.
2.3.1 Low Attenuation Loss
Electrical distribution of high-frequency microwave signals through either
free space or transmission lines always causes problems besides its high cost. In free
space, losses due to absorption and reflection increase with frequency, where as in
transmission lines, the rise of impedance with frequency leads to very high losses.
Therefore, distributing high frequency radio signals electrically over long distances
requires expensive regenerating equipment, as for mm-waves, their distribution via
the use of transmission lines is not feasible even for short distances.
The alternative solution for this problem is to distribute baseband signals or
signals at low intermediate frequencies (IF) from the switching centre (headend) to
the BS [1]. The baseband or IF signals are up-converted to the required microwave,
or mm-wave frequency at each base station and amplified before being radiated. This
system configuration is the same as the one used in the distribution of narrowband
mobile communication systems. Since optical fiber offers very low loss, RoF
technology can be used to achieve both low-loss distribution of mm-waves, as well
as simplification of RAUs at the same time.
Single Mode Fibers (SMFs) made from glass (silica), have attenuation losses
below 0.2 dB/km and 0.5 dB/km in the 1550 and 1300 nm windows, respectively as
shown in Figure 2.2 [6].
9
Figure 2.2. Operating regions of optical fiber [2]
2.3.2 Large Bandwidth
Optical fibers offer enormous bandwidth. There are three main transmission
windows, which offer low attenuation in the wavelength region of 850, 1310, and
1550 nm respectively [6] as shown in Figure 2.2.
For a single SMF optical fiber, the combined bandwidth of the three windows
is in the excess of 50 THz. commercial systems utilize only a fraction of this capacity
(1.6 THz) [5].
The high optical bandwidth enables high speed signal processing that may be
more difficult or impossible to do in electronic systems. Furthermore, signal
processing in the optical domain makes it possible to use cheaper low bandwidth
optical components such as laser diodes and modulators; in addition, it is still
capable to handle high bandwidth signals.
The utilization of enormous bandwidth, which is primary source of receiver
and transmission data, offered by optical fibers is however, severely hampered by the
limitation of bandwidth in electronic systems. This problem is referred to as the
electronic bottleneck [3]. The solution of the electronic bottleneck lies in effective
10
multiplexing Optical Time Division Multiplexing (OTDM) and DWDM techniques.
In analogue optical systems, including RoF technology, the Sub-Carrier Multiplexing
(SCM) is used to increase optical fiber bandwidth utilization. In SCM, several
microwave subcarriers, which are modulated with digital or analogue data, are
combined and used to modulate the optical signal, to be carried on a single fiber.
This makes RoF systems cost-effective.
2.3.3 Immunity to Radio Frequency Interference
Immunity to ElectroMagnetic Interference (EMI) is a very attractive property
of RoF technology, especially for microwave transmission. This is so because signals
are transmitted in the form of light through the fiber. Due to this immunity, fiber
cables are preferred even for short connections at mm-waves. EMI immunity is the
immunity to eavesdropping, which is an important characteristic of optical fiber
communications as it provides privacy and security.
2.3.4 Easy Installation and Maintenance
In RoF systems, complex and expensive equipments are kept at the headend,
thereby making the Remote Antenna Unit (RAUs) simpler. For instance, most RoF
techniques eliminate the need for a local oscillator and related equipments at the
RAU. In such cases a photodetector, an RF amplifier and an antenna make up the
RAU. Modulation and switching equipment is kept in the headend and is shared by
several RAUs. This arrangement leads to smaller and lighter RAUs by effectively
reducing system installation and maintenance costs. Easy installation and low
maintenance costs of RAUs are very important requirements for mm-wave systems,
because of the large number of the required RAUs. In applications where RAUs are
not easily accessible, the reduction in maintenance requirements leads to a major
operational cost savings [10]. The usage of smaller number of RAUs also leads to a
reduced environmental impact.
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2.3.5 Reduced Power Consumption
Reduced power consumption is a consequence of having simple RAUs with
reduced equipments. Most of the complex equipments are kept at the centralized
headend. In some applications, the RAUs are operated in passive mode. For instance,
some 5 GHz Fiber-Radio systems employing pico-cells can have the RAUs operate
in a passive mode [10]. Reduced power consumption at the RAU is significant
considering that the RAUs are sometimes placed in remote locations and have not
been fed by the power grid.
2.3.6 Multi-Operator and Multi-Service Operation
RoF offers system operational flexibility. Depending on the microwave
generation technique, the RoF distribution system can be made signal-format
transparent. The Intensity Modulation and Direct Detection (IM-DD) technique can
be made to operate as a linear system and, therefore, as a transparent system. This
can be achieved by using low dispersion fiber (SMF) in combination with pre-
modulated RF subcarriers (SCM). In that case, the same RoF network can be used to
distribute multi-operator and multi-service traffic resulting in huge economic savings
[11]. The principle of Optical Frequency Multiplication (OFM) can also be used to
achieve multi-service operation in combination with either WDM or SCM, because
its tolerance to chromatic dispersion.
2.3.7 Dynamic Resource Allocation
Since the switching, modulation, and other RF functions are performed at a
centralized headend, it is possible to allocate the capacity dynamically. In a RoF
distribution system for Global System for Mobile communications (GSM) traffic,
more capacity can be allocated to a certain area during the peak times and then re-
allocated to other areas when off-peak. This can be achieved by allocating optical
12
wavelengths, through WDM [1]. Allocating the capacity dynamically as the need for
it arises, obviates the requirement for allocating permanent capacity, which would be
a waste of resources in the cases where traffic loads vary frequently by large
margins. Furthermore, having the centralized headend facilitates the consolidation of
other signal processing functions such as mobility functions and macro diversity
transmission [1].
2.4 The Applications of Radio-over-Fiber Technology
Some of the applications of RoF technology include satellite
communications, mobile radio communications, broadband access radio, Multipoint
Video Distribution Services (MVDS), Mobile Broadband System (MBS), vehicle
communications and control, and wireless LANs over optical networks. Two of the
main application areas of RoF technology are briefly discussed below.
2.4.1 Cellular Networks
The field of mobile networks is an important application area of RoF
technology. The ever-rising number of mobile subscribers coupled with the
increasing demand for broadband services have kept sustained pressure on mobile
networks to offer increased capacity. Therefore, mobile traffic (GSM) can be relayed
cost effectively between the SCs and the BSs by exploiting the benefits of SMF
technology. Other RoF functionalities such as dynamic capacity allocation offer
significant operational benefits to cellular networks.
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Figure 2.3 These robust RAPs are connected to the central base station via the
RoF links [10]
2.4.2 Satellite Communications
Satellite communication was one of the first practical applications of RoF
technology. One of the applications involves the remoting of antennas to suitable
locations at satellite earth stations. In this case, small optical fiber links of less than
1km and operating at frequencies between 1 GHz and 15 GHz are used [10]. By
doing so, high frequency equipment can be centralized.
The second application involves the remoting of earth stations themselves.
With the use of RoF technology, the antenna needs not to be within the control area
(e.g. Switching Centre). They can be sited many kilometers away for the purpose of
improved satellite visibility or reduction of interference from other terrestrial
systems. The Switching equipment may also be appropriately sited, taking in to
consideration the environmental or accessibility reasons or reasons relating to the
cost of premises, without requiring to be in the vicinity of the earth station antennas.
CBS
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2.5 RoF Multiplexing Techniques
RoF multiplexing techniques is the process of multiplexing wavelength of
different frequency onto a single fiber. This operation cerates many virtual fibers,
each capable of carrying different signal.
RoF multiplexing uses wavelengths to transmit data parallel by bit or serial
by character, which increases the capacity of the fiber by assigning incoming optical
signals to specific frequency (wavelengths) within designated frequency band and
then multiplexing the resulting signal out on to one fiber.
2.5.1 Sub-Carrier Multiplexing in RoF Systems
Subcarrier Multiplexing (SCM) is a simple and cost effective approach for
exploiting optical fiber bandwidth in analogue optical communication systems in
general and in RoF systems in particular. In SCM, the RF signal is used to modulate
an optical carrier at the transmitters side. This results in an optical spectrum
consisting of the original optical carrier f0, plus two side-tones located at f0 fSC, ,
where fSC is the subcarrier frequency. If the subcarrier itself is modulated with data
(analogue or digital), then sidebands centered at f0 fSC are produced as illustrated in
Figure 2.4.
Figure 2.4 SubCarrier multiplexing of mixed digital and analogue signals [11]
2.4 GHz
15
In order to multiplex multiple channels of mixed digital and analogue signals
to one optical carrier, the multiple sub-carriers are first combined and then used to
modulate the optical carrier as shown in Figure 2.3. At the receivers side the sub-
carriers are recovered through direct detection and then radiated. Different
modulation schemes may be used on separate sub-carriers. One sub-carrier may carry
digital data, while the other may be modulated with an analogue signal such as video
or telephone traffic. therefore, SCM is found to support the multiplexing of various
kinds of mixed mode broadband data. Modulation of the optical carrier may be
achieved by either directly modulating the laser, or by using external modulators.
SCM may be used in both IM-DD and Remote Heterodyne Detection (RHD)
RoF techniques. SCM in combination with IM-DD has been used in RoF systems fed
by multimode fiber. However, these systems have been used mainly for transmitting
WLAN signals at frequencies below 6 GHz [11].
2.5.2 Wavelength Division Multiplexing in RoF Systems
WDM are passive devices that combine light signals with different
wavelengths, coming from different fibers, onto a single fiber. They include dense
wavelength division multiplexers (DWDM), devices that use optical (analog)
multiplexing techniques to increase the carrying capacity of fiber networks beyond
levels that can be accomplished via time division multiplexing (TDM)
The use of WDM for the distribution of RoF signals as illustrated in figure,
has gained importance recently. WDM enables the efficient exploitation of the fiber
networks bandwidth. These systems can achieve capacities over 1 Tb/s over a single
fiber. At the same time, bit rates on a single channel have risen to 10 Gb/s and
systems operating at 40 Gb/s channel rates are becoming commercially available.
The channel spacing in WDM can be decreased to 50 GHz or even to 25 GHz and
thus, it is possible to use hundreds of channels. However, if the channel spacing is
dropped to 50 GHz instead of 100 GHz, it will become much harder to upgrade the
systems to operate at 40 Gb/s due to the nonlinear effects.
16
Figure 2.5 WDM system using multiple wavelength channels and optical
amplifiers [10]
However, the transmission of RF signals is seen as inefficient in terms of
spectrum utilization, since the modulation bandwidth is always a small fraction of the
carrier signal frequency. Therefore, methods to improve the spectrum efficiency have
been proposed. RoF on WDM systems have been reported. Carriers modulated with
mm-waves are dropped from and added to a fiber ring using Optical Add-Drop
Multiplexers (OADM). The OADM are placed at base stations and tuned to select
the desired optical carriers to drop [10] [11].
17
CHAPTER 3
NON-LINEAR EFFECTS
3.1 Introduction
The fundamental component that makes the optical communication possible
is the optical fiber. The phenomenon which guides the light along the optical fiber is
the total internal reflection. It is an optical phenomenon which occurs when the
incident light is completely reflected. In case of materials with different refractive
indices, light will be reflected and refracted at the boundary surface. This will occur
only from higher refractive index to a lower refractive index such as light passing
from glass to air. This phenomenon forms the basis of optical communication
through fibers.
An optical fiber is a dielectric waveguide, it is cylindrical, and guides the light
parallel to the axis. The cylindrical structure is dielectric with a radius a and
refractive index of n
1
is the called the core of the fiber and the layer that
encompasses this structure is called the cladding. The Cladding has a refractive index
n
2
which is lesser than n
1
. This helps in providing mechanical strength and
reducing scattering losses. It also prevents the core from surface contamination.
cladding doesnt take part in light propagation.
18
3.2 Types of Fibers
Fibers can be classified according to the cores material composition. If the
refractive index of the core is uniform and changes abruptly at the cladding boundary,
then it is called as Step-index fiber. If the refractive index changes at each radial distance,
then it is called as Graded-index fiber. These fibers can be divided into single mode and
multi mode fibers. The single mode fibers operate in only one mode of propagation.
Multimode fibers can support hundreds of modes.
Both laser diodes and light emitting diodes (LED) can be used as light wave
sources in fiber-optical communication systems. When compared to Laser diodes, LEDs
are less expensive, less complex and have a longer lifetime; however, their optical
powers are typically small and spectral linewidths are much wider than that of laser
diodes. In multimode fibers different modes travel with different speed, which is
commonly referred to as intermodal dispersion, giving room to pulse spreading. In single
mode fibers, different signal frequency components travel in different speed within the
fundamental mode and this result in chromatic dispersion. Since the effect of chromatic
dispersion is proportional the spectral linewidth of the source, laser diodes are often used
in high-speed optical systems because of their narrow spectral linewidth.
3.3 Fiber Losses
For efficient recovery of the received signal, the signal to noise ratio at the
receiver must be considerably high. Fiber losses will affect the received power eventually
reducing the signal power at the receiver. Hence optical fibers suffer heavy loss and
degradation over long distances. To overcome these losses, optical amplifiers were
invented, which significantly boosted the power in the spans in between the source and
receiver. However, optical amplifiers introduce amplified spontaneous emission (ASE)
noises which are proportional to the amount of optical amplifications they provide; low
19
loss in optical fibers is still a critical requirement in long distance optical systems to
efficiently recover the signal at the receiver.
Attenuation Coefficient is a fiber-loss parameter, which expressed in the units of
dB/Km. For short wavelengths; the loss may exceed 5 dB/Km and makes it unsuitable for
long distance transmission [2]. These losses are mainly due to material absorption and
Rayleigh scattering. Material absorption is the phenomenon exhibited by silica fibers.
The intrinsic absorption is caused by the fused silica and the extrinsic absorption is
caused by the impurities in silica. The other contributing factor is the Rayleigh scattering
which is caused by the density fluctuations in the fiber. These fluctuations change the
refractive index on a smaller scale. Light scattering in such medium is called Rayleigh
scattering [7].
In multi-mode fibers, intermodal dispersion is the dominant contributor of signal
waveform distortion. Although intermodal dispersion is eliminated in single mode fibers,
different frequency component of optical signal carried by the fundamental mode still
travel in slightly different speed giving rise to a wavelength-dependent group delay. As
the group delay depends on wavelength, different amount of time is taken for the
different spectral components to reach a certain distance. Due to this effect, the optical
signal with a certain spectral width spreads with time when it travels through the fiber.
This pulse spreading is important and needs to be determined.
3.4 Fiber Nonlinearities
Even though optical networks are fast, robust, and error free, still nonlinearity
obstacles exist, which prevent it from being a perfect medium.
The nonlinear effects of the fibers play a detrimental role in the light propagation.
Nonlinear Kerr effect is the dependence of the refractive index of the fiber on the power
20
that propagating through it. This effect is responsible for self phase modulation (SPM),
cross phase modulation (XPM) and four wave mixing (FWM). The other two important
effects are stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS).
3.4.1 Self Phase Modulation
In fibers, the refractive index always has some dependence on the optical intensity
which is the optical power per effective area. This relation can be given as [6]:
0 2 0 2
................................................................ (3. ........ ) . 1
eff
P
n n n I n n
A
= + = +
where n
o
is the ordinary refractive index , n
2
is the nonlinear refractive index co-efficient,
Aeff is the effective core area, and P is the power of the optical signal.
This nonlinearity is known as Kerr nonlinearity. This produces Kerr effect in
which the propagating signal is phase modulated by the carrier. This leads to a
phenomenon called Self-phase modulation that converts power fluctuations into phase
fluctuations in the same wave [8].
In a material where the refractive index depends on a varying signal intensity
propagating along the fiber, it will produce time varying refractive index. Higher
refractive index at the peak of the pulse is produced, when compared to the edges of the
pulse. These results a time varying phase change d/dt. Due to this change, the frequency
of the optical signal undergoes a frequency shift from its initial value. This effect is
known as frequency chirping, in which different parts of the pulse undergo different
phase change as shown in Figure 3.1 [8]. The rising edge experiences a shift towards the
higher frequency and the trailing edge experiences a shift towards the lower frequency.
Since this effect depends heavily on the signal intensity, SPM has more effect on high
intensity signal pulses.
21
Figure 3.1 Frequency chirping effect
In case of fibers having the group velocity dispersion (GVD) effects, the pulse
normally broadens which leads to difficulty in the receiver side to decode the signal.
When the chromatic dispersion is negative, the edges of frequencies which experienced
higher shifts tend to move away from the centre of the pulse. The edges of the
frequencies which experienced lower shifts tend to move away from the centre in the
opposite direction. Thus the GVD affected pulse will be broadened at the end of the fiber,
and the chirping worsens due to this effect. Therefore the SPM can worsen the
performance of the optical system in the case of long haul transmission.
3.4.2 Cross Phase Modulation
As with Equation 3.2, the refractive index of the fiber depends on the time
varying signal intensity, which results time varying refractive index. This phenomenon
22
leads to an effect called XPM. XPM has more pronounced effect in the case of WDM
systems in which more optical channels are transmitted simultaneously. In the case of
XPM, the phase shift depends on the power of other channel. The total phase shift can be
represented as [6].
..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... . 2 ..... ..... ..... .... ( . 3.2)
NL
j eff j m
m j
L P P u
=
| |
= +
|
\ .

where is the non-linear phase shift for the j

th
channel, M=(N
3
-N
2
) varies from 1 to
5 W
-1
/Km, L
eff
is the effective length of the fiber, and P
j
and P
m
are the power for the
channels i and j respectively.
On the right-hand-side of Equation 3.2, the first term represents effect of SPM
and the second term represents that of XPM. The factor of 2 in this equation implies that
XPM is twice as effective as SPM for the same amount of power [7]. The phase shift
which is directly created by XPM at the end of the fiber depends on the bit patterns and
powers of the neighboring channels. The effect of XPM also depends on the wavelength
separation between the signal channel and the neighboring channel. If the channels are
separated widely, then the XPM effects are relatively weak because the two bit streams
walk-off from each other quickly. In case of the DWDM systems, the channel
wavelength separation is very narrow, which leads to strong XPM effect. Since XPM
results in an inter channel crosstalk, its effect, to some extent, also depends on the bit
pattern of the two channels.
To analyze the effect of XPM and SPM, the nonlinear Schrdinger equation can
be used which represented as [2]:
2
2
2
2
...............................................................(3.3)
2 2
i A A
A i A A
z t
| o

c c
+ = +
c c
23
By increasing the effective area, nonlinearities can be reduced. A
eff
is about 80
m
2
for standard fibers and 50 m2 for dispersion shifted fibers [6].
3.4.3 Four Wave Mixing
FWM is a phenomenon that occurs in the case of DWDM systems in which the
wavelength channel spacing are very close to each other. This effect is generated by the
third order distortion that creates third order harmonics. As shown in Figure 3.2, these
cross products interfere with the original wavelength and cause the mixing. In fact, these
spurious signals fall right on the original wavelength which results in difficulty in
filtering them out. In case of 3 channel system, there will be 9 cross products, where 3 of
them will be on the original wavelength. This is caused by the channel spacing and fiber
dispersion. If the channel spacing is too close, then FWM occurs. If the dispersion is
lesser, then FWM is higher since dispersion is inversely proportional to mixing
efficiency. As can be seen in Figure 3.2, the cross product lies right on the original signal
which poses problem when filtering.
In general, for N wavelengths input channel there will be M cross mixing
products and are given by [22]
( )
2
......................................................................................... 1 (3.4)
2
.
N
M N =
24
Figure 3.2 Four wave mixing products
If the WDM system is considered as a sum of N monochromatic plane waves, it is
possible to solve the arising channels angular frequencies. Considering a simple three-
wavelength (1, 2, and 3) system that is experiencing FWM distortion, nine cross
products are generated near 1, 2, and 3 see Figure 3.3 that involve two or more of the
original wavelengths. There are additional products generated, however they fall well
away from the original input wavelengths.
25
Figure 3.3 (a) two input signals 1 and 2 (b) three input signals 1, 2 and 3
and the arising new frequency components due to FWM
Assuming that the input wavelengths are
1
= 1551.72 nm,
2
= 1552.52 nm, and

3
= 1553.32 nm. The interfering wavelengths generated around the original three
wavelength system are:

1
+
2
-
3
= 1550.92 nm

1
-
2
+
3
= 1552.52 nm

2
+
3

1
= 1554.12 nm

1
-
2
+
3
=1552.52 nm
2
1
-
3
= 1550.12 nm
2
3
-
1
= 1554.92 nm

2
+
3
-
1
= 1554.12 nm
2
2
-
1
= 1553.32 nm
2
3
-
2
= 1554.12 nm
It can be seen that three of the interfering products fall right on top of the original three
signals and the remaining six products fall outside of the original three signals. These six
wavelengths can be optically filtered out. The three interfering products that fall on top of
the original signals are mixed together; and cannot be removed by any means. Figure 3.2
shows the results graphically. The three tall solid bars are the three original signals. The
shorter cross-hatched bars represent the nine interfering products. The number of the
interfering products increases as (N
3
-N
2
) where N is the number of signals.
26
Figure 3.4 show that the number of the interfering products rapidly becomes a very large.
Since there is no way to eliminate the products that falling on top of the original signals,
the priority is to prevent them from forming in the first place.
Figure 3.4 FWMproducts versus channel count [22]
Therefore two factors strongly influence the magnitude of the FWM products, referred to
as the FWM efficiency. The first factor is the channel spacing; where the mixing
efficiency increases dramatically as the channel spacing becomes closer. Fiber dispersion
is the second factor, and the mixing efficiency is inversely proportional to the fiber
dispersion, being strongest at the zero-dispersion point. In all cases, the FWM mixing
efficiency is expressed in dB, and more negative values are better since they indicate a
lower mixing efficiency.
Figure 3.5 shows the magnitude of FWM mixing efficiency versus fiber
dispersion and channel spacing. If a system design uses NDSF with dispersion of 17
ps/nm/km and the minimum recommended International Telecommunication Union
(ITU) DWDM spacing of 0.8 nm, then the mixing efficiency is about -48 dB and will
have little impact. On the other hand, if a system design uses DSF with a dispersion of 1
ps/nm/km and a non-standard spacing of 0.4 nm, then the mixing efficiency becomes -12
dB and will have a severe impact on the system performance, perhaps, making the
recovery of the transmitted signal impossible. The magnitude of the mixing efficiency
27
will vary widely as these parameters vary. The data presented is intended to illustrate the
principles only.
Figure 3.5 FWM mixing efficiency in single-mode fibers [22]
FWM is independent of the used bit rate; however, it is critically dependent on channel
spacing and chromatic dispersion. Therefore, the effects of FWM must be considered
even at moderate-bit-rate systems, if the channel spacing is small or the chromatic
dispersion of the fiber is low. Thus, it is possible to minimize the effects of FWM by
increasing the channel spacing and the chromatic dispersion of the fiber.
3.4.4 Stimulated Brillouin Scattering (SBS)
SBS falls under the category of inelastic scattering in which the frequency of the
scattered light is shifted downward. This results in the loss of the transmitted power along
the fiber. At low power levels, this effect will become negligible. SBS sets a threshold on
the transmitted power, above which considerable amount of power is reflected. This back
reflection will make the light to reverse direction and travel towards the source. This
usually happens at the connector interfaces where there is a change in the refractive
28
index. As the power level increases, more light is backscattered since the level would
have crossed the SBS threshold. The parameters which decide the threshold are the
wavelength and the line width of the transmitter.
Lower line width experiences lesser SBS and the increase in the spectral width of
the source will reduce SBS. In the case of bit streams with shorter pulse width, no SBS
will occur. The value of the threshold depends on the RZ and NRZ waveforms, which are
used to modulate the source. It is typically 5 mW and can be increased to 10 mW by
increasing the bandwidth of the carrier greater than 200 MHz by phase modulation [8].
3.4.5 Stimulated Raman Scattering (SRS)
SRS occurs when the pump power increases beyond the threshold, however SRS
can happen in either direction, forward and backward. The molecular oscillations set in at
the beat frequency and the amplitude of the scattering increases with the oscillations. The
equations that govern the feedback process are [8]:
..............................................................................(3.9)
p
R p s p p
dI
g I I I
dz
o =
............................................................................ ( .. 3.10)
s
R p s s s
dI
g I I I
dz
o =
where gR is the SRS gain. Ip and Is are intensities of Pump and stokes field.
In case of the threshold power, the P
th
is given by [8],
2
........................................................................ 16 ( ) / . (3.11) ........
th R
P w g o t =
where w
2
is the effective area of the fiber core and w is the spot size.
Even though there are some detrimental effects posed by these two effects,
SBS and SRS can also be used in a positive way. Since both deal with transferring
energy to the signal from a pump, they can be used to amplify the optical signal.
Raman gain is also used in compensating losses in the fiber transmission. Table 3.1
shows comparison of property behavior under the influence of SBS and SRS.
Table 3.1 Comparison between SBS and SRS
Property SBS SRS
Direction of
scatter
Only in backward
direction
In both forward and backward
direction
Frequency shift About 10 GHz About 13 THz
Spectrum width Narrow width Broad spectrum width
29
CHAPTER 4
METHODOLOGY
4.1 Introduction
This chapter highlights the techniques and methods employed to study the
nonlinear effects of FWM in WDM for RoF as well as to analyze the modelling
results obtained. Details of the methods will be given in the proceeding sections.
4.2 Simulation using Optisystem Software
OptiSystem software is a numerical simulation enables users to plan, test and
simulate almost every type of optical link in the physical layer across the broad
spectrum of optical networks. Algorithms are included for dispersion map design, bit
error rate calculation, system penalty estimations, and link budget calculations.
Each layout can have certain component parameters assigned to be in sweep
mode. The number of sweep iterations to be performed on the selected parameters
could be defined. The value of the parameter changes through each sweep iterations;
which produces a series of different calculation results, based on the parameter
values. These processing parameters effect on the results are channel pacing, input
power, effective area and dispersion of the fiber
30
4.3 The Simulation Model
There are two technologies for modulation, direct or without external
modulation as shown in Figure 4.1 which the RF signal directly varies the bias of a
semiconductor laser diode
Figure 4.1 Direct modulation
The other technology is the external modulators are typically either integrated
Mach-Zehnder interferometers or electroabsorption modulators as shown in Figure
4.2 which the constant wave (CW) laser (always on bright), and the light is
modulated by an external lithium-niobate electro-optic modulator. External
modulation is currently preferred over any other form of modulation because it has
best performance, in spite of high cost.
Figure 4.2 External modulation
31
Using Optisystem software, two types of simulation models have been
developed to study FWM effects. The two models are with external modulated signal
and without external modulated signal as shown in the Figure 4.3 and 4.4,
respectively.
The frequency of the phase modulator drive signal was kept at 2.4 GHz. The
phase modulator has been used to sweep the optical frequency, it was necessary to
first integrate the drive signal [11].
.
Figure 4.3 Simulation model with external modulated signal
32
Figure 4.4 Simulation model without external modulated signal
The simulation models were modified according to the related parameters or
components for different types of simulation process as given below
i. Effect of channel spacing.
ii. Effect of different Power Level of the signals Sources
iii. Effect of increase dispersion of the Fiber Optic
iv. Effect of Increase Effective Area of the Fiber optic
4.4 Simulation of the Four Wave Mixing effect
Each component in both simulation models, shown in Figures 4.3 and 4.4,
has its own role, to play in the process.
The Pseudo Random Bit Sequence Generator is a device or algorithm, which
outputs a sequence of statistically independent and unbiased binary digits.
33
NRZ Pulse Generator (non-return-to-zero) refers to a form of digital data
transmission in which the binary low and high states, represented by numerals 0 and
1, are transmitted by specific and constant DC (direct-current) voltages.
In positive-logic NRZ, the low state is represented by the more negative or less
positive voltage, and the high state is represented by the less negative or more
positive voltage. In negative-logic NRZ, the low state is represented by the more
positive or less negative voltage, and the high state is represented by the less positive
or more negative voltage.
The continues wave (CW) Generator is a generator of continuous-wave
millimeter-wave optical signals. The spectral linewidth of the generated millimeter-
wave signals is 2 kHz. The power of the measured cw millimeter-wave signals is
almost in proportion to the power multiplication of the two input optical signals.
The Mach-Zehnder Modulator, is a modulator, which has two inputs, one for
the laser diode and the other for the data from the channels.
The WDM Multiplexer is a method of transmitting data from different
sources over the same fiber optic link at the same time whereby each data channel is
carried on its own unique wavelength.
The Optical Fiber is a component, used in the simulation is a single mode fiber
(SMF-28), where the dispersive and nonlinear effects are taken into account by a
direct numerical integration of the modified nonlinear Scrdinger (NLS) equation.
Besides the above components there are three types of components, which used
for visualizing purposes:
i. Optical Power Meter Visualizer
ii. Optical Spectrum Analysis
iii. WDM analyzer
Below are the tables for parameters setting. Table 4.1 shows the set of the
global parameters; and Table 4.2 shows the parameters, set for the CW laser sources.
The parameters set in the WDM MUX are shown in Table 4.3. There are many tabs
34
for the optical fiber parameter settings, where Table 4.4 gives the setting for the main
and the dispersion tabs, Table 4.5 gives the setting for the nonlinear tab, and Table
4.6 gives the setting for the numerical and PMD tabs in optical fiber respectively.
Table 4.1 Global parameters
Table 4.2 CW Laser sources parameters
35
Table 4.3 WDM 2x1 multiplexer parameters
Table 4.4 Main tab and dispersion tab parameters are set for optical fiber
Table 4.4: Main tab and Dispersion tab Parameters for Optical Fibers
36
Tables 4.5 Nonlinear tab parameters for optical fiber
Table 4.6 Numerical tab and PMD tab parameters for optical fiber
37
4.5 Simulation of FWM for higher number of channels
Sources in the simulation model were increased to three or four channels.
Figures 4.5 and 4.6 show the sources increased in the new simulation model based on
direct modulation [22].
Figure 4.5 Simulation model with three channels
Figure 4.6 Simulation model with four channels
38
4.6 Effect of Different Power Level of the Signals Sources
The main requirement from a wireless communication system is that the
transmitted electro magnetic (EM) wave must reach the receiver with ample power to
allow the receiver to distinguish the wave from the background noise.
Another common property used to describe signal strength is the S/N ratio.
The S/N ratio does not describe the absolute power in the signal, but instead
describes the power of the signal in comparison to the power of the background
noise. The higher the S/N ratio, the better or more powerful the signal. Since the S/N
ratio accounts for the level of background noise, it is a very valuable and widely used
indicator of signal strength.
In the simulation process, the power at the simulation model sources was
varied from 20 dBm to -10 dBm with step of -10 dBm to in order try different
simulations.
4.7 Effect of Increase dispersion of the Fiber Optic
Wavelength dispersion, is a signal dispersion, which occurrs primarily in
single-mode fiber. A significant amount of the light launched into the fiber is leaked
into the cladding. This leaked amount is wavelength dependent and also influences
the speed of propagation. High volume communication lines have carefully timed
spacings between individual signals. Fortunately, wavelength dispersion can be
minimized by careful designation of fiber refractive index.
The dispersion parameter of the fiber optic in the simulation model was
varied from 1 ps/nm/km to 16.75 ps/nm/km. This has been done in order to compare
the results with different dispersion parameters and the power level of sources set at
0 dBm.
39
4.8 Effect of Increase Effective Area of the Fiber optic
The effective area (A
eff
) of the single-mode fiber is an important
measurement parameter. It is the area of the cross section of the beam arrived into
the fiber. The effective area evaluation requires the measurement of the field
distribution in the fundamental mode
The effective area parameter of the fiber optic in the simulation model has
been changed from 64 m
2
to 76.5 m
2
, in order to compare the results with different
effective area parameters as the power level of sources set at 0 dBm.
.
4.9 Modelling the Effect of FWM
Matlab program is used to develop the analytical model of the effect of FWM
in WDM for RoF. The modelling is meant to study the nonlinear effects due to the
FWM in WDM for RoF when the light passing through the medium. Figure 4.6
shows the steps that will be followed in the modeling process.
The total polarization P is nonlinear with respect to the electric field E,
however, it can be written as:
( )
(1) (2) (3)
0
...................... . . . . . . . ....... . ........ ....... .........(4.1) P c _ _ _ = E + E E+ E EE +
where
0
is the vacuum permittivity and
(j)
(j = 1,2,) is jth order susceptibility.
When light propagates in a transparent medium, its electric field causes some
amount of polarization in the medium. While at low light intensities the polarization
is linear with the electric field, nonlinear contributions become important at high
optical intensities, so the polarization equation consists linear terms as well as
nonlinear terms. The first order susceptibility
(1)
represents the linear term, and
nonlinearities can have strong effects in fibers at the third order susceptibility
(3)
. So,
only the nonlinear effects in the optical fibers, which originate from the third-order
susceptibility
(3)
,
will be considered and the other terms will be neglected. The
40
programming will start from the third-order susceptibility
(3)
.
Thus the electric field of
the signal can be written as [6]:
( ) ( )
1
................................................................. , cos .(4.2) ....
N
i i i
i
r t E t z e |
=
E =

Where is the propagation constant, and is angular frequencies

Substituting Equation 4.2 into Equation 4.1, and if only the term of the third
order susceptibility is taken into account, the nonlinear dielectric polarization
(
( )
,
NL
P r t ) can be written as [6]:
( )
( )
( )
( )
( )
3
1 1 1
, cos cos cos
n n n
NL o i i i j j j k k k
i j k
P r t E t z E t z E t z c _ e | e | e |
= = =
=

( )
( )
3
2
1 1
..............................
3
2 .( 1) cos ..........
4
n n
o
i i j i i i
i j
E E E E t term z
c _
e |
= =
(
= +
(


( )
( )
3
3
1
....................................................... cos .... 3 3
4
.. ( ) . . . . 2
n
o
i i i
i
E t z term
c _
e |
=
+

( )
( ) ( )
( )
3
2
1 1
...................
3
cos 2 3 ( 3) 2 .
4
... .
n n
o
i j i i i j
i j
E E t z t z term
c _
e | | |
= =
+

( )
( ) ( )
( )
3
2
1 1
3
cos 2 3 .......................
4
.( 4) 2
n n
o
i j i i i j
i j
E E te t z t z rm
c _
e | | |
= =
+ + +

( )
( ) ( ) (
3
1
........................................ ...
3
4
cos c 5 . ) s ( o
n n n
o
i j k
i j i k j
i j k i j k
E E E
t z term
c _
e e e | | |
= > >
+
+ + + +

( ) ( )
................ ......... cos cos ............... .( 6 .. )
i j k i j k
ter t z m e e e | | | + + +
( ) ( )
................ ......... cos cos ............... ( 7 ... )
i j k i j k
ter t z m e e e | | | + + +
( ) ( )
)
............. ......... cos cos ............ ( ...... 8)
i j k i j k
z rm t te e e e | | | +
(4.3)
The nonlinear susceptibility of the optical fiber generates new waves at the
angular frequencies r s t (r, s, t = 1, 2,). Term 1, in the above equation
represents the effects of SPM and XPM.
41
Terms 2, 4 and 5 can be neglected, due to lack of phase matching. The remaining terms can
satisfy the phase matching condition. The power transferred due to the FWM to new
frequencies after light has propagated distance L in the fiber can be estimated from equation
4.4 [6]:
( )
2
3
2
................................................................................. (4. ........ )
8
.. 4
ijk ijk
ijk i j k
eff eff
d
P PP P L
A n c
e _
| |
= |
|
\ .
where n
eff
is the effective index, A
eff
is the effective area, P
i
, P
j
and P
k
are the input
powers at
i
,
j
and
k
. The factor d
ijk
depends on the number of channels affecting
the FWM
The efficiency of FWM and noise performance are analyzed, taking into
account the effects of difference channel spacing. Equation 4.5 is presented to
evaluate the efficiency of the FWM [23].
2
2
2
( )
eff
n
A D
q

(
=
(
A
(

(4.5)
Equation 4.6 is used to investigate the relationship between the efficiency and
the power of the FWM [23].
( ) ( )
2
2
2
exp( )
9
ijk ijk i j k eff
P d p p p L L

o q
| |
=
|
\ .
(4.6)
where L
eff
is effective length, which can be calculated by using Equation 4.7.
1
l
eff
e
L
o
o

= (4.7)
where is the Angular frequency, d is the degeneracy factor,
(3)
is the third order
susceptibility, A
eff
is the effective Area, n2 is the nonlinear reflective index, c is the
speed of light, D is the dispersion, is the channel space, is the fiber loss
coefficient and L is total fiber length.
42
The third order susceptibility
(3)
,
which includes self-phase modulation
(SPM) and cross-phase modulation (XPM) as well as four-wave mixing (FWM).
Therefore, the SPM and XPM will be considered as zero, thus, their effects on FWM
modeling are neglected. Term1 representing XPM and SPM will be considered as of
zero effect and will be neglected too.
The four-wave mixing, require the phase matching to be efficient. Essentially
this is mean to ensure a proper phase relationship between the interacting waves.
FWM will be a peak at the phase matching spectrum. Equation 4.8 satisfies the
condition of phase matching:
= (
1
)+ (
2
)- (
3
)- (
4
) (4.8)
Where
j
is the propagation constant. If = 0 the phase matching condition is
satisfied, otherwise mismatching occurs.
The model in this study will use only two wavelengths, therefore the phase matching
condition will be = (
2
) - 2 (
1
) =0 in order to satisfy the phase matching
requirement as shown in Figure 4.7.
Figure 4.7 The phase matching condition of two different wavelengths [8]
Term2, term4, and term5 in the polarization Equation 4.3 are considered as
mismatching terms. After neglecting the terms representing the effects of SPM, XPM
that lack phase matching, the remaining terms in the nonlinear equation, which
satisfy the phase matching condition, will be used later to model the FWM.

1

43
CHAPTER 5
RESULTS AND DISCUSSIONS
5.1 Introduction
This chapter presents and discusses the results obtained from the simulation
model by using Optisystem as numerical simulation and Matlab as analytical
simulation. The numerical simulation is simulated accordingly as mentioned in the
previous chapter, with and without external modulated laser.
5.2 Simulation of the Four Wave Mixing Effect
In the FWM simulation model layout, two types of visualiser tools have been
used. The optical spectrum analyzer and the WDM analyzer were fixed after MUX
and at the end of the fiber optic. The results obtained after the multiplexer are same
as the input power level shown before the nonlinear effect. The nonlinear effect
occurs only during the propagation of signals through the fiber. The optical spectrum
analyzer has been used to show the waveform whereby the WDM analyzer has been
used to display signal power (dBm), noise power (dBm) and OSNR (dB).
44
5.3 Simulation Results without the External Modulated Signal
In this simulation two CW lasers were used as signals sources, the
frequencies were set at 1550 and 1550.1 nm, where as the power was set at 0 dBm.
The linewidth has been set at 0, due to the interest in measuring only the total power
of the sideband frequencies, where the shape of the spectrum is not required. The
input signals have propagated through 25 km of nonlinear fiber.
5.3.1 Effect of Channel Spacing variation
Figure 5.1 shows the signal at the input channel when the channel spacing is
set at 0.1 nm.
Figure 5.1 Optical spectrum at the input of the fiber when channel spacing is set
at 0.1 nm
The result obtained from the simulation is depicted in Figure 5.2. From this
figure, the FWM effect is obviousl because the simulation without external
modulated laser is simpler compared to the simulation model with external
modulated laser. The interfering wavelengths generated around the original two
45
wavelength systems are 1549.9 nm and 1550.2 nm, thereby the power of the each
FWM sideband is approximately -59 dBm
Figure 5.2 Optical spectrum at the output of the fiber when channel spacing is set
at 0.1 nm
Figure 5.3 shows the signal at the input channel when the channel spacing is
set at 0.2 nm.
Figure 5.3 Optical spectrum at the input of the fiber when channel spacing is set
at 0.2 nm
When the channel spacing is increased to 0.2 nm, the result obtained from the
simulation is depicted in Figure 5.4. The interfering wavelengths generated around
47
the original two wavelength system are 1549.8 nm and 1550.4 nm, thereby the power
of the each FWM sideband is approximately -61 dBm.
Figure 5.4 Optical spectrum at the output of the fiber when channel spacing is set
at 0.2 nm
Similarly, Figures 5.5 shows the signal at the input channel when the channel
spacing is increased to 0.5 nm.
Figure 5.5 Optical spectrum at the input of the fiber when channel spacing is set
at 0.5 nm
Figure 5.6 shows the interfering wavelengths generated around the original
two wavelength system of 1549.5 nm and 1551 nm; thereby the power of each FWM
sideband is approximately -71 dBm.
48
Figure 5.6 Optical spectrum at the output of the fiber when channel spacing is set
at 0.5 nm
Therefore, as the spacing between channels is increased the effect of the
FWM is decreased
5.3.2 Effect of Different Power Level of the Signals Sources
In the following process, the power level of the input sources was varied from
20 dBm to -10 dBm with step -10 dBm while other parameters such as the dispersion
and the effective area were kept unchanged.
The result obtained from the simulation when the input source power is set at
20 dBm is depicted in Figure 5.7.
49
Figure 5.7 Optical spectrum at the output of the fiber when input power is set at
20 dBm
The result obtained from the simulation when the input source power is set at
10 dBm is depicted in Figure 5.8.
Figures 5.8 Optical spectrum at the output of the fiber when input power is set at
10 dBm
The result obtained from the simulation when the input source power is set at
-10 dBm is depicted in Figure 5.9.
50
Figures 5.9 Optical spectrum at the output of the fiber when input power is set at
-10 dBm
From the results, given it is clear that when the power level is increased to 20
dBm the effect of the FWM becomes very severe as shown in the Figure 5.7. As the
power level of the signal sources is decreased to -10 dBm the FWM becomes less
effective, as shown in the Figure 5.9, therefore, the FWM becomes significantly
effective at high optical power levels.
5.3.3 Effect of Increase Dispersion of the Fiber Optic
The dispersion parameter of fiber optic was changed from 1.0 ps/nm/km
to16.75 ps/nm/km, at input power of 0 dBm. The results were taken at the end of the
fiber optic.
Simulation results at dispersion of 16.75 ps/nm/km at input power of 0 dBm
is shown in Figures 5.10.
51
Figure 5.10 Optical spectrum at the output of the optical when the dispersion of
fiber optic is set at 16.75 ps/nm/km
The results obtained at the end of the fiber when the power level is set at 0
dBm and the dispersion is set at 16.75 ps/nm/km as shown in Figure 5.10, was
compared with the result obtained at the same power level and dispersion of 1
ps/nm/km as shown in Figure 5.4, these result show that the FWM products were
reduced when the dispersion parameter is increased. It is important to mention that
the dispersion parameter can not be set at too high value because it does bring
limitation in bandwidth in the WDM model.
5.4 Simulation Results with the External Modulated Signal
In this simulation two CW lasers were used as signals sources, the
frequencies were set at 1550 and 1550.1 nm, as shown in Figure 4.1, where as the
power was set at 0 dBm, due to the interest in measuring only the total power of the
sideband frequencies, where the shape of the spectrum is not required. The input
signals have propagated through 25 km of nonlinear fiber.
52
5.4.1 Effect of Channel Spacing variation
Figure 5.11 shows the signal at the input channel when the channel spacing is
set at 0.1 nm.
Figure 5.11 Optical spectrum at the input of the fiber when the channel spacing is
set at 0.1 nm
The result obtained from the simulation is depicted in Figure 5.12. The FWM
effect is not quite obvious because the external modulation produce sideband.
53
Figure 5.12 Optical spectrum at the output of the fiber when the channel spacing
is set at 0.1 nm
Figure 5.13 shows the signal at the input channel when the channel spacing is
set at 0.2 nm.
Figure 5.13 Optical spectrum at the input of the fiber when the channel spacing is
set at 0.2 nm
From Figures 5.14, the FWM effect is quite obvious when the channel
spacing is increased to 0.2. The power of the FWM sideband is approximately -72
dBm
54
Figure 5.14 Optical spectrum at the output of the fiber when the channel spacing
is set at 0.2 nm
Figure 5.15 shows the signal at the input channel when the channel spacing is
set at 0.5 nm.
Figure 5.15 Optical spectrum at the input of the fiber when the channel spacing is
set at 0.5 nm
Also in Figures 5.16, the FWM effect is quite obvious when the channel
spacing is increased to 0.5 nm. The power of the FWM sideband is approximately -
87 dBm
55
Figure 5.16 Optical spectrum at the output of the fiber when the channel spacing
is set at 0.5 nm
Therefore, as the spacing between channels is increased the effect of the
FWM is decreased
5.4.2 Effect of Different Power Level of the Signals Sources
In the following process, the power level of the input sources was varied from
20 dBm to -10 dBm with step -10 dBm while other parameters such as the dispersion
and the effective area were kept unchanged.
The result obtained from the simulation when the input source power is set at
20 dBm is depicted in Figure 5.17.
56
Figure 5.17 Optical spectrum at the output of the fiber when input power is set at
20 dBm
The result obtained from the simulation when the input source power is set at
10 dBm is depicted in Figure 5.18.
Figure 5.18 Optical spectrum at the output of the fiber when input power is set at
10 dBm
The result obtained from the simulation when the input source power is set at
-10 dBm is depicted in Figure 5.19.
57
Figure 5.19 Optical spectrum at the output of the fiber when input power is set at -
10 dBm
From the results, given it is clear that when the power level is increased to 20
dBm the effect of the FWM becomes very severe as shown in the Figure 5.17. As the
power level of the signal sources is decreased to -10 dBm the FWM becomes less
effective, as shown in the Figure 5.19, therefore, the FWM becomes significantly
effective at high optical power levels.
The new generated mixing products have high possibilities of falling directly
on the original signal, which produce crosstalk.
5.4.3 Effect of Increase Dispersion of the Fiber Optic
Simulation results with the use of the external modulated laser at dispersion
of 16.75 ps/nm/km at input power of 0 dBm is shown in Figures 5.20.
58
Figure 5.20 Optical spectrum at the output of the fiber when input power is set at
0 dBm
The results obtained at the end of the fiber when the power level is set at 0
dBm and the dispersion is set at 16.75 ps/nm/km as shown in Figures from 5.20.
were compared with the result obtained at the same power level and dispersion of 1
ps/nm/km as shown in Figure 5.12, these result show that the FWM products were
reduced when the dispersion parameter is increased. It is important to mention that
the dispersion parameter can not be set at too high value because it does bring
limitation in bandwidth in the WDM model.
5.4.4 Effect of Increase Effective Area of the Fiber Optic
Simulation results with the use of the external modulated laser at effective
area of 76.5 m
2
at input power of 0 dBm are shown in Figure 5.21.
59
Figure 5.21 Optical spectrum at the output of the fiber when the effective area of
the fiber optic is set at 76.5 m
2
Results obtained at the end of fiber where the power level is set at 0 dBm, and
the effective area is increased to 76.5m
2
is shown in Figure 5.21 is compared with
Figure 5.12 which the effective area is set at 64 m
2
. It is found that the increasing of
the effective area can reduce the FWM effect.
5.5 Simulation of Four Wave Mixing for Higher Number of Channels
This section presents the simulation results as the number of channels is
increased to four in the simulation model, with or without the use of external
modulated laser.
60
5.5.1 Simulation Results for Four Signal Source without External Modulated
Signal
The simulation results for four channels, without use of external modulated
laser, Figure 5.22 shows input signal when number of channels is increased to four
and the channel spacing is set at 0.1 nm.
Figure 5.22 Four optical spectrum at the intput of the fiber when the channel
spacing is set at 0.1 nm
The result obtained from the simulation when the number of channel is
increased is depicted in Figure 5.23. The number of FWM also is increased
61
Figure 5.23 Four output optical spectrum channels when the channel spacing is set
at 0.1 nm
The result obtained from the simulation when the number of channel is
increased and the channel spacing is set at 0.5 nm is depicted in Figure 5.24. The
number of FWM also is increased
Figure 5.24 Four output optical spectrum channels when the channel spacing is
set at 0.5 nm
62
5.5.2 Simulation Results for Four Signal Source with External Modulated
Signal
The simulation results for four channels, when using External modulated
Laser, at different channel spacing..
Figure 5.25 shows input signal when number of channels is increased to four
and the channel spacing is set at 0.1 nm.
Figure 5.25 Four Input optical spectrum channels when the channel spacing is set
at 0.1 nm
The result obtained from the simulation when the number of channel is
increased and the channel spacing is set at 0.1 nm is depicted in Figure 5.26. The
number of FWM is also increased.
63
Figure 5.26 Four output optical spectrum channels when the channel spacing is set
at 0.1 nm
The result obtained from the simulation when the number of channel is
increased and the channel spacing is set at 0.5 nm is depicted in Figure 5.27. The
number of FWM is also increased but with less effect.
Figure 5.27 Four output optical spectrum channels when the channel spacing is set
at 0.5 nm
64
5.6 Discussions
Based on the results presented, The FWM effects increase as the number of
channels is increased. The number of spurious signals due to FWM increase
geometrically and given by
M= (N
3
-N
2
)/2 (5.1)
where N is the number of channels and M is the number of the newly generated
sidebands. The new generated mixing products have high possibilities fall directly on
the original signal, this could produce crosstalk.
Therefore, as the spacing between channels is reduced or remained equal the
effect of the crosstalk is found to become greater. When the spacing between the
channels is unequal, showed that the mixing products have low power level and
highly possible not to falls on the original signal, which makes them easy to be
filtered, and in turn improve the system performance.
Results obtained at the end of fiber where the power level is set at 0 dBm, and
the effective area is increased to 76.5m
2
are shown in Figures 5.10. It is found that
the OSNR obtained is better than before increasing the effective area as shown in
Figure 5.4.
As general, the increase of the effective area can reduce the FWM effect and
give higher OSNR value compared to the simulation result obtained with the same
power level.
The effective area refers to the equivalent area of the fiber in which the
optical power is transmitted. In the case of single mode fiber, this is roughly
proportional to the core area. Fiber with a large effective area offers reduced optical
power density, which raises the power threshold for the FWM penalties.
In addition, the effective area parameter and the dispersion parameter can be
used to calculate the FWM efficiency as follows:
65
= n
2
/(A
eff
x D x
2
) (5.2)
where is the FWM efficiency, n
2
is the nonlinear index coefficient, A
eff
is the
effective area, D is the dispersion and is the spectral width.
5.7 Analytical Modelling
Matlab based program has been developed using Equations 4.4 to 4.6 in order
to design analytical model (Appendix A), which assists to predict the expected FWM
power in different channel spacing. The designed model can give the expectation
value of the FWM power in different input signal power level.
The analytical results have been compared to the results obtained from the
numerical simulation, as shown in Figures 5.28 and 5.29.
Figure 5.28 Power per channel vs. FWM power
5 10 15 20 25 30 35 40
-125
-120
-115
-110
-105
-100
-95
-90
power per channel in mill watt
F
W
M
p
o
w
e
r
(
d
B
m
)
66
Figure 5.29 Channel spacing versus FWM power
These results show that when power per channel is increased the spurious
power increase, too. The power of the FWM produced is found to be inversely
proportional to the square of the channel spacing, when all channels have the same
input power. Furthermore, the FWM effects increase exponentially as the level of the
optical power from the signal sources is increased, as shown in the Figure 5.28
Based on results presented, it is clear that when the channel spacing is smaller
the FWM effect becomes more significant due to the phase matching, as shown in
Figure 5.29.
5.8 Four Wave Mixing Reduction
One way to combat the FWM process is to use unequal channel spacing, so
that the mixing products do not coincide with signal frequency, and to use low input
power, or high effective area. Fiber dispersion management is a very effective way,
helpful not for FWM but also is the case of other nonlinear phenomena, that degrade
0. 1 0. 15 0. 2 0. 25 0. 3 0. 35 0. 4 0. 45 0. 5 0. 55 0. 6
-80
-75
-70
-65
-60
-55
c hannel s pac i ng
F
W
M
p
o
w
e
r
(
d
B
m
)
Anal y t i c al s im ulat ion
numeri c al s im ulat ion
67
transmission performance in the fiber, also FWM can be mitigated by increasing the
effective area of the fiber [19].
5.8.1 Effect of Unequal Channels
Figure 5.30 shows input signal when the channel spacing is unequal.
Figure 5.30 Optical spectrum at the input of the fiber when the channel spacing is
unequal
When the spacing between the channels is unequal, showed that the mixing
products have low power level and highly possible not to falls on the original signal,
which makes them easy to be filtered, and in turn improve the system performance.
As shown Figure 5.31.
68
Figure 5.31 Optical spectrum at the output of the fiber with unequal channel
spacing
5.8.2 Effect of Increase Effective Area of the Fiber Optic
The effective area parameter of fiber optic has been changed from 64 m
2
to
76.5 m
2
at the power level set at 0 dBm. The results were taken at the end of the
fiber optic.
Simulation results at effective area of 76.5 m
2
at input power of 0 dBm are
shown in Figures 5.32.
Figure 5.32 Optical spectrum at the output of the fiber when the effective area of
the fiber optic is set at 76.5 m
2
69
Results obtained at the end of fiber where the power level is set at 0 dBm, and
the effective area is increased to 76.5m
2
s shown in Figure 5.32. It is found that the
increasing of the effective area can reduce the FWM effect.
70
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusion
Future wireless systems it will be targeting towards providing broadband
access and personal area multimedia services to large number of subscribers. Radio
over fiber (RoF) network accompanied with wavelength division multiplexing
(WDM) can provide a simple topology, easier network management, and an
increased capacity by allocating different wavelengths to individual remote nodes.
The performance of WDM networks is strongly influenced by nonlinearity
characteristic inside the fiber. Therefore the nonlinearity effects of fiber optics pose
additional limitation in WDM systems.
It is well known that FWM in WDM for RoF signals are mostly generated by
non-degenerate FWM process regardless of the number of input signals. In this study
only two and four input signals were launched into the optical fiber. The FWM effect
has been investigated analytically and numerically simulated. Simple equations to
determine the spectral linewidth, the FWM power due to channel spacing and the
power of the FWM components due to the input power have been deduced.
The numerical simulation results obtained have shown the spectral
characteristics of the FWM in WDM for RoF where the effects of FWM are
pronounced with decreased channel spacing of wavelengths or at high signal power
levels.
71
The numerical simulation model results and the analytical model results were
compared. The numerical simulated results clearly demonstrate that the degradation
due to FWM can be minimized by ensuring that the phase matching does not occur.
This has been achieved by increasing the channel separation and supplying low
signal power level. The high effective area is also found to the decrease FWM effect.
It is noticed that the FWM also causes inter-channel cross talk for equally spaced
WDM channels. Thus, FWM can be mitigated using unequal channel spacing.
It could be concluded that results obtained from this study will provide useful
information for identifying the fundamental limit of the capacity of the WDM
systems.
6.2 Recommendations for Future Work
FWM in WDM for RoF effects are likely to become the main source of
performance degradation in contemporary and future fiber optical communications,
therefore future studies in attempt to overcome such problems, the following could
be recommended.
Investigation of FWM effect using more than eight sources is essential
because most technologies nowadays use DWDM in order to meet the huge capacity
demands
Crosstalk is the transfer of power from one channel to another, can occurs
due to nonlinear effect. FWM can produce crosstalk between wavelength channels.
This crosstalk is strongly dependent on channel separation and optical power.
Therefore it is important to estimate how large the cross talk is.
72
7. References:
[1] Hamed Al-Raweshidy, Radio over Fiber Technologies for Mobile
Communications Networks , Artech House, 2002.
[2] Guo, Y., Kao, C. K. and Chiang, K. S. Nonlinear photonics: nonlinearities
in optics, optoelectronics and fiber communications. Springer-Verlag, 2002.
Berlin, Germany.
[3] Govind P.Agrawal, Fiber-Optic communication system McGraw-Hill
December 2001.
[4] Robert, C. E. Optical Networking A beginers guide McGraw-
Hill/Osborne 2004
[5] Yannis, L. G. New optical Microwave Up-Conversion Solution in Radio
over Fiber Network Journal of lightwave technology, 24 (3) (2006) 1277-
1282
[6] Antti Lamminp, Measurement of nonlinearity of optical fiber. Master
thesis, Helsinki University of Technology, 2003.
[7] D. Marcuse, Effect of Fiber Nonlinearity on Long-Distance Transmission,
Journal of lightwave technology, 9 (1) (1991) 121-128.
[8] Remigius Zengerle, Modeling of Nonlinear Phenomena in Optical Multi-
channel Trasmission system Master thesis, University of Kaiserslautern,
2005.
[9] A. V. Yulin, D. V., and P. St. J. Russell Four-wave mixing of linear waves
and solitons in fibers with higher-order dispersion Journal of lightwave
technology, 29 (3) (2004) 950-955.
[10] Ajung Kim, Young Hun Joo, and Yungsoo Kim, 60GHz Wireless
Communication Systems with Radio-over-Fiber Links for Indoor Wireless
LANs Journal of lightwave technology, 20, (4), (2004) 517-521.
[11] Anthong Nooma, Radio over Fiber Technology for Broadband wireless
communication systems Master thesis, Eindhoven University of Technology,
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[12] Takuo Tanemura and Kazuro Kikuchi, Unified analysis of modulational
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lightwave technology, 20 (12) (2003) 2502-2513.
73
[13] Caiqin Wu and Xiupu Zhang, Impact of Nonlinear Distortion in Radio Over
Fiber Systems With Single-Sideband and Tandem Single-Sideband
Subcarrier Modulations Journal of lightwave technology, 24 (5) (2006)
2076 2090.
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[19] Vrizlynn L. L. Thing, P. Shum, and M. K. Rao, Bandwidth-Efficient WDM
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74
APPENDIX A
MATLAB PROGRAM FOR FWM POWER
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% this program is used to compute power per channel versus FWM power
% and to compute channe spaing versus FWM channel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% variables
%
% X = third order susceptibility
% lemda = wavelength in vacuum
% c = speed og light in vacuum
% Aeff= effecive area of the optical fiber
% n= nonlinear reflective inex
% alfa = fiber loss
% D= degeneracy factor
% eff = FWM efficiency
% Leff = effctive length
%
x=6*10^-15;
lemda=0.5*10^-6;
c=3*10^8;
Aeff=6.4*10^-11;
n=1.48;
75
alfa=.0461;
eff=.05;
Leff=22*10^3;
D=3;
k=(32*(pi)^3*x)./(n^2.*lemda*c)*(Leff/Aeff)
P=eff*(D.*k).^2*(1*10^-3)^3*exp(-alfa*75)
Pdb= 10*log10(P/10^-3)
plot(x,y)
hold on
y1 = [-59.5 -61.2 -65.5 -68 -72.5 -80];
plot(x,y1,'r')