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Direct modulation

Consider the static optical power-versus-current characteristic of a laser diode; if

we bias at point IB and then superimpose modulation, then the optical power will
Electrical-to-optical conversion: modulators track changes in this. We show it here for sinusoidal modulation:

Stavros Iezekiel PL (mW)

Department of Electrical and IL
PL = P0 (1 + m cos ω mt ) = P0 + p (t )
Computer Engineering PL (t ) = s L I L (t )
University of Cyprus
P0
PL

IL (mA)

I L = I B [1 + m cos ωmt ] = I B + i (t )
• HMY 645 IB
• Lecture 08
• Spring Semester 2015

3 4

Although the method of direct modulation is a useful one, it suffers a number of

problems:

1. As well as the intensity of the light, the wavelength is modulated. (This

phenomenon is called chirp.) Along with fibre dispersion, this leads to a chirp- Ti-diffused optical waveguide
induced dispersion limit on transmission distance. CW light Electrodes

2. The maximum bandwidth we can modulate up to is only a few tens of GHz at the
very best.

3. The maximum quantum efficiency (η) in theory is 100%, and this places an upper
limit on the slope efficiency (and therefore the “gain”). Lithium
niobate
Modulated light
hc substrate
sL = η
qλ
EXTERNAL MODULATION
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In addition to direct modulation, we can also modulate the light from a laser with an external One advantage of external modulation is that it can be used to implement optical
component known as a modulator. Hence the terms external modulation and external modulator.
phase modulation, which opens up the possibility of coherent optical communications
and therefore increased receiver sensitivity.
External modulation
Laser emits constant optical power. This then
External passes through an optical modulator (external
modulator Modulated modulator) – this is a voltage driven device. As
light we adjust the voltage, the amount of optical
output power absorbed will vary. In this way, we
CW achieve modulation of the optical power
RF input
Laser coming out of the modulator.
+ Bias

Bias point and

modulation depth
Optical chosen to give
power incrementally linear
slope P0 + p (t )
This will
depend on the
CW laser
output power
as well as drive
conditions Vπ V

VB + v(t )

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Other advantages of external modulation compared to direct modulation: Material Considerations

• Laser diodes suffer from chirp which then introduces dispersion penalty. Not an issue Obviously the key requirement is that some optical property of the material must
with external modulation. change in response to a changing electrical parameter.

• It is possible to produce formats such as single sideband (SSB) or double-sideband • Electro-optic effect
suppressed carrier (DSB-SC) • An applied electric field changes the refractive index
• This leads to phase changes
• Slope efficiency of laser diodes is limited by fundamental quantum efficiency (100% • Can also produce intensity modulation
max), whereas for external modulation the slope efficiency scales with CW laser power. when combined with an interferometer

• Laser diodes limited to 30 GHz max (unless optical injection locking is used), whereas • Acousto-optic effect
up to at least 100 GHz has been reported with modulators. • A sound wave (resulting from electric field applied to a piezoelectric) changes
the refractive index
• Many Mach-Zehnder modulators are based on lithium niobate and are difficult to
integrate with other components, but electro-absorption modulators lend themselves to • Electro-absorption effect
monolithic integration with driver electronics. • Applied electric field changes the absorption

• Recent work by Intel, for example, on silicon modulators paves the way for integration
with CMOS electronics.
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To date, the dominant type of modulator is the lithium niobate Mach-Zehnder, which
Comparison of electro-optic materials
is based on the electro-optic effect.

Electro-optic effect:

A small change in refractive index n results from an electric field E:

1 1
= + rE + RE 2 + ...

Moodie, CIP
n 2 n02

Pockels effect Kerr effect

Only certain crystalline solids show the Pockels effect, Observed in all optical materials with varying
as it requires lack of inversion symmetry magnitudes, but generally weaker than Pockels
It is linear with respect to electric field and hence effect.
Apart from presence of electro-optic effect, other important material properties include
voltage
optical loss, maximum optical power handling capability and stability (thermal and
In general, the Pockels effect is used since it is stronger (Kerr effect is primarily optical).
exploited for optical fibre solitons).
Modulators can be made from inorganic materials, semiconductors or polymers
The Pockels coefficients rij are elements of a 6 x 3 tensor

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However, for the moment lithium niobate (an inorganic material) dominates, not
because it excels with respect to loss, stability, maximum optical power or electro-optic
sensitivity, but because it offers the best compromise between all four key parameters.

Lithium niobate is also relatively cheap since it is also widely used in surface acoustic
wave filters. It can be grown using the Czochralski process in wafer sizes large enough to
accommodate the relatively long and narrow structures required for Mach-Zehnder
modulators.

Polymer modulator fabricated using SU-8 based

rubber stamp as a potential route to low cost
manufacturing.
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Light from a laser can be described by its electric field. To keep things simple we
consider a purely monochromatic laser (i.e. a “perfect” laser), for which the emitted
field at some fixed distance from the laser is given by:

E (t ) = Eo (t )e j (ωo ( t ) t +φo ( t ))
Lucent

Optical phase

Amplitude (complex quantity)

Optical frequency (i.e. 100’s of THz)

In analogy with electronic communications, we are able to modulate amplitude,

frequency or phase.

MACH-ZEHNDER Amplitude modulation in optical communications is known as intensity modulation,

and this is the most common approach. It can be achieved either through direct or
MODULATORS external modulation.

Frequency and phase modulation can only be achieved with an external modulator,
and can only be detected with a coherent photoreceiver. We will not consider these
techniques any further here.

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The optical intensity is directly proportional to the square of the electric field External modulators that are based on the interferometer principle are known as
magnitude. The optical power emitted by the laser is, in turn, directly proportional Mach-Zehnder modulators (MZM). To understand the basic principle, we need to
to the intensity. So we can write: remember something about superposition (and constructive and destructive
interference).
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optical power ∝ E (t ) = Eo (t ) Consider some examples:

So the optical power varies only with variations in the amplitude of the electric field,
and this is achieved either through direct modulation or an external modulator.
Constructive Destructive "Quadrature phase" ±90°
interference: interference: interference:
We will now consider the operation of an external modulator based on the principle
of an interferometer: 1.0 1.0 1.0
Electrical input (modulation) + + +
0.2 -0.2 -0.2i
Unmodulated = = =
light from laser
1.2 0.8 1-0.2i

Modulator
time time time
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Now consider the optical waveguide structure of a MZM: The waveguides are formed from titanium which is diffused onto a layer of lithium niobate,
which forms the substrate. Lithium niobate is a material that has a strong electro-optic effect –
The two waveguide arms have equal if we apply a voltage to it, then its refractive index changes. We can show that this is equivalent
length, so the delay and hence phase to introducing a phase shift.
shift is equal for both paths.
Input light
Ti-diffused optical waveguide
CW light Electrodes

Output light
Lithium
Y-junction. The incoming light is niobate
split equally into two paths at substrate Modulated light
this point. So the light on each Second Y-junction. Here light from the two arms
of these paths for an ideal is combined in phase. However, the optical power
device will be 3 dB less in In the MZM shown above, a voltage applied to the electrodes will introduce a phase shift into
of the output will be lower than that of the input
optical power compared to the the upper arm. For zero volts there is no phase shift and we have constructive interference, but
due to losses in the waveguides and at the Y-
input light. junctions. We refer to this as the insertion loss of if we increase the voltage to some value (called Vπ) then there is a π radians relative phase shift
the MZM leading to total extinction. Values in between will lead to varying levels of absorption.

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Just as we have a light-current characteristic for a laser diode, we have a voltage-light The transfer characteristic is given by:
characteristic for a MZM:

Po Pi Po T ff   πVm 
Po = T ff Pi
= 1 + cos 
Pi 2   Vπ 
1 T ff < 1
Reduction due to If we apply a bias voltage of nVπ/2 (where n is odd) and a small-signal
optical insertion loss modulation component given by vm(t), then linearization of the above equation
of modulator
around the bias point will yield:
T ff
Po T ff   π (VB + vm (t ) )  T ff  π vm (t ) 
= 1 + cos  ≈ 1 ± 
Pi 2   Vπ  2  Vπ 

from which the slope efficiency (in W/V) is obtained as:

0 Vm Vπ dPo T ff π
1 2 3 4 = Pi
0 dvm 2Vπ
So by increasing the optical power from the CW laser, we can increase the
Vm = Vπ efficiency of the modulator.
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Choice of the bias point is an important consideration, because the sinusoidal shape of the So if we use an appropriate bias point (say 3Vπ/2), and then apply modulation, we
MZM transfer characteristic means there are no linear parts to the curve, so if we want to have the following:
have almost linear operation we must choose points on the curve that are good
approximations to a straight line. Also, we can show that the best bias points will be those for Po Pi
which the slope of the characteristic is maximised (in order to prove efficiency).
Bias point and modulation
If we assume constant CW input power, then: 1 depth chosen to give
incrementally linear slope
Reduction due to
optical insertion loss
T ff Pi   πVm  of modulator
Po = 1 + cos  T ff
2   Vπ  Po + p (t )
 π
Pi
dPo T ff Pi  πVm 
= − sin  
dVm 2  Vπ  Vπ 

Finding the maxima/minima for this derivative yields the following as suitable bias points: 0 Vm Vπ
0 1 2 3 4
Vm 1 3 5
= , , ,..... VB + v(t )
Vπ 2 2 2
Vπ