08 modulators 2015 - ucy · amplitude modulation in optical communications is known as intensity...
TRANSCRIPT
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Electrical-to-optical conversion: modulators
• HMY 645
• Lecture 08
• Spring Semester 2015
Stavros IezekielDepartment of Electrical and
Computer Engineering
University of Cyprus
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PL (mW)
IL (mA)
[ ] )(cos1 tiItmII BmBL +=+= ω
BI
( ) )(cos1 00 tpPtmPP mL +=+= ω
0P
)()( tIstP LLL =
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
track changes in this. We show it here for sinusoidal modulation:
Direct modulation
LI
LP
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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-
induced dispersion limit on transmission distance.
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”).
λη
q
hcsL =
EXTERNAL MODULATION
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CW light
Modulated light
Ti-diffused optical waveguide
Lithium
niobate
substrate
Electrodes
In addition to direct modulation, we can also modulate the light from a laser with an external
component known as a modulator. Hence the terms external modulation and external modulator.
VVπ
Bias point and
modulation depth
chosen to give
incrementally linear
slope
Optical
power
This will
depend on the
CW laser
output power
as well as drive
conditions
)(tvVB +
)(0
tpP +
External
modulator
CW
LaserRF input
+ Bias
External modulation
Modulated
light
output
Laser emits constant optical power. This then
passes through an optical modulator (external
modulator) – this is a voltage driven device. As
we adjust the voltage, the amount of optical
power absorbed will vary. In this way, we
achieve modulation of the optical power
coming out of the modulator.
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One advantage of external modulation is that it can be used to implement optical
phase modulation, which opens up the possibility of coherent optical communications
and therefore increased receiver sensitivity.
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Other advantages of external modulation compared to direct modulation:
• Laser diodes suffer from chirp which then introduces dispersion penalty. Not an issue
with external modulation.
• It is possible to produce formats such as single sideband (SSB) or double-sideband
suppressed carrier (DSB-SC)
• Slope efficiency of laser diodes is limited by fundamental quantum efficiency (100%
max), whereas for external modulation the slope efficiency scales with CW laser power.
• Laser diodes limited to 30 GHz max (unless optical injection locking is used), whereas
up to at least 100 GHz has been reported with modulators.
• Many Mach-Zehnder modulators are based on lithium niobate and are difficult to
integrate with other components, but electro-absorption modulators lend themselves to
monolithic integration with driver electronics.
• Recent work by Intel, for example, on silicon modulators paves the way for integration
with CMOS electronics.
Material Considerations
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Obviously the key requirement is that some optical property of the material must
change in response to a changing electrical parameter.
• Electro-optic effect
• An applied electric field changes the refractive index
• This leads to phase changes
• Can also produce intensity modulation
when combined with an interferometer
• Acousto-optic effect
• A sound wave (resulting from electric field applied to a piezoelectric) changes
the refractive index
• Electro-absorption effect
• Applied electric field changes the absorption
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To date, the dominant type of modulator is the lithium niobate Mach-Zehnder, which
is based on the electro-optic effect.
Electro-optic effect:
A small change in refractive index n results from an electric field E:
...11 2
2
0
2+++= RErE
nn
Pockels effectOnly certain crystalline solids show the Pockels effect,
as it requires lack of inversion symmetry
It is linear with respect to electric field and hence
voltage
Kerr effectObserved in all optical materials with varying
magnitudes, but generally weaker than Pockels
effect.
In general, the Pockels effect is used since it is stronger (Kerr effect is primarily
exploited for optical fibre solitons).
The Pockels coefficients rij are elements of a 6 x 3 tensor
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Moodie
, C
IP
Comparison of electro-optic materials
Apart from presence of electro-optic effect, other important material properties include
optical loss, maximum optical power handling capability and stability (thermal and
optical).
Modulators can be made from inorganic materials, semiconductors or polymers
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Polymer modulator fabricated using SU-8 based
rubber stamp as a potential route to low cost
manufacturing.
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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.
MACH-ZEHNDER
MODULATORS
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Lu
ce
nt
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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:
))()(()()(
tttj
oooetEtEφω +=
Amplitude (complex quantity)Optical frequency (i.e. 100’s of THz)
Optical phase
In analogy with electronic communications, we are able to modulate amplitude,
frequency or phase.
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
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
magnitude. The optical power emitted by the laser is, in turn, directly proportional
to the intensity. So we can write:
22)()( tEtE o=∝ power optical
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.
We will now consider the operation of an external modulator based on the principle
of an interferometer:
Modulator
Electrical input (modulation)
Unmodulated
light from laser
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External modulators that are based on the interferometer principle are known as
Mach-Zehnder modulators (MZM). To understand the basic principle, we need to
remember something about superposition (and constructive and destructive
interference).
Consider some examples:
+
=
time
1.0
-0.2
0.8
Destructive
interference:
1.0
0.2
1.2
+
=
time
Constructive
interference:
+
=
time
"Quadrature phase" ±90°
interference:
1.0
-0.2i
1-0.2i
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Now consider the optical waveguide structure of a MZM:
Input light
Y-junction. The incoming light is
split equally into two paths at
this point. So the light on each
of these paths for an ideal
device will be 3 dB less in
optical power compared to the
input light.
The two waveguide arms have equal
length, so the delay and hence phase
shift is equal for both paths.
Second Y-junction. Here light from the two arms
is combined in phase. However, the optical power
of the output will be lower than that of the input
due to losses in the waveguides and at the Y-
junctions. We refer to this as the insertion loss of
the MZM
Output light
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CW light
Modulated light
Ti-diffused optical waveguide
Lithium
niobate
substrate
Electrodes
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 –
if we apply a voltage to it, then its refractive index changes. We can show that this is equivalent
to introducing a phase shift.
In the MZM shown above, a voltage applied to the electrodes will introduce a phase shift into
the upper arm. For zero volts there is no phase shift and we have constructive interference, but
if we increase the voltage to some value (called Vπ) then there is a π radians relative phase shift
leading to total extinction. Values in between will lead to varying levels of absorption.
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0 1 2 3 4
0
1
πVVm
io PP
ffT
Reduction due to
optical insertion loss
of modulator
Just as we have a light-current characteristic for a laser diode, we have a voltage-light
characteristic for a MZM:
πVVm =
1<
=
ff
iffo
T
PTP
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The transfer characteristic is given by:
+=
π
πV
VT
P
P mff
i
o cos12
If we apply a bias voltage of nVπ/2 (where n is odd) and a small-signal
modulation component given by vm(t), then linearization of the above equation
around the bias point will yield:
( )
±≈
++=
ππ
ππV
tvT
V
tvVT
P
P mffmBff
i
o )(1
2
)(cos1
2
from which the slope efficiency (in W/V) is obtained as:
i
ff
m
o PV
T
dv
dP
π
π
2=
So by increasing the optical power from the CW laser, we can increase the
efficiency of the modulator.
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Choice of the bias point is an important consideration, because the sinusoidal shape of the
MZM transfer characteristic means there are no linear parts to the curve, so if we want to
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
which the slope of the characteristic is maximised (in order to prove efficiency).
If we assume constant CW input power, then:
+=
π
πV
VPTP miff
o cos12
−=
ππ
ππV
V
V
PT
dV
dP miff
m
o sin2
Finding the maxima/minima for this derivative yields the following as suitable bias points:
,.....2
5,
2
3,
2
1=
πV
Vm
22
0 1 2 3 4
0
1
πVVm
io PP
ffT
Reduction due to
optical insertion loss
of modulator
Bias point and modulation
depth chosen to give
incrementally linear slope
πV
tvVB )(+
i
o
P
tpP )(+
So if we use an appropriate bias point (say 3Vπ/2), and then apply modulation, we
have the following: