08 modulators 2015 - UCY · Amplitude modulation in optical communications is known as intensity modulation, and this is the most common approach. It can be achieved either through

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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

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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: