Simulation of Traveling Wave Electroabsorption Modulators ...546777/FULLTEXT01.pdf · the project have been so far limited to Amplitude Modulation / On-Oﬀ Keying. It is worthwhile

Simulation of Traveling Wave Electroabsorption Modulators for

Phase Modulation

Prasanna Ramaswamy

Promotor(s): Prof. Urban WestergrenAssisting supervisor(s): Prof. Urban Westergren

Master dissertation submitted in order to obtain the academic degree of

Erasmus Mundus Master of Science in Photonics

Royal Institute of Technology KTH, StockholmAcademic year 2011-2012

Erasmus Mundus MSc in Photonics Erasmus Mundus

Simulation of Traveling Wave

Electroabsorption Modulators for Phase

Modulation

PRASANNA RAMASWAMY

Master’s Thesis

Supervisor: Prof. Urban Westergren

iii

Abstract

Electro-Absorption Modulators (EAMs) have been instrumental in achieving

ultrafast modulation speeds of over 100 Gb/s, and in particular, segmented

Travelling-Wave (TWEAMs) designs offer excellent compatibility with standard

microwave technology due to their characteristic impedance being closer to 50Ω.

The TWEAM device fabricated as part of the European Project HECTO, has

been succesful is field trials at 112 Gb/s using On-Off Keying (OOK). Achiev-

ing phase modulation using a TWEAM offers not only significant improvements

over OOK in terms of higher bit rate, but also a great advantage against other

phase modulators that use electro-optic effects which need much stronger drive

signals and also present issues with chip-integration. The existing model for the

TWEAM has been modified to incorporate a variable delay line to simulate en-

hanced electro-optic effects in the active quantum well layer. Simulations were

performed for Binary and Quadrature Phase Shift Keying, and 8-Quadrature

Amplitude Modulation. Clear constellation diagrams are obtained at 10 Gb/s

with Error Vector Magnitude of around -19 dB at 10 Gb/s and -10 dB at 50

Gb/s. Results from this thesis emphasize the need for further optimization of

the model and fabricating a TWEAM that is capable of advanced modulation

formats.

iv

Acknowledgements

I would like to express my gratitude to my supervisor, Prof. Urban Westergren,

for his constant guidance throughout the course of this thesis work. I would also

like to thank all the professors in Belgium and Stockholm, whose courses helped

me increase my knowledge in the area of photonics and which I thouroughly

enjoyed. I am very thankful to the European Commission and the EMMP con-

sortium that provided me with scholarship, without which my stay and study in

Europe would have been simply impossible. A sincere thanks to all my friends

in Belgium and Stockholm who made these two years memorable.

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Background 4

2.1 Direct and External Modulation . . . . . . . . . . . . . . . . . . . 4

2.1.1 Electro-optic and Electro-absorption Modulators . . . . . . 5

2.2 Electro-absorption Mechanisms . . . . . . . . . . . . . . . . . . . 5

2.2.1 Franz-Keldysh Effect . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Quantum Confined Stark Effect . . . . . . . . . . . . . . . 6

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Electro-Absorption Modulators 9

3.1 Device Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Device Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . 11

3.2.2 Modelling Optical Absorption . . . . . . . . . . . . . . . . 13

3.3 Electro-optic effect in TWEAMs . . . . . . . . . . . . . . . . . . . 14

3.3.1 Relation between Optical Absorption and change in Re-

fractive Index . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.2 Transmission line model for voltage dependent delay . . . 16

3.4 Summary and Simulation Setup . . . . . . . . . . . . . . . . . . . 18

v

CONTENTS vi

4 TWEAM as a Phase Modulator 20

4.1 Simulating Phase Shift Keying . . . . . . . . . . . . . . . . . . . . 21

4.1.1 Binary Phase Shift Keying . . . . . . . . . . . . . . . . . . 21

4.1.2 Quadrature Phase Shift Keying . . . . . . . . . . . . . . . 29

4.2 Quadrature Amplitude Modulation . . . . . . . . . . . . . . . . . 33

4.3 Limitations and Summary . . . . . . . . . . . . . . . . . . . . . . 36

5 Conclusions and Future Work 38

Appendices 38

A Netlist Generation 39

A.1 Large Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 39

A.2 Voltage-dependent Delay line . . . . . . . . . . . . . . . . . . . . 42

B Circuit Schematic 44

Bibliography 44

List of Figures

1.1 Internet traffic through the years. Data sourced from [3] . . . . . 2

2.1 Schematic of an Optical Transmitter [6] . . . . . . . . . . . . . . . 5

2.2 Band to band absorption involving the Franz Keldysh Effect . . . 6

2.3 Band diagram of a quantum well under zero and non-zero electric

field, illustrating QCSE [9] . . . . . . . . . . . . . . . . . . . . . 6

2.4 Band diagram of a quantum well under zero and non-zero electric

field, illustrating QCSE [10] . . . . . . . . . . . . . . . . . . . . . 7

3.1 Schematic of a TWEAM [12] . . . . . . . . . . . . . . . . . . . . 9

3.2 (a) Circuit depicting a Segmented TML structure (b) Impedance

variation along the length [12] . . . . . . . . . . . . . . . . . . . . 10

3.3 (a) Entire device structure (b) Vertical cross section including the

DC bias configuration [13] . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Equivalent circuit representation of a slice of the (a) active section

(b) passive section [13, 14] . . . . . . . . . . . . . . . . . . . . . . 12

3.5 Optical absorption as a function of voltage showing a fit using the

empirical relation in Equation 3.1 [12] . . . . . . . . . . . . . . . 14

3.6 Transmission line model using lumped LC elements . . . . . . . . 16

3.7 Schematic of the delay line implementation . . . . . . . . . . . . . 17

3.8 Summary of the structure of the TWEAM and the models used . 19

4.1 Comparison of modulators with a RQW and a 3-Step QW active

region [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

vii

LIST OF FIGURES viii

4.2 Constellation Diagram for BPSK . . . . . . . . . . . . . . . . . . 22

4.3 Schematic of a BPSK Demodulator . . . . . . . . . . . . . . . . . 23

4.4 Modulated BPSK output signals corresponding to the two bit lev-

els . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.5 Error Vector Magnitude versus Length for Achieved BPSK at 10

Gb/s and 50 Gb/s . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.6 Constellation diagrams for the achieved BPSK (a) with 2×100 µm

active segments at 10 Gbps (b) 2×150 µm active segments at 50

Gbps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.7 Error Vector Magnitude versus Optical input power for Achieved

BPSK at 10 Gb/s and 50 Gb/s . . . . . . . . . . . . . . . . . . . 27

4.8 Constellation diagrams showing poor BPSK modulation with large

input optical power of 10 mW at (a) 10 Gb/s (b) 50 Gb/s . . . . 27

4.9 Error Vector Magnitude versus Bias Voltage for Achieved BPSK

at 10 Gb/s and 50 Gb/s . . . . . . . . . . . . . . . . . . . . . . . 28

4.10 Constellation diagrams for achieved BPSK with 2.5V bias voltage

for (a) 10 Gb/s (b) 50 Gb/s . . . . . . . . . . . . . . . . . . . . . 29

4.11 Constellation Diagram for QPSK . . . . . . . . . . . . . . . . . . 30

4.12 Schematic of a QPSK demodulator . . . . . . . . . . . . . . . . . 31

4.13 Modulated QPSK output signals corresponding to the four symbols 31

4.14 Constellation diagrams for achieved QPSK at (a) 10 Gb/s (b) 50

Gb/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.15 Constellation Diagrams for 8-QAM . . . . . . . . . . . . . . . . . 33

4.16 Constellation diagrams for achieved 8-QAM at (a) 10 Gb/s (b) 50

Gb/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.17 Modulated 8-QAM output signals corresponding to the 8 bit levels 35

4.18 Normalised impulse response of a segmented TW-EAM[20] . . . . 36

4.19 Modulated signal showing peak and settling time . . . . . . . . . 37

A.1 Schematic of the delay line implementation . . . . . . . . . . . . . 42

B.1 Schematic of the modulator circuit . . . . . . . . . . . . . . . . . 44

Chapter 1

Introduction

1.1 Motivation

Communication has played an important role in the development of socities all

along the course of history. The sophistication of the communication systems

increased with increase in the distances over which communication was required,

and also with the increase in the amount of data that was needed to be conveyed

across.

In the past century, it was shown that telecommunication using optical sig-

nals offered many advantages over prevailing methods of using electrical and radio

signals. Beginning with the invention of the laser in the 1960s [1] and the fiber

optic cable in the 70s [2], there has been a steady growth in the area of telecom-

munications, fuelled by availability of smaller and more compact light sources,

transmission media with lower losses, dispersion compensating fibers, optical am-

plifiers and so on. And interlinked to this development, came a rapid increase in

demand for much more data to be squeezed into communication networks. As

can be seen from Figure 1.1, with ever increasing penetration of the internet, and

with increase in bandwidth-intensive services like video on demand, there is a

continued research interest in building transmission links with higher data rate

capabilities.

1

CHAPTER 1. INTRODUCTION 2

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110

0.5

1

1.5

2

2.5

3x 10

4

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110

0.5

1

1.5

2

2.5

3x 10

4

Fix

ed In

tern

et T

raffi

c(P

B/m

onth

)

2000 2002 2004 2006 2008 2010 20120

100

200

300

400

500

600

Year

Mob

ile In

tern

et T

raffi

c(P

B /

mon

th)

Figure 1.1: Internet traffic through the years. Data sourced from [3]

The European project, HECTO (High-Speed Electro-Optical Components for

Integrated Transmitter and Receiver in Optical Communication) which concluded

in 2009, developed photonic components, transmitters and receivers for high-

speed and cost-effecient communication systems, that were field-tested at 112

Gb/s [4]. The studies carried out on the electro-absorption modulator as part of

the project have been so far limited to Amplitude Modulation / On-Off Keying.

It is worthwhile to look at the chirp properties and investigate if a complete

transition to Phase modulation / Phase Shift Keying can be achieved which offer

much higher data rates compared to On-Off Keying.

1.2 Outline of the Thesis

We have, so far, looked at the motivation to carry forward research into high-

speed modulators. And since phase shift keying offers even higher data rates

for a given bandwidth, we look at the possibility of achieving phase modulation

with good quality using a modified model for Travelling Wave Electro-Absorption

Modulators in this thesis. Chapter 2 provides the necessary background to under-

stand electro-absorption. In Chapter 3, travelling-wave electro-absorption mod-

CHAPTER 1. INTRODUCTION 3

ulators are discussed in detail including their structure and the electrical models

developed for them. We also introduce a model for the voltage dependent delay

and explain the simulation setup. The results of the study on phase modula-

tion are discussed extensively in Chapter 4 which include simulating Binary and

Quadrature Phase Shift Keying and 8-Quadrature Amplitude Modulation, and

the thesis concludes with a short summary and scope for future work in Chapter

5.

Chapter 2

Background

2.1 Direct and External Modulation

Information is coded on to an optical carrier using optical modulators. Mod-

ulation can be classified into two types - Direct Modulation, where the current

driving the optical source is varied, and External Modulation, where a continuous

wave output from an optical source is modulated externally by a device which

usually contains a material whose optical properties can be varied.

Direct modulation suffers from various drawbacks, the most important of them

being chirping. Frequency chirping occurs during transition of the modulating

signal between low and high levels, which is called Transient chirping, and also

because of temperature effects on the optical source, called Adiabatic chirping.

Chirping leads to dispersion during propagation through an optical fiber, which

limits the trasmission distance severely. Several methods have been used to re-

duce frequency chirping, like injection locking, pulse-shape tailoring etc. The

maximum bandwidth recorded for a directly modulated VCSEL is 40 GHz using

Injection-locking techniques [5].

External modulation, on the other hand, offers better freedom of design since

it is virtually independent of the laser source. Figure 2.1 shows a schematic of

an optical transmitter including the position of an external modulator within it.

4

CHAPTER 2. BACKGROUND 5

Driver

Optical SourceExternal

Modulator

Channel

Coupler

Electrical

Input

Optical

output

Figure 2.1: Schematic of an Optical Transmitter [6]

External modulators usually involve materials whose optical properties can

be changed with the application of electric field. Depending on the properties

used to modulate the light, they can be divded into two groups - Electro-optic

(refractive) modulators and Electo-absorption (absorptive) modulators.

2.1.1 Electro-optic and Electro-absorption Modulators

Electro-optic modulators involve materials whose real part of the refractive

index changes with the application of electric field, due to Pockels Effect where

the change in refractive index is linearly proportional to the applied electric field,

or Kerr effect where the change in refractive index is proportional to the square

of the applied electric field, or a combination of both.

Electro-absorption modulators, involve materials whose imaginary part of

the refractive index changes with the application of electric field, which is ba-

sically change in the degree of absorption of the material. Physically, this is

explained through two phenomena namely Franz-Keldysh effect and Quantum

Confined Stark Effect (QCSE) which are discussed in the next sections.

2.2 Electro-absorption Mechanisms

2.2.1 Franz-Keldysh Effect

The application of an electric field causes a tilt in the band structure of bulk

semiconductors, that leads to a higher probability of photon absorption due to


the possibility of tunneling from a lower to a higher enegry level. This effect was

studied by Franz and Keldysh [7, 8]. This is schematically shown in Figure 2.2.

Figure 2.2: Band to band absorption involving the Franz Keldysh Effect

Additionally, Coulomb interaction between electrons and holes results in exci-

ton resonances. These resonances are, however, quickly broadened or suppressed

with the increase in the applied electric field due to ionisation of the excitons [9].

2.2.2 Quantum Confined Stark Effect

Figure 2.3: Band diagram of a quantum well under zero and non-zero electric

field, illustrating QCSE [9]


Unlike bulk semiconductors, the spatial separation between electrons and holes

in a quantum well structure is confined within the potential barriers around the

quantum well. This results in stronger Coulomb interaction, which means that

the exciton resonances cannot be broken even with a stronger applied electric

field. Figure 2.3 shows band diagrams of a quantum well without and with

applied electric field.

Figure 2.4: Band diagram of a quantum well under zero and non-zero electric

field, illustrating QCSE [10]

The band structure is tilted by applying a reverse bias perpendicular to the

quantum wells, which decreses the effective band gap. This, further, results in

the exciton peak shifting towards longer wavelengths. In addition, the overlap

between the wave functions of electrons and holes decreases due to their opposite

direction of movement in the presence of an electric field, which finally results in

a reduction in the absorption. Both these effects can be seen in Figure 2.4.

2.3 Summary

Electro-absorption modulators present distinct advantages over electro-optic mod-

ulators. They are much more compact and easier to integrate, especially with


DFB lasers, compared to electro-optic modulators, which are mostly made out

of LiNbO3, a difficult material when it comes to chip-integration. Also, the drive

voltage needed for electro-absorption modulators is lesser than that for electro-

optic modulators [9]. This is due to the strong interaction between the elctric

and optical fields, which also help in faster modulation speed, lower insertion loss

and higher extinction ratio. The chapters that follow consider electro-absorption

modulators employing quantum-well structures.

Chapter 3

Electro-Absorption Modulators

Electro-absorption modulators (EAMs) can be designed in two configurations -

lumped and travelling wave configurations. The speed of the lumped configura-

tion is severely limited by RC time constant of the structure. Moreover, a longer

interaction length between the electric and optical fields is required for better

modulation. But with lumped structures, the performace only gets worse with

increase in length due to increase in the device capacitance. A bandwidth of

50 GHz using a modulation length of 63 µm has been shown using a lumped

structure [11].

Figure 3.1: Schematic of a TWEAM [12]

To overcome this limitation, a travelling wave structure is used where the

9

CHAPTER 3. ELECTRO-ABSORPTION MODULATORS 10

transmission line capacitance is compensated by the electrode inductance [12].

The Travelling-Wave (TW) regime occurs when load impedance is matched to the

characterstic impedance of the TML-EAM (Zl = Z0), that is, there is no reflection

at the load and the electrical and the optical signals can co-propagate along the

transmission line structure. A schematic of a TW-EAM is shown in Figure 3.1.

It turns out that the characterstic impedance for such a TML-EAM is generally

15 - 25Ω. To achieve a more standard impedance of 50Ω, a segmented structure

is used with alternating high and low impedances, illustrated in Figure 3.2.

AC

High Z

Low Z

Position

Imp

ed

an

ce

(a) (b)

Figure 3.2: (a) Circuit depicting a Segmented TML structure (b) Impedance

variation along the length [12]

3.1 Device Structure

The device fabricated as part of the HECTO project uses an InP substrate, to

enable easier intergration with a laser diode. The active material is a strain-

compensated multiple quantum well layer between a low-doped buffer layer (n -

5 × 1017 cm−3) and an n - InP upper cladding with a thin n− InGaAs layer on

top. The active sections are selectively p-doped by zinc diffusion. The vertical

cross-section of the device is shown in Figure 3.3 (b).


AC

Electrode

p - InP

AC GndSiN Isolation

Active MQW

n - InP Buffer

Substrate n - InP

BCB

AC Gnd

BCB

i - InP SiN Isolation

DC

-

+

On-ChipOff-Chip

(a) (b)

Figure 3.3: (a) Entire device structure (b) Vertical cross section including the

DC bias configuration [13]

The depletion layer thickness is estimated to be 0.45 µm. A thick intrinsic

layer that provides lower capacitance, i.e. higher impedance is used to overcome

the RC limitation due to the p-cladding resistance and the active layer capaci-

tance. The thickness has a trade off with the modulation efficiency, since a thicker

intrinsic layer also results in a lower field across the quantum well structure. The

passive section has an upper cladding that in slightly n-doped. As discussed ear-

lier, we need the passive section to have a higher charateristic impedance. This is

achieved by a 6 µm thick layer of BenzoCycloButene (BCB) layer that is used to

separate the ground plane and the top electrode and to form a planar structure.

The device is optimised for a 50 Ω load. For operation with a 35 Ω load, a NiCr

resistor is used to achieve the required matching [13].

3.2 Device Modelling

3.2.1 Equivalent Circuits

In order to run computer simulations, the device structure desribed above, has

to be represented in the form of an equivalent electrical circuit. The active and

the passive sections are modelled using circuits shown in Figure 3.4. These are


the equivalent circuits for a single slice of the active and passive segments, and a

number of such slices form a complete segment.

Act

ive

Sec

tion

Passiv

e T

ML

(a) (b)

Figure 3.4: Equivalent circuit representation of a slice of the (a) active section

(b) passive section [13, 14]

Segment Parameter Value

Active L 280 pH/mm

Rp 1.25 Ω-mm

RC 2.05 Ω/(mm√GHz)

Cint 518 fF/mm

Cext 125 fF/mm

Passive Lp 354 pH/mm

Cp 64 fF/mm

Rδl 4.9 Ω-mm

RCp 5 Ω/mm + 0.8 Ω/(mm√GHz)

Table 3.1: Values of the componenets in the equivalent circuits [13]

Each slice of the active section has series impedance ZSM that consists of

a series resistance RSC , a frequency dependent resistance RC which models the

skin effect athigh frequencies and an inductacne L for the electrode. The shunt

impedance YPM consists of a resistance Rp due to the p-doped region, a capaci-


tance Cint due to the intrinsic region where the interaction between the optical

and electric fields takes place, and an external capacitance Cext. This model

works well for moderate levels of optical power. But for higher optical power

levels, the photocurrent due to absorption of light is modelled as a current source

Iphoto and the transit time delay, that is, the time taken for the photo-generated

carriers to travel across the intrinsic region, becomes important at high-speed

operations and is included in series in the circuit model.

The passive section is essentially a transmission line structure consisting of

lumped LC sections. In addition to the inductance and capacitance, each slice

ot the passive section consists of a series resistance RCp that also includes the

frequency dependent skin effect, a shunt resistance Rδl due to the BCB layer

between the top and the bottom elctrodes.

The values of the components described above has been empirically extracted

in given in Table 3.1, which will be used for further simulations [13]. In every

slice of the active section, there is a partial absorption of the electric field, and

the remaining power is transmitted to the next slice. In the passive section, the

propagation is modelled by a transmission line delay corresponding to the unit

length of the section divided by the optical group velocity.

3.2.2 Modelling Optical Absorption

To model the optical absorption in the active segment, we use the empirical

relation between electric field and optical absorption proposed in [12].

∆α ≈ p(E − E0)c = p

(

V − V0

hi

)c

(3.1)

where ∆α is the change in absorption, V0 is the low field bias point that corre-

sponds to a transmitted ‘1’ signal, V is the driving voltage , hi is the thickness

of the intrinsic region and p is a proportionality constant. This relation is shown

to be a good fit to the absorption curves of various devices [12] as shown in


Figure 3.5.

Figure 3.5: Optical absorption as a function of voltage showing a fit using the

empirical relation in Equation 3.1 [12]

3.3 Electro-optic effect in TWEAMs

3.3.1 Relation between Optical Absorption and change in

Refractive Index

The real and the imaginary parts of the refractive index of a material are coupled,

and the mathematical relationship between them is given by the Kramers-Kronig

relation (Equation 3.2). This coupling introduces a change in the refractive in-

dex when there is a change in the optical absorption. This induces a parasitic

frequency chirp in an electroabsorption modulators.

∆n(λ0, V ) =λ2

0

2π2PV

∫

∞

−∞

∆α(λ′, V )

λ20− λ′2

dλ′ (3.2)

where ∆n and ∆α are the changes in refractive index and optical absorption

respectively. For small signal modulation, this equation can be further simplified


to

∆n(λop, V ) = αmat(λop)λop

4π∆α(λop, V ) (3.3)

where αmat is the material chirp factor and λop is the operating wavelength [15].

Using the empirical model for the absorption in the modulator from Equation 3.1,

we get,

∆n(λop, V ) = αmat(λop)λop

4πp

(

V − V0

hi

)c

(3.4)

We can club together the constants at given wavelength, and incorporate the fact

the for low field bias V0 ≈ 0, and rewrite the equation as

∆n(λop, V ) = kV c (3.5)

At low field bias, the curvature paramter for the fabricated modulator is c = 1.5

- 1.8 [12]. Therefore, the change in refractive index can be assumed to be linear

over a small interval. This change in refractive index can be modelled as a time

delay in the signal given by

τdelay =n(V )Lm

c(3.6)

where Lm is the length of the modulator and c is the speed of light in vacuum.

The modelling of this delay using an electrical circuit simulator is discussed in

the following section.


3.3.2 Transmission line model for voltage dependent de-

lay

Figure 3.6: Transmission line model using lumped LC elements

A lossless transmission line is generally modelled using an infinte number of

lumped LC elements as shown in Figure 3.6 where L and C are the inductance

per unit length and capacitance per unit length respectively. The charaterstic

impedance Z0 of the line is given by

Z0 =

√

L

C(3.7)

and the velocity of propagation of the electromagnetic wave is given by

v =1

√LC

(3.8)

Comparing the above equation with the definition of refractive index of a material,

we have

n =c

v(3.9)

⇒ n(V ) = c√

LC(V ) (3.10)

To make the velocity of propagation dependent on voltage, we can make either

the inductance or the capacitance dependent on voltage [16]. From the previous

section (Equation 3.5, we see that we require a linear depenance of the delay

on the voltage. So, if the capacitance (or inductance) values are proportional

to the square of the voltage, we get a linear dependance of the delay on voltage


(Equation 3.10). So the time delay becomes

τdelay = Lm

√

LC(V ) (3.11)

The circuit simulator PSPICE allows to implement a capacitance that is propor-

tional to the square of the voltage across it. From the PSPICE reference manual,

we find the equation model for a capacitance is

C(V ) = C0 ×K(1 + aV + bV 2)(1 + x(T − Tnom) + y(T − Tnom)2) (3.12)

where C0 is the capacitance at zero voltage, a and b are the voltage-dependent

coeffecients and x and y are the temperature-dependent coeffecients. By choosing

an appropriate value for the We can choose an appropriate value for b and by

imposing that a, x, y = 0 , K = 1

band bV 2 ≫ 1 we have

C(V ) = C0V2 (3.13)

∴ n(V ) = c√

LC0V 2 (3.14)

= c√

LC0V (3.15)

The final schematic of the delay line implementation is shown below in Figure 3.7.

R R

R

LC section High Pass Filter

Figure 3.7: Schematic of the delay line implementation

In the above schematic, the microwave signal is much stronger than the optical

signal. The delay will be, thus, controlled mainly by the microwave signal. The

change in capacitance values due to change in modulating voltage does help in

controlling the delay, but also results in a change in impedance for the line. This


is solved by placing a large resistor on both sides of the line that act as attenuators

and reduce the reflections due to variations in the impedance. Finally, a high pass

filter is placed at the end to remove any changes in the component of the signal,

and to allow only the optical carrier with the induced delay to pass through at

the end.

3.4 Summary and Simulation Setup

In this chapter so far, we have seen the device structure, and electrical and optical

modelling procedure of the Travelling Wave Electro-Absorption modulators. An

implementation of the same in PSPICE was available from previous work. As

part of this thesis work, the large signal model of the TWEAM was rewritten in

the form of a user-controlled script that would automatically generate the SPICE

netlist required for the same. As mentioned earlier, each segment of the modula-

tor, both passive and active, is modelled using a number of slices of incremental

sections. The script allows for the user to input the number of slices and the

lengths of each of the segments. This dynamic generation of the netlist allows

for quicker and easier efficient control of the device model rather than modifying

the circuit schematic or the netlist manually.

Furthermore, the change in refractive index that is present along with the op-

tical absorption was discussed in this chapter along with modelling of the same

using a transmission line with variable delay. To implement the model of the

delay line in PSPICE, a script was written which takes in the number of LC

segments required for the line, and returns the netlist as the output. This was

incorporated in the script written for the large signal model of the TWEAM men-

tioned above, to form a model of the modulator that incorporates both change

in optical absorption and in refractive index. These scripts is further explained

in Appendix A.

The follwing diagram summarises schematically how the different models dis-

cussed in this chapter are put together in the generated output from the script to


form a complete model of the modulator, which can be analysed using a electrical

ciruit simulator software such as PSPICE.

Active Section

TML

Input Optical Signal

Output Optical Signal

Figure 3.8: Summary of the structure of the TWEAM and the models used

Chapter 4

TWEAM as a Phase Modulator

As discussed in the introduction section, the previous work done involving the

Electro-absorption modulators was limited to amplitude modulation, i.e. On-

Off Keying. By modifying the structure of the Quantum Well layer, the relative

strengths of optical absorption and change in the refractive index can be varied. A

conventional rectangular quantum well structure gives a low change in refractive

index for a higher change in absorption, but it has been shown that a 3 step

quantum well structure shows a higher change in refractive index for a low change

in absorption [17].

Figure 4.1: Comparison of modulators with a RQW and a 3-Step QW active

region [17]

20

CHAPTER 4. TWEAM AS A PHASE MODULATOR 21

This gives us a flexibility to switch between an amplitude modulator and a

phase modulator, or having a mixture or the two, which in turn leads to the

possibility of achieving modulation foramts such as Phase shift keying (PSK),

Quadrature Amplitude Modulation (QAM) etc., that have better data rate ca-

pabilities than a single channel On-Off Keying. To achieve this, different active

segments of the modulator can be fabricated to have different quantum well struc-

tures, so that the strengths of amplitude modulation and phase modulation can

be controlled independently. The rest of the work is concentrated on simulating

the performance of the modulator for these schemes.

4.1 Simulating Phase Shift Keying

In phase modulation, the phase of the carrier wave is modulated according to

the signal that needs to be transmitted. The digital version of phase modula-

tion is called Phase Shift Keying. Generally, the different levels that need to be

transmitted are encoded as different phase shifts of the carrier. Mathematically

speaking, a set of orthogonal basis functions are chosen for a particular modu-

lation scheme. A linear combination of these functions can be used to represent

any vector in the signal space. The chosen linear combinations form a symbol in

the signal space. The symbols are reperesented by constellation diagrams.

4.1.1 Binary Phase Shift Keying

Binary Phase Shift Keying (BPSK) is the simplest form of PSK, which uses a sin-

gle sinusoid as the basis function. This form of PSK modulates 1 bit/symbol. In

the time domain, the transmitted signal simply consists of an in-phase (with the

carrier) sinusoid and an out of phase sinusoid for the 2 bit levels to be transmitted

respectively. The modulated signal can be represented by

sn(t) =

√

2Eb

Tb

cos(2πfct+ π(1− n)), n = 0, 1. (4.1)


where Eb is the energy per bit, Tb is the bit duration and fc is the frequency of the

carrier. The constellation diagram for BPSK is shown in Figure 4.2. Ideally, the

points on the constellation are exact, but due to propagation medium, limitations

in the trasmitter side or at the receiver end, the points become blurred.

Quadrature

In phase

Figure 4.2: Constellation Diagram for BPSK

To analyse the performace of the modulator, a mathematical demodulation

was performed on the resulting signal (Equation 4.1). A schematic of the demod-

ulation algorithm is shown in Figure 4.3. The modulated signal is multiplied with

the carrier, which results in a waveform whose average value is directly related

to the phase of the modulated signal as shown in the equation below [18].

sk =< (sin(ωct) + sin(ωct+ φk))2 >

= 1 + cos(φk) (4.2)

This is realised by the integration over a bit period. In a real-world demodulator,

this is further passed through a comparator which decides the level of the received

bit. Since we need to look at the performace of the modulator, we need to look

look at the signal obtained before the comparator block and analyse its quality.


Comparator

Figure 4.3: Schematic of a BPSK Demodulator

For the simulations, a modulator device with four active segments was con-

sidered, two of which were modelled to be electro-absorption segments, and the

other two to be phase modulation segments. A schematic of the same is shown

in Appendix B. The two modulator blocks were driven and biased independently,

and also each of them had their own microwave terminations. It is of practical

use to have the two sections functioning independently of each other not only

so that the relative strengths of amplitude modulation and phase modulation

can be tweaked to achieve the required modulation format, but also so that each

of them can be independently optimised based on their own microwave responses.

To simulate BPSK, the absorption modulator part was ‘turned off’ by setting

low bias and drive voltages, so that the optical field propagates without having

any influence from the active segments. The voltage-variable refractive index is

controlled by the variable capacitances of the delay lines present in the slices of

the active segments of the phase modulation block. The delay line was configured

to have a π shift in phase for the two levels of the signal, and other parameters

of the modulator model were varied to see their effect on the modulation quality.

To visualise modulation quality, the constellation diagrams of the modulated

optical carrier were plotted. The degree of fuzziness of the constellation points

was estimated using a quantity called the Error Vector Magnitude (EVM) as

defined below:

EVM(dB) = 10 log10

(

Perror

Preference

)

(4.3)


where Perror is the Root Mean Squared power of the error vector (the vector dif-

ference between the observed and the corresponding ideal constellation points)

and Preference is, generally, the power of the outermost point in the refernce signal

constellation.

Figure 4.4 shows the output signal from the simulation in the time domain in

blue. This is visualised along with the carrier shown in red. The two diagrams

show represent the output for the two bit levels. It is visually observable that the

output corresponding to one bit level is in phase with the carrier and the output

corresponding to the other bit level is out of phase with the carrier.

5.44 5.445 5.45 5.455 5.46 5.465 5.47 5.475 5.48

x 10−12

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

2.044 2.0445 2.045 2.0455 2.046 2.0465 2.047 2.0475 2.048

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

Figure 4.4: Modulated BPSK output signals corresponding to the two bit levels


Effect of Active Segment Length

The proposed model for the modulator is simulated for various lenghts of the

active segment. Changing the lengths of the segments changes the characteristic

impedance of the model, which, in turn changes the microwave characteristics.

The behaviour of the Error Vector Magnitude with varying active segment lengths

is shown in Figure 4.5 for 10 Gb/s and 50 Gb/s data rates. A ringing in the im-

pulse response of the modulator causes degradation of the quality of the phase

modulation as the data rate increases, that is, the frequency of the microwave

signal increases. This is further discussed at the end of this chapter. We also

observe that the modulator performs better around an optimal length region

around 100 µm at both data rates. Figure 4.6 shows the constellation diagrams

of the achieved modulation for the lengths that introduced least distortion in the

constellation diagrams. The constellation point on the right corresponds to the

lower modulating votage level , and the one on the left corresponds to the higher

level. This explains the difference in the phase noise between the two points.

0.05 0.1 0.15 0.2 0.25 0.3−20

−18

−16

−14

−12

−10

−8

−6

Active segment length (mm)

EV

M (

dB)

10 Gb/s50 Gb/s

Figure 4.5: Error Vector Magnitude versus Length for Achieved BPSK at 10

Gb/s and 50 Gb/s


−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase

(a) (b)

Figure 4.6: Constellation diagrams for the achieved BPSK (a) with 2×100 µm

active segments at 10 Gbps (b) 2×150 µm active segments at 50 Gbps

Effect of Input Optical Power

Figure 4.7 shows the variation of the Error Vector Magnitude with variation in

the input optical power. We could, in general, expect the quality of modulation

to get worse as the optical input power increases beyond a certain point, due

to the fact that the photogenerated current causes more voltage to be dropped

across the p-doped region of the device, instead of the active layer.

Also noticeable from the plot is that, for 50 Gbps the modulation quality more

or less remains the same. This could be related to the LC nature of the modulator,

that causes a resonance effect. This resonance frequency becomes higher as the

input optical power increases. This movement of the frequency to the right

causes a frequency range where the frequency response of the modulator remains

almost unchanged for different optical powers. This phenomenon is inferred from

simulation results from previous work [19].


0.5 1 1.5 2 2.5−20

−18

−16

−14

−12

−10

−8

−6

−4

Input Optical Power (mW)

EV

M (

dB)

10 Gb/s50 Gb/s

Figure 4.7: Error Vector Magnitude versus Optical input power for Achieved

BPSK at 10 Gb/s and 50 Gb/s

−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase

(a) (b)

Figure 4.8: Constellation diagrams showing poor BPSK modulation with large

input optical power of 10 mW at (a) 10 Gb/s (b) 50 Gb/s


Effect of Bias Voltage

The behaviour of the quality of modulation represented by the Error Vector

Magnitude, with bias voltages is plotted in Figure 4.9, and constellation diagrams

corresponing to two of the poorer qualities of achieved modulation are shown in

Figure 4.10. Irrespective of the bias, the change in voltage required for a π phase

shift remains the same, but, unlike the previous cases, we see an increased phase

noise in both the constellation points. This is due to the fact that the two voltage

levels for the bit symbols are comparatively much higher than the previous cases

due to the bias voltage already being set at a high level.

0.5 1 1.5 2 2.5−20

−18

−16

−14

−12

−10

−8

−6

Bias Voltage (V)

EV

M (

dB)

10 Gb/s50 Gb/s

Figure 4.9: Error Vector Magnitude versus Bias Voltage for Achieved BPSK at

10 Gb/s and 50 Gb/s


−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase

(a) (b)

Figure 4.10: Constellation diagrams for achieved BPSK with 2.5V bias voltage

for (a) 10 Gb/s (b) 50 Gb/s

4.1.2 Quadrature Phase Shift Keying

Quarature Phase Shift Keying (QPSK), also known as 4-PSK, is the second sim-

plest form of PSK after BPSK (analysed in the previous section). QPSK uses 4

levels of phase shift, which means that it can encode two bits per symbol. In other

words, if BPSK has two levels of phase shift to transmit a 0 and a 1, QPSK uses

4 levels that can transmit, for example, 00 01 10 and 11. Mathematically, it is,

therefore, possible to show that QPSK can be used to transmit at twice the data

rate for a given bandwidth or at the same data rate using only half the bandwidth.

The modulated signal can be represented by

sn(t) =

√

2Es

Ts

cos(

2πfct+ (2n− 1)π

4

)

, n = 1, 2, 3, 4. (4.4)

where Es is the energy per symbol, Ts is the symbol duration and fc is the


frequency of the carrier. This results in two basis functions, namely

φ1(t) =

√

2

Ts

cos(2πfct) (4.5)

φ2(t) =

√

2

Ts

sin(2πfct) (4.6)

Quadrature

In phase

Figure 4.11: Constellation Diagram for QPSK

Figure 4.11 shows QPSK as a constellation diagram. We observe that, we

can interpret QPSK as two combined BPSK carriers that are orthogonal to each

other. In the time domain, the signal will ideally look like a sinusoid with 4

varying levels of phase shift (0, 90, 180 and 270). A part of the time domain

plot resulting from the simulations of our model is shown in Figure 4.13.

The demodulation of QPSK is done following the schematic shown in Fig-

ure 4.12 in practical applications. The modulated signal is split into two parts,

each of which is multiplied with a filter matched to the corresponding basis func-

tion (Equation 4.5). These are then sampled at intervals corresponding to a

symbol duration. This is then passed through a decision device that decides the

level of the bits (symbol), and finally the two streams are multiplexed to form a

single data stream.


Figure 4.12: Schematic of a QPSK demodulator

With regard to our simulation of the modulator model, the demodulation was

performed in a similar fashion as BPSK. This was because, the purpose of the

demodulation, in our case, was to visualise the modulation characteristics of the

modulator and not to actually demodulate a signal with the intent of deciding

the bit levels. Thus, it is sufficient to have a single reference sinsusoid, and look

at the phase shifts induced in the carrier for the different bit levels, using the

same algorithm as was employed for BPSK, and then visualising the same using

constellation diagrams.

5.44 5.445 5.45 5.455 5.46 5.465 5.47 5.475 5.48

x 10−12

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

1.445 1.446 1.447 1.448 1.449

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

2.449 2.4495 2.45 2.4505 2.451 2.4515 2.452 2.4525 2.453

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

3.449 3.45 3.451 3.452 3.453

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

CarrierOutput

Figure 4.13: Modulated QPSK output signals corresponding to the four symbols


Figure 4.13 shows regions of the simulated output from PSPICE correspond-

ing to the phase shifts for different symbols. As was in the case of BPSK, the

phase shifts are also visually apparent in the moudulated signal. As mentioned

earlier, QPSK can be interpreted as BPSK on two orthogonal carriers, and thus,

the figures on the left can be interpreted as BPSK on the sine carrier and the

figures on the right can be interpreted as BPSK on the cosine carrier. The charac-

terstic behaviour of the modulator would be essentially be the same as described

above in the section dealing with BPSK. Constellation diagrams for the best

achieved modulation quality (1mW optical power, 1V Bias and 2×100µm (for 10

Gb/s and 2×150µm for 50 Gb/s) active section lengths) are shown in Figure 4.14.

The steps of the drive voltage were chosen to be linear. A useful quality of the

moulator that can be observed in the constellation diagrams is the linearity of

phase variations achieved. This shows us that the voltage-dependent delay is

indeed linear as it was modelled to be.

−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase

(a) (b)

Figure 4.14: Constellation diagrams for achieved QPSK at (a) 10 Gb/s (b) 50

Gb/s

Another notable feature from the constellation diagrams is behaviour of the

phase noise. Starting from the constellation point at the right, the phase noise

increases as we move counter clockwise along the circle. This can be attributed


to the increasing levels of the modulating voltage along the same contour.

4.2 Quadrature Amplitude Modulation

The modulation schemes discussed in the previous section encode the transmit-

ted signal purely in the phase of the optical carrier. When this is combined

with amplitude modulation, it allows for more data to be squeezed through. For

example, consider the constellation diagram for QPSK from Figure 4.11. The

amplitude of the carrier in each of the constellation points is the same. Suppose

we introduce two levels of amplitude to this instead of just one, we obtain an

8-QAM constellation shown in Figure 4.15 (a). This results in the possibility of

transmitting 3 bits per symbol. Additionally, this can be easily implemented by

cascading an amplitude modulator and a phase modulator. The 8-QAM constel-

lation shown in Figure 4.15 (b), however, has more sepration of the constellation

points than (a), which is useful when it comes to reducing the bit error rate for

tranmsmissions, but this constellation would also be much more complicated to

modulate and demodulate than (a).

Quadrature

In phase

Quadrature

In phase

(a) (b)

Figure 4.15: Constellation Diagrams for 8-QAM

To implement this, the amplitude modulator segments are now switched on.

The parameters used for this segment are the optimised parameters drawn from

[19]. The drive to the amplitude modulator (AM) part is decoupled from the


phase modulator (PM) part. The information that needs to be encoded on the

amplitude of the carrier is used to drive the active segments of the AM and

the information that needs to go onto the phase of the carrier is used to drive

the active segments of the PM. Figure 4.17 shows the time domain output of the

achieved modulation. The four levels of phase shift are, once again, clearly visible

in the different rows of the figure matrix and the two levels of amplitude can be

seen along the two columns. The constellation diagrams of the achieved 8-QAM

are plotted in Figure 4.16. The phase noise characteristics appear to be similar

to that achieved in QPSK. Since the optical absorption part of the modulator is

optimised for frequencies upto 100 GHz, the output does not show any significant

amplitude noise.

−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In−Phase

(a) (b)

Figure 4.16: Constellation diagrams for achieved 8-QAM at (a) 10 Gb/s (b) 50

Gb/s


5.44 5.45 5.46 5.47 5.48

x 10−12

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

1.445 1.446 1.447 1.448 1.449

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

2.449 2.45 2.451 2.452 2.453

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

3.449 3.45 3.451 3.452 3.453

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

5.53 5.54 5.55 5.56 5.57

x 10−12

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

1.469 1.47 1.471 1.472 1.473

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

2.459 2.46 2.461 2.462 2.463

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

3.434 3.435 3.436 3.437 3.438

x 10−11

−2

−1

0

1

2x 10

−4

Time

Am

plitu

de

Figure 4.17: Modulated 8-QAM output signals corresponding to the 8 bit levels


4.3 Limitations and Summary

The quality of the phase modulation achieved using the presented model is rea-

sonable at bit-rates upto around 50 Gb/s. There exists a peaking in the impulse

reponse of a modulator followed by a ringing, which leads to the presence of a

settling time in the phase modulated output. This impulse response is shown in

Figure 4.18 [20]. The output signal in the time range corresponding to a transi-

tion between two levels of the modulating signal for the phase modulator block is

shown in Figure 4.19. When it comes to amplitude modulation, the settling time

does not seem to be an issue, but in the use as a phase modulator, this leads to

a lot of variation in the phase shifts during this transition time. This ringing in

the impulse response, which has a time period of about 10 ps, is probably the

cause of the settling time of also around 10 ps in the modulated output, and this

is comparable to the bit duration at 100 Gb/s which is also 10 ps. In the case

when this ringing is not due to this impulse response, it could have been due to

the Bragg resonance created by the periodic TML structure of the modulator.

To investigate this, the number of slices in the models of the segments was in-

creased, but the settling time was, however, observed to be still present in the

output signal.

Figure 4.18: Normalised impulse response of a segmented TW-EAM[20]


1 1.05 1.1 1.15 1.2

x 10−10

−1

0

1

2x 10

−4

Time

Opt

ical

Pow

er

Figure 4.19: Modulated signal showing peak and settling time

Another issue was the sheer amount of data and computing time needed to

run the simulations close to 200 THz (approximate frequency corresponing to

the optical telecom wavelengths). The previous work done at KTH with the elec-

troabsorption modulators did not take into account the phase information of the

carrier, because as far as the electrical simulation is concerned, only the envelope

of the modulated signal matters. Some of the longer simulations presented in

this thesis were carried with a lower frequency for the carrier, of course, taking

into account the change in behaviour of the THz frequency dependent part of

the model. This approach does not introduce errors and it was confirmed by

checking with the simulated output using 200 THz carrier frequency. In fact, the

time domain plots presented in this thesis use a carrier frequency 200 THz.

This chapter presented a detailed report on the investigation of phase modula-

tion using variable delay line model added to the existing model of the TWEAM.

Chapter 5

Conclusions and Future Work

The work done as part of this thesis has been an attempt at investigating the pos-

sibility of modifying the model of a travelling wave electro-absorption modulator

to achieve phase modulation. The proposed model was simulated with successful

phase modulation at data rates of upto about 50 Gb/s. This makes it imperative

to carry out further research into using TWEAMs for phase modulation.

The simulation results were presented for BPSK, and the effect of some circuit

and design parameters were analysed. Additionally, the model was successfully

simulated to perform QPSK and 8-QAM. Some limitations of the model were also

presented. The electrical simulation was carried out using commercial the circuit

simulator PSPICE. In order to make the voltage variable delay line model more

robust, it could be worthwhile to look into ways to model the circuit manually or

in a more fundamental way. Though this could be tedious, having a better control

on circuit components could result in getting rid of some modelling artifacts. For

example, a complete control on the inductances and capacitances in the delay

line would allow to implement an idea proposed in [21] to model a transmission

line with variable delay, but constant characterstic impedance. Furthermore, the

next step could be to charaterise the optical and microwave behaviour of the

phase modulator segment in detail, and finally to fabricate the step quantum

well structures and characterise the device.

38

Appendix A

Netlist Generation

A.1 Large Signal Model

The PSPICE netlist for the large signal model (the small signal model has a

similar script generator developed in [22]) of the modulator was generated using

a PHP script according to the number of slices required in each segment. The

order of the blocks in the generated netlist is: Bias circuitry → (Active and pas-

sive segments) → Load termination. An excerpt from the source code, which

generates the netlist for the active segments of the modulator, is shown below.

<?php

$fh = fopen("active_segment.net", ’w’);

fwrite($fh,"

.SUBCKT activetml P1 P2 OPI POp1

+ PARAMS:Length=0 L=0 RC=0 Rp=0 CInt=0

+ Cext=0 N=0 Optlength=0");

for ($i=0; $i<=$slices-1; $i++)

fwrite($fh, "\nX_A".(string)($i));

if($i==0)fwrite($fh," P1");

elsefwrite($fh," N".(string)(($i-1)*10))."\n+ ";

39

APPENDIX A. NETLIST GENERATION 40

if($i==$slices-1) fwrite($fh," P2a ");

elsefwrite($fh," N".(string)($i*10)."\n+ ");

fwrite($fh," PC$i activesegment

+ PARAMS:");

if($i==0)fwrite($fh,"RC = RC/2 L = L/2");

elsefwrite($fh,"RC = RC L = L ");

fwrite($fh,"

+ CINT = CINT RP = RP CEXT = CEXT LENGTH = LENGTH/$slices

+ X_TL$i PC$i ");

if($i==0) fwrite($fh," PT0 OPI ");

elseif($i==$slices-1) fwrite($fh," POp1 PT".(string)($slices-2)." ");

elsefwrite($fh," PT".(string)($i)." PT".(string)($i-1)." ");

fwrite($fh," OpticalLine PARAMS:N=N

+ LENGTH = OPTLENGTH+

+ ($slices-".(string)($i+1)." +0.5)*LENGTH/$slices");

fwrite($fh,"

X_AE P2a P2 activesegmentend PARAMS: RC=RC/2 L=L/2

+ Length=Length/$slices

.ENDS \n");

fwrite($fh,"

.SUBCKT OpticalLine P1 P2 OPI PARAMS: N=0 Length=0

E_E1 Ngg 0 VALUE (V(P1)-V(0)-Voffset)

R_R1 Ngg N001 1

D_LIMIT N001 0 Dlimit

E_ABM11 N002 0 VALUE EXP(-K3a*EXP(1.5*LOG(-V(N001))))

R_Rdum1 N002 0 1

G_ABM2I P1 0 VALUE (-R_AW*(1-V(N002))*K1a*V(OPI))

E_ABM21 N003 0 VALUE (2*K1a*V(N002)*V(OPI))

R_ROPO N004 N003 1

T_T1 N004 0 N005 0 Z0=1 TD=N*Length/3e8

X_DEL N005 N004 P2 delayline

R_R2 0 P2 1


.ENDS \n");

fwrite($fh,"

.SUBCKT activesegment P1 P2 PCINT PARAMS: Length=0 L=0 RC=0

+ Rp=0 CInt=0 Cext=0

L_TMLASeg_L P1 N001 L*Length*1e3

G_TMLASeg_Rc N001 P2 LAPLACE V(N001)-V(P2)

+ 1/(".(string)($active_Rc_t)."RC*Length*1e3*sqrt(abs(s)/6.28/1G))

R_TMLASeg_Rdum N001 P2 1k

R_TMLASeg_Rp PCINT P2 Rp/Length/1e3

C_TMLASeg_Cint 0 PCINT CInt*Length*1e3

C_TMLASeg_Cext 0 P2 CExt*Length*1e3

.ENDS

.SUBCKT activesegmentend P1 P2 PARAMS: Length=0 L=0 RC=0

+ Rp=0 CInt=0 Cext=0

L_TMLASegEnd_L P1 N001 L*Length*1e3

G_TMLASeg_Rc N001 P2 LAPLACE V(N001)-V(P2)

+ 1/(".(string)($active_Rc_t)."RC*Length*1e3*sqrt(abs(s)/6.28/1G) )

R_TMLASegEnd_Rdum N001 P2 1k

.ENDS \n");

fclose($fh);

?>


A.2 Voltage-dependent Delay line

A PHP script to generate the voltage dependent delay line (Figure A.1) was

written, which takes in the number of LC sections and the values of the total

inductance and capacitance as input. The program places the inductances and

capacitances using a loop construct and finally ends the line with an appropriate

high pass filter that passes only the optical carrier removing any DC components.

R R

R

LC section High Pass Filter

Figure A.1: Schematic of the delay line implementation

<?php

$fh = fopen("delay.net", ’w’);

$number = 102; // Number of LC sections

fwrite($fh,"

.MODEL Cbreak-X1 CAP(C=1E-03 VC2=1E+03)

.SUBCKT delayline V01 VM1 OUT

E_EO N001 N002 VO1 0 1

E_EM N002 0 VM1 0 1

R_Rscale N001 v1 Rscale

R_Rmatch1 v1 0 R_match1\n");

for($i=0; $i<=$number-1;$i++)

if($i==$number-1)

fwrite($fh,"L_L".(string)($i+1)." v".(string)($i+1)."

+ vend ldelay\n");

fwrite($fh,"C_C".(string)($i+1)." 0 vend Cbreak-X1

+ cdelay\n");


else

fwrite($fh,"L_L".(string)($i+1)." v".(string)($i+1)."

+ v".(string)($i+2)." ldelay\n");

fwrite($fh,"C_C".(string)($i+1)." 0 v".(string)($i+2)."

+ Cbreak-X1 cdelay\n");

fwrite($fh,"

R_Rmatch2 vend 0 R_match2

C_hp1 vend vhp1 100f

R_hp1 vhp1 0 1

C_hp1 vhp1 vhp2 100f

R_hp1 vhp2 0 1

R_end vhp2 OUT 1

C_end OUT 0 1f

.ENDS \n");

fclose($fh);

?>

Appendix B

Circuit Schematic

Figure B.1: Schematic of the modulator circuit

44

Bibliography

[1] T. H. Maiman, Stimulated Optical Radiation in Ruby, Nature 187, 493 (1960).

[2] F. P. Kapron, D. B. Keck, and R. D. Maurer, Radiation losses in glass opticalwaveguides, Appl. Phys. Lett. 17, 423 (1970)

[3] Visual Networking Index, Cisco. http://www.cisco.com/go/vni

[4] High-Speed Electro-Optical Components for Integrated Transmitter and Re-ceiver in Optical Communication, http://www.hecto.eu/

[5] Lukas Chrostowski et al, 40 GHz Bandwidth and 64 GHz Resonance Frequencyin Injection-Locked 1.55 µm VCSELs. IEEE Journal of Selected topics inQuantum Electronics, Vol. 13, No. 5, September/October 2007

[6] Govind P. Agrawal. Fiber-Optic Communication Systems. John Wiley & Sons,Inc., 3 edition, 2002

[7] W. Franz, Einfluß eines elektrischen Feldes auf eine optische Absorption-skante, Z. Naturforschung 13a (1958) 484489.

[8] L. V. Keldysh, Behaviour of Non-Metallic Crystals in Strong Electric Fields,J. Exptl. Theoret. Phys. (USSR) 33 (1957) 9941003, translation: SovietPhysics JETP 6 (1958) 763770.

[9] Shengzhong Zhang. Traveling-wave Electroabsorption Modulators. PhD Dis-sertation, University of California, 1999

[10] I. Kotaka, K. Sato, K. Wakita, M. Yamamoto, and T. Kataoka, High-speed(20 Gb/s), low-drive voltage (2 V/sub p-p/) strained InGaAsP MQW modu-lator/DFB laser light source, Electron. Commun. Jpn. 2, Electron. , vol. 78,pp. 1-9, 1995

[11] T. Ido, S. Tanaka, M. Suzuki, M. Koizumi, H. Sano, and H. Inoue,Ultra-high-speed multiple-quantum-well electro-absorption modulators with in-tegrated waveguides, J. Lightwave Technol., vol. 14, pp. 2026-2034, 1996

45

BIBLIOGRAPHY 46

[12] Robert Lewen, High-Speed Electroabsorption Modulators and p-i-n Photodi-odes for Fiber-Optic Communications, Doctoral Dissertation, Royal Instituteof Technology, Department of Microelectronics and Information Technology,Stockholm 2003

[13] Robert Lewen, Stefan Irmscher, and Urban Westergren. Segmentedtransmission-line electroabsorption modulators. Journal of Light wave Tech-nology, 22(1):172-179, January 2004.

[14] R. Lewen, S. Irmscher, and U. Eriksson, Microwave CAD circuit model-ing of a traveling-wave electro-absorption modulator, IEEE Trans. MicrowaveTheory Tech., vol. 51, pp. 11171128, Apr. 2003

[15] Ivan P. Kaminow, Tingye Li, Alan E. Willner, Optical Fiber Telecommuni-cations V A: Components and Subsystems, Elsevier, 2008

[16] Akinwumi Abimbola Amusan, Simulation of Traveling Wave Electro-absorption Modulators Suitable for 100Gbps, MSc Thesis, Royal Institute ofTechnology, Stockholm 2011

[17] H. Mohseni, H. An, Z. A. Shellenbarger, M. H. Kwakernaak, and J. H.Abeles, Enhanced Electro-Optic Effect in GaInAsP-InP Three- Step QuantumWells, Applied Physics Letters, Volume 84, Number 11, 2004

[18] Roel Baets, Gunther Roelkens,Photonics, Ghent University - course syllabus,2009-2010

[19] Gebirie Yizengaw Belay, nvestigation of Large Signal Effects on TravellingWave Electroabsorption Modulator Performance and Optimization , MSc The-sis, Royal Institute of Technology, Stockholm 2010

[20] Yongbo Tang, Yichuan Yu, Yuqian Ye, Urban Westergren, Sailing He, De-sign and optimization of an arbitrarily segmented traveling wave electrode foran ultrahigh speed electroabsorption modulator, Optics Communications 281(2008) 51775182

[21] Fallside F., Bickley D.T.,Nonlinear delay line with a constant characteristicimpedance, Proceedings of the Institution of Electrical Engineers, Volume 113, Issue 2, (1966) 263- 270

[22] Myles Darlington Heiland, Modeling of Device Characteristic Effects onTraveling-Wave Electroabsorption Modulator Performance, MSc Thesis,Royal Institute of Technology, Stockholm 2009

Documents

Simulation of Traveling Wave Electroabsorption Modulators ...546777/FULLTEXT01.pdf · the project have been so far limited to Amplitude Modulation / On-Oﬀ Keying. It is worthwhile