© Bahareh Sherafati, 2018

Polarization management : An efficient polarization rotator splitter on silicon-on-insulator platform

Mémoire

Bahareh Sherafati

Maîtrise en génie électrique - avec mémoire

Maître ès sciences (M. Sc.)

Québec, Canada

ii

Polarization management An efficient polarization rotator splitter on silicon-on-insulator

platform

Mémoire

Bahareh Sherafati

Sous la direction de :

Leslie Ann Rusch, directrice de recherche Wei Shi, codirecteur de recherche

iii

Résumé

Ce mémoire vise à étudier la gestion de la polarisation et est axé sur la conception, la

simulation et la fabrication d'un rotateur séparateur de polarisation (PSR) sur des plates-formes

en silicium en utilisant une structure combinant un cône adiabatique à deux niveaux et un

coupleur adiabatique.

Après une introduction sur les systèmes de communication optique, spécifiquement sur les

systèmes photoniques intégrés, nous introduisons le silicium sur isolateur (SOI) comme plate-

forme la plus attrayante pour notre circuit photonique intégré. Bien que la propriété intrinsèque

de contraste élevé de SOI entraîne la petite taille de la puce, cette propriété entraîne également

une forte dépendance de polarisation pour les dispositifs silicium photoniques (SiP). Pour

résoudre le problème et supprimer cette dépendance, des circuits de diversité de polarisation

ont été proposés et il est important de traiter la gestion de la polarisation sur la puce.

Dans ce mémoire, le principe général de fonctionnement de la gestion de la polarisation est

étudié en profondeur. Comme la rotation de polarisation est la fonction la plus importante de

la gestion de la polarisation, nous nous concentrons sur les principes de base de la rotation de

polarisation dans un dispositif à section unique. Nous discutons également de différents types

de rotateurs de polarisation et donnons une introduction à l'évolution historique des rotateurs

de polarisation. Enfin, les séparateurs de polarisation sont présentés comme le deuxième

élément important dans la gestion de la polarisation, et différents types de séparateurs de

polarisation sont présentés.

Pour gérer efficacement la polarisation, il est essentiel de développer un PSR haute

performance. Par conséquent, nous introduisons une structure efficace qui est basée sur la

conversion de mode TM0-TE1 dans une conicité (taper) à deux niveaux sur SOI. Nous

expliquons et motivons ce choix. Ensuite, nous décrivons la modélisation avec le logiciel

Lumerical Finite Difference Time Domain (FDTD) ; les résultats de la simulation fournissent

l'évolution des profils d'intensité des modes le long du dispositif. Par la suite, nous présentons

les détails de la disposition sur la carte (layout) pour la fabrication et la caractérisation

éventuelle des conceptions utilisant des coupleurs de bordure (edge couplers), ainsi que des

conceptions utilisant des coupleurs à réseau (grating couplers). Pour évaluer la performance

du PSR conçu pour deux applications différentes, nous proposons un modèle mathématique et

iv

les matrices de transfert. Enfin, la performance du PSR proposé est analysée dans un système

de communication optique.

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Abstract

This thesis aims to study polarization management, and focuses on design, simulation and

fabrication layout of a polarization splitter rotator (PSR) on silicon platforms by utilizing a

structure combining an adiabatic bi-level taper and an adiabatic coupler.

Following an introduction about optical communication systems and specifically integrated

photonic systems, we introduce silicon-on-isolator (SOI) as the most attractive platform for our

integrated photonic circuit. Although the intrinsic high-index contrast property of SOI leads to

a very small footprint, this property also results in high polarization dependence for silicon

photonic (SiP) devices. To solve the problem and remove this dependency, polarization

diversity circuits have been proposed and it is important to deal with on-chip polarization

management.

In this thesis, the general operating principle of polarization management is thoroughly

studied. As polarization rotation is the most important function of polarization management,

we concentrate on the basic principles of polarization rotation in a single section device. We

also discuss different types of polarization rotators and give an introduction to the historic

evolution of polarization rotators. Finally, polarization beam splitters are introduced as the

second important element in polarization management, and different types of polarization

splitters are presented.

To efficiently manage polarization, it is critical to develop a high performance PSR.

Therefore, we introduce an efficient structure that is based on TM0-TE1 mode conversion in a

bi-level taper on SOI. We explain and motivate that choice. Afterwards, we describe the

modeling in Finite Difference Time Domain (FDTD) Lumerical software; simulation results

provide the evolution of mode intensity profiles along the device. Subsequently, we present the

layout details for fabrication and eventual characterization for designs using edge couplers, as

well as designs using grating couplers. To evaluate the performance of the designed PSR for

two different applications, we propose a mathematical model and the transfer matrices. Finally,

the performance of the proposed PSR is analyzed in an optical communication system.

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Contents

Résumé ................................................................................................................................ iii

Abstract ................................................................................................................................. v

List of Tables ....................................................................................................................... ix

List of Figures ....................................................................................................................... x

List of abbreviations ............................................................................................................ xii

Acknowledgments ............................................................................................................. xiii

Chapter One: Introduction .................................................................................................... 1

1.1. Optical Communication ......................................................................................... 2

1.2. Photonic Integrated Circuits with Different Platforms .......................................... 4

1.3. Silicon Photonics Platforms for PICs .................................................................... 5

Chapter Two: Polarization Management .............................................................................. 7

2.1. Introduction ............................................................................................................ 8

2.2. TE and TM Polarization Modes ............................................................................. 8

2.3. Polarization Management .................................................................................... 11

2.4. Polarization Rotator ............................................................................................. 12

2.5. Operation Principles of Polarization Rotator ....................................................... 14

2.6. Polarization Beam Splitter ................................................................................... 17

2.7. Summary .............................................................................................................. 18

Chapter Three: PSR Based on TM0-TE1 Mode Conversion in a Bi-level Taper on SOI .. 19

vii

3.1. Introduction .......................................................................................................... 20

3.2. Selecting a High Performance PSR ..................................................................... 20

3.3. Modeling and Simulation ..................................................................................... 23

3.3.1. Functionality ................................................................................................ 23

3.3.2. Simulation .................................................................................................... 23

3.4. Chip Layout Design ............................................................................................. 28

3.4.1. Input and Output Coupling .......................................................................... 28

3.4.1.1. Edge Couplers .......................................................................................... 28

3.4.1.2. Grating Couplers ...................................................................................... 29

3.4.2. Fabrication Process ...................................................................................... 31

3.4.3. Complete Layout with Multiple Designs ..................................................... 32

3.5. Summary .............................................................................................................. 35

Chapter Four: Application of PSR in Optical Systems ....................................................... 36

4.1. Introduction .......................................................................................................... 37

4.2. Applications ......................................................................................................... 37

4.3. Mathematical Model ............................................................................................ 38

4.4. Loss, Crosstalk, and Desired Outputs .................................................................. 40

4.5. Scattering Parameters Extraction and Model Development ................................ 42

4.6. Performance of the Designed Bi-level PSR ......................................................... 44

4.7. Summary .............................................................................................................. 47

viii

Chapter Five: Conclusion and Outlook ............................................................................... 49

Appendix ............................................................................................................................. 51

References ........................................................................................................................... 55

ix

List of Tables

Table 1.1: Technology comparison between InP, SiP, and SiN as the PIC platform based on

their ability to build different blocks, (+ + +: Very good, + +: Good, +: Modest, -: challenging,

- -: Very challenging). ................................................................................................................ 4

Table 1.2: Performance comparison between InP, SiP, and SiN as the platform for PIC based

on their characteristics, (+ + +: Very good, + +: Good, +: Modest, -: challenging, - -: Very

challenging), 1 with edge coupler, 2with grating coupler [1]. .................................................... 5

Table 2.1: Effective refractive indices and propagation constants for TE and TM modes. 11

Table 4.1: The correspandance between outputs and the elements of transfer matrices. ... 41

Table A.1: Geometrical parameters of the designed PSR based on bi-level taper and

adiabatic coupler. ..................................................................................................................... 51

Table A.2: Geometrical parameters of the designed PSRs with various changes in some

dimensions. .............................................................................................................................. 52

Table A.3: Geometrical parameters of the designed PSRs with various changes in some

dimensions. .............................................................................................................................. 53

x

List of Figures

Figure 1.1: A schematic of a simple optical communication system. ................................... 2

Figure 2.1: Three layer waveguide with confinement in y axis (a) asymetric dielectric planer

waveguide (b) rectangular strip waveguide. .............................................................................. 9

Figure 2.2: A ridge waveguide with the light propagation through z-axis and light

confinement along x-axis and y-axis. ...................................................................................... 10

Figure 2.3: Polarization diversity technology with two PSRs and two identical circuits. .. 12

Figure 2.4: Different categories of polarization rotators. .................................................... 13

Figure 2.5: Polarization rotation in a birefringent waveguide after a half- beat length

propagation. ............................................................................................................................. 15

Figure 2.6: TE to TM mode exchange in a birefringent waveguide after a half- beat

length. ....................................................................................................................................... 16

Figure 3.1: The top view of schematic configuration of a directional coupler-based PSR

based on an asymmetrical directional coupler [53]. ................................................................ 21

Figure 3.2: The top view of schematic configuration of a PSR based on a bi-level taper and

an adiabatic coupler [17]. ......................................................................................................... 22

Figure 3.3: Top view of the PSR in FDTD, color gradient represents the power intensity in

the structure. ............................................................................................................................. 24

Figure 3.4: Top view of the power intensity in PSR when inputting TE mode only .......... 25

Figure 3.5: Top view of the power intensity in PSR when inputting TM mode only ......... 25

Figure 3.6: Schematic of the power evolution and mode profiles at different cross-sections

of the bi-level PSR. .................................................................................................................. 26

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Figure 3.7: PSR (presented by blue box) with edge couplers on left, in gray on right is test

structure with edge couplers. ................................................................................................... 29

Figure 3.8: (a) PSR (presented by blue box) with grating couplers. (b) Test structure with

grating couplers. ....................................................................................................................... 31

Figure 3.9: Geometrical parameters of the designed PSR based on bi-level taper and

adiabatic coupler. ..................................................................................................................... 32

Figure 4.1: Integrated polarization diversity system [8] consisting of an input PSR, a

photonic structure, and an output PSR. .................................................................................... 38

Figure 4.2: Transfering data from FDTD Lumerical software to Interconnect Lumerical

software. ................................................................................................................................... 43

Figure 4.3: Looking at the performance of the PSR with ONA in Interconnect Lumerical,

Inputting TE. ............................................................................................................................ 43

Figure 4.4: Transmission (dB) in TE output port when a mix of TE and TM modes

enters. ....................................................................................................................................... 44

Figure 4.5: Transmission(dB) in TM output port when a mix of TE and TM modes

enters. ....................................................................................................................................... 45

Figure 4.6: Desired TE Transmission and TM conversion ................................................. 46

Figure 4.7: Calculated PCE for the designed bi-level PSR. ................................................ 47

Figure A.1: Geometrical parameters of the designed PSR based on bi-level taper and

adiabatic coupler. ..................................................................................................................... 51

Figure A.2: looking at the performance of the PSR with ONA in Interconnect Lumerical,

Inputting TE. ............................................................................................................................ 54

Figure A.3: looking at the performance of the PSR with ONA in Interconnect Lumerical,

Inputting TM. ........................................................................................................................... 54

xii

List of abbreviations

CMOS Complementary Metal-Oxide-Semiconductor

E-beam Electron Beam

ER Extinction Ratio

FDTD Finite Difference Time Domain

IME Institute of Microelectronics

LED Light-Emitting Diodes

MIMO Multiple Input Multiple Output

MMI Multimode Interference Coupler

MZI Mach Zehnder Interferometer

ONA Optical Network Analyzer

PCE Polarization Conversion Efficiency

PIC Photonic Integrated Circuits

PSR Polarization Splitter Rotator

SiP Silicon Photonics

SOI Silicon On Isolator

S-parameters Scattering parameters

TE Transverse Electric

TM Transverse Magnetic

xiii

Acknowledgments

Firstly, I would like to express my sincere gratitude to my supervisor, Prof. Leslie Ann

Rusch and my co-supervisor, Dr. Wei Shi for the continuous support of my master study and

related research, for their patience, motivation, and immense knowledge. Their guidance

helped me in all the time of research and writing of this thesis. I could not have imagined

having better advisors and mentors for my master study. Also I want to thank all my colleagues

and friends in COPL at Université Laval for their intellectual and friendly supports. And last

but not least I want to thank my dear husband for every single moment and also my family,

although faraway their warm encouragement and support have always been with me.

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Chapter One: Introduction

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1.1. Optical Communication

At the present time, optical and wireless communication systems are the two complementary

systems to supply the increasing demand of high speed and high capacity data transfer. In

optical communication systems, light is the main element. Instead of electrical current, light is

used to carry the signal. In fact, the signal is modulated on light and is transmitted through an

optical fiber. The fundamental devices are optical fibers, transmitter/modulators,

receiver/demodulators, and some other devices such as amplifiers, filters, polarization

controllers, etc.

The optical communication system has some advantages and disadvantages compared to

traditional electrical communication with copper cables. The first distinguishing point is the

low attenuation in optical fibers, which makes it perfect for long distances. Typically, the

attenuation in optical fibers is lower than 1 dB/km, which is much lower than dozens of dB/km

in copper cables. Another positive point is that they have no electromagnetic interference, so

this system is reliable in a noisy environment. Moreover, its wide range of bandwidth makes

this system more popular. The other advantages are that the optical fibers are small, not heavy,

and they are cheaper than the copper cables. However, optical systems have some negative

points such as expensive transmitter, receiver, and other support equipment. In addition,

installing and implementing an optical communication system requires expertise and skill for

cable installation and interconnection.

In the following section, a short introduction to the building blocks of an optical

communication system is presented.

Figure 1.1: A schematic of a simple optical communication system.

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1- Optical fiber: Basically, single-mode and multi-mode fibers are the two main types

of optical fibers. Single-mode fibers are suitable for long and high performance links.

However, as they have a diameter less than 10 µm, more expensive interconnects and

methods are required. On the other hand, multi-mode fibers have a larger diameter,

typically more than 50 µm, so cheaper connectors, transmitters, and receivers can be

used. The drawback of multi-mode fibers is their limited bandwidth and limited link

length as there is multi-mode distortion in these types of fibers. In addition, multi-

mode fibers have high attenuation. Typically, the optical fibers are not polarization

maintaining, thus the polarization of the light can change through propagation.

2- Transmitter: As depicted in Fig. 1.1, at the transmitter side, the data is sent to

a modulator driver which creates a high frequency voltage that corresponds to the

transmitted data. This high frequency voltage and also the light that comes out from

the laser are the two inputs of electro-optical modulator. In the modulator, the signal

gets modulated on the light and finally is launched through the optical fiber. The

source of light can be a laser diode or a semi-conductor transmitter such as light-

emitting diodes (LEDs). The laser diodes produce coherent light while LEDs produce

incoherent light.

3- Receiver: At the receiver side, there is a photodetector which converts light to

electricity via photo-electric effect. Basically, a photodetector is a reverse biased

semiconductor-based photodiode. The photodetector receives the transmitted light

and creates an electrical signal like the one at the output of the driver in the transmitter

side. Finally, the original logical data is recreated using electrical signal processing.

4- Some other secondary devices are utilized in an optical communication system to

enhance the performance of the system such as amplifiers, filters, wave-division

multiplexer/demultiplexer, polarization controller, etc.

Because of fiber attenuation and fiber distortion, the transmission distance of a fiber-

optic communication system is limited. To overcome this limitation, amplifiers can

be used, which directly amplifies the optical signal without converting into the

electrical signal. An amplifier is typically a rare-earth mineral erbium doped fiber,

which is pumped with a laser light with a wavelength shorter than the wavelength of

communications signal. Furthermore, optical filters can be utilized to selectively

transmit or filter the light with a specific wavelength. In addition, to improve and

better use the capacity of an optical channel, wave-division multiplexing (WDM)

plays a critical role. WDM is a technique which multiplexes a number of optical

4

signals onto a single optical fiber via sending each data over a different central

wavelength. Other multiplexing techniques such as polarization multiplexing and

mode division multiplexing can be utilized simultaneously with WDM, but usually

special fibers and/or complex signal processing are required. Moreover, in the

polarization dependent systems, polarization controller devices can solve the problem

of polarization dependency as we will explain in the next chapters. As a result, all

these devices and techniques increase the performance of an optical communication

system.

1.2. Photonic Integrated Circuits with Different Platforms

The previous section was an introduction on traditional optical communication systems. In

the following section we discuss about more modern optical systems with photonic integrated

circuits (PIC). In traditional optical communication systems, devices are discrete components

and they are bulky compared to integrated devices. However, recently all or some of these

devices or functions are integrated in one microchip which is called a PIC. As a result, PICs

reduce assembly cost and the overall system is cheaper. They are more robust and have better

functionality, improved performance, and reduced power consumption.

There are different materials that can be used as the platform for PICs, such as Indium

phosphide (InP), Silicon Photonics (SiP), and SiN. Each has its own advantages and

disadvantages. In the Table 1.1 and Table1.2, a comparison between these materials is shown

[1].

Table 1.1: Technology comparison between InP, SiP, and SiN as the PIC platform based on their ability to build different blocks, (+ + +: Very good, + +: Good, +: Modest, -: challenging, - -: Very challenging).

Building block InP SiP SiN Passive components + + + + + + Lasers + + + - - Modulators + + + + + + Switches + + + + + + + Optical amplifiers + + + - - Detectors + + + + + + -

As it is clear from Table 1.1, InP-based PICs are one of the most powerful technologies. A

full photonic functionality in a single chip including high-performance lasers, detectors,

5

modulators, optical amplifiers, and a variety of passive components, can be realized by InP-

based platforms [1]. Indium phosphide is the most commercially utilized material for active

and passive chips. Nevertheless, it is obvious from Table 1.2 that devices on SiP platforms

have the smallest footprint, the lowest chip cost of fabrication and also the lowest cost of

packaging with grating couplers. Most importantly, SiP is compatible with complementary

Metal-Oxide-Semiconductor (CMOS). In the next section, we discuss more about SiP which

is one of the most attractive platforms based on above-mentioned advantages.

Table 1.2: Performance comparison between InP, SiP, and SiN as the platform for PIC based on their characteristics, (+ + +: Very good, + +: Good, +: Modest, -: challenging, - -: Very challenging), 1

with edge coupler, 2with grating coupler [1].

Characteristic InP SiP SiN Footprint + + + + + + Chip cost + + + + + CMOS compatibility - - + + + Low cost packaging - - 1 /+ + 2 + +

1.3. Silicon Photonics Platforms for PICs

As it is discussed in the previous section, SiP platform has received much attention in recent

years due to its compatibility with CMOS technology, which makes the mass production of

photonics devices cost-effective. The devices on SiP platforms have the lowest cost for chip

fabrication and packaging with grating couplers. Moreover, having high optical confinement

enables a variety of applications for silicon waveguides. The intrinsic high-index contrast

property of SiP allows for photonics with very small footprint, which is highly desirable for

system integration.

Researchers and engineers around the world have developed various kinds of SiP devices

in the last decade. SiP devices such as waveguides, detectors, modulators, and wavelength

filters have been designed and demonstrated. The performance of these SiP devices are almost

the same as the conventional photonic devices but they are on a wafer with a small footprint.

Electronic–photonic circuits play a significant role in different areas such as optical

communications within data centers and computers, high-speed communications for mobile

devices, medical applications, and sensor systems. Currently SiP is at the same period of

expansion that electronics was in the 1970s and 1980s. However, existing silicon foundries that

6

fabricate high-quality wafers have facilitated SiP chip fabrication. We are currently in an

important transition when academics and industry both have access to SiP fabrication by the

multi-project wafer services offered by CMC Microsystems, Institute of Microelectronics

(IME), ePIXfab, etc. [2]

Although fabrication of a wafer is very expensive, cost sharing of fabrication in a multi-

project wafer makes it accessible for a lot of industries and research groups. Therefore, when

different groups combine their designs and fabricate their multi-project wafer together, the cost

is reasonable. The procedure is to design and simulate the SiP integrated circuits with a

simulation software such as Lumerical or PheoniX Software or any other. Fortunately, there

are some Process Design Kit (PDK) libraries for CMOS UV-lithography foundry services such

as CMC Microsystems, IME, ePIXfab, imec, OpSIS, and LETI, which help researchers to use

some rules and some optimized devices such as waveguides, couplers, bends, Y-branches, etc.

Therefore, it is not required to start from scratch for each project. These libraries make the

projects much more convenient and faster. The next step of the procedure is fabrication, and

finally testing the chips in the laboratory. Normally, the process can be repeated different times

to improve and optimize a device or system.

In SiP wafers, typically silicon lies on top of a layer of silica which is known as silicon on

isolator (SOI). SOI is a structure that supports both electric and photonic circuits. After SOI

fabrication, a top cladding of silica it is added. Typical physical parameters for a SiP wafer are

an 8-inch diameter, 220 nm top Si layer (core), and 2 µm silica (cladding).

The main reason of SiP small footprint is the high refractive index contrast between the

silicon and silica. However, this high intrinsic contrast also causes severe polarization

dependency for the SiP chips. As a result, some photonic integrated devices support only one

type of polarization mode. Therefore, polarization management and designing an efficient PSR

is essential to remove this dependency. In the next chapter, polarization management is

discussed in detail.

7

Chapter Two: Polarization Management

8

2.1. Introduction

In traditional optical communication using intensity modulation with direct detection

(IMDD), the polarization of the light is not exploited. The polarization alters during

transmission in single mode fiber (SMF) and as a result, the output light is randomly polarized.

A random polarization state does not damage the quality of the signal in a system that is

insensitive to polarization. SiP is growing in popularity and SiP chips are sensitive to

polarization. Consequently, polarization management is an important issue to consider in

silicon subsystems. SiP integrated devices only support one kind of polarization mode.

In the following chapter, firstly polarization states in waveguides are introduced and the

requirement for on-chip polarization management is discussed. Finally, different approaches

regarding polarization conversion are presented and the basic principles of polarization mode

conversion is studied.

2.2. TE and TM Polarization Modes

In this section, the definition of TM (Transverse Magnetic) and TE (Transverse Electric)

modes for planar and ridge waveguides is introduced and explained in detail. In planar

waveguides1, light propagation is determined by Maxwell’s equations. Optical modes of a

waveguide are the result of Eigen-solutions of Maxwell’s equations under appropriate

boundary conditions in the waveguide with specific geometry. Figure 2.1 illustrates a three-

layer asymmetric dielectric slab waveguide. It consists of a core layer, and upper cladding and

lower cladding which provide the boundary conditions for the solution of the wave equations.

A planar waveguide with its basic axes is illustrated in Fig. 2.1.a. In this case, light is

confined in the y-axis and propagates in the plane of x-z. Based on their field distribution, two

orthogonally modes of TE and TM exist. When the electric field is in the plane of the core layer

and it is perpendicular to the propagation direction, the light has TE mode. In TE mode case,

the electric fields in z and y axes and also the magnetic field in x axis are equal to zero

1 Planar waveguides, also called slab waveguides, are made of three layers with different material and different dielectric constants.

Directions parallel to their interfaces can be considered essentially infinite. So, the light is confined only in one direction and is guided in a

plane.

9

(Ey = Ez = Hx = 0). On the other hand, the light has TM mode when the magnetic field is in the

plane of the core layer and it is perpendicular to the propagation direction. In TM mode case,

the magnetic fields in z and y axes and also the electric field in x axis are equal to zero

(Hz = Hy = Ex = 0) [3].

Figure 2.1: Three layer waveguide with confinement in y axis (a) asymetric dielectric planer waveguide (b)

rectangular strip waveguide.

In PICs, one dimensional waveguides like planer waveguides are not conventional. Two

dimensional waveguides like strip waveguide2 (as shown in Fig.2.1.b) and ridge waveguides3

(as shown in Fig.2.2) are commonly used in PICs. In this case, light is confined in both y-axis

and x-axis and the propagation direction is along the z-axis. In these types of waveguides,

optical modes are again the result of Eigen-solutions of Maxwell’s equations based on the

boundary condition in both x-axis and y-axis. So, the equations for planar waveguides are not

valid for these other geometries. In two dimensional waveguides, pure TE and pure TM does

not exist anymore and hybrid modes are defined. When Ex and Hy components have the most

power, the light mode is called “TE-like mode”. When Ey and Hx are dominate, the light mode

is defined “TM-like mode” [3].

2 Strip waveguide is a strip of a layer sandwiched between cladding layers. A rectangular strip waveguide is the simplest strip waveguide.

3 Ridge waveguide is a uniform rectangular strip waveguide with one or two (double ridge) rectangular on the top and/or on the bottom.

10

Figure 2.2: A ridge waveguide with the light propagation through z-axis and light confinement along x-axis and y-axis.

In a perfectly symmetric rectangular ridge waveguide, as can be seen in Fig. 2.2, the

propagation constants of the two orthogonal fundamental modes (TE and TM) are identical, as

the boundary conditions are the same for both modes. However, waveguides are not usually

designed to be symmetric, and even when they are, there are always some external factors like

fabrication defects, temperature variations, or stress, which cause differences in the

characteristics of the two modes. Thus, TE and TM modes have different effective refractive

indices (neff), creating waveguide birefringence. The propagation constant for each mode can

be calculated by

𝛽 = 𝑛%&& 2𝜋𝜆 (2.1)

where, λ is the light wavelength.

Typically, the strip waveguides are 500 nm wide and 220 nm thick. For this typical

waveguide geometry, neff is calculated at the wavelength of 1550 nm in a commercial numerical

solver of Maxwell’s equations, Lumerical MODE. Numerical results are summarized in table

2.1 for a SOI strip waveguide. The obtained values are on the order of effective refractive

indices found in the literature [4].

11

Table 2.1: Effective refractive indices and propagation constants for TE and TM modes.

neff 𝜷 (1/µm)

TE 2.36086 9.57014

TM 1.66372 6.744148

From Table 2.1, the difference between the effective refractive indices of the two modes is

0.7, and the propagation constants are different. Accordingly, the two modes of light travel

with different propagation constants through the waveguide experiencing birefringence.

Therefore, these two polarization modes are not able to couple to each other and they have a

phase difference as they propagate. This phenomena changes total polarization of the wave [3,

5].

2.3. Polarization Management

Devices based on polarization-diversity technology are required to address the problem of

polarization sensitivity in PICs [6, 7]. In this section, requirements for on-chip polarization

management, as well as different approaches to polarization management, are studied. In

addition, basic principles of polarization conversion are investigated in detail.

Polarization of light varies when light propagates through optical fibers. Therefore, receiver

side optical integrated circuits see light without a fixed polarization; received signals are

randomly polarized. Most of the devices on SiP integrated circuits are polarization sensitive,

e.g., a lot of structures such as filters [8], modulators [9], on-chip lasers [10] require a unique

polarization state; typically polarization is not problematic at the transmitter side where is can

be easily manipulated. As PICs need to be compatible with traditional fiber optic systems, on-

chip polarization management including splitting, rotating, and combining different

polarizations becomes an important issue.

From another point of view, with on-chip polarization management it is possible to better

use capacity of a channel by exploiting polarization division multiplexing (PDM) with coherent

detection; such a strategy increases spectral efficiency and subsequently communication

capacity. Therefore, high-performance polarization-management devices with small footprints

are also of interest for coherent optical applications [11].

12

Figure 2.3 illustrates basic principles of polarization-diversity technology. In this system,

input light is separated into two polarized TE and TM beams by a polarization splitter. One of

the outputs, the TM mode, is rotated into the other (TE) by a polarization rotator. The two

beams with the same polarization modes, are separately launched into two identical circuits.

The characteristics of the two branches of the subsystem are expected to have identical

properties. Afterward, by another PSR, one of the outputs is rotated to the TM polarization

mode (e.g. TE which used to be TM is rotated back to TM).

Figure 2.3: Polarization diversity technology with two PSRs and two identical circuits.

2.4. Polarization Rotator

Polarization rotator is the key component in polarization management systems. The main

idea in a polarization rotator is to tilt the optical axis of the waveguide by creating some kind

of anisotropy and asymmetry. This tilting of the optical axis is the main cause of coupling

between polarization states and results in polarization rotation.

In general, there are two types of polarization rotators, called active and passive devices, as

shown in Fig. 2.4. Active polarization rotators are based on material anisotropy, while passive

polarization rotators are typically based on an asymmetric geometry. The most important

methods to realize active polarization rotators exploit the photo-elastic [12, 13] and electro-

optic [14, 15] effects. Some anisotropic materials, such as quartz, do not require active

elements. The constant application of stress can induce a permanent anisotropic state. Other

passive polarization rotators make asymmetric geometries by using discontinuities and

asymmetries in the structures, such as steps, tapers, junctions, and bends, to introduce power

exchange between polarization states in the resultant hybrid mode [16]. Passive polarization

rotators are more attractive and more commonly used as their fabrication process is easier than

that of active polarization rotators; they also typically have a wider bandwidth.

13

Figure 2.4: Different categories of polarization rotators.

Passive polarization rotators are categorized into mode-coupling and mode-evolution

devices. Devices based on the mode-evolution method can be realized by either using a bi-

level taper in its structure [17, 18], or by using either a silicon nitride or an amorphous silicon

as the top layer. These structures break the vertical symmetry of the waveguide in passive

devices [19-22]. The main idea of mode-evolution is to rotate the main axis of the structure

together with that of the fundamental polarization mode along transition. In order to

adiabatically couple the modes through these types of devices, typically an excessively long

structure is needed, and their fabrication process is complex. However, mode-evolution devices

have attracted much attention because of their robust fabrication and broad band wavelength

range.

The other category of passive polarization rotators is mode-coupling structures; it is also

based on a tilted optical axis. In this method, one polarization mode rotates to the other after a

specific length along the waveguide structure. This specific length is a function of different

parameters of the waveguide geometry and of the propagated light; these issues are discussed

in detail in the next section. Therefore, mode-coupling structures are very sensitive to

fabrication geometry variations and errors, and they are absolutely wavelength dependent.

However, advantages such as ease of fabrication process and smaller footprint in comparison

to the other structures, have made mode-coupling structures attractive.

14

Various passive polarization rotators have been offered and constructed based on different

designs of anisotropy and asymmetry in the waveguide geometry. The main idea is based on

the fact that hybrid modes can have a power exchange between different polarization modes

by employing some asymmetries and discontinuities. In 1991, the first experimental results for

polarization rotation were reported by Shani et. al. [23] by utilizing periodic asymmetric-loaded

rib waveguides. However, in their report, the theory of the polarization rotation was not

mentioned. In the next year, Haung and Mao [24] theoretically analyzed the structure by using

hybrid supermode, based on scalar modes. According to their report, an asymmetric cross-

section makes a perturbation to the principle axes of the waveguide, and by periodically

exchanging the loaded layer in longitudinal direction, polarization rotation is accumulated

coherently until full conversion is obtained. In 2001, Obayya et. al. [25, 26] designed a

polarization rotator based on cascaded bent sections. In this design, the insertion loss in the

structure is high as there are a lot of junctions between sections, thus, the scattering and the

mode-mismatching is large. Moreover, the device is very long and the fabrication is complex.

Some other structures have only one single straight section to make a simple polarization

rotator [27-34]. Their low insertion loss, small footprint, and simple geometry makes them

interesting devices in comparison to periodic asymmetric-loaded rib waveguides. In 2003, a

polarization rotation using SOI ridge waveguides with slanted sidewalls was proposed by Chan

et. al. [32]. Several devices based on similar structure were proposed later in 2006 [33, 34]. In

2014, Sacher et. al. [17] proposed and fabricated a single-section PSR based on mode-evolution

on SOI using a bi-level taper. The completely adiabatic structure of this design causes a low

insertion loss and less sensitivity to dimension variations. Although this device is around

500 µm long, it is one of the most popular designs up to now.

2.5. Operation Principles of Polarization Rotator

As is expressed in the previous sections, polarization management is essential in photonic

integrated systems and a polarization rotator is one of the key elements. In this section, the

operating principles of polarization rotation in passive polarization rotators are explained in

detail.

In any passive polarization rotation structure, a geometrical anisotropy is the main cause of

polarization rotation. As is shown in section 2.2, different polarization states have different

effective indices. Therefore, after propagation, the phase difference of two modes is different

15

and is a function of the difference in their propagation constants Δβ, and propagation length L

[35]:

Δ𝜑 = ΔβL (2.2)

Based on (2.2), the phase delay between two modes is repeated after integer multiples of Lb

which is called polarization beat length:

𝐿- =2𝜋

(𝛽/ − 𝛽1) (2.3)

where β0 and β1 are the propagation constants of the two modes. Half-beat length,𝐿𝜋,is the

propagating distance when the phase delay becomes ±π:

𝐿5 =𝐿-2 =

𝜋(𝛽/ − 𝛽1)

= 𝜋

𝑛%&&/ − 𝑛%&&1 𝐾0=

𝜆

2 𝑛%&&/ − 𝑛%&&1

(2.4)

As shown in Fig. 2.5, any linearly-polarized light can be decomposed into two components

along the main axes which are called fast and slow birefringence axes in the transverse plane.

When light propagates at a distance equal to a half-beat length, the phase difference between

the two modes is ±π degrees. In Fig. 2.5, after propagation of L9, the vertical component

toward up rotates π degrees and goes toward down. Consequently, if linearly-polarized light is

launched into a birefringent waveguide at an angle of 𝜑 to one main optical axis, after

propagating L9, the output polarization with respect to the same axis is -𝜑 [16].

Figure 2.5: Polarization rotation in a birefringent waveguide after a half- beat length propagation.

The rotation of the optical axis after a half-beat length propagation is the basis of the idea

of rotating two orthogonal modes transforming one into the other. In an asymmetric structure,

the two lowest-order eigenmodes are hybridized and their electric and magnetic fields are tilted

from the vertical axis due to the new boundary conditions in solving Maxwell’s equations.

16

Without loss of generality, it can be assumed that the electric field of the TE and TM modes

are aligned in the x and y directions respectively, and the optical axis has been rotated. The

optical axis can be tilted by any angle that can be realized by a correct optimization of the

waveguide parameters, i.e. proper choice of the geometry and refractive index of the

asymmetric waveguide. In a single-section polarization rotator, the asymmetric waveguide is

optimized to have an optical axis tilted to exactly 45°. Under this condition, the TE mode

rotates by 90° and rotates to TM mode. In next paragraph, this theory is explained in detail.

We assume, without loss of generality, that light is launched along the x-axis. As shown in

Fig. 2.6, x-y is considered as the electrical axes and x’-y’ as the optical axes. This asymmetric

waveguide is optimized to have optical axes (x’ and y’) rotated 45 degrees with respect to the

electrical axes (x-y). Thus, at the starting point of the waveguide, the polarization of light is

TE. This mode has an angle of 𝜑 = -45° with respect to the optical axes. In this situation, two

eigenmodes are excited, and each mode is transmitted with propagation constants, β1 and β2,

respectively. As is explained in the previous paragraph, after a propagation of a half beat-

length, light polarization is rotated to a new angle of 𝜑 = -(- 45°) = +45°. Therefore, in total a

90° rotation of the polarization is obtained, and accordingly, the polarization of output light is

along y-axis, i.e. TM mode [16, 36].

Figure 2.6: TE to TM mode exchange in a birefringent waveguide after a half- beat length.

In order to check the performance and efficiency of a polarization rotator, polarization

conversion efficiency (PCE) and extinction ratio (ER) are critical parameters. PCE is calculated

as follows for the case of TM to TE conversion.

𝑃𝐶𝐸=>→=@ = 𝑃=@ABC

𝑃=@ABC + 𝑃=>ABC

(2.5)

17

In (2.5), 𝑃=@ABC and 𝑃=>ABCare the powers of the output TE mode and the output TM mode,

respectively. It is worth mentioning that insertion loss is not considered in PCE.

ER is another parameter to evaluate the efficiency of a polarization rotator which is defined

as [16, 37]:

𝐸𝑅 = 10𝐿𝑜𝑔(1 − 𝑃𝐶𝐸𝑃𝐶𝐸 ) (2.6)

Equation (2.6) can be written as follows for the case of TM to TE conversion.

𝐸𝑅 = 10𝐿𝑜𝑔𝑃=>ABC

𝑃=@ABC,𝑊ℎ𝑒𝑛𝑇𝑀𝑖𝑠𝑡ℎ𝑒𝑖𝑛𝑝𝑢𝑡 (2.7)

A polarization conversion with higher PCE and lower ER has better performance and

efficiency. A typical requirement is for PCE over 92% [38], leading to a typical target ER of

10.61dB. In the last chapter these parameters are calculated for a PSR based on TM0-TE1

mode conversion in a bi-level taper.

2.6. Polarization Beam Splitter

A Polarization beam splitter is another key element of a polarization diversity system, as

well as optical systems for imaging, sensing, and signal processing. The basic structures that

can be employed to realize a polarization beam splitter are multi-mode interference (MMI)

couplers [39, 40], Mach-Zehnder interference (MZI) couplers [41, 42], and directional couplers

[43, 44]. Directional couplers have attracted more attention as they have the advantage of ease

of design and fabrication. For instance, a directional coupler beam splitter is proposed by

Fukuda [44] in which the TE mode has a significantly longer coupling length than the TM

mode. Thus, the TE mode goes through the waveguide with very slight coupling, while the TM

mode is cross-coupled completely. To have a polarization beam splitter with a higher extinction

ratio, it is possible to use a cascaded structure. The disadvantage of the cascaded approach is

its long structure and small bandwidth [44]. A better substitution for cascaded directional

coupler beam splitters is an asymmetrical directional coupler, such as the ones reported by Lin

et. al. [45] and Dai et. al. [46]. Typically, in directional coupler structures a big birefringence

of around 10−2 ∼10−1 is necessary and can be attained by SOI with an ultrahigh index contrast

18

and ultra-small cross-section. Therefore, deep-ultra-violet (deep-UV) or Electron Beam (E-

beam) lithography is needed for fabrication [47]. Another flexible and practical structure is an

MZI coupler [48]; which can realize a polarization beam splitter in waveguides with a small

birefringence. In addition, the fabrication process can be a regular lithography process [49].

The other approach is a polarization beam splitter based on MMI coupler which has a complex

structure. As MMI couplers consist of a lot of junctions, normally their insertion loss is high

[50-52].

2.7. Summary

In this chapter TE and TM modes were defined in two basic types of waveguides. Then, the

general operating principle of polarization management was thoroughly studied. Subsequently,

the key elements of a polarization management system were discussed. Firstly, different types

of polarization rotators were introduced and an introduction to the historic evolution of

polarization rotators was provided. Afterwards, the basic principles of polarization rotation in

a single section device were defined. Finally, polarization beam splitters were introduced and

their different types were presented.

In the next chapter, the focus is on a high performance structure based on TM0-TE1 mode

conversion in a bi-level taper on SOI. In this chapter we explained and motivated that choice.

Subsequently, the simulation results as well as the layout details for fabrication will be

expressed.

19

Chapter Three: PSR Based on TM0-TE1 Mode

Conversion in a Bi-level Taper on SOI

20

3.1. Introduction

As discussed in chapter two, polarization management is a critical issue and it is important

to design photonic integrated systems with efficient PSRs. In the following chapter, we

investigate different PSRs. A high performance PSR is introduced based on TM0-TE1 mode

conversion in a bi-level taper on a SOI platform. We report results of modeling and simulation

in Finite Difference Time Domain (FDTD) Lumerical software. Finally, we present the layout

of the design that has been sent for fabrication and eventual characterization.

3.2. Selecting a High Performance PSR

As stated in chapter two, there are several structures to realize a polarization rotator and a

polarization splitter. The advantages and disadvantages of each structure were discussed. The

goal of this section is to identify and select a high performance PSR architecture. A high

performance PSR has a high extinction ratio, high polarization conversion efficiency, low

insertion loss, wide bandwidth, high fabrication tolerance, compact footprint, and is CMOS

compatible. As discussed in chapter one, among materials used for photonic integrated

platforms, SOI is an interesting platform in high demand. Thus, the investigation to find a high

performance PSR is done only among the ones based on the SOI platform.

Polarization rotators can be categorized as active or passive devices. Since the active

polarization rotators are not based on the SOI platform, we do not consider them. The passive

polarization rotators are more common as their fabrication processes are more robust and their

bandwidths are wider. As a result, we focus on the following two passive devices:

• Directional-Coupler-based PSR: Although these types of PSRs are ultra-small (~100 µm)

and CMOS compatible, they are very sensitive to fabrication errors and there are strict

constraints on waveguide width and coupler length [53, 54].

• Mode-evolution PSR: These PSRs consist of a bi-level taper4 and an adiabatic coupler.

Mode-evolution PSRs are very robust to fabrication errors and have low insertion loss due

4 In photonic waveguides, a taper is a waveguide whose size gradually changes. For example, it can be used to connect two different sized waveguides using a gradual transition.

21

to their adiabatic structure. This type of PSRs is compatible with CMOS technologies,

however, it has a large footprint (~500 µm) [17, 18, 55, 56].

Consider the first option, a directional coupler-based PSR, in 2011, Dai et. al. [53] designed

an ultra-compact (less than 100 µm) directional coupler-based PSR that consists of an

asymmetrical directional coupler and an adiabatic taper. As is shown in Fig. 3.1, the TM0 mode

rotates to the TE1 mode in the adiabatic taper because of the mode coupling between two

modes. The TE0 mode, however, does not change through the adiabatic taper. In the second

section, the asymmetrical directional coupler acts as a splitter, where the TE1 mode is coupled

to the adjacent waveguide, and changes to the TE0 mode. The TE0 mode coupling to the

adjacent waveguide can be avoided by introducing a phase mismatch.

Figure 3.1: The top view of schematic configuration of a directional coupler-based PSR based on an asymmetrical directional coupler [53].

In Dai et. al.’s directional coupler-based PSR [53], a silicon nitride (Si3N4) top layer is used

to break the vertical symmetry of the waveguide, however, this process is not available at most

foundries. A solution for this limitation is to fabricate the device with an air cladding process

and to deposit the Si3N4 layer on top later. However, the air cladding process is not available

at IME that fabricates the chips for this work. Even if the air cladding process was available,

Si3N4 deposition equipment in COPL laboratory causes a lot of fabrication errors. Another

issue is that it is more interesting to have a silica layer on top instead of a silicon nitride top

layer in photonic integrated circuit. Therefore, although Dai et. al.’s PSR [53] is an ultra-small

and high performance device, we did not select it for this work as it is difficult to fabricate and

is not robust to fabrication errors.

22

We next consider a mode-evolution PSR based on Sacher et. al.’s design [17]. As explained

in chapter two, mode-evolution PSRs are also in the category of passive polarization rotators.

Mode-evolution is commonly used as it has a wide bandwidth and the fabrication process is

robust. Although mode-evolution polarization rotators are typically long, they have low

insertion loss and have the advantage of being CMOS compatible. Due to these advantages, a

mode-evolution PSR based on bi-level taper was selected for this work.

We select the PSR based on Sacher et. al.’s design [17] that consists of a bi-level taper as

TM0-TE1 mode rotator and an adiabatic coupler as a TE1-TE0 mode splitter. This PSR is

similar to Dai et. al.’s design [53], however, as the bi-level taper has a symmetric SiO2 cladding,

no extra layer or material are required. Thus, the fabrication process is robust and simple. In

Dai et. al.’s design [53], a directional coupler is used for splitting the TE0 and TE1 modes.

While in Sacher et. al.’s design [17], the two modes are divided into two waveguides by an

adiabatic coupler similar to a Y-Branch approach . In addition, Sacher et. al.’s PSR [17] is

completely adiabatic, decreasing the insertion loss, reducing the sensitivity to variations in

waveguide dimensions, and having a wider bandwidth. These parameters make Sacher et. al.’s

design [17] more interesting than previous designs. The total length of the bi-level taper based

PSR is around 495 µm, consisting of a 115 µm long bi-level taper and a 380 µm long adiabatic

TE1-to-TE0 coupler. Furthermore, polarization crosstalk is less than -13 dB over a bandwidth

of 50 nm [17].

The bi-level taper PSR is depicted in Fig. 3.2, where the partially-etched level of Si is shown

by the darker regions, and the fully etched level of Si is displayed by the lighter regions. The

thickness of the top silicon region is 220 nm and the partially-etched thickness is 90 nm, which

is designed for IME baseline.

Figure 3.2: The top view of schematic configuration of a PSR based on a bi-level taper and an adiabatic coupler [17].

23

3.3. Modeling and Simulation 3.3.1. Functionality

The main operating principle of the bi-level PSR is mode-evolution. If light with TE0

polarization is launched in the device, it propagates through the adiabatic bi-level taper and

exits the taper without any change. Afterwards, the TE0 mode enters the main branch of the

adiabatic coupler and exits the upper port without any change, exploiting the phase mismatch

between TE0 and higher modes.

If light with a TM0 polarization is launched at the input, it is rotated to a hybrid mode with

TM0 and TE1 features during the adiabatic bi-level taper (center region in device of Fig. 3.2).

The vertical symmetry of the bi-level taper is broken with the partially-etched slab waveguide,

causing a large change in the effective indices of the modes along the central section of the

structure [53, 57]. These effective indices differences force the TM0 mode to rotate to the

hybrid mode (with both TE1 and TM0 features), and then the hybrid mode is forced to rotate

to the TE1 mode at the interface with the coupler. The TE1 mode then couples to the lower

branch of the adiabatic coupler; and the TE0 mode exits from the lower output port after a

bend. The adiabatic coupler avoids crosstalk between TM0 and TE1 modes. The output of

each of the two branches is in the TE0 mode [17].

3.3.2. Simulation

We simulated the PSR based on an adiabatic bi-level taper (with dimensions specified in

[17]) in FDTD 3D software from Lumerical . The parameters of the design are reported in

Fig. 1 and Table A.1 in Appendix for easy reference. Figs. 3.3, 3.4, and 3.5 show a color map

of the signal intensity from a top view of the PSR as calculated in FDTD Lumerical software,

where x- and y-axis refer to the physical dimensions of the PSR. The length of the device is

495 µm, and the width varies along its length. Color gradient illustrates the power intensity of

the modes that propagate in the structure, as given by the accompanying scale.

Later figures will present the optical intensity along the structure, but we begin here by

focusing only on the input and output intensities in Fig. 3.3. The internal signal intensities are

occluded so that we may easily identify port locations in this top view orientation. While the

intensities are not shown within the main body of the bi-level taper (they are presented in the

24

following), the intensities are shown at the input and output port for illustration of the case of

inputting a mixed signal with both TE and TM present.

Figure 3.3: Top view of the PSR in FDTD, color gradient represents the power intensity in the structure.

Figure 3.4 is generated when simulating a TE mode alone at the input. There is no rotation

and no coupling throughout propagation for this input. The power intensity at the output is the

same as at the input, while we observe the intensity within the bi-level taper decrease as the

waveguide is widens, and increase again as the waveguide narrows; the mode profile stretches

out somewhat. We observe virtually no intensity at the lower output port.

25

Figure 3.4: Top view of the power intensity in PSR when inputting TE mode only

Figure 3.5 is generated when simulating a TM mode alone at the input. The TM mode rotates

to a hybrid mode across the bi-level taper and then couples to the lower branch of the adiabatic

coupler. A bend in the waveguide leads the converted TM signal to the lower output port where

it exits the device. We observe virtually no intensity at the upper output port.

Figure 3.5: Top view of the power intensity in PSR when inputting TM mode only

26

Mode evolution [55, 56] is the operating principle of this PSR. Figure 3.6 provides a cross-

section view at various points along the bi-level taper. In the center column of Fig. 3.6, the top

view sketch is provided as a reference to indicate where the cross-section view is taken. The

cross-sections demonstrate the evolution of TE and TM modes along the length of the device.

Two scenarios are presented in Fig. 3.6. In the left column, are intensities in cross-section for

the case of inputting the TE mode alone. In the right column of Fig. 3.6 are the intensities in

cross-section for the case of inputting only the TM mode.

The red points in the power intensity profiles are the maxima, whose numerical values in

dB are written to the side. Note that the color bar scale changes at each point to enhance

visibility. Both cases in Fig. 3.6 have the same input power. As the modes expand in the

waveguide whose width is varying, the maximum powers changes. At the input and output

ports the waveguide width is identical. Hence, scales match at input and output. The maximum

power of a specific profile mode is proportional to its total power when the cross-section is

constant.

Figure 3.6: Schematic of the power evolution and mode profiles at different cross-sections of the bi-level PSR.

In observing the leftmost column, we see that when the TE mode alone is input, almost all

the input power exits from the main output (output port for the signal on TE at input). The

27

maximum input power of TE mode is 32 dB (point A) and it is again 32 dB for TE mode at the

output (point D). Some leakage is observed at point E, where the maximum power of TE mode

on the lower output port (output port for signal on TM at input) is 0.01 dB. The leakage was

not visible in the previous plot (Fig. 3.4) as the color scale was fixed. The maximum power

intensity within the bi-level taper (point B and C) decreases because the waveguide is wider

and the mode profile stretches out.

The rightmost column of Fig. 3.6 shows the power evolution when the TM mode alone is

input. At point A, the mode profile of the TM mode is visible. In the center of the bi-level taper

(point B), we see two intensity spots, as the hybrid mode with TM0 and TE1 features is visible.

At the beginning of the adiabatic coupler (point C), the hybrid mode continues to evolve. The

lower output (output port for signal on TM mode at input) has a high intensity (point E) as

expected. At Point D, the upper output (output port for signal on TE mode at input), a little TM

mode leakage can be seen (0.08 dB).

The TM input shows a higher leakage in comparison with the TE input. This means that the

conversion efficiency is not 100%. In chapter four, the conversion efficiency of this design is

calculated. Note that simulation running time to generate data in Figs 3.3-3.6 took more than

24 hours on the cmc-node server and required ~6 GB of memory. Therefore, this simulation

technique is inappropriate for sweeping design parameters for device optimization.

To improve this design (increase the bandwidth and reduce the crosstalk), there are three

avenues to explore. The blunt-tip at the starting point of the adiabatic coupler causes waveguide

discontinuity. To eliminate any mode coupling as a result of the discontinuity, this blunt-tip

can be replaced by a large radius arc. Therefore, a PSR with an arc instead of the blunt-tip at

the beginning of the adiabatic coupler was designed in the final layout. A second improvement

could be reducing the gap in the adiabatic coupler, which reduces the crosstalk by reducing the

effective index difference between the TE0 and TE1 modes [55, 56]. However, as our

fabrication process is UV lithography, the minimum feature size is 200 nm. Thus, it is not

possible to improve the performance of this design by reducing the adiabatic coupler gap.

Finally, the widths and length of the bi-level taper can be optimized, since the incomplete TM0-

TE1 mode conversion in the bi-level taper is the source of the crosstalk. Therefore, to check

the fabrication tolerance and to improve the first design, various PSRs with different

dimensions were designed in the final layout. The dimensions are provided in Table A.2 and

Table A.3 of Appendix.

28

3.4. Chip Layout Design

The simulation results from the previous section confirm that the designed PSR has

acceptable performance, which is also confirmed based on the results presented in chapter four,

for example PCE of 94.5%. Therefore, we design a layout to send for fabrication. A layout, or

mask layout, is a 2D top-view representation of a physical design that is used in optical

lithography manufacturing. The layout we present include two different options for coupling

the light into the chip. These two options are described in section 3.4.1, as well as our

motivation in including both. In section 3.4.2, we describe the two potential fabrication process

and the reason of choosing deep-ultraviolet (UV) lithography method for our work.

The file format used to share a layout is GDS or GDSII. In this work, the layout was created

by Mentor Graphic Pyxis tool with the help of a script. The designed PSRs were saved as

“ample” files. A “do” file was created to do the placement of the objects. Finally, the routing

was done manually. The layout is presented in section 3.4.3.

3.4.1. Input and Output Coupling

Typically, there are two methods for coupling the light into the SiP chips. Edge couplers

that are polarization insensitive may be used, and grating couplers that are polarization

sensitive may be used. Our application clearly calls for the use of a polarization insensitive

method in order to send and receive both the TE mode and the TM mode through the same

input or output. However, edge couplers are risky as their alignments are more difficult and

requires more sophisticated test equipment. Therefore, we also fabricate devices with grating

couplers as a backup method. Some features of the device could be characterized with grating

coupler inputs (leakage, routing, etc.). However, a complete characterization (performance on

a mixed polarization input) requires the use of edge couplers.

3.4.1.1. Edge Couplers

Depicted in the left side of Fig. 3.7, is the case of edge coupling. One edge coupler is

sufficient for each input or output, as it is not sensitive to polarization. Edge coupling is the

preferred method as it has less insertion loss and it is polarization insensitive. The input port is

in the middle of the PSR geometry, and both TE and TM modes are launched from this port.

The leftmost edge coupler is the “output port for signal on TE at input” and the rightmost edge

29

coupler is the “output port for signal on TM at input”. A test structure is used to find the

insertion loss of the edge couplers (no PSR, only couplers) and of the y-branch alone. These

characterizations can be used to normalize the results for the PSR structure. A test structure

with edge couplers is shown in gray on the right side of Fig. 3.7.

Figure 3.7: PSR (presented by blue box) with edge couplers on left, in gray on right is test structure with edge couplers.

3.4.1.2. Grating Couplers

Figure 3.8a illustrates the backup method with grating couplers to characterize the designed

PSR. The grating couplers are sensitive to polarization and can be designed to support either

TE or TM modes. For each input and output, we design a pair of couplers, one supporting TE

and one supporting TM, and a Y-branch to combine the light to/from them. The input ports are

at the bottom; two polarization modes are launched separately and then combined together with

a Y-branch. Two pairs of output ports are visible above the input ports. In the middle, the output

ports are for the “signal on the TE at the input” (TE output port). At the top, the output ports

are for the “signal on TM at the input” (TM output port). The output signals are divided by a

30

Y-branch and a pair of TE and TM grating couplers provide access to the two modes in each

output port.

In the ideal case, when inputting TE only, all the input power exits from the TE grating

coupler at the TE output port. When inputting TM only, all the input power exits from the TE

grating coupler of the TM output port. In this ideal case, no power will be at the remaining two

output couplers. Note that at the top and bottom of the structure a pair of alignment mark with

TE grating coupler is placed to make sure that the fiber arrays is well aligned while doing the

measurements.

In Fig. 3.8b is the test structure for characterizing the grating couplers alone. There is a pair

of TE alignment marks on top and a pair of TM alignment marks at the bottom. For

measurements, the fiber array is aligned to the grating couplers and the best angle of fiber and

coupler is fixed. The optimal angle of grating couplers and fiber array is designed to be

20 degrees, but in experiment, it is necessary to check and find the best angle with the lowest

loss. These alignment marks are also necessary for automatic measurements. These alignment

marks are placed at multiple points in the layout. Moreover, in the middle, there is a

combination of TE and TM couplers and a Y-branch to measure the summation of insertion

loss and the loss of Y-branch to normalize the whole PSR structure loss.

31

Figure 3.8: (a) PSR (presented by blue box) with grating couplers. (b) Test structure with grating couplers.

3.4.2. Fabrication Process

For SOI fabrication, E-Beam lithography and deep-ultraviolet (UV) lithography are the two

potential technologies. As they use different ways to pattern the photoresist, they are different

in flexibility, resolution, cost, and fabrication delay. UV lithography supports the bi-level

fabrication we require for our device [58] ; E-beam was not available at the time the design

was completed, hence we opted for UV lithography. We discuss the two processes to highlight

the compromises we made by opting for UV lithography.

As E-Beam lithography can be done only by a few steps and the required equipment is

available in many facilities, the delivery time for fabrication is around one month. Moreover,

the resolution of minimum feature sizes is typically under 50 nanometers, a very fine

resolution. In UV lithography, once the mask is fabricated, it is possible to repeat the pattern

at a low cost which makes UV lithography process suitable for mass production. The minimum

feature size is larger than E-Beam process, usually 100 nm to 200 nm, because of the larger

wavelength and diffraction effects of ultra-violet light compared to electrons.

32

Although the resolution of E-Beam run is higher, and it has shorter delivery time, E-Beam

is not suitable for our bi-level PSR, since a double etched process is needed. Thus, for this

work, IME Singapore fabricates the designed chip using UV lithography technique.

3.4.3. Complete Layout with Multiple Designs

Fig. 3.9 shows the various parameters involved in the design of the PSR. The default

parameters are listed in Table1 of the Appendix. Figure 3.9 shows the complete layout where

different PSRs with different dimensions are designed and placed. The details of dimensions

can be found in Table A.2 and Table A.3 of Appendix. Multiple designs with variations in

dimensions are included to determine the effect of these variations on the performance of the

PSR.

Figure 3.9: Geometrical parameters of the designed PSR based on bi-level taper and adiabatic coupler.

W2, W3, L2 and L3 are the dimensions of the bi-level taper in gray in Fig. 3.9. The width

and length of bi-level taper can be optimized, since the incomplete TM0-TE1 mode conversion

in the bi-level taper is the source of crosstalk. The default values are W2 = 1.55 µm,

W3 = 0.85 µm, L2 = L3 = 50 µm. In each new PSR we change one parameter, leaving the

others untouched. In PSR1 to PSR4, W2 is 1 µm, 1.4 µm, 1.7 µm, and 2 m, respectively. In

PSR5 and PSR6, W3 is 0.800 µm and 0.900 µm, respectively. In PSR7 and PSR8, L2 and L3

are 0.4500 µm and 0.550 µm, respectively. These variations range from 10% to 30% of the

default values.

The length of the adiabatic directional coupler is L4 with the default value of 300 µm. In

PSR9 and PSR10, L4 changed to 280 µm and 320 µm, respectively. PSR11, PSR12, PSR14,

and PSR15 are related to some changes in the length of the bend and the balance of the bend.

The balance of the bend is related to the radius of the curves within the bend. The balance can

vary between 0 and 1, corresponding respectively to an almost flat (no bend) coupler and a

33

curved coupler (90 degree bend). L5 is the length of the bend and we changed the default value

of 70 µm to 60 µm and 80 µm in PSR11 and PSR12, respectively. The balance of the bend is

0.5 by default and we changed it to 0.9 and 0.2 in PSR14 and PSR15.

The last improvement is related to the blunt-tip at the starting point of the adiabatic coupler.

For eliminating any mode coupling as a result of the waveguide discontinuity, this blunt-tip

can be replaced by a large radius arc. Therefore, we designed a PSR13 with an arc instead of

the blunt-tip at the beginning of the adiabatic coupler.

34

Figure 3.10: Complete layout with different PSRs and some test structures.

The waveguide width on SOI is typically 500 nm and in this work all the waveguides are

500 nm wide. The radius of the waveguide bends is 25 µm to make sure that the bend loss is

sufficiently small. This is especially important for TM polarization as its bend loss is normally

higher than the bend loss of the TE polarization [59].

35

In the designed layout, the pitch between two grating couplers is 127 µm. Typically fiber

arrays have 127 µm or 250 µm gap between two adjacent fibers. The pitch for edge couplers is

125 µm. The pitch for edge couplers can be a multiple of 125 µm. We selected these pitches

based on the existing fiber arrays and transposers in our laboratory. Finally, with these

dimensions, the total area that we require for the chip is 2.8 mm × 3.0 mm including edge

couplers on one of the sides.

At last, it is necessary to do the silicon tiling to avoid density errors. In addition, there are

lots of standards and rules to follow during the layout design such as minimum feature size,

minimum bend radius, etc.

3.5. Summary

In this chapter, a high performance PSR based on TM0-TE1 mode conversion in a bi-level

taper on SOI platform was introduced. We presented the evolution of modes intensity profiles

along the device using modeling and simulation in FDTD Lumerical software. We discussed

the use of edge couplers vs. grating couplers for the fabricated devices. Finally, we presented

the design layout for fabrication and strategies for characterization of fabricated devices. In the

next chapter, performance of this PSR in a system will be simulated in two different

applications.

36

Chapter Four: Application of PSR in Optical Systems

37

4.1. Introduction

Polarization is important for two reasons. First, physically polarization is an element of the

electrical field which is modified by the components it touches, whether via the fiber through

which it propagates or the modulator which imprints the data, all these devices will have an

impact on the polarization. Secondly, it is also important because different communication

systems try to take advantage of polarization in different ways, to design polarization diversity

components, it is important to understand the requirements for a given system. Some optical

systems transmit data without regards to polarization, and are tolerant to an arbitrary state of

polarization. Other communication systems try to exploit polarization states to increase the

data capacity, placing distinct data streams on each polarization. In the following chapter, the

PSR to be designed under these two different contexts and applications is examined.

4.2. Applications

To analyze the role and performance of a PSR we must specify the system. We need to

define the main applications of PSR and then the parameters to evaluate the performance in a

system.

We first address a polarization-insensitive system. In traditional long distance fiber-optic

signal transmission, the polarization of light is not exploited. Under this condition, the

polarization varies from input to output, and performance is expected to be independent of

polarization state. For instance, in a communication system using traditional on-off keying,

polarization is not controlled in any manner. Polarization freely rotates and the photodetectors

detect the signal no matter what polarization it is on.

When designing on-chip silicon photonics, polarization management is an important issue.

Different polarization states possess different properties and some photonic integrated devices,

such as ring resonators, only support one polarization state. One solution for SiP integrated

chips is to use two PSRs to remove polarization dependency. As depicted in Fig. 4.1, an

arbitrary combination of TM and TE modes (i.e., an arbitrary polarization state) is launched to

the chip. At the beginning, the TE and TM modes are separated. On one path, the TM mode

rotates to TE mode. Now there are two separate paths each now carrying a signal in the TE

mode, which is well supported on chip. These two paths together carry the totality of the

incoming signal. They propagate through two identical photonic circuits than can be designed

38

to provide any needed functionality, such as filtering. Once the appropriate function has been

accomplished on the chip, the two separate paths can be rotated back to their original

polarization state via a second PSR, and coupled into an optical fibre.

Figure 4.1: Integrated polarization diversity system [8] consisting of an input PSR, a photonic structure, and an output PSR.

The second important application of a PSR is in support of dual polarization

multiplexing. In this case, two distinct data streams are sent on TE and TM modes to increase

the data capacity. The requirements are very different in this application. In these systems the

two states of polarization may mix during transmission, however they remain orthogonal to

one another. At the receiver multiple input multiple output (MIMO) processing is utilized to

undo the polarization rotation that occurs. This polarization mixing is described by a Jones

matrix, which is a unity matrix. Because of its unity, it is easy for the receiver to undo the

polarization rotation, which means there is no loss in one polarization relative the other. If the

SiP chip uses a polarization diversity approach it is important that the PSR device also have

the response of a Jones matrix, i.e., a unity matrix. If it is not a unity matrix, this component

could make it more difficult for the receiver to separate the data streams. Nonetheless, due to

polarization dependent loss, data transmission on any but the principle state of polarization will

lead to some mismatch. In the following sections, first we define the transfer matrices of a PSR;

then we discuss about the parameters which are important in the performance of each system.

4.3. Mathematical Model

In this section, we define the inputs/outputs of a PSR in an optical system and introduce the

transfer matrices of a PSR. The input and outputs are depicted and defined in Fig. 3.8. A

39

combination of TE and TM modes is sent through the input port of PSR and we analyze the

two outputs. The first output port is called the TE output port because when a signal with only

TE mode is sent, the light is meant to exit from this port without any changes. The second

output port is called the TM output port because when an isolated TM mode is launched, it is

rotated to TE, processed if needed and then sent to exit from this port once returned to the TM

state. In our analysis, each TM and TE output port is monitored for TE and TM content. To

summarize, for the TE output port we would examine:

1. Inputting TE only, observing TE content (desired) 2. Inputting TE only, observing TM content (undesired) 3. Inputting TM only, observing TM content on (undesired; can be acceptable

depending on the application) 4. Inputting TM only, observing TE content on (undesired)

and a similar observation would be made on the TM output port.

The previous discussion can be cast in a mathematical model for mode rotation on chip. The

input is a linear combination of TE and TM modes which is given by vector X.

𝑋 = 𝑋=@𝑋=>

, (4.1)

where 𝑋=@ is the TE mode content at the input, and 𝑋=> is the TM mode content at the input.

We call the vector for the TE output port

𝑌 = 𝑌=@𝑌=>

. (4.2)

We define the transfer matrix for TE output port as

𝐴 = 𝐴11 𝐴1W𝐴W1 𝐴WW

(4.3)

such that

𝑌 = 𝐴×𝑋 è 𝑌=@𝑌=>= 𝐴11 𝐴1W

𝐴W1 𝐴WW× 𝑋=@𝑋=>

(4.4)

Similarly, for the TM output port:

𝑍 = 𝑍=@𝑍=>

, (4.5)

40

𝐵 = 𝐵11 𝐵1W𝐵W1 𝐵WW

, (4.6)

𝑍=@𝑍=>

= 𝐵11 𝐵1W𝐵W1 𝐵WW

× 𝑋=@𝑋=>

. (4.7)

The PSRs are typically wavelength dependent. Therefore, the matrices A and B are a function

of wavelength. In section 4.6, we present the simulation results of the designed bi-level PSR in

Interconnect software for a range of wavelengths.

4.4. Loss, Crosstalk, and Desired Outputs

In this section we discuss the two applications presented in section 4.2 and the ideal behavior

of matrices A and B for each application.

In the first scenario (arbitrary polarization for one signal), polarization diversity is desired.

In this application, the TM and TE outputs will be combined before leaving the chip. There is

no discussion of crosstalk for this application, as there is only one channel of data on the input

signal.

Suppose we consider the TE output port:

• Inputting TE, observed TE content: Desired TE • Inputting TE, observed TM content: Loss • Inputting TM, observed TE content: Leakage TE (acceptable) • Inputting TM, observed TM content: Loss

If we input TE only, but observe some TM content at the output port, this content will not

be coupled to the output, because the coupler only can output TE mode. So this content is loss.

If we are inputting TM and observe content on the TE output port in the TE mode, this is totally

acceptable. It is on the TE mode in the TE port, so this light will be coupled to the output. Since

all light is coupled together at the output whether it originates in the TE output port or the TM

output port is irrelevant. However, if we input TM and observe TM content on the TE output

port this will be loss. We could simply say that for this application, any light on TM in the TE

mode is loss, since it does not get coupled to the output.

A similar summary covers the TM output port:

• Inputting TE, observed TE content: Leakage TE (acceptable) • Inputting TE, observed TM content: Loss • Inputting TM, observed TE content: Desired TE from TM input

41

• Inputting TM, observed TM content: Loss

The second scenario is dual polarization multiplexing. In this case we want to maintain

orthogonality of the input polarization states. When inputting TE only, any part of the TE mode

exiting from the TM port is crosstalk. Similarly, when inputting TM only, any part of the TM

mode rotating to TE and exiting from the TE port is again crosstalk. In brief:

TE output port:

• Inputting TE, observed TE content: Desired TE • Inputting TE, observed TM content: Loss • Inputting TM, observed TE content: Crosstalk on TE input • Inputting TM, observed TM content: Loss

TM output port:

• Inputting TE, observed TE content: Crosstalk on TM input • Inputting TE, observed TM content: Loss • Inputting TM, observed TE content: Desired TE from TM input • Inputting TM, observed TM content: Loss

Table 4.1, shows the correspondence between the elements of transfer matrices and the

outputs that we defined.

Table 4.1: The correspandance between outputs and the elements of transfer matrices.

Output ports

Transfer matrices

Output components Polarization diversity application

Dual polarization multiplexing application

TE

output

port

A11 Inputting TE, TE content Desired TE Desired TE

A21 Inputting TE, TM content Loss Loss

A12 Inputting TM, TE content Leakage TE (acceptable) Crosstalk on TE input

A22 Inputting TM, TM content Loss Loss

TM

output

port

B11 Inputting TE, TE content Leakage TE (acceptable) Crosstalk on TM input

B21 Inputting TE, TM content Loss Loss

B12 Inputting TM, TE content Desired TE Desired TE

B22 Inputting TM, TM content Loss Loss

42

Based on our discussion in section 4.3, ideally 𝐴 = 1 00 0 and 𝐵 = 0 1

0 0 . Specifically, for

polarization diversity application: A21, A22, B21 and B22 should be small in order to limit loss.

A12 and B11 are free parameters; any values provide acceptable performance. For dual

polarization application: A21, A22, B21 and B22 should be small in order to limit loss. A12 and

B11 should be small in order to limit crosstalk.

The next section explains how we simulate the PSR device in the FDTD Lumerical software

of a specific wavelength. Results for a range of wavelengths are then transferred to Interconnect

Lumerical software for analysis.

4.5. Scattering Parameters Extraction and Model

Development

There is one length two input vector and two length two output vectors, hence a vector of

six signals to track. We find a matrix S of scattering parameters (s-parameters) for these six

signals using FDTD Lumerical software.

𝑋=@𝑋=>𝑌=@𝑌=>𝑍=@𝑍=> ABC[BC

= 𝑆

𝑋=@𝑋=>𝑌=@𝑌=>𝑍=@𝑍=> ]^[BC

(4.8)

The matrix S is a 6×6. S-parameters can be extracted for any desired wavelength. In this

project, 100 wavelengths between 1530 nm and 1580 nm (1530, 1530.5, 1531, …) are

considered, and S-parameters were extracted from the FDTD Lumerical results for each

wavelength. From S we can extract the matrices A and B defined in the previous section.

The obtained S-parameters matrices from FDTD Lumerical software were exported to

Interconnect Lumerical software to test the PSR in a system. Interconnect Lumerical software

created a three-port object based on the transferred data at 100 different wavelengths.

Figure 4.2 presents transferring data from FDTD Lumerical software to Interconnect Lumerical

software. Thus, a PSR element is built by using simulation results from FDTD Lumerical

software.

43

Figure 4.2: Transfering data from FDTD Lumerical software to Interconnect Lumerical software.

Plots of PSR transfer matrix elements as a function of wavelength are generated by using a

virtual optical network analyzer (ONA). The ONA excites the input port, and observes the two

output ports. In one case, the ONA excites only the TE mode (orthogonal identifier = 1 and

four components coming from the TE and TM output ports are measured (two mode contents

from each output port). The two outputs from TE output port are A11 and A21 and the two

outputs from TM output port are B11 and B21. In another case, the ONA excites only the TM

mode (orthogonal identifier=2), and again the same outputs are measured. In this case, the two

outputs from TE output port are A12 and A22 and the two outputs from TM output port are B12

and B22. Figure 4.3 shows the Lumerical Interconnect simulation environment when the input

is TE mode. The ONA sweeps wavelengths. In the next section we discuss about the simulation

results of our model in Interconnect software.

Figure 4.3: Looking at the performance of the PSR with ONA in Interconnect Lumerical, Inputting TE.

44

4.6. Performance of the Designed Bi-level PSR

In this section, the simulation results of the designed bi-level PSR in Interconnect Lumerical

software is presented.

Figure 4.4 shows all the power outputs from TE output port. The curves demonstrate the

elements of transfer matrix (A) of the TE output port in dB scale. As is expected, for TE output

port, A11 is near 0 dB which shows a high transmission. A21 and A22 show losses which are low,

below -19 dB and they are not too much wavelength dependent. The dashed line is an

acceptable output in polarization diversity application and a high value of A12 could be still a

desired output. However, A12 is crosstalk in dual polarization multiplexing application. This

parameter is more wavelength dependent but still is low, below -20 dB. In total, in TE output

port, cross talk and all the losses and are small.

Figure 4.4: Transmission (dB) in TE output port when a mix of TE and TM modes enters.

Figure 4.5 shows all the power outputs from TM output port. The curves demonstrate the

elements of transfer matrix (B) of TM output port in dB scale. As is expected, for TM output

port, B12 is near 0 dB which shows a high transmission. B21 and B22 show loss which are low,

below - 10 dB, however the variation of B22 is around 15 dB in this range of wavelength, which

shows the variation in the amount of loss. For the TM output port, between crosstalk and losses,

B22 is the dominant component. As we discussed in chapter three, during the adiabatic bi-level

45

taper, TM mode shall rotate to a hybrid mode with TM0 and TE1 features and through the

coupler TM0 rotates to TE1 and exits from TM output port. In fact, it is expected that B22

would have the maximum value between the other elements, because this parameter is related

to the TM input which is not able to rotate to TE and without rotation couples to the second

output port and exits as the TM mode. The dashed line (B11) is an acceptable and desired output

in polarization diversity application. However, B11 is crosstalk in dual polarization

multiplexing application. B11 is also wavelength dependent and it is low, below - 20 dB.

Figure 4.5: Transmission(dB) in TM output port when a mix of TE and TM modes enters.

Figure 4.6 focuses on only A11 and B12. Ideally A11 and B12 should be 0 dB. A11 shows the

performance of TE mode propagation in PSR. B12 shows the performance of TM mode

propagation and polarization rotator. It is not unexpected that B12 does not perform as well as

A11 since B12 passes through the rotator while A11 does not; the rotator is not 100% efficient.

46

Figure 4.6: Desired TE Transmission and TM conversion

As an example, when the wavelength is equal to 1550 nm, the transfer matrices in dB scale

are as below, and are similar to the target behavior:

𝐴 = 0.08 −24.51−26.37 −18.93 » 1 0

0 0 (4.9)

𝐵 = −23.52 −0.74−29.80 −14.42 » 0 1

0 0 (4.10)

As defined in chapter two, polarization conversion efficiency (PCE) and extinction ratio

(ER) are two convenient parameters to evaluate the performance of a polarization rotator. For

the TM to TE mode rotator, PCE and ER are calculated as follow,

𝑃𝐶𝐸 =𝑃=@ABC

𝑃=@ABC + 𝑃=>ABC=

(𝑌=@ + 𝑍=@)(𝑌=@ + 𝑍=@) + (𝑌=> + 𝑍=>)

= (𝐴11×𝑋=@ + 𝐴1W×𝑋=>) + (𝐵11×𝑋=@ + 𝐵1W×𝑋=>)

[(𝐴11×𝑋=@ + 𝐴1W×𝑋=>) + (𝐵11×𝑋=@ + 𝐵1W×𝑋=>)} + {(𝐴W1×𝑋=@ + 𝐴WW×𝑋=>) + (𝐵W1×𝑋=@ + 𝐵WW×𝑋=>)]

(4.11)

When the input is only TM mode, we have Xkl = 0. Then, PCE will be as follow,

𝑃𝐶𝐸 =𝐴1W×𝑋=> + 𝐵1W×𝑋=>

(𝐴1W×𝑋=> + 𝐵1W×𝑋=>) + (𝐴WW×𝑋=> + 𝐵WW×𝑋=>)

=𝐴1W + 𝐵1W

(𝐴1W + 𝐵1W) + (𝐴WW + 𝐵WW)

(4.12)

ER will be equal to

𝐸𝑅 = 10𝐿𝑜𝑔1 − 𝑃𝐶𝐸𝑃𝐶𝐸

(4.13)

In the case of ideal A and B matrices, PCE is 100% and ER is -∞.

47

Figure 4.7 shows the variation of the PCE (%) as a function of wavelength. PCE varies less

than 11.85% in over the range of wavelengths. The average of PCE from 1530 nm to 1580 nm

is equal to 93.86%. The typical requirement for PCE is over 92% [38] and our PSR has a 94.5%

PCE at the wavelength of 1550 nm. We conclude thatur PSR has achieved high efficiency.

This high value of efficiency confirms the low losses and crosstalk in Fig. 4.4 and Fig. 4.5.

Figure 4.8 demonstrates the variation of ER as a function of wavelength. The average ER is -

13 dB; lower ER is better. It is worth mentioning that an acceptable requirement of ER is less

than -10.61 dB and for our PSR it is -12.35 at the wavelength of 1550 nm. In fact, ER is

essentially a way of evaluating the efficiency in a dB scale. The observed periodic behaviour

can be attributed to the splitter.

Figure 4.7: Calculated PCE for the designed bi-level PSR. Figure 4.8: Calculated ER for the designed bi-level PSR.

As an example, at the wavelength of 1550 nm, if we convert dB to Watt, the PCE will be

equal to:

𝑃𝐶𝐸 =(0.00354 + 0.84333)

(0.00354 + 0.84333) + (0.01279 + 0.03614) = 0.945

→ 𝑃𝐶𝐸 = 94.5%

(4.14)

and as it is defined in chapter two, the ER will be equal to

𝐸𝑅 = 10𝐿𝑜𝑔1 − 𝑃𝐶𝐸𝑃𝐶𝐸 = 10𝐿𝑜𝑔

1 − 0.9450.945 = −12.35𝑑𝐵

(4.15)

4.7. Summary

In this chapter, we evaluated the performance of the designed PSR for two applications. We

proposed a mathematical model and the transfer matrices are calculated for a given wavelength.

48

We swept wavelength and examined the evolution of PSR performance. Finally, PCE and ER

were calculated to check the performance of our PSR.

49

Chapter Five: Conclusion and Outlook

50

The focus of this master’s thesis is on-chip polarization management and its application in

optical communication systems. We concentrated on a PSR based on TM0-TE1 mode

conversion in a bi-level taper on SOI.

Our interest was motivated by the polarization sensitivity of SOI platforms. As polarization

rotation is the most important function of polarization management, we examined different

types of polarization rotators, finally opting to implement an efficient structure based on TM0-

TE1 mode conversion in a bi-level taper on SOI. We presented the layout details for fabrication

and eventual characterization with both edge couplers and grating couplers. We simulated

performance by extracting S-parameters in FDTD Lumerical software.

The results show a high transmission of TE to TE exits from TE output port and a high

transmission of TM to TE exits from TM output port. TM to TE transmission is not as high as

TE to TE. Because of all the manipulations on the TM input, it is normal that the performance

of TM to TE transmission would be lower than the TE to TE transmission. In general, the losses

and cross-talks are low and the average of PCE which is 93.86% confirms this fact. Some

components are more wavelength dependent but still they are low enough. Among cross-talks

and losses, the dominant component is B22. This parameter is related to the TM input which is

not able to rotate to TE and without rotation couples to the TM output port and exits as the TM

mode. As a result, it is expected that B22 would have the maximum value among the other

elements.

One can use the PSR design to make a polarization insensitive device. For example, one can

make a polarization insensitive ring resonator by placing this PSR before the ring resonator. In

this regard, one can split the two modes and rotate TM to TE mode to send only TE mode to

ring resonator, so a polarization insensitive ring resonator will be created. Moreover, one can

use this PSR to develop a dual polarization multiplexer, as discussed in chapter four.

The chip sent for fabrication has now arrived in the laboratory. The fabricated chip will be

characterized in the lab. The design presented has already been incorporated in other systems

that have also been recently received and will be undergoing characterization. The swept

parameters during fabrication will allow future systems to use the optimized dimensions for

the PSR structure.

51

Appendix

Figure A.1: Geometrical parameters of the designed PSR based on bi-level taper and adiabatic coupler.

Table A.1: Geometrical parameters of the designed PSR based on bi-level taper and adiabatic coupler.

Parameters PSR0 (µm)

W0 0.500

W1 0.550

W2 1.550

W3 0.850

W4 0.650

W5 0.500

W6 0.200

W7 0.500

Gap 0.200

L1 15

L2 50

L3 50

L4 300

L5 70

L6 10

Balance bend 0.5

52

Table A.2: Geometrical parameters of the designed PSRs with various changes in some dimensions.

Parameters PSR0

(µm)

PSR1

(µm)

PSR2

(µm)

PSR3

(µm)

PSR4

(µm)

PSR5

(µm)

PSR6

(µm)

PSR7

(µm)

PSR8

(µm)

W0 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

W1 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550

W2 1.550 1.000 1.400 1.700 2.000 1.550 1.550 1.550 1.550

W3 0.850 0.850 0.850 0.850 0.850 0.800 0.900 0.850 0.850

W4 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650

W5 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

W6 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200

W7 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

Gap 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200

L1 15 15 15 15 15 15 15 15 15

L2 50 50 50 50 50 50 50 45 55

L3 50 50 50 50 50 50 50 45 55

L4 300 300 300 300 300 300 300 300 300

L5 70 70 70 70 70 70 70 70 70

L6 10 10 10 10 10 10 10 10 10

Balance

bend 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

53

Table A.3: Geometrical parameters of the designed PSRs with various changes in some dimensions.

Parameters PSR9

(µm)

PSR10

(µm)

PSR11

(µm)

PSR12

(µm)

PSR13

(µm)

PSR14

(µm)

PSR15

(µm)

PSR16

(µm)

PSR17

(µm)

W0 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

W1 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550

W2 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550 1.550

W3 0.850 0.850 0.850 0.850 0.850 0.850 0.850 0.850 0.850

W4 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650

W5 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

W6 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.300 0.200

W7 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

Gap 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.300

L1 15 15 15 15 15 15 15 15 15

L2 50 50 50 50 50 50 50 50 50

L3 50 50 50 50 50 50 50 50 50

L4 280 320 300 300 300 300 300 300 300

L5 70 70 60 90 70 70 70 70 70

L6 10 10 10 10 10 10 10 10 10

Balance

bend 0.5 0.5 0.5 0.5 0.5 0.9 0.2 0.5 0.5

comments

Blunt-

tip

coupler

replace

d by an

arc

54

Figure A.2: looking at the performance of the PSR with ONA in Interconnect Lumerical, Inputting TE.

Figure A.3: looking at the performance of the PSR with ONA in Interconnect Lumerical, Inputting TM.

55

References

1. Smit, M., Past, present and prospects of InP-based photonic integration. 2017: Technical university of Eindhoven, Netherlands.

2. Chrostowski, L. and M. Hochberg, Silicon Photonics Design: From Devices to Systems. 2015: Cambridge University Press.

3. Samadian, P., Photonic Integrated Circuits Challenges & Solutions: Homogenization, Polarization Management and Coupling. 2015, University of Ottawa.

4. Xu, Q., et al., Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material. Optics letters, 2004. 29(14): p. 1626-1628.

5. Dai, D., et al., Polarization management for silicon photonic integrated circuits. Laser & Photonics Reviews, 2013. 7(3): p. 303-328.

6. Barwicz, T., et al., Polarization-transparent microphotonic devices in the strong confinement limit. Nature Photonics, 2007. 1(1): p. 57-60.

7. Fukuda, H., et al., Silicon photonic circuit with polarization diversity. Optics express, 2008. 16(7): p. 4872-4880.

8. Popovíc, M.A., et al., Multistage high-order microring-resonator add-drop filters. Optics letters, 2006. 31(17): p. 2571-2573.

9. Watts, M.R., et al., Vertical junction silicon microdisk modulators and switches. Optics express, 2011. 19(22): p. 21989-22003.

10. Purnawirman, J.S., T N Adam, G Leake, D Coolbaugh, J D B Bradley, E Shah Hosseini, and M R Watts., C- and L-band erbium-doped waveguide lasers withwafer-scale silicon nitride cavities. . Optics letters, 38(11):1760, 2013.

11. Pfau, T., et al., Coherent digital polarization diversity receiver for real-time polarization-multiplexed QPSK transmission at 2.8 Gb/s. IEEE Photonics Technology Letters, 2007. 19(24): p. 1988-1990.

12. Yamanouchi, K., K. Wakazono, and K. Shibayama, Optical surface wave mode converters and modulators utilizing static strain-optic effects. IEEE Journal of Quantum Electronics, 1980. 16(6): p. 628-634.

13. Yamanouchi, K., K. Higuchi, and K. Shibayama, TE- TM mode conversion by interaction between elastic surface waves and a laser beam on a metal- diffused optical waveguide. Applied Physics Letters, 1976. 28(2): p. 75-77.

14. Alferness, R.C. and L.L. Buhl, Waveguide electro- optic polarization transformer. Applied Physics Letters, 1981. 38(9): p. 655-657.

15. Alferness, R.C., Guided-wave devices for optical communication. IEEE Journal of Quantum electronics, 1981. 17(6): p. 946-959.

16. Deng, H., Design and characterization of silicon-on-insulator passive polarization converter with finite-element analysis. 2005.

17. Sacher, W., T. Barwicz, and J.K. Poon. Silicon-on-insulator polarization splitter-rotator based on TM0-TE1 mode conversion in a bi-level taper. Optical Society of America.

18. Sacher, W.D., et al., Polarization rotator-splitters in standard active silicon photonics platforms. Opt Express, 2014. 22(4): p. 3777-86.

19. Zhang, H., et al., Efficient and broadband polarization rotator using horizontal slot waveguide for silicon photonics. Applied physics letters, 2012. 101(2): p. 021105.

20. Vermeulen, D., et al., Silicon-on-insulator polarization rotator based on a symmetry breaking silicon overlay. IEEE Photonics Technology Letters, 2012. 24(6): p. 482-484.

21. Xiong, Y., et al., Robust silicon waveguide polarization rotator with an amorphous silicon overlayer. IEEE Photonics Journal, 2014. 6(2): p. 1-8.

22. Chen, L., C.R. Doerr, and Y.-K. Chen, Compact polarization rotator on silicon for polarization-diversified circuits. Optics letters, 2011. 36(4): p. 469-471.

56

23. Shani, Y., et al., Polarization rotation in asymmetric periodic loaded rib waveguides. Applied Physics Letters, 1991. 59(11): p. 1278-1280.

24. Huang, W. and Z.M. Mao, Polarization rotation in periodic loaded rib waveguides. Journal of lightwave technology, 1992. 10(12): p. 1825-1831.

25. Obayya, S.S.A., et al., Beam propagation modeling of polarization rotation in deeply etched semiconductor bent waveguides. IEEE Photonics Technology Letters, 2001. 13(7): p. 681-683.

26. Obayya, S.S.A., et al., Improved design of a polarization converter based on semiconductor optical waveguide bends. Applied optics, 2001. 40(30): p. 5395-5401.

27. Holmes, B.M. and D.C. Hutchings, Realization of novel low-loss monolithically integrated passive waveguide mode converters. IEEE photonics technology letters, 2006. 18(1): p. 43-45.

28. Beggs, D.M., M. Midrio, and T.F. Krauss, Compact polarization rotators for integrated polarization diversity in InP-based waveguides. Optics letters, 2007. 32(15): p. 2176-2178.

29. Fontaine, M., Cross-phase modulation phenomena in strongly guiding waveguides: a theoretical approach revisited. JOSA B, 1998. 15(3): p. 964-971.

30. Huan, Z., et al., Realization of a compact and single-mode optical passive polarization converter. IEEE Photonics Technology Letters, 2000. 12(3): p. 317-319.

31. Deng, H., et al., Design rules for slanted-angle polarization rotators. Journal of lightwave technology, 2005. 23(1): p. 432.

32. Chan, P.S., H.K. Tsang, and C. Shu, Mode conversion and birefringence adjustment by focused-ion-beam etching for slanted rib waveguide walls. Optics letters, 2003. 28(21): p. 2109-2111.

33. Deng, H., et al., Fabrication tolerance of asymmetric silicon-on-insulator polarization rotators. JOSA A, 2006. 23(7): p. 1741-1745.

34. Brooks, C., et al., Passive silicon-on-insulator polarization-rotating waveguides. Optical engineering, 2006. 45(4): p. 044603-044603.

35. Filippov, V.N., O.I. Kotov, and V.M. Nikolayev, Measurement of polarisation beat length in single-mode optical fibres with a polarisation modulator. Electronics Letters, 1990. 26(10): p. 658-660.

36. Kim, S.-H., et al., Single-trench waveguide TE-TM mode converter. Optics express, 2009. 17(14): p. 11267-11273.

37. El-Refaei, H. and D. Yevick, An optimized InGaAsP/InP polarization converter employing asymmetric rib waveguides. Journal of lightwave technology, 2003. 21(6): p. 1544-1548.

38. Gao, L., et al., Ultra-compact and low-loss polarization rotator based on asymmetric hybrid plasmonic waveguide. IEEE Photonics Technology Letters, 2013. 25(21): p. 2081-2084.

39. Rahman, B.M.A., et al., Design of optical polarization splitters in a single-section deeply etched MMI waveguide. Applied Physics B: Lasers and Optics, 2001. 73(5): p. 613-618.

40. Shi, Y., D. Dai, and S. He, Proposal for an ultracompact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler. IEEE Photonics Technology Letters, 2007. 19(11): p. 825-827.

41. Soldano, L.B., et al., Mach-Zehnder interferometer polarization splitter in InGaAsP/InP. IEEE photonics technology letters, 1994. 6(3): p. 402-405.

42. Liang, T.K. and H.K. Tsang, Integrated polarization beam splitter in high index contrast silicon-on-insulator waveguides. IEEE photonics technology letters, 2005. 17(2): p. 393-395.

43. Kiyat, I., A. Aydinli, and N. Dagli, A compact silicon-on-insulator polarization splitter. IEEE photonics technology letters, 2005. 17(1): p. 100-102.

44. Fukuda, H., et al., Ultrasmall polarization splitter based on silicon wire waveguides. Optics Express, 2006. 14(25): p. 12401-12408.

57

45. Lin, S., J. Hu, and K.B. Crozier, Ultracompact, broadband slot waveguide polarization splitter. Applied Physics Letters, 2011. 98(15): p. 151101.

46. Dai, D., Z. Wang, and J.E. Bowers, Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler. Optics letters, 2011. 36(13): p. 2590-2592.

47. Dai, D., et al., Compact broadband polarizer based on shallowly-etched silicon-on-insulator ridge optical waveguides. Optics express, 2010. 18(26): p. 27404-27415.

48. Dai, D., Z. Wang, and J.E. Bowers, Considerations for the design of asymmetrical Mach–Zehnder interferometers used as polarization beam splitters on a submicrometer silicon-on-insulator platform. Journal of Lightwave Technology, 2011. 29(12): p. 1808-1817.

49. Dai, D., et al., Compact polarization beam splitter using an asymmetrical Mach–Zehnder interferometer based on silicon-on-insulator waveguides. IEEE Photon. Technol. Lett., 2012. 24(8): p. 673-675.

50. Jiao, Y., et al., Shortened polarization beam splitters with two cascaded multimode interference sections. IEEE Photonics Technology Letters, 2009. 21(20): p. 1538-1540.

51. Tu, Z., et al. A compact SOI polarization beam splitter based on multimode interference coupler. Optical Society of America.

52. Hong, J.M., et al., Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application. IEEE Photonics Technology Letters, 2003. 15(1): p. 72-74.

53. Dai, D. and J.E. Bowers, Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires. Opt Express, 2011. 19(11): p. 10940-9.

54. Ding, Y., et al., Fabrication tolerant polarization splitter and rotator based on a tapered directional coupler. Optics express, 2012. 20(18): p. 20021-20027.

55. Watts, M.R. and H.A. Haus, Integrated mode-evolution-based polarization rotators. Optics letters, 2005. 30(2): p. 138-140.

56. Watts, M.R., H.A. Haus, and E.P. Ippen, Integrated mode-evolution-based polarization splitter. Optics letters, 2005. 30(9): p. 967-969.

57. Dai, D., Y. Tang, and J.E. Bowers, Mode conversion in tapered submicron silicon ridge optical waveguides. Optics express, 2012. 20(12): p. 13425-13439.

58. St-Yves, J., Contra-directional couplers as optical filters on the silicon on insulator platform. 2015, Laval University

59. Rickman, A.G. and G.T. Reed, Silicon-on-insulator optical rib waveguides: loss, mode characteristics, bends and y-junctions. IEE Proceedings-Optoelectronics, 1994. 141(6): p. 391-393.