Design and simulation of wideband photonic intergrated circuits for multimode (DE) multiplexing and conversion747

vii List of Mathematical Symbols nc Refractive effective index of cladding la yer ns Refractive effective index of substrate layer nr Refractive effective index of core yer la neff Effe

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

-0 -

TRAN TUAN ANH

DESIGN AND SIMULATION OF WIDEBAND PHOTONIC INTEGRATED CIRCUITS

AND CONVERSION

DOCTORAL DISSERTATION

HANOI 2020 –

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

-0 -

TRAN TUAN ANH

DESIGN AND SIMULATION OF WIDEBAND PHOTONIC INTEGRATED CIRCUITS

PROF DR TRAN DUC HAN

DR TRUONG CAO DUNG

HANOI 2020 –

i

DECLARATION OF AUTHORSHIP

I, Tran Tuan Anh, declare that this dissertation entitled, "Design and simulation of wideband photonic integrated circuits for multi mo- de (de)multiplexing and conversion", and the work presented in it is my own

- Where I have consulted the published work of others, this is always clearly attributed

-Where I have quoted from the work of others, the source is always given

- With the exception of such quotations, this dissertation is entirely my own work

- I have acknowledged all main sources of help Where the dissertation is based on work done by myself jointly with others, I have made exactly what was done by others and what I have contributed myself

ii

Acknowledgment

First and foremost, I would like to thank my supervisor Prof Dr Tran Duc Han for his support and advice throughout my research time in Hanoi University of Science and Technology (HUST) His encouragement and full support led me to every success

of my study I have been able to learn a lot from him about being a good teacher and researcher

I would like to express my gratitude to my supervisor, Dr Truong Cao Dung, for guiding and motivating me since I was an undergraduate student at HUST He has given me the very first guidance until I finished my doctoral dissertation

I special thanks to Prof Dr Vu Van Yem for his constant help during my study postgradua courses and sincere advi for my future career te ces

Finally, I would like to express my grateful thanks to my parents, Mr Tran Quoc Hung and Mrs Tran Thi Huong, and my uncle, Mr Tran Quoc Dung, for their support and encouragement

TRAN TUAN ANH

iii

Table of Contents

INTRODUCTION 1 CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS AND FABRICATION 8

1.1 Shapes and functions of silicon-on-insulator waveguide _8 1.2 Optical waveguide analysis and simulation methods 12

1.2.1 Wave equations _ 12 1.2.2 Effective index method _ 15 1.2.3 Finite Difference Method _ 17 1.2.4 Beam Propagation Method 18 1.2.5 Finite Difference Beam Propagation Method 19

1.3 Silicon-on-insulator waveguide fabrication 21

1.3.1 Separation by implanted oxygen (SIMOX) 21 1.3.2 Bond and Etch-back SOI (BESOI) 23 1.3.3 Wafer Splitting _ 24 1.3.4 Silicon Epitaxial Growth 25 1.3.5 Fabrication of surface etched features 25

1.4 Silicon-on-insulator waveguide structure used for MDM functionality _27

1.4.1 Directional coupler 27 1.4.2 Multimode interference _ 32 1.4.3 Asymmetric Y-junction waveguide _ 41

1.5 Conclusion _43

CHAPTER 2 MODE DIVISION MULTIPLEXER BASED ON ASYMMETRIC

DIRECTIONAL COUPLER _ 45

2.1 Two mode division (De)multiplexer based on an MZI asymmetric silicon waveguide _45

2.1.1 Design and structural optimization 45 2.1.2 Simulation and performance analysis 49

3.2.1 Design and structural optimization 56 3.2.2 Simulation and performance analysis 64

3.3 Conclusion _68

CHAPTER 4 MODE DIVISION MULTIPLEXER BASED ON TILT BRANCHED

BUS STRUCTURE SILICON WAVEGUIDE 70

4.1 Three-mode multiplexed device based on tilt branched bus structure using silicon

waveguide 70

4.1.1 Design and structural optimization 70

iv

4.1.2 Simulation and performance analysis 74

4.2 Four-mode multiplexed device based on tilt branched bus structure using silicon

waveguide 78

4.2.1 Design and structural optimization 78 4.2.2 Simulation and performance analysis 83 4.2.3 Proposal of experimental diagram _ 85

4.3 Conclusion _89

DISSERTATION CONCLUSION AND FUTURE WORKS _ 92 PUBLICATIONS 94 UNDER REVIEW PAPER 94 REFERENCE 95

v

Abbreviation

CMOS Complementary Metal Oxide Semiconductor

FD-BPM Finite Difference Beam Propagation Method

FFT-BPM Fast Fourier Transform Beam Propagation Method

vi

OEICs Opto-electronic Integrated Circuits

PECVD Plasma-enhanced chemical vapor deposition

vii

List of Mathematical Symbols

nc Refractive effective index of cladding la yer

ns Refractive effective index of substrate layer

nr Refractive effective index of core yer la

neff Effective refractive effective index

cm Excitation coefficient of m- order mode th

NxM Matrix dimension with and N M

q Sum from 0to (N-1) of variable q

m Propagation constant of m-th order mode

Operation wavelength in waveguide F

x Differential equation of function by variable F x

mn Uncoupl coefficients of m-th order mode at n-ed th

order output port

mn Coupled coefficients of m-th order mode at n-th order

output port

ix

List of Figures

Fig a Set up initial parameters of SOI waveguide and simulation method in RSoft 4

Fig b Pathway monitoring power at each output port of a design 5

Fig 1.1 Schematic of non-planar optical waveguides High index is indicated by darker color 8

Fig 1.2 Schematic of SOI waveguide 10

Fig 1.3 Schematic of SOI Rib waveguide 10

Fig 1.4 Scheme of the effective index method for solving the propagation constant of a step-index channel waveguide Starting from a 2D waveguide, the problem is split into two step-index planar waveguides 16

Fig 1.5 The cross-section of the waveguide is made discrete with a rectangular grid of points which have identical spacing 18

Fig 1.6 Comparison between BPM (left) and FFT-BPM (right) simulation FD-BPM under TBC gives better simulation result as the simulated wave is smoother 20 Fig 1.7 Comparison between FD-BPM simulation time depending on computed step of grid size 0.05μm (a) verse grid size 0.01μm (b) 21

Fig 1.8 Variation of the oxygen profile during the SIMOX process (a) Low-dose; (b) high-dose (peak is at the stoichiometric limit for SiO2); and (c) after implantation and annealing at high temperature for several hours 22

Fig 1.9 The bond and etch-back process to form BESOI: (a) oxidation; (b) bonding; and (c) thinning 23

Fig 1.10 (a) Thermally oxidized wafer is implanted with a high dose of hydrogen (b) A second wafer is bonded to the first as in the BESOI process (c) Thermal processing splits the implanted wafer at a point consistent with the range of the hydrogen ions 24

Fig 1.11 (a) Schematic of a silicon rib waveguide (b) Electron micrograph of a silicon rib waveguide Reproduced by permission of Intel Corporation 26

Fig 1.12 Schematic of a confined AC-generated plasma suitable for silicon processing The processed wafer in placed on the lower, grounded electrode 27

Fig 1.13 Directional coupler consisting of slab optical waveguide 29

Fig 1.14 Periodic exchange of power between waveguide 1 and 2 30

Fig 1.15 Simulation of periodic exchange of power between waveguide 1 and 2 using BPM 30

Fig 1.16 Power transfer ratio verse phase mismatch parameter 31

Fig 1.17 The schematic configuration of MMI waveguide 33

Fig 1.18 Two-dimensional representation of a MMI waveguide 34

Fig 1.19 Power distribution of GI-MMI with (left), (middle), -BPM simulation 38

(right) using FD Fig 1.20 Power distribution of 2x2 PI-MMI, input access waveguide is at with (left), (right) using FD-BPM simulation 40

Fig 1.21 Power distribution of SI-MMI showing 1- -3-way splitting (left) and 1- -to to 1 imaging (right) having same length and different width using FD-BPM simulation 41

Fig 1.22 Oscillating field pass through boundary between two isotropic media 41

x

Fig 1.23 Schematic structure of tilt branch bus waveguide 43

Fig 2.1 Schematic of the mode synthesizer based silicon waveguide 46Fig 2.2 BPM simulation for the height of waveguides of the asymmetric directional 47Fig 2.3 BPM simulation for power ratio as a function of the waveguide height 48Fig 2.4 Transmission characteristic of dependence of the coupling length of the asymmetric directional coupler by BPM simulation 48Fig 2.5 Electric field patterns for the mode (de)MUXer 49Fig 2.6 Wavelength response of the mode DMUXer in the C-band 49Fig 2.7 1- -wavelength spectrum in the side of mode multiplexer 50nmFig 2.8 Crosstalk of the modes in the structure for MUXer and deMUXer devices as

a function of the etched depth tolerance: H=h1=500 nm 50Fig 2.9 Sidewall roughness loss calculation for two modes and two polarization states of the waveguide in two cases: a) σ = 2 nm, Lcor = 50 µm and b) σ = 0.4 nm,

Lcor = 10 µm 52

Fig 3.1 Schematic of cascade NxN GI MMI used for switching optical signal 54Fig 3.2 Proposed schematic of a three mode (de)multiplexer based on a trident coupler and two multimode interference couplers on the platform of silicon on insulator waveguides 56Fig 3.3 Schematic diagram and transmittance properties of the trident coupler: a) schematic diagram and b) BPM simulation for transmittance properties of the

trident coupler as a function of the length of the sinusoidal 59Fig 3.4 BPM simulation for the phase angle Φ is a function of the central width of the phase shifter 64Fig 3.5 Electric field patterns of the proposed three - mode (de)MUXer for:

fundamental mode (a), first-order mode (b), second-order mode (c), and total of three modes (d) 65Fig 3.6 Performances dependence on the wavelength of the proposed three modes-(de)MUXer: (a) insertion loss and (b) crosstalk 66Fig 3.7 Influence of branching angles of the trident coupler on optical performances

of the proposed (de)MUXer: a) insertion loss, and b) crosstalk 67Fig 3.8 Fabrication tolerances of the proposed (de)MUXer: a) length tolerance of the second MMI coupler LMMI2, and b) width tolerance of the input width W0 67Fig 3.9 Insertion loss and crosstalk in the proposed structure for three mode -

(de)MUXer device as functions of the etched depth tolerance 68

Fig 4.1 The proposed design of the three-mode channel separation device 71Fig 4.2 Dependence of effective index of the main bus waveguide on variation of the main waveguide width Wm at the height h of 220 nm 71Fig 4.3 The results of transmission characteristic of proposed device at the first tilted waveguide as a function of the width Wa (nm), which passively affects the mode selective coupling coefficients 73

xi

Fig 4.4 The results of transmission characteristic of proposed device at the second tilted waveguide as a function of the width Wa (nm), which passively affects the mode selective coupling coefficients 74Fig 4.5 Simulated electric field patterns for the proposed three mode (de)multiplexer for: fundamental mode (a), first-order mode (b), second-order mode (c) 74Fig 4.6 The characteristic optical performance of the device depends on the

wavelength, showing the I.L and Cr.T of each three mode outputs 75Fig 4.7 Variation of optical transmission performance of the proposed waveguide depended on width tolerance ΔW (nm) 76Fig 4.8 Variation of optical transmission performance of the proposed waveguide depended on height tolerance Δh (nm) 76Fig 4.9 Transmissions at three output ports PO1, PO2 and PO3 as a function of two simultaneous variables Δh (nm) and ΔW (nm) of the bus waveguide when three modes are excited: (a), (b), (c) for mode TE0, (d), (e), (f) for mode TE1 and (g), (h), (i) for mode TE2 77Fig 4.10 The proposed schematic of a four-mode (de)multiplexer device a) Top view b) Size view 78Fig 4.11 Dependence of effective indices by using numerical simulation for

different modes on variation of the waveguide width 79Fig 4.12 The results of transmission characteristic of proposed device for mode selective coupling coefficients a) at the A1 b) at the A2 and c) at the A3 82Fig 4.13 Simulated electric field patterns for the proposed four mode

(de)multiplexer for: a) fundamental mode, b) first-order mode, c) second-order mode, d) third-order mode 83Fig 4.14 The characteristic optical performance of the device depends on the

wavelength of the four-mode a) Insertion loss (I.L) b) crosstalk (Cr.T) 84Fig 4.15 Power of the proposed device at four output ports O1, O2, O3 and O4 are functions of two simultaneous variables Δh (nm) and ΔW (nm) of the bus

waveguide when four modes are excited (a), (b), (c), (d) for mode TE0; (e), (f), (g), (h) for mode TE1; (i), (j), (k), (l) for mode TE2 and (m),(n),(o),(p) for mode TE3 85Fig 4.16 System level simulated setup for the mode demultiplexer measurement The optical and the electrical connections are shown as gold and blue lines,

respectively PRBS: Pseudo Random Binary Sequence, PPG: Programmable Pattern Generator, PC: Polarization Controller, EDFA: Erbium Doped Fiber Amplifier, DUT: Device under test, BPF: Band-pass filter, PD: Photodetector, BERT: bit error rate tester, CLK: clock synthesizer, VOA: Variable Optical Attenuator, BERT: Bit error rate tester Gain1=10dB, Gain2=3dB 86Fig 4.17 Eye diagrams of the four-mode demultiplexer for four desired output ports corresponding to injected four modes, respectively 87Fig 4.18 BER factor is a function of transmit power Tx of the tunable multimode laser 87Fig 4.19 The BER was surveyed according to the bit rate of the communication system when the transmit power Tx = -1dBm 88Fig 4.20 The BER factors are functions of wavelength in 100nm of the wavelength band in the third telecom windows 89

as optical splitters, (de)multiplexers, switches … The conventional way to construct those components is to put each component into an individual temperature controlled package and connect them to corresponding functional units However, this method

is difficult to assemble and accounts for the major percentage of cost of the whole device After that, thanks to advanced technology and well developed semiconductor fabrication technology, planar lightwave circuits (PLCs) had solved some major problems such as polarization dependence, temperature sensitivity and optical loss,

of FTTH networks Power splitters are used to divide the optical power from input ports to different channels, while (de)multiplexers are for combining and separating different wavelengths Different types of power splitters based on PLC technology

had been proposed, such as Y-Branches [1], Mach-Zehnder Interferometer [2], Multimode Interference (MMI) [3] PLCs based devices are superior to conventional fused-fiber type splitters in terms of low cost and mass producing ability Regarding multiplexing function, one of the popular components used in FTTH networks the is optical network unit (ONU), which is located at each users’ places ONU contains a triple wavelength i.e 1310nm, 1490nm, 1550nm, (de)multiplexer, and opto-electronics devices such as laser diodes and photo detectors Most of current practical triplexer transceivers are bulky modules built on discrete optical components, which

is difficult to integrate with other devices and to package PLCs technology presents

to be a solution for realizing triplexers with good performance and lower layout complexity Recently, there are some studies in this field using MMI structure [4] [5] Hence, PLCs long term reliability for optical telecommunication has been already established

born of information networks, have been proposed There are some available techniques, such as WDM [6], [7] multilevel modulation format [8], polarization division multiplexing (PDM) Until nowadays, WDM technology is still very popular

in optical communication systems, because this technology supports simultaneously

a lot of traffic wavelengths However, the available channel numbers in the C and L bands for dense-WDM systems has been fully utilized In addition, there are still some limitations that need to be solved in WDM regarding fiber nonlinearity, such as four-

wave mixing (FWM), cross phase modulation (XPM) phenomena or stimulated scattering effects On the other hand, mode division multiplexing (MDM) technology has been being pa attention as an emerging technology to enhance the capacity of idoptical communication system [9] [13] be– sides the mentioned above technologies In

but these structures need phase shifters, in which a difference of propagation constants of spatial modes can lead to mismatch of the haft beat lengths, thus causing significant crosstalk and loss Others based on asymmetric directional couplers [34]–[37] and symmetric Y-junctions couplers [38] [39] are relatively complex to manufacture in terms of making the mask in manufacturing process and have quite large insertion loss Recently, Dai et.al [40] proposed a four mode on-chip MDM structure which based on adiabatic asymmetric directional couplers However, these devices have some drawbacks, e.g., high-order modal loss and modal dispersion while guiding into the waveguides, so they have difficulty in coupling with multimode fiber links or other planar lightwave circuits Moreover, many adiabatic couplers often required a relatively large footprint and were complicated to fabricate Similarly,

Research objects and scope

This dissertation focuses on designing new MDM structures based on SOI waveguides Three most common SOI waveguide structures will be studied, namely asymmetric directional coupler, multimode interference coupler and asymmetric Y-junction waveguide, due to their vast applications for different functionalities in PIC field, especially MDM and mode converter The scope of this study is limited within passive devices made from silicone rib/ridge waveguide structure used for mode (de)multiplexing function only Rib/ridge waveguide height is designed based on CMOS fabrication standard, while width and length are determined according to the number of desired supporting modes and devices working principles respectively

Passive devices are considered due to its simplicity and no need of routing or switching optical signals for MDM function alone Silicon material is suitable for

Fig a Set up initial parameters of SOI waveguide and simulation method in RSoft

In MDM, the most important features of the devices are low loss, low crosstalk, high bandwidth, capability to support a few modes, hence all devices performance will be assessed according to those criteria They are defined as follows:

5

I L 10log out

in

P

Fig b Pathway monitoring power at each output port of a design

I.L and Cr.T will be deployed to evaluate devices fabrication and bandwidth tolerance Although there still no international unified criterion assessing whether isthe devices meet standard requirements or not because this research field is still in

demonstrate pros and cons of the proposed designs as well as potential further improvements or future research

Scientific contributions and practical applications

The dissertation has three main contributions as follows:

6

1) We proposed a new design based on asymmetric directional coupler SOI waveguide, which can (de)multiplex fundamental mode and 1st-order mode The result has been published in International Conference on Advanced Technologies for Communications (ATC), 2016

2) We proposed a new design based on 3x3 MMI couplers and trident SOI waveguide, which can (de)multiplex fundamental mode, 1st-order mode and 2nd-order mode The result has been published in Optical and Quantum Electronic

3) We proposed a new mode sorting design based on branch tilt SOI waveguides diverted from bus SOI waveguide, which can (de)multiplex multi high-order modes Our designs can (de)multiplex up-to 4 modes so far, hence show a high potential for multimode (de)multiplexing development One of the results has been published in

Photonics and Nanostructures-Fundamentals and Applications

All of our designs can operate within band C range with low insertion loss and crossta have small footprint, thus can be promising candidates for high bitrate lk;MDM systems as well as on- p photonic integrated circuits chi

Dissertation structure

The dissertation consists of 4 chapters and is organized as follows:

- In chapter 1, SOI waveguides will be mentioned, regarding its common shapes, applications in PLCs components and their advantages compared to other materials used in PLCs Then different numerical simulation methods are summarized The finite difference method is developed to solve the eigenmodes of the waveguide structure The beam propagation method is used to investigate the light propagation

in different waveguide structures Effective index method can be used in waveguide with arbitrary shape and refractive index distribution to simplify the calculation and save computing capacity After that, SOI waveguide fabrication process will be

briefly introduced Finally, working principles of three types of SOI waveguide structures used in this dissertation are introduced sequentially First , the theory of lycoupling between two directional waveguides will be introduced, covering from thesimplest case, which is symmetric co-directional coupler, to general cases, which can

be applied to mode excitation coupling in asymmetric coupler Secondly, MMI coupler working principles are introduced, especially its self-image properties will govern the applications in MDM as well as other functionalities The last structure is Y-junction waveguide, in which MDM function can be achieved based on its phase matching conditions

7

- chapter 2, a new structure of two-mode on chip (de)multiplexing devices (TM-In (de)MUXer) is proposed, built in the form of a compact Mach-Zehnder interferometer (MZI) by using asymmetric directional coupler silicon waveguides

- In chapter 3, caded MMI working principle in optical switching is introduced casThen, a new mode (de)muxer structure based on cascaded MMI presented MMI iswill solve the major challenge in MDM systems, which selectively injecting or isextracting individual modes of a multimode link, using its self-imaging properties and phase shift Furthermore, MMI devices have functions of converting high order ersmodes from the input port to fundamental modes at the output ports so as to be compatible with optical single mode fiber as well other network-on chip systems, thus

be able to reach high flexibility of light signals processinging [42] MMI coupler also meets the requirements of an effective optical device namely broadband, low loss and large tolerance fabrications, hence being recently used for MDM [31], [33], [38]

- In chapter 4, a new MDM structure, which designed based on multi-branch bus isSOI waveguide for selecting and converting guided modes, are introduced The

designs function of converting high order modes from the bus input port to ’fundamental mode at the output ports also prove the feasibility of compatibility thebetween the proposed designs and single mode optic fiber and network on-chip alsystems Those designs show some improvements compared to the designs using MMI coupler [31], [43] which are still relatively complex as its structure requires low

fabricating tolerant passive phase shifters, and the designs based on asymmetric directional coupler [44], [45] which can only (de)multiplex 2 modes

8

CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS

1.1 Shapes and function s of silicon -on-insulator waveguide

Optical waveguide is basic unit of photonics components in PLCs Optical waveguide allows optical signal transfer along its propagation direction and confines the light within the high refractive index region There are several non-planar schematics of waveguide shown in Fig 1.1 as

Fig 1.1 Schematic of non-planar optical waveguides High index is indicated by darker

Rib waveguide: consists of a slab waveguide and a strip waveguide, with the same refractive index, superimposed on it Although a rib waveguide cannot be a single-mode waveguide technically, however well designed one can make power of high-order mode leak out after very short propagation distance and thus only fundamental

is defined by the distribution of the dopants

Optical waveguide can be made of different materials such as: LiNbO3 [46], SiO2

[47], [48], Silicon on Insulator [49], [50], Polymer [51], InP [52] [53], etc The , features of each material are summarized in Table 1.1.1

LiNbO3 High Electro-Optic coefficient,

non-linear effect, excellent high

device

Si High refractive index contrast,

high integration density and compatible with Si electronics

Indirect bandgap

Polymer Ease of fabrication, low cost, high

Electro-Optic and Thermal-Optic performance

Low life expectancy

InP Direct bandgap, good for high

speed modulation and light emitters

High cost, complex technology, large foot print

due to low refractive index contrast between core and cladding layers

Table 1.1 Pros and Cons of different materials used in fabricating PLCs devices Apart from the materials mentioned in the table, another mater commonly used in ial optical waveguide is chalcogenide (As2S3), of which effective refractive index is significantly high and sensitive power intensity according to Kerr effect [54], thus tocan be applied in nonlinear directional coupler However, in this dissertation, SOI is used for all of our designs as it is the most favorable choice for passive devices with outstanding features such as low cost, low loss, high density integration due to its high refractive index contrast and good matching for single mode fiber Furthermore, optical power loss of C-band in silicon waveguide, which is used as the input signal for all of our designs and very popular in practical applications in analog CATV signal overlay, is significantly low Schematic structure of SOI slab waveguide is shown in Fig 1.2, in which a uniform layer of SiO2 is placed in the middle between thin silicon

Silicon substrate

Surface silicon guiding layer Buried SiO 2 cladding

Fig 1.2 Schematic of SOI waveguide

H

h0

Hd

Si, nr=3.45SiO2, nc=1.46

Fig 1.3 Schematic of SOI Rib waveguide There are several basic blocks and optical elements that perform some basic common functions in many PLCs as below:

1 Interconnect This basic element serves to connect optically two points of a photonic chip It can also act as a spatial filter, maintaining a Gaussian-like mode throughout the chip architecture In order to interconnect different elements which are not aligned with the optical axis of the chip, a bend WG is needed, and therefore

a bend WG is often called an offset WG These are also used to space channel WGs

at the chip end faces, so that multiple fibers may be attached to it

2 Power splitter 1x2 A power splitter 1x2 is usually a symmetric element which equally divides power from a straight WG between two output waveguides The simplest version of a power splitter is a Y-branch A different version of a power splitter is the MMI element The advantage of this design is the short length of the

11

if one needs the reflection to occur only for a particular wavelength or a grating period

WG under Bragg condition

4 Directional coupler This element has two input ports and two output ports and is composed of two closely spaced WGs The working principle of the coupler is based

on the periodical optical power exchange that occurs between two adjacent waveguides through the overlapping of the evanescent waves of the propagating modes This effect is described by the coupled mode formalism By setting design parameters, including waveguide spacing and coupler length, the ratio of powers between the two output ports may be set during the fabrication process between zero and one

5 Polarizer A waveguide polarizer allows passing light having a well-defined polarization character, either TE or TM light, by filtering one of them The fabrication

of a waveguide polarizer is simple as depositing a metallic film onto a waveguide

6 Polarization beam splitter In some integrated optical devices, it is necessary to divide the input light into its two orthogonal polarizations TE and TM, into separate waveguide output ports An integrated optical element based on a lithium niobate substrate can perform this function

7 Phase modulator An integrated optical phase modulator performs a controlled shift on the phase of a light beam and consists of a channel WG fabricated on a substrate with a possibility of changing its refractive index by means of an externally applied field (thermal, acoustic, electric, etc.) The most common phase modulator is based on the electro-optic effect: an electric field applied to an electro-optic material,

such as LiNbO3, induces a change in its refractive index, then the propagation constant of the propagating mode also changes; therefore, the light travelling through that region undergoes a certain phase shift

8 Intensity modulator One of the most important functions of an optical chip is intensity modulation of light at very high frequenc One of the simplest ways to iesperform this task is to build an integrated Mach-Zehnder interferometer (MZI) on an electro-optic substrate

9 TE/TM mode converter In a normal situation, TE and TM modes are orthogonal and then the power transfer between them cannot occur Nevertheless, TE to TM conversion can be achieved by using electro-optic substrate, which must have non-zero off-diagonal elements in the electro-optic coefficient matrix If Lithium Niobate

is used as a substrate, a period electrode is required because this crystal is birefringence, and therefore the TE, TM modes have different effective refractive

indices (propagation speeds) By combining phase modulators and a TE/TM converter, a fully integrated polarization controller can be built

The photonic elements can be found in an optical passive or active device Examples

of passive devices are the power splitter, directional couplers, frequency converter, the arrayed waveguide grating (AWG), the integrated acousto-optic tunable filters (AOTF), etc Examples of active devices are the integrated optical amplifier, the integrated laser, etc

1.2 Optical waveguide a ysis and simulation methods nal

Analysis and simulation play a very important role in proposing efficient designs that provide good performance, namely low signal loss and crosstalk effect, compactness, and making the cost for product development reduce dramatically It also helps to

In this dissertation, several different numerical methods have been developed for the design of PL devices Effective index method (EIM) is used to save computing Cscapacity by simplifying the three-dimension waveguide into two-dimension waveguide; Beam propagation method (BPM) and Finite Difference Method (FDM)

13

and H r t , is electrical field and magnetic field respectively Maxwell’s equation in

a medium is presented as follows:

B r t

t

D r t r t

B r t r t

(1.2.1)

where

and is electric and magnetic current density respectively, and ,

e r t and m r t is electric and magnetic charge density, respectively

in whichPis the polarization density andM is the magnetization density, and the

s the magnetic permeability,

dielectric permittivity and magnetic permeability, respectively

In free space, where the is no free charges nor current sources thenre P=0,M =0,

,,

, 0, 0

o r

o r

E r t

H r t

t

H r t

E r t

t

E r t

H r t

(1.2.3)

Together with following vector identity:

E r t , E r t , 2E r t , (1.2.4)Where and is nabla and Laplacian operator, respectively, denoted as follows:

Replacing vector identity (1.2.4) to Maxwell equation in free space, we have:

2 2

2 2 0

1 u 0u

c t (1.2.7) This equation is called wave equation, where is speed of light in free

space and u represents any of the three components ( ) of E r t , and

( ) of H r t , .

In the scope of this section, monochromatic electromagnetic waves are considered

All the components of the electric and magnetic are harmonic functions of time of the

is angular frequency Substituting in Maxwell’s equations, in the case of

linear, homogenous, non-dispersive and isotropic medium, we obtain:

00

x coordinate in such a way that the other coordinates (the y coordinate) acts as a parameter In this way, we obtain a y-dependent effective index profile; this generated index profile is treated once again as a one-dimensional problem from which the effective index of the propagating mode is finally obtained

Considering a channel w eguide where field propagates in z axis of Cartesian avcoordinate, electric and magnetic fields take the form as below:

u x y z t , , , u x exp j t j z (1.2.12) Given a refractive index distribution n(x,y) that defines the channel waveguide, the equations for the electromagnetic fields are reduced and this enables exact solutions

E x y E x y

k n x y E x y

16

With EIM, we assume that the field E(x,y) could be expressed as:

E x y , X x Y y (1.2.15) Substitute Eq (1.2.15) into Eq (1.2.14) and divide it by (XY)

k n x

X x (1.2.17b)

is called the effective index distribution corresponding to x direction and can

be solved with Eq (1.2.17a) by using the method the slab dielectric waveguide inThe propagation constant then can be solved in equation (1.2.17b) and the final solution is defined by two integer number and , reflecting the (in x direction) q p qthand pth (in y direction) order solution (modes) of equations (1.2.17a) and (1.2.17b ).Following example in Fig 1.4 will show how effective index mode works in practice The depth and width of the core waveguide are a and respectively b

n r

a b

Channel Waveguide x

y z

n c

n s

p I

N

p I

as the planar waveguide I, and the effective index associated with the pthguided mode for this waveguide is denoted by

The second step is to consider a symmetric step-index planar waveguide, denoted as waveguide II, formed by a core film of thickness b, whose refractive index is the effective index calculated previously The film is surrounded on both sides by a medium with refractive index equal to the substrate refractive index ns The new waveguide can easily be solved by conventional methods applied to planar structures The effective index of the q th order guided mode calculated by this planar waveguide corresponds to the modal effective index for the channel waveguide 1.2.3 Finite difference method

An arbitrary electromagnetic field propagating along a waveguide can be decomposed into many elementary discrete guided modes, which can be also called eigenmodes Besides Maxwell’s equation, numerical methods help to solve

eigenmodes in complicated waveguide geometrics and Finite Difference Method (FDM) is one of the Eigenvalue Mode Solver (EMS) methods Numerical methods will simplify the calculation by maximizing the approximation of the exact solution

and minimizing errors at the same time With FDM, the cross section of the waveguide is made discrete with a rectangular grid of points which might be of identical or variable spacing as illustrated in Figure 1.2.2 In each of the subdivisions,

-a two-dimension-al w-ave equ-ation is repl-aced with -appropri-ate Finite Difference anrelationship which is derived from a five-point Taylor series formula Each grid of points is assigned to an arbitrary electric field value Due to the subdivisions being rectangular, thus the FDM is appropriate for rectangular waveguide structure As shown in Figure 1.2.2, by defining to be electric field component to be calculated, uthe relationships are shown in equations below:

It is a good approximation if there is a large index discontinuity at the edge Nevertheless, it effectively reflects back the radiation to the analysis domain To eliminate the back reflections or incoming fluxes into the analysis window, the TBC

is applied It effectively allows radiation to pass through the boundary freely and leaves the analysis domain without appreciable reflection In this way, the unwanted interference in the core layer can be prevented [57]

n-1 n n+1

m+1

m m-1

X

Y

Fig 1.5 The cross-section of the waveguide is made discrete with a rectangular grid of

points which have identical spacing

1.2.4 Beam propagation method

FDM can solve the waveguide eigenmode, but cannot be used to solve propagation characteristics in integrated optics or fiber optics The Beam Propagation Method (BPM) is a widely used and indispensable numerical technique in today’s modeling and simulation of evolution of electromagnetic fields in arbitrary inhomogeneous an medium BPM is eligible to apply in complex geometries and automatically consider

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Propagation in z direction and refractive index changes along this direction, then electrical field can be presented as the complex field u of slow axial variation of

( , , z)

u x y multiplied by a fast oscillating wave exp( jkn z0 ) moving in z direction:

E x y z ( , , ) u x y( , ,z)exp( jkn z0 ) (1.2.20) Where no is the refractive index of cladding Substituting equation (1.2.20) to (1.2.19), we have:

Assumption of weakly guiding condition, such that , equation (1.2.21) can be written as:

2

0 0

Under restriction of propagation to a narrow ranges of angles, 2u2 0

dz , equation (1.2.22) can be written as:

1.2.5 Finite difference beam propagation method

To simplify the calculation, we analyze BPM based on FDM in 2D only, hence direction dependency can be omitted Equation (1.2.23) can be rewritten as:

2 2 2

0 2

u A( , ) x z 2u2 B x z u( , )

z x (1.2.25) which can be calculated approximately by FDM:

0

1 2

kn (1.2.29)

2 2

0 0

in z propagation, boundary condition also need to be imposed into analysis window

Fig 1.6 Comparison between FD-BPM (left) and FFT-BPM (right) simulation FD-BPM under TBC gives better simulation result as the simulated wave is smoother

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TBC is used in -BPM simulation to eliminate the back reflections or incoming FDfluxes into the analysis window, in which radiation disappears into the boundary without any reflection when reaching the edge of the simulation window Although FFT-BPM is not analyzed in this dissertation, Fig 1.7 is shown as an example of

comparing between FFT-BPM and FD-BPM with TBC Simulation of field propagation along Y-branch with equal shape arms is taken into consideration It is clear that FD-BPM with TBC gives better results, which explains the reason that we

yand z are set as 0.05μm as can be seen in Fig 1 (a)7

Fig 1.7 Comparison between FD-BPM simulation time depending on computed step of

grid size 0.05 μm (a ) verse grid size 0.01 μm (b )

1.3 Silicon-on-insulator waveguide fabrication

1.3.1 Separation by implanted oxygen (SIMOX)

The SIMOX process is the most common method to fabricate a massive quantity of

SOI material The essential part in manufacturing SOI the SIMOX method is inimplanting a large amount of oxygen ions below the surface of a silicon wafer The most common way to illustrate the total volume of any ion species embedded into a wafer is by the implanted ion dose The dose is just the whole amount of ions passing

through one square centimeter of the wafer surface and is measured in units of ions/cm2 der normal room-temperature conditions upper layer Un of silicon crystal might change to an unwanted amorphous stage during the implantation of the oxygen ions To avoid this effect, the silicon substrate is retained at a certain high temperature

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during implantation To have the first glance of the relative amount of the dose required for SIMOX, it can be compared with the dose implanted in a typical doping process for the creation of source and drain contacts in manufacturing complementary metal-oxide semiconductor (CMOS) transistors

There is a need of high energy in order to implant oxygen ions into crystalline silicon The depth of the SiO2 and consequently the thickness of the silicon upper layer depends on that energy Figure 1.8 shows the schematic development of the oxygen concentration as a function of depth from the uppermost silicon wafer surface The graphs are simply meters of the growth of oxygen concentration versus depth at typical execution stages Similar to all implanted species, the oxygen concentration

can be illustrated by a shape according, but not identical, to that of a Gaussian function (Figure 1.8a) As the implantation proce continues and the dose rises, the ssultimate concentration of oxygen ions (O+), saturates to a plague figure of that found

in stoichiometric SiO2 (Figure 1.8b) With further implantation the oxygen ions cannot be more condensed, forming a solid, continuous layer of SiO2 After being implanted with oxygen to a dose up to the concentration level, the silicon wafer is

Sub-SiO2 Stoichiometric

SiO formation 2 concentration

SiO formation 2 concentration

Depth from Si wafer surface (b)

Depth from Si wafer surface (c)

Fig 1.8 Variation of the oxygen profile during the SIMOX process (a) Low -dose; (b) high-dose (peak is at the stoichiometric limit for SiO2); and (c) after implantation and

annealing at high temperature for several hours The implant energy determines the depth and thickness of the buried SiO2 layer To make the scopes of this structure more appropriate for the manufacture of wider cross-section waveguides, epitaxial growth technique is used to increase the thickness of silicon layer up to several microns[61]

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1.3.2 Bond and Etch-back SOI (BESOI)

A very strong bond of two SiO2 wafers appears when their surfaces are brought into physical contact and this phenomenon managed to form the BESOI process The

assembly of BESOI has three phases presented schematically in Figure 1.9: (a) oxidation of the two wafers to be bonded; (b) formation of the chemical bond; (c) thinning (etching) of one of the wafers

Wafer thinning can be achieved via a number of two common methods The most popular one is chemical mechanical polishing (CMP) technique, which is used widely

in making wafer planar in microelectronics The wafer surface must be weakened and then detached during a single processing step CMP method In general, the in thesilicon surface, which needs to be polished, is handled with a rotating pad, and at the

to the etchant, leaving a silicon upper layer whose depth and uniformity are defined

by the foundation of the doped layer

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to eradicate the exposure of p-type layer resulting from the selective etch The the

final wafer structure is the one of an undoped silicon upper layer on the buried SiO2 1.3.3 Wafer Splitting

A thermally oxidized wafer is implanted with hydrogen to a certain concentration The implanted hydrogen ions concentration function has the form similar to Gaussian profile The distance from the wafer surface the highest condense to of the profile relies on the H+ ion energy, but is normally in the range of a few hundred nanometers

to a few microns The H+ ions are at their maximum concentration at this depth, in

After the implantation step, the wafer is brought into interaction with a second handling wafer, which surface may or may not be cover ed by thermal SiO2 From the contact, room-temperature bonding happens similar to that of the BESOI method Subsequent impacted thermal the same degree in which of SIMOX process at firstly separates the implanted wafer along the high concentration of the implanted H+ ions profile, then reinforces the bond between the former and latter wafer

A careful CMP process deployed to decrease roughness of SOI surface After that, is epitaxial silicon growth can build up the thickness of the silicon upper layer if needed The inhomogeneity thickness of the implanted hydrogen profile peak are only a few percent Importantly, although the upper layer is implanted with a high dose quantity, the small mass of the hydrogen ions guarantees th negligible remaining destruction e

at the end of the thermal treatment The buried SiO2 thickness may be varied from nanometers to several microns due to the termination of the thermal oxidation deprocess

The adaptability, high quality and efficient use of silicon presented from this method makes it a brilliant platform fabricate silicon photonics with low cost to

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1.3.4 Silicon Epitaxial Growth

‘Epitaxial’ is from Greek word where “epi” means “above” and “taxy” means “in order manner”, hence the whole word depicts the process of growing a mono-crystal layer in an order, especially when fabricating mic - or opto-electrical devices The rodeployment of epitaxial silicon as the waveguide medium has the supplementary benefit of doping and defect levels below ones found in wafers cut

The most popular epitaxial silicon growth technique is chemical vapor deposition (CVD) CVD is a method which places a solid film on the surface of a silicon wafer

by the reaction of a gas mixture on that surface Regarding licon deposition, the si

1.3.5 Fabrication of surface etched features

1.3.5.1 Photolithography

Photolithography is the standard method of printed circuit board (PCB) and microprocessor fabrication The process uses optical radiation, which changes the photoresist layers, to make the conductive paths of a PCB layer and the paths and electronic components in the silicon wafer of microprocessors

The width of a rib waveguide shown in Figure 1.11 is mainly created by the photolithographic process, so the regulator of the photo process is one of the most vital tasks in silicon photonic manufacture Moreover, it is not enough to guarantee

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microns and, by cautious select of the objective dimensions, CD control can be widen

to several hundred nanometers [66] However, the silicon photonics manufacturer may insist on the very strict CD when fabricating more complicated shape submicron-dimension devices or waveguides

Photolithography technique uses deep ultraviolet light to transfer a mask pattern to the surface of a wafer The pattern is printed on the wafer using a photoresist Many formulas and procedure variants have been introduced to guarantee good, application-specific photolithography, but the primary structure of all photo-processes depends

on specific common steps, namely wafer preparation, photoresist application, soft bake, exposure to ultraviolet light, photoresist developing and hardbake

Fig 1.11 (a) Schematic of a silicon rib waveguide (b) Electron micrograph of a silicon

rib waveguide Reproduced by permission of Intel Corporation 1.3.5.2 Silicon etching

Etching process is executed preciseto ly remove redundant material from the silicon wafer surface by a chemically reactive or physical method There are two general approaches: wet and dry etching Each approach has benefits and drawbacks, however dry etching prevails in reproducing structures of submicron scales Low-loss silicon waveguides, having dimensions typically >1µm, have been shaped by both wet [67] and dry [68] etching, but with the requirement for flexible process capability, tight tolerances and reproducible production, dry etching is regarded as the most suitable

solution

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Dry etching is done through the development of a low pressure plasma The physical processes, which consist of the formation and stabilization of a plasma, are out of the scope of this dissertation However, because of the prevalence of plasmas in silicon

in an isolated chamber, can be achieved by the application of either DC or AC power

to a process gas Although DC one is infrequently used in practical applications because it is unsuitable with insulating electrodes causing surface charging and an unbalanced plasma AC power avoids this issue by accumulating charges in one half-

Fig 1.12 Schematic of a confined AC -generated plasma suitable for silicon processing

The processed wafer in placed on the lower, grounded electrode

CF4 gas is normally used to derive plasma in the silicon etching process F atoms, which can be dissociated from CF4 at certain conditions, are used as active elements

to etch both Si and SiO2 However, using plain CF4 a plasma environment will asslow down the etching rate as CF3 and F can recombine to form the original stage

CF4 Hence, O2 is added into the gas mix to promote significantly the etching rate due

to the reaction of oxygen with CF3 inhibiting F recombination and hence increasing the free F concentration

1.4 Silicon-on-insulator waveguide structure used for MDM functionality

1.4.1 Directional coupler

Coupling theory has been applied extensively in guided-wave optics as a

mathematical tool for the analysis of electromagnetic wave propagation and