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P E R P U S T A K A A N KUi T T H O
3 OOOO 00117408 9
PSZ 19:16 (Pind. 1/97) UNIVERSITI TEKNOLOGI MALAYSIA
BORANG PENGESAHAN STATUS TESIS •
JUDUL : DEVELOPMENT OF OPTICAL DEVICES SIMULATION
SOFTWARE USING FINITE DIFFERENCE METHOD
SESIPENGAJIAN: 2003/2004
Saya RAHMAT BIN TALIB
(HURUF BESAR)
mengaku membenarkan tesis (PSM/Saijana/Doktor Falsafah)* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:
1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan
pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara institusi
pengajian tinggi. 4. ** Silatandakan(V)
SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972)
(Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/badan di mana penyelidikan dijalankan)
TERHAD
TIDAK TERHAD
"(TAN
Alamat Tetap :
40, KAMPUNG SAUJANA
BATU 29, LENGA
84040 MUAR, JOHOR
AN PENULIS)
Disahkan olel'
P.M. DR. NORAZAN BIN MOHD KASSIM
Nama Penyelia
Tarikh 11 MAC 2004 Tarikh : II MAC aooif-
CAT AT AN : * Potong yang tidak berkenaan. ** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak
berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.
• Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Saijana secara penyelidikan, atau disertasi bagi pengajian secara keija lcursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM).
"I hereby declare that I have read this thesis and in
my opinion this thesis is sufficient in terms of scope and
quality for the award of the degree of Master of Engineering
( Electrical- Electronics & Telecommunications )
Signature :
Name of Supervisor
Date: J L M C
ssoc. Prof. Dr. Norazan bin Mohd. Kassim
200 b
DEVELOPMENT OF OPTICAL DEVICES SIMULATION SOFTWARE
USING FINITE DIFFERENCE METHOD
RAHMAT BIN TALIB
A project report submitted in partial fulfilment
of the requirements for the award of the degree of
Master of Engineering (Electrical - Electronics & Telecommunications)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
MARCH, 2004
ii
I declare that this thesis entitled "Development of Optical Devices Simulation
Software using Finite Difference Method" is the result of my own work except as
cited in the references. The thesis has not been accepted for any degree and is not
concurrently submitted in candidature of any other degree.
Signature :
Name : Rahmat bin Talib
Date: 11th March 2004
iii
To my beloved wife and daughter.
iv
ACKNOWLEDGEMENT
Praise be to Allah S.W.T the Most Gracious, the Most Merciful, whose
blessing and guidance have helped me through my thesis smoothly. Peace and
blessing of Allah be upon our Prophet Muhammad S.A.W who has given light to
mankind.
I would like to express gratitude to my supervisor Assoc. Prof. Dr. Norazan
bin Mohd. Kassim for all the idea, guidance, motivation and support that he had
given to me during this project.
I am grateful to Mr. Hanif bin Ibrahim and Mr. Asrul Izam bin Azmi for all
information, knowledge and guidance regarding my project.
I also would like to express gratitude to my wife, Hasnah bt Hj.
Ibrahim@Berahim and my daughter, Iffah Irdina for their patience.
Finally, I would like to thank all my friends and all those whoever has helped
me to complete my thesis.
V
ABSTRACT
Optical devices are very important part in optical communication system that
makes the system work. Reliability, quality, cost and new functionalities become
important factors for acceptance of optical devices in telecommunication network as
a whole. Optical devices such as switch and coupler, consist of common element is
called as waveguide. Thus, the functions of each optical device depend on
parameters of the waveguide. In this project, simulation software of the rib
waveguide will be developed to obtain optimize parameters for fabrication process,
thus minimize the error and cost. Purpose of the simulation is to obtain the electric
profile and effective refractive index of the waveguide by input the parameters such
as dimension of waveguide structure, refractive index of material and operated
wavelength. The mathematic model of waveguide is obtained by using Finite
Difference Method based on Scalar Wave Equation. The simulation software is
developed using current version of C language, Visual C++ 6. It is provided with
new features suitable for Window-Based program. The performance of the developed
simulation software is verified by using well established rib waveguide structure.
The results obtained from simulation are agreeable with other researcher. It shows
that the developed software is comparable with other software available in market.
vi
ABSTRAK
Peranti optik merupakan komponen yang sangat penting dalam sistem
perhubungan optik bagi membolehkan sistem itu beroperasi. Kebolehharapan,
kualiti, kos dan fungsi-fungsi baru menjadi faktor penting kepada penerimaan
sesuatu peranti optik dalam keseluruhan jaringan telehubungan. Peranti optik seperti
suis dan penganding terdiri dari unsur yang dipanggil pandu gelombang. Oleh itu,
fungsi-fungsi setiap peranti optik bergantung kepada parameter-parameter pandu
gelombang tersebut. Dalam projek ini, perisian simulasi bagi pandu gelombang
tetulang akan dibangunkan untuk mendapatkan parameter yang optimum bagi proses
fabrikasi, justeru itu kesilapan dan kos dapat diminimumkan. Tujuan simulasi ini
ialah untuk mendapatkan profil medan elektrik dan indek biasan berkesan pada
pandu gelombang dengan memasukan beberapa parameter seperti ukuran struktur,
indek biasan bahan dan panjang gelombang. Model matematik bagi pandu
gelombang diperolehi menggunakan Kaedah Pembezaan Terhingga berdasarkan
Persamaan Gelombang Skalar. Perisian simulasi dibangunkan menggunakan versi
terkini bahasa C iaitu Visual C++ 6. Ia dilengkapi dengan ciri-ciri baru sesuai untuk
aturcara Berasakan-Tetingkap. Prestasi perisian simulasi yang dibangunkan disahkan
dengan menggunakan struktur pandu gelombang terkemuka. Hasil keputusan
simulasi yang diperolehi adalah menyetujui dengan penyelidik lain. Ini membuktikan
perisian yang dibina setanding dengan perisian lain dalam pasaran.
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE PAGE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES x
LIST OF FIGURES xi
LIST OF SYMBOLS xiv
LIST OF APPENDICES xvi
1 INTRODUCTION 1
1.1 Introduction 1
1.2 Project Objective 3
1.3 Structure of Thesis 3
2 BASIC THEORY OF ELECTROMAGNETICS 5
2.1 Electromagnetic Theorems 5
2.2 The Wave Equation 7
2.2.1 The Time-Independent Wave Equation 8
2.3 Full-Vectorial,Semi-Vectorial and Scalar Wave 9
Equation
viii
3 OPTICAL WAVEGUIDE & OVERVIEW OF 13
NUMERICAL METHOD FOR ANALYSIS
OF WAVEGUIDE
3.1 Optical Waveguide 13
3.1.1 Planar Waveguide 14
3.1.2 Waveguide Modes 15
3.1.3 Waveguide Cut-off 15
3.1.4 Channel Waveguide 17
3.2 Numerical Methods 19
3.2.1 Effective Index Method 19
3.2.2 Finite Difference Method 21
4 MATHEMATIC MODEL OF WAVEGUIDE 24
4.1 Finite Difference Schemes 24
4.2 Finite Difference Scalar Wave Equation 26
4.3 Finite Difference Semi-Vectorial Wave Equation 28
5 VISUAL C++ PROGRAMMING & SOFTWAVE 31
DEVELOPMENT
5.1 C Language Programming 31
5.1.1 Programming Universals 31
5.1.2 Editing, Compiling & Running 32
Visual C++ Programs
5.1.3 Visual C++Concept 34
5.1.3.1 Defining Classes 34
5.1.3.2 Data Hiding & Encapsulation 35
5.1.3.3 Polymorphism 35
5.1.3.4 Inheritance 36
5.1.3.5 Template Functions 36
5.1.3.6 Overloading Functions 37
5.2 Microsoft Visual C++6.0 37
5.3 Software Development 39
5.3.1 Component of Application 39
5.3.2 Flow Chart of Application Software 40
5.3.3 Development Stages 42
5.4 Simulation Manual of WaveGuideCADTool 43
6 RESULTS AND DISCUSSIONS 47
6.1 Standard Rib Waveguide for Analysis 47
6.2 Results and Discussions 51
6.2.1 Two Layer Rib Waveguide 51
6.2.2 Three layer Rib Waveguide 60
6.2.3 Directional Coupler 62
6.3 Beam Propagation Method(BPM_CAD) 66
7 CONCLUSIONS 68
REFERENCES 70
APPENDIX A: Source Code of Visual C++ 72
Version 6for WaveGuideCADTool simulation
software
V
LIST OF TABLES
TABLE NO TITLE PAGE
5.1 Categories of input 39
5.2 Processing data 39
6.1 The parameters of the rib waveguide (Figure 6.1) 48
6.2 The parameters of the rib waveguide (Figure 6.2) 49
6.3 The parameters of the rib waveguide (Figure 6.3) 50
6.4a Comparison effective index, Neff for rib waveguide 55
in Figure 6.1 using FD(VC++) with EI, IPM and
VFE [1]
6.4b Comparison Normalized propagation constant,b for 56
rib waveguide in Figure 6.1 using FD(VC++) with
EI, IPM and VFE [1]
6.5 Result for waveguide in Figure 6.2 with Ax=0.05|_im 60 Q
and Ay=0.1|_im when changes on b<lxl0"
6.6 Comparison normalized propagation constant b, for 61
the waveguide of Figure 6.2 with other method[2]
6.7 Coupling length for directional coupler in Figure 6.3 62
with ?lo = 1.55jim
6.8 Comparison coupling length(mm) of the directional 63
coupler
6.9 Result for waveguide in Figure 6.3 with Ax=0.05|j.m, 64 Q
Ay=0.1|j.m and s=1.0fim when changes on b< lx l0 '
for even mode
6.10 Result for waveguide in Figure 6.3 with Ax=0.05|im, 65
Ay=0.1|im and s=1.0(im when changes on b<lxl0"8
for odd mode
A1
LIST OF FIGURES
FIGURE NO TITLE PAGE
3.1 An example of an integrated optic device 13
3.2 Planar waveguide 14
3.3 Several of modes in planar waveguide 15
3.4 2 dimension confinement of channel waveguide 17
3.5a Buried Channel 17
3.5b Rib Guide 18
3.5c Embedded Strip 18
3.5d Raised Strip 18
3.5e Ridge Guide 18
3.6 A rib waveguide is divided to three slab waveguide 20
3.7 Symmetric slab for rib waveguide since ncm = ncin 21
3.8 Finite Difference mesh for modelling of a rib 22
waveguide
4.1 The slope or derivative of/(x) at point C using 24
forward, backward and central difference
4.2 Mesh point for Finite Difference Method of 26
waveguide structure window with size N x M
5.0 Input-Processing-Storage-Output 32
5.1 Steps for running a program 33
5.2 The Visual C++ Main Menu 38
5.3a Flow Chart of Application software 40
5.3b Flow Chart of Application software 41
5.4 Main window of WaveGuideCADTool application 43
software
5.5a Input parameters dialog box for 2 layer rib waveguide 44
Xll
5.5b Input parameters dialog box for 3 layer rib waveguide 45
5.5c Input parameters dialog box for 3 layer rib waveguide 45
directional coupler
5.5d Context menu 46
6.1 GaAs rib waveguide structure operating at X=\. 15^m 48
6.2 InP/InGaAsP rib waveguide structure operating at 49
A,=1.55|j.m
6.3 InP/InGaAsP rib waveguide structure operating at 50
X = \ , 5 5 | j . m
6.4a Comparison of difference Xs 52
6.4b Comparison of difference Ys 52
6.4c Comparison of difference mesh size, Ay with others 53
method[l]
6.4d Comparison of difference mesh size, Ay 53
6.4e Comparison of difference mesh size, Ay versus 54
time(s)
6.4f Comparison of difference mesh size, Ay versus 54
iteration
6.4g A comparison of effective index versus t(fim) for the 55
structure in Figure 6.1 using EI, IPM and VFE [1]
6.4h A comparison of normalised propagation constant,b 56
versus t(jim) for the structure in Figure 6.1 using EI,
IPM and VFE [1]
6.5(a) and (b) 3D plot and contour of the electric field distribution 57
for waveguide in Figure 6.1 using given parameters
with Ay =0.1 |am, Ax=0.05jim and t=0.1fim
6.6(a) and (b) 3D plot and contour of the electric field distribution 58
for waveguide in Figure 6.1 using given parameters
with Ay =0.1|am, Ax=0.05|j.m and t=0.5fim
6.7(a) and (b) 3D plot and contour of the electric field distribution 59
for waveguide in Figure 6.1 using given parameters
with Ay =0.1|itn, Ax=0.05(im and t=0.9|am
6.8(a) and (b) 3D plot and contour of the electric field distribution
for waveguide in Figure 6.2 using given parameters
with Ay =0.1 (im and Ax=0.05|im
6.9(a) and (b) 3D plot and contour of the electric field distribution
for waveguide in Figure 6.3 using given parameters
with Ay =0.1|am, Ax=0.05jim and s =1.0)j.m
6.10(a) and (b) 3D plot and contour of the electric field distribution
for waveguide in Figure 6.3 using given parameters
with Ay =0.1 [im, Ax=0.05jam and s =1.0(im
6.11 The electric field and refractive index of the rib
waveguide Figure 6.1 using BPM_CAD software
6.12 The electric field and refractive index of the rib
waveguide Figure 6.1 using WaveGuideCADTool
software
x i v
LIST OF SYMBOLS
B - Magnetic flux density (Wb/m2)
c0 - Speed of light ( 3 x 108 mis)
d - Distance of slab waveguide (m)
D - Electric flux density (C/m2)
E - Electric field strength (V/m)
H - Magnetic field strength (A/m)
j - V^T
J - Current density (A/m2)
k0 - Free space propagation constant (rad/m)
n - Refractive index
nc - Refractive index of cladding
ng - Refractive index of guiding medium
ns - Refractive index of substrate
t - Time (s)
TE - Transverse electric wave
TM - Transverse magnetic wave
TEM - Transverse electromagnetic wave
(3 - Propagation constant in propagation direction (rad/m)
s0 - Free space permittivity (8.8542 x 10"12 F/m )
(p - Total internal reflection phase shift (rad)
X - Wavelength (m)
Ho - Free space permeability (Atl x 10"7 H/m)
9C - Critical reflection angle (°)
p - Charge density (C/m )
co - Angular frequency (rad/s)
¥ - Field distribution
Partial differential
Gradient operator
Curl operator
Divergence operator
Laplacian operator
xvi
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Source Code of Visual C++ Version 6 72
for WaveGuideCADTool simulation software
CHAPTER 1
INTRODUCTION
1.1 Introduction
The rapid growth of optical communications system makes the optical
devices great demand all over the world. Reliability, quality, cost and new
functionalities become important factors for acceptance of optical devices in
telecommunication network as a whole. Optical communications systems promise
for high bandwidth, high speed, low loss and low cost. The optical communications
give opportunity for development of new applications. Many research efforts have
been done to improve the quality of the communications system in order to fulfill the
demand of customer and market competition. There are many research works
involved such as simulation, characterization, fabrication and measurement.
In this project, simulation has been chosen because by simulation, an
optimize parameters of waveguide can be obtained for fabrication process, thus
minimize the error and cost. Simulation is veiy important process in designing
optical devices because it can avoid many problems in the early stage and hence help
the designer to undertake necessary action.
2
From the literature review, solving waveguide problem is actually to solve
wave equation which is derived from the well known Maxwell's equation. The
analysis of waveguide can be done in Scalar[l][2][3], Semivectorial[3][4] or
Vectorial[5] Wave Equation. The difference between theses wave equation are due to
several assumptions have been made during derivation of equation and each of them
have difference level of complexity. The scalar wave equation is the simplest
equation compared the other two. In this project, only weakly-guiding waveguide
and polarization direction is appropriately chosen. Thus, the scalar wave equation
will be used.
There are many numerical methods available to solve the waveguide problem
in order to determine the effective refractive index, normalized propagation constant
and field profile. Among the popular methods are Effective Index (EI) Method,
Finite Difference Method (FDM) and Finite Element Method (FEM). The Effective
Index (EI) Method does not give good results when the structure operates near cut-
off[2]. Finite Element Method (FEM) may appear the troublesome of spurious
solutions [6]. Thus, FDM is chosen for this project because considering above
mentioned problems.
The FDM to solve the scalar wave equation can be implemented by computer
programming such as FOTRAN, C and others. FOTRAN becomes not popular
nowadays because the existing more powerful computer language such as C. C
language has been used for numerical method in electromagnetic problems [7]. C
language can generate "stand alone" program. Current version of C language, Visual
C++ (VC++) can be used to develop Window-based program and Graphical User
Interface (GUI) with very small effort. Due to above reason, VC++ will be used in
this project.
3
1.2 Project Objective
The main objective of this project is to develop simulation software using
Visual C++ based on Finite Difference Method (FDM) to solve the Scalar Wave
Equation in optical devices. Other objective is to evaluate the performance and
accuracies of the software with other standard software such as Beam Propagation
Method (BPM CAD).
1.3 Structure of Thesis
There are seven chapters in this thesis. Chapter 1 will have a brief description
about project introduction, methodology, objective and related topics that will
include in each chapter.
Chapter 2 will focus on the basic theoiy of electromagnetic as a foundation
for the formulation of wave equation. The derivation of scalar, semi-vectorial and
vectorial wave equations form well known the Maxwell's equations.
Chapter 3 will explain about optical waveguide application in integrated
optics, planar waveguide, modes and cut-off. The description about two dimension
confinements of channel waveguide and several channel waveguide geometry
available. Explain the numerical methods such as EIM and FDM that available to
solve wave equation.
Chapter 4 will explain more detail how the mathematic model for waveguide
is derived form the Scalar and Semivectorial Wave Equation to the FD form.
4
Chapter 5 will focus on the Visual C++ programming concept such as classes,
inheritance and others, development of software, flow chart of program and
operation manual of software.
Chapter 6 will consist of simulation results and discussions. Two rib
waveguide structures and a directional coupler used as samples where the
performance and accuracies of the simulation software are compared with other
researcher and BPM_CAD.
Chapter 7 will conclude overall achievement of the project, suggestions to
improve the software for future work.