Development of optical devices simulation software using finite difference method

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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.

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Signature :

Name of Supervisor Date: J L M C

ssoc. Prof. Dr. Norazan bin Mohd. Kassim

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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

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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

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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.

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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

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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

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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

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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

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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

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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

6.4a 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 < l x l 0 '

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

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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

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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

with Ay =0.1|am, Ax=0.05|j.m and t=0.5fim

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6.8(a) and (b) 3D plot and contour of the electric field distribution

with Ay =0.1 (im and Ax=0.05|im

with Ay =0.1|am, Ax=0.05jim and s =1.0)j.m

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

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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)

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Partial differential

Gradient operator

Curl operator

Divergence operator

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A Source Code of Visual C++ Version 6 72

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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.

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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.

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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.

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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.