126_mohdmuzafarbinismail2008.pdf

iii

ANALYSIS OF BURIED OPTICAL WAVEGUIDE CHANNEL USING

FINITE DIFFERENCE METHOD

MOHD MUZAFAR BIN ISMAIL

This thesis submitted in partial fulfillment of the requirement for the award of the

degree of Bachelor of Electrical Engineering (Telecommunication)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

April 2008

��

�

Special dedicated to

Apple of my eyes; my beloved parents, brothers and sister.

all my friends, teachers and lectures

for their support and encouragement

vi

ACKNOWLEDGEMENT

Alhamdulillah….

Praise to Allah S.WT The Most Gracious, The Most Merciful, there is no

power no strength save in Allah, The Highest and The Greatest, whose blessing and

guidance have helped me through the process of completing this project. Peace and

blessing of Allah be upon our prophet Muhammad S.A.W who has given light to

mankind.

My deepest gratitude goes to my supervisor Assoc. Prof. Dr. Abu Sahmah

Mohd Supa’at for all the knowledge, motivation and support that he had given me in

completing this thesis. Lots of love from deepest of my heart goes to my family

especially my parents whom always given me their love and warm support.

I sincerely and almost thanks all of my teachers, lecturers and all of my

friends for helping directly or indirectly.

May Allah bless all of you. Ameen

Thank you very much.

vii

ABSTRACT

Optical waveguides have been known as basic structure in integrated optics.

Result of the optical waveguide an analysis is very useful before fabrication process.

Therefore, ongoing development in the area of optoelectronic design have required

accurate, reliable and powerful tools for the analysis of it’s constitute wave guiding

elements as well as for entire circuits. This project focuses on modeling optical

waveguide (buried channel) which is the main component of optical devices.

Modeling is a very crucial process in designing optical devices because it can avoid

many problems in early stage and hence help the designer to undertake necessary

action. In this project, optical propagation characteristic of straight waveguide on

light intensity distribution within the structures has been investigated at 1.55

micrometer window. The purpose of the simulation is to obtain the electric field

profile and effective refractive index, neff of the waveguide that varies according to

input parameters such as dimension of waveguide structure, refractive index of

material and operated wavelength. The analysis has been analyzed using a numerical

method based on finite difference approach and be calculated with efficiently using

on the personal computer. Graphic user interface (GUI) had been applied in

developing this simulation program using MatlabR2006a. The factors that contribute

to the accuracy of simulation results were obtained and these results are agreeable

with theory.

viii

ABSTRAK

Pandu gelombang optik telah lama dikenali sebagai struktur asas dalam

struktur optik bersepadu. Keputusan analisis pandu gelombang ini amat berguna bagi

aplikasi sebelum memulakan proses fabrikasi. Oleh itu perkembangan yang

berterusan dalam bidang optoelektronik memerlukan perisian yang tepat dan boleh

dipercayai bagi membuat analisis pandu gelombang dan litar keseluruhan. Projek ini

difokuskan kepada pemodelan pandu gelombang (saluran tertanam) yang merupakan

komponen utama dalam peranti optik. Permodelan adalah sangat penting didalam

proses merekacipta peranti optik kerana ia dapat mengelakkan banyak masalah pada

peringkat awal dan ini dapat membantu pereka untuk mengambil tindakan yang

sepatutnya. Dalam projek ini, ciri taburan cahaya perambatan optik yang melalui

struktur pada tingkap panjang gelombang 1.55 micrometer dalam perambatan lurus

dikaji. Tujuan simulasi adalah untuk mendapatkan profil medan elektrik dan indeks

biasan berkesan, neff pada pandu gelombang yang berubah mengikut parameter

masukan seperti ukuran struktur, indek biasan bahan dan panjang gelombang dalam

projek ini. Analisis pengiraan di lakukan melalui penghampiran pembezaan

terhingga permodelan dalam pendekatan kaedah berangka yang mana boleh dikira

secara berkesan dengan menggunakan komputer peribadi. Pengantaramuka grafik

pengguna telah diaplikasikan dalam pembangunan program simulasi ini dengan

menggunakan perisian Matlab R2000a. Faktor-faktor yang menentukan ketepatan

hasil simulasi juga diperoleh dan dipersetujui dengan teori.

ix

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION v

ACKNOWLEDGEMENT vi

ABSTRACT vii

ABSTRAK viii

TABLE OF CONTENTS ix

LIST OF TABLES v

LIST OF FIGURES xiii

LIST OF SYMBOLS xvi

LIST OF APPENDICES xviii

1 INTRODUCTION

1.1 Introduction 1

1.2 Objectives 2

1.3 Scope of the work 2

1.4 Problem Statement 3

1.5 Motivation of the work 4

1.6 Methodology 4

1.7 Structure of Thesis 7

x

2 OPTICAL WAVEGUIDE

2.1 Introduction 8

2.2 Background 8

2.3 Buried Optical waveguide 9

2.4 Type of waveguides 11

2.4.1 2-D Optical Waveguides 11

2.4.2 3-D Optical waveguides 13

2.5 Optical waveguide application 14

2.5.1 Fabrication process 15

2.6 Optical waveguide analysis techniques 16

2.6.1 Analytical approximation solutions for

Optical waveguide 17

2.6.2 Numerical solutions for optical

waveguides 18

3 MATHEMATICAL ANALYSIS

3.1 Overview of numerical method 19

3.2 Finite Difference Methods 20

3.3 Numerical methods solve Maxwell’s

Equation exactly 24

4 MATLAB AND GUI DEVELOPMENT

4.1 Introduction of MATLAB software 29

4.1.1 Basic MATLAB features 29

4.2 Basic Graphical User Interface (GUI) 33

4.2.1 User of guide 33

4.2.2 Starting GUIDE 34

4.3 ‘My GUI’ concept 34

xi

5 RESULT, ANALYSIS AND DISCUSSION

5.1 Result Process 53

5.1.1 First stage 53

5.1.2 Second stage 55

5.2 Calculation result and Buried optical

waveguide figure presentation 55

5.3 Effective index, neff and normalized

propagation constant, b analysis 66

5.4 Comparison with previous analysis 68

5.5 Discussion 69

6 CONCLUSION AND RECOMMENDATION

6.1 Conclusion 72

6.2 Recommendation 73

REFERENCES 74

APPENDIX A: Source code for Buried

Waveguide modeling by

Using MATLAB 76

xii

LIST OF TABLES

TABLE NO TITLE PAGE

1.1 Differentiation before software developed

and after software developed 3

5.1 Categories of input 54

5.2 Processing data 54

5.3 Final output 54

5.4 9 samples of data from GUI calculation 66

xiii

LIST OF FIGURES

FIG NO. TITLE PAGE

1.1 Overview project flow 4

1.2 Gantt Chart of PSM 1 5

1.3 Gantt Chart of PSM 2 6

2.1 Buried optical waveguide 10

2.2 Buried waveguide for integrated circuitry 10

2.3 Three layer dielectric waveguide 12

2.4 2-D optical buried waveguide channel 12

2.5 Plane of symmetry 12

2.6 The cross-sectional profile of the air-clad buried waveguide 13

2.7 3-D buried waveguide channel 13

2.8 NASA’s Glenn research centre (fabrication process) 15

3.1 Typical finite difference mesh 21

3.2 Locting node (a) on centre (b) on mesh point 21

4.1 The flow chart show how the MATLAB work 31

4.2 The flow chart of programming process 32

4.3 Overview plan of ‘My GUI’ 35

4.4 Main page of ‘My GUI’ 36

4.5 Main page for EXAMPLE section- waveguide (3 x 3) 37

4.6 Refractive index profile button- n core (3.44),n cladding (3.34) 37

and n air (1)

4.7 Optical Normalized Power button - 0.7010 38

4.8 E-field profile button 38



and n air (1)

xiv





and n air (1)



4.17 Calculation part in ‘My GUI’ 43

4.18 Analysis section in ‘My GUI’ 44

4.19 neff graph (left) and b Graph (right) 44

4.20 Main page of application in ‘My GUI’ 45

4.21 Optical concept button 46

4.22 Symmetry waveguide and ray transmission button 46

4.23 Mathematical Equation button 47

4.24 Material application button 48

4.25 Figure 1 (left) and figure 2 (right) from material

application button 48

4.26 Main pages of optical devices application button 49

4.27 APD Preamplifier application button 50

4.28 Photo diode application button 50

4.29 Optical fiber application button 51

4.30 Fiber Spec Corning application button 51

4.31 Laser diode application button 52

4.32 Fabrication Process button 52

5.1 Buried optical waveguide structure plan view 56

5.2 (a) neff and b at waveguide (3 x 3) calculation result 57

(b) Figure of refractive index, E-field and E-field contour 57

5.3 (a) neff and b at waveguide (3.5 x 3.5) calculation result 58






xv











5.11 (a) Effective Index, neff graph 67

(b) Normalized propagation constant,b graph 67

5.12 Dispersion characteristic for the lowest four modes of an

anisotropic rectangular dielectric waveguide 69

xvi

LIST OF SYMBOLS

b - Normalized propagation constant

c - Speed of light; Phase velocity [m/s]

B - Magnetic flux-density complex amplitude [Wb/m2]

d - Differential

div - Divergence

D - Electric flux density [C/m2]

E - Electric field [V/m]

F - Force [kgms-2

]

H - Magnetic-field complex amplitude [A/m]

H - Magnetic field [A/m]

j - (-1)1/2

integer

J - Electric current density [A/m2]

k0 - Free space propagation constant [rad/m]

l - length [m]

m - number of modes

M - Magnetization density [A/m]

n - Refractive index

ng - Refractive index of guiding layer

ns - Refractive index of substrate layer

nc - Refractive index of cladding layer

NA - Numerical Aperture

ρ - Electric polarization density [C/m2]

Q - Electric charge [C]

T - Time [s]

TE - Transverse electric wave

TM - Transverse magnetic wave

TEM - Transverse electromagnetic wave

xvii

ϕ - Total internal reflection phase shift [rad]

V - Voltage [V]

β - Propagation constant [rad/m]

� - Electric permittivity of medium [F/m]

�0 - Electric permittivity of a free space [F/m]

�r - Relative dielectric constant of the material[F/m]

� - Angle

�c - Critical angle

� - Wavelength [m]

�0 - Free space wavelength [m]

� - Magnetic permeability [H/m]

�0 - Magnetic permeability of free space [H/m]

� - Angle in a cylindrical coordinate system

� - Angular frequency [rad/s]

∂ - Partial differential

∇ - Gradient operator

∇ . - Divergence operator

∇ x - Curl operator

∇ 2 - Laplacian operator

xviii

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Source code for Buried waveguide modeling by 76

using MATLAB

CHAPTER 1

INTRODUCTION

1.1 Introduction

The use of optical signals as a means for carrier in telecommunications is

evident since the invention of laser in 1960 [2]. It was in 1969, Miller introduced the

term ‘Integrated Optics’ involves the realization of the optical and electro optic

elements which may be integrated in the large numbers on one chip means of the

same processing techniques used to fabricated integrated electronic circuits [7].

Demand for integrated optic circuits comes from the side of the light wave

communication system which required in addition to laser source, components such

as optical switches, modulators and power splitters.

Material science and fabrication technology have advanced in recent years at

an explosive rate, creating a strong interest in the possibility of extending and

replacing several functions traditionally performed by electronics with optical

devices. Day by day, new optical devices are being design, investigated and

demonstrated in research laboratories throughout the world .This development,

combined with the rapidly increasing demand for more sophiscated and widespread

telecommunication services, has put very strong pressure on the continuous

development of accurate and efficient methods for the analysis of the devices and

systems involved.

2

Dielectric waveguide are fundamental components of devices and systems both

in microwave and optics, and as such, a full understanding of how electromagnetic

waves propagate in complicated waveguide structures is essential. While in

microwaves dielectric waveguides constitute only one of the types of waveguide in

use, in optics they are practically the only form of waveguide structure. They play an

essential role in optoelectronics, being in the form of optical fibers, fiber lasers and

amplifies or in integrated optics where most devices are made from optical

waveguides of different configurations properties.

Buried optical waveguide channel are higher-index guiding layers are

selectively formed near the substrate surface by metal in diffusion, ion exchange, ion

implementation, and light/electron-beam irradiation. The buried type of 3-D

waveguide has the advantages that the propagation loss is typically lower than

1db/cm with a smooth guide surface and that planar electrodes are easily placed on

the waveguide to achieve light modulation and switching. The buried 3-D waveguide

is thus the most suitable for optical waveguide devices.

1.2 Objectives

The objective of this project is to develop simulation software for buried

waveguide structure. It also to analyst buried waveguide channel using finite

difference method and to aim for educational study on computer analysis and design.

1.3 Scope of the work

Scope of this project begins with:

i) Understanding the optical waveguide concept (buried optical waveguide).

ii) Understanding the finite difference method as a chosen method for analyzing

the waveguide.

iii) Understanding the MATLAB and GUI (graphical user interface) software as

a tool to build the simulation program and to get the accurate result.

3

1.4 Problem Statement

The propagations characteristic of optical waveguides can be calculated by

solving Maxwell’s equation, but this is difficult task and time consuming also

involve tedious or rigorous mathematically. Furthermore, Mathematical analysis not

many software available for characterization of optical waveguide and expensive

software available and also needs high speed computer such as mainframe computer.

In this project, numerical solution, finite difference method using computer (matlab

software) provide the solutions to overcome the problems and give advantages over

analytical approximation solutions. Table 1.1 shows the differentiation analysis of

optical waveguide between before software analysis and after software analysis.

Table 1.1: Differentiation before software developed and after software

developed

Before software developed After software developed

Formulation

Fundamental laws explained

briefly

Formulation

Exposition of relationship of

problem to fundamental laws

Solution

Elaborate an often complicated

method to make problem tractable

Solution

Easy-to-use computer method

Interpretation

In-depth analysis limited by time-

consuming solution

Interpretation

Ease of calculation allows holistic

thought and intuition to develop;

system sensitivity behavior can be

studied

4

1.5 Motivation of the Work

The analysis where this software simulation hopefully can be used in the

laboratory or classroom as a friendly user tool. Besides that, this analysis given

accurate, fast, effective, low cost and can be used using personal computer. The

mathematical is formulated so that with give accurate results but not involves tedious

or rigorous mathematical equation.

1.6 Methodology

Implementation and works of the project are summarized into the flow chart as

shown in Figure 1.1. Gantt charts as shown in Figure 1.2 and Figure 1.3 show the detail

of the works of the project that had been implemented in the first and second semester.

Figure 1.1: Overview Project Flow

Research an optical waveguide generally

and buried optical waveguide specifically

Study the mathematical equation with

finite difference method solution (FDM)

to get parameter and characteristic for

optical waveguide analysis.

MATLAB programming and GUI

development

Result and analysis

Thesis writting

5

Figure 1.2: Gantt chart PSM 1

n

o

ACTIVITY w

1

w

2

w

3

w

4

W

5

w

6

w

7

w

8

w

9

w

1

0

w

1

1

w

1

2

w

1

3

w

1

4

w

1

5

1 Meeting with

supervisor

2 Thesis title

confirmation

3 Making

proposal-

objective

4 Making

proposal-

Methodology

&

Approaches

5 Making

proposal -

Expected

Result

6 Complete and

submit PSM1-

1 form

7 Create The

Gantt Chart

8 Study optical

waveguide &

buried

waveguide

9 Study

Maxwell

equation and

finite

difference

method

10 Study Matlab

simulation

and GUI

11 Preparation

for PSM 1

seminar

12 PSM 1

seminar

13 Writing final

report of

PSM1

14 Submit final

report PSM 1

6

Figure 1.3: Gantt Chart for PSM 2

N

O ACTIVITY W

1

W

2

W

3

W

4

W

5

W

6

W

7

W

8

W

9

W

1

0

W

1

1

W

1

2

W

1

3

W

1

4

W

1

5

1 Meeting with

supervisor

2 Thesis writing-

chapter1

(introduction)

3 Thesis writing-

chapter2

(literature review)

4 Thesis writing-

chapter3

(mathematical

analysis)

5 Submit the progress

project form2-0

6 Run MATLAB

simulation and

build GUI

7 Result and analysis

8 Thesis Writing-

chapter4

(MATLAB and

GUI development)

9 Thesis writing-

chapter5

(result and analysis)

10 Thesis writing-

chapter6

(conclusion and

recommendation)

11 Submit a brief

project formPSM2-

1

12 PSM2 –TOP

Exhibition (

seminar and demo)

13 Final check and

submit final draft

14 Submit the

hardcopy and the

softcopy

7

1.7 Structure of thesis

This thesis consists of six chapters including this introduction follow the

university thesis standard. In second chapter present overview of an optical

waveguide structure. Dielectric waveguides are the structures that confine and guide

the light in the guided-wave devices and circuits of the integrated optic in a region of

higher effective index that surrounding media. Buried structure waveguide, which

are integrated optical component and as well as methods for analyzing the

electromagnetic fields. The analytical methods for describing propagation along

waveguides using the single modes are presented.

Analysis of optical waveguide will be present at chapter three. Based on the

Maxwell equations, a set of scalar wave equations governing the propagation of E-

field and H-field in the straight waveguides are derived. The propagation

characteristic of buried waveguide with straight and bending structure have been

investigated at wavelength of 1.55 micrometer. Then, an optical waveguides have

been analyzed using the numerical method based on finite difference approach.

Meanwhile the chapter 4 focused on propagation characteristic and the field

of the guided modes can be calculated very efficiently on a personal computer with

modest computational time. Three dimensional (3D) figure plot and contour profile

field in waveguide using MATLAB software will be determine as result analysis.

Beside that chapter 5 present on the analysis of the result and discussion which

analysis the performance in terms of the waveguide modes and its confinement

depends on parameters that include dimension on the core waveguide and

relationship between core and the cladding refractive index will be an optimized.

Finally, the main contributions are summarized in chapter six to conclude this thesis.

CHAPTER 2

OPTICAL WAVEGUIDE

2.1 Introduction

The increasing complexity of modern devices in optics rules out accurate

analytical treatment and so it has maintained a critical demand for accurate and

efficient computer modeling. Computer modeling techniques that allow an accurate

simulation of the behavior of real devices have become increasingly more common

and popular with the availability of cheaper and ever more powerful computer

resources. Optical waveguide had been used widely and becoming fast as a major

reason in development of optical circuit that gives more advantages than

conventional way. Thus, the analysis and modeling optical waveguides had been

given special attentions by researchers as important step before waveguides can be

practically used.

2.2 Background

The rapid development in fields such as fiber optics communication

engineering and integrated optical electronics have expanded the interest and

increased expectations about guided-wave optics, in which optical waveguides play a

central role. Optical waveguides for optical fibers and optical integrated circuits

utilize a wave phenomenon that traps the light locally and guides it in any direction,

9

although their propagation lengths differ greatly [2]. In order to develop new optical

communication systems or optical devices, we need to fully understand the principle

of optical guiding, while obtaining accurate quantitative propagation characteristic of

waveguides and utilizing them effectively in actual design. The generally meaning

optical waveguide is the��physical structure that guides electromagnetic waves in the

optical spectrum. Common types of optical waveguides include optical fiber and

rectangular waveguides. Channel of optical waveguide such as buried, ridge, rib, slab

and surface embedded. It is used as components in integrated optical circuit or as the

transmission medium in local and long haul optical communication system.

2.3 Buried Optical Waveguide channel

A buried waveguide is made by modifying the properties of the substrate

material so that a higher refractive index is obtained locally. Most fabrication process

results in a weak, graded index guide buried just below the surface. Diffusion is often

used to fabricate this type of guide. For example Titanium metal can be diffused into

Lithium Niobate substrates, by putting the metal strip about 10000A thickness follow

by higher temperature (approach 10000

C) for three to nine hours. This is known as

Ti:LiNbO3 [5] process as shown in figure 2.1. The additional of that metal act as an

impurities that cause a change of the refractive index.

Figure 2.2 illustrate configuration of a dielectric channel waveguide (buried). The

surrounded channel with the refractive index n1

greater than n2, n3

, and n4, is called

the core, or, the guiding channel. And the other areas with the lower refractive

indices are called the claddings, or, index buffering layers. This whole structure is

usually built on a substrate, such as silicon wafer, silica, glass or PC board.

In the structure shown in Figure 2.2, n2, n

3, and n

4 can be the same, which

makes the structure a buried channel waveguide. n2

and/or n3

may be air. Depending

on the geometric structure, refractive indices, and wavelength, certain modes can be

supported and light can therefore propagate through the waveguide [4].

10

Ti:LiNbO3

Figure 2.1: Buried optical waveguide

Figure 2.2: Buried Optical waveguide for integrated circuitry

11

2.4 Types of Waveguides

Optical waveguides can be classified according to their:

• geometry (planar, strip, or fiber waveguides)

• mode structure (single-mode, multi-mode)

• refractive index distribution step or gradient index)

• material (glass, polymer, semiconductor)

2.4.1 2-D Optical waveguides

Waveguides that trap the light only in the direction of thickness are called 2-

D optical waveguides or slab waveguides. It can be stepped or graded optical

waveguides based on distribution of its refractive index. Figure 2.3 shows the

simplest three layer waveguide structure. It is the simplest, most basic waveguide

structure.

Here, nf, ns and nc represent the refractive indexes of the thin film, substrate,

and upper cladding, respectively. When the upper cladding is air, as in most cases,

nc=1. This type of optical waveguide is called a three layer dielectric waveguide or

an asymmetric slab waveguide. The relationship among the refractive indexes is

nc<ns<nf , and the light is trapped inside the thin film [1] . In the case of rectangular

waveguide geometry the presence of the air-semiconductor interface also reduces the

symmetry, to only x-direction, as shown in Fig.2.5.

The cross-sectional profile of a buried waveguide with rectangular core cross

section, lying near to the air-semiconductor boundary is given in Fig.2.6. The

waveguide of core refractive index n1, width 2W and thickness 2H, is buried in a

semiconductor of refractive index n2 at a depth D below the air boundary. The cross

section is divided in two regions: region I which encloses the rectangular waveguide

core, ( | x | < W) and region II ( | x | > W) [6] .

12

y

nc= cladding refractive index

z

nf =film refractive index

ns=substract refractive index

Figure 2.3: Three layer dielectric waveguide

Figure 2.4: 2-D optical buried waveguide channel

Figure 2.5: Planes of symmetry of (a) deeply buried waveguide, (b) shallowly

Buried waveguide

13

Figure 2.6: The cross-sectional profile of the air-clad buried waveguide

2.4.2 3-D Optical Waveguides

A 2-D optical waveguides can trap light in the direction of the thickness (y

direction), but allows light to spread in the horizontal direction(x direction). In order

to facilitate the construction of optical integrated circuits, various types of 3-D

optical waveguides as shown in fig.2.7, or optical channel waveguides, which trap

the light in both x and y directions, have been devised.

Figure 2.7: 3-D Buried waveguide channel

14

2.5 Buried Optical Waveguides Application

The buried optical waveguide is a very important component and suitable for

integrated optical technologies, finding widespread and significant inferometers,

splitters, and switches and also as an optical interconnects such as bends and

junction. The higher index guiding layers are selectivity formed near subtracts

surface by metal in diffusion, ion exchange, on implantation and light beam

radiation. The buried type of channel waveguide has the advantages that that the

propagation loss in typically lower in 1 dBm with smooth surface. It’s usually

suitable for bend waveguide with small curvature radii due to its characteristic that

strongly transverse confinement of scattering loss due to waveguide wall roughness

[3].

An optical waveguide that is uniform in the direction of propagation, as

shown in Fig.2.1 is the most basic type of waveguide, but this alone is not sufficient

for construction of an optical waveguides is placed on the substrate to construct an

optical circuit with desired features. Corner –bent waveguides, S-shaped waveguides,

and bent waveguides are used to change the direction of the light wave. Tapered

waveguides are used to change the width of waveguides; branching waveguides and

crossed waveguides are used for splitting, combining, and interference; and optical

waveguide directional couplers and two mode waveguide couplers are used for

coupling. Waveguide gratings, with a periodic structure in the direction of

propagations, play many important roles in the optical integrated circuit, such as

wavelength filter, mode converter, reflector, resonator, demultiplexer, etc.

Waveguide gratings are also used widely as a laser element, such as a distributed

Bragg reflector (DBR) laser or a distributed feedback (DFB) laser.

15

2.5.1 Fabrication process.

Semiconductor device fabrication is the process used to create chips, the

integrated circuits that are present in everyday electrical and electronic devices. It is

a multiple-step sequence of photographic and chemical processing steps during

which electronic circuits are gradually created on a wafer made of pure

semiconducting material. Silicon is the most commonly used semiconductor material

today, along with various compound semiconductors.

The entire manufacturing process from start to packaged chips ready for

shipment takes six to eight weeks and is performed in highly specialized facilities

referred to as fabs [ ]8 .

Figure 2.8: NASA’s Glenn Research Center (fabrication process)

16

2.6 Optical Waveguide Analysis techniques

The propagation characteristics of optical waveguides can be calculated by solving

Maxwell’s equations but this is not easy task. There are many reasons that optical

waveguide analysis is difficult; some of the major reasons are listed below:

1) Optical waveguides have complex structures.

2) The general propagation mode is the hybrid mode.

3) Some optical waveguides have an arbitrary refractive index distribution (graded

Optical waveguides), as in doped optical waveguides and non –uniform core

optical fiber.

4) The range of electromagnetic field distribution is open, or infinite.

5) Anisotropic materials and nonlinear optical materials are used to increase the

range of performance.

6) Materials with a complex refractive index, such as semiconductors and metals,

are used. To overcome these difficulties, various methods have been developed

for the analysis of optical waveguides. Such methods may be roughly classified it

analytical approximation solutions and numerical solutions using computer.

17

2.6.1 Analytical Approximation Solutions for Optical Waveguides

An exact analytical problem solution can be obtained for stepped 2-D optical

waveguides and stepped optical fibers .if, however, the waveguide has an arbitrary

refractive index distribution and exact analysis is no longer possible. Therefore,

various types of analytical approximation solutions have been developed for 2-D

optical waveguides in which the refractive index changes gradually in the thickness

direction, and for optical fiber whose refractive changes gradually only in the radial

direction.

In the case of 3-D optical waveguides for optical integrated circuits and non

axisymmetrical optical fiber, hybrid mode analysis is required to satisfy the boundary

conditions, even if the individual materials that constitute the waveguide are

homogenous. However, the analytical approximation solutions developed for these

optical waveguides generally do not treat them as hybrid mode, and therefore, the

accuracy of the solution deteriorates near the cutoff frequency. The Marcatili method

(MM) and the effective index method (EIM), known as typical analytical

approximation solutions for 3-D optical waveguides, and the equivalent network

method (ENM), which enables hybrid-mode analysis [9].

18

2.6.2 Numerical solutions for Optical Waveguides.

Numerical solutions can be grouped into the domain solution, which includes

the whole domain as the operational area, and the boundary solution, which includes

the whole domain as the operational area, and the boundary solution, which includes

only the boundaries as the operational area. The former is also called a differential

solution, and the latter, an integral solution. The domain solutions include the finite

element method (FEM), finite difference method (FDM), variation method (VM) and

multilayer approximation method(BEM), point matching method (PMM) and mode-

matching method(MMM).For the analysis of graded optical waveguides, the use of

boundary solutions is difficult. The finite difference method (FDM) is a simple

numerical technique used in solving problem that uniquely defined by three things:

1) A partial differential equation such as Laplace’s or Poisson’ equation

2) A solution region

3) Boundary and/or initial conditions

A finite difference method to Poisson’s or Laplace’s equation, for example, proceeds

in three steps:

1) Dividing the solution region into a grid of nodes

2) Approximating the differential equation and boundary conditions by a set of

Linear algebraic equations (called difference equations) on grid points within

solution region.

3) Solving this set of algebraic equations.

CHAPTER 3

MATHEMATICAL ANALYSIS

3.1 Overview of numerical method

Numerical methods solve Maxwell’s equations exactly and the results the

provide are often regarded as benchmarks. Integrated waveguides, by contrast, are

usually rectangular structures which confine the light in both directions. Because

they do not have planar or cylindrical symmetry, the eigenmodes of these structures

cannot be computed analytically. Instead, numerical techniques must be used to solve

the eigenvalue equations. There are many different numerical techniques for solving

partial differential equations such as the Finite Difference (FD), Finite Elements (FE)

and Finite Difference Beam Propagation (FDBPM) methods which are robust,

versatile and applicable to a wide variety of structures. Unfortunately, this is often

achieved at the expense of long computational times and large memory requirements,

both of which can become critical issues especially when structures with large

dimensions are considered or when used within an iterative design environment.

20

3.2 Finite Difference Methods (FDM)

The FD method is one of the most frequently used numerical techniques

[6].Its application to the modeling of optical waveguides dates from early eighties,

originally evolving from previous FD models for metal waveguides [8]. The FD

method discretisizes the cross-section of the device being analyzed and is therefore

suitable for modeling arbitrarily shaped optical waveguides which could be made out

of isotropic homogeneous, inhomogeneous, anisotropic or lossy material. In the finite

difference technique, differential operators are replaced by the difference equations,

as example, the first derivative of a function f (x) could be approximated as

( ) ( )'( )

f x x f xf x

x

+ ∆ −≈

∆ (1)

This is a very intuitive approximation and mostly elementary calculus define

the fist derivative of a function to be just such a finite difference in the limit that

x !"0 .This equation (44) fails entirely if the function f (x) is discontinuous in the

interval x !"x #" x .Maxwell equations predict that the normal component of the

electric field are discontinuous across abrupt dielectric interfaces. Therefore in order

to develop an accurate model for eigenmodes of an optical waveguide, it must

construct a finite difference scheme which accounts for the discontinuities in the

eigenmodes [7].

The essence of the FD is to map the structure onto a rectangular mesh [8] [9]

as example shown in Figure 3.3illustrates a typical finite difference mesh for ridge

waveguide, allowing for the material discontinuities only along mesh lines. The

refractive index profile has been broken up into small rectangular elements or pixels,

of size x $" y .Over each of these elements, the refractive index is constant.

Thus, discontinuities in the refractive index profile occur only at the boundaries

between adjacent pixels. Because of the index profile is symmetry about the y -axis,

only half of the waveguide needs to be included in the computational domain [7].

21

The computational window must extend far enough outside of the waveguide

core in order to completely encompass the optical mode. The finite difference grid

points, which the discrete points at fields are sampled, are located at the centre of

each cell. Some finite difference schemes instead choose to locate at the grid points

at the vertices of the each cell rather than at the centre. This approach works well for

finite difference schemes involving the magnetic field H which is continuous across

all the dielectric interfaces. However, the normal component of the electric field E is

discontinuous across an abrupt dielectric interface, may leads to an ambiguity if the

grid points are placed at cell vertices. Figure 3.4 shows that the possible ways of

placing nodes on the mesh with a constant refractive index [10] and that node can be

associated to maximum of four different refractive indices [9].

Figure 3.1: A typical finite difference mesh for an integrated waveguide. The

refractive index profile n(x, y) has been divided into small rectangular cells over

which n(x, y) is taken to be constant.

Figure 3.2: Locating nodes (a) on centre of a mesh cell or (b) on mesh points.

22

We will begin by deriving the finite difference equations for the scalar

eigenmode approximation. Recall in this approximation nave been replaced by a

single scalar eigenmode equation for one of the transverse field components denoted

%(x, y) as equation (49).This approximation is valid for “weakly-guiding”

waveguides in which the refractive index contrast is small.

2 2

2 2

02 20k

x yβ

� �∂ ∂+ + Φ − Φ =� �

∂ ∂� � (2)

Or

22 2

2 20

Tk

x y

� �∂ ∂+ Φ + Φ =� �

∂ ∂� � (3)

The parameter kT determines the propagation constant &" through,

2 2 2

Tk ω µε β= − In order to translate this partial differential equation into a set of

finite difference equations, we must approximate the second derivatives in terms the

values of %(x, y) at surrounding grid points as

(4)

This approximation can be derived by performing a second order Taylor expansion

of field about the grid point under consideration, P. With this notation, the central

difference approximations of the derivatives of %"at the ( i, j ) th node are

2

( 1, ) 2 ( , ) ( 1, ),

( )xx

i j i j i ji j

x

Φ + − Φ + Φ −Φ ≈

∆ (5)

2

( , 1) 2 ( , ) ( , 1),

( )tt

i j i j i ji j

t

Φ + − Φ + Φ −Φ ≈

∆ (6)

''

2

( ) 2 ( ) ( )( )

f x x f x f x xf x

x

+ ∆ − + − ∆≈

∆

23

The differential of scalar, semivectorial or vector polarized wave equation is then

approximated, usually with a five point FD form in terms of the fields at the nodes of

the mesh point. For improved convergence more accurate difference forms can be

used [6].Taking into account the continuity and discontinuity conditions of the

electric and magnetic field components at the grid interface the eigenvalue problem

becomes of the form

[ ] 2A βΦ = Φ

(7)

where 'A ! is a band matrix which is symmetric for scalar modes [6] or non

symmetric for semivectorial[10][13] and vector modes. "! , the modal propagation

eigenvalue and #!is the eigenvector representing the modal field profile. Whilst FD

method is in principle straightforward to implement, numerical modeling of the open

boundaries, typical of optical waveguides needs care. The problem is overcome by

either (a) enclosing a structure in a sufficiently large rectangular box which does not

disturb the penetration of the field and on which the zero field condition is imposed

or (b) imposing an open boundary or matched boundary condition on the box sides

for example by assuming exponential decay of the field in the outward normal

direction. However when the device operates near cut-off the size of the box for both

cases has to be sufficiently large to allow for substantial penetration of the field into

the substrate. The accuracy of the method therefore depends on the mesh size, the

assumed nature of the electromagnetic field and the order of the FD scheme used. In

this projects work open boundary or matched boundary condition and non-uniform

meshes have been proposed such that a finer mesh is applied in the region where the

field changes rapidly and a coarser mesh for regions where field is stationary to make

the FD method more flexible for modeling of large and complex geometries The

variational method is used to establish the eigenvalues and the eigenvectors and the

successive over relaxation method (SOR)[11]]has been considered as the

acceleration factor as an improvement that speed the convergence process.

24

3.3 Numerical methods solve Maxwell’s equation exactly

The basic formulation that governs the propagation of light in the optical

waveguide isa Maxwell’s equations that consist of the following [10]:

. 0

. V

d BX E

d t

d DX H J

d t

B

D ρ

−∇ =

∇ = +

∇ =

∇ = (8)

Where:

E : Electric field intensity

H : Magnetic field intensity

D : Electric field

B : Magnetic field density

Vρ : Electric charge density

J : Current density

Assuming that the waveguide is made of isotropic, homogeneous and free of source

medium, Equation (8) will become:

. 0

. 0

d BX E

d t

d DX H

d t

B

D

∇ = −

∇ =

∇ =

∇ = (9)

25

Manipulating Equation (9) will produce a so-called Helmholtz wave equation that

adequately describes the propagation of electromagnetic wave. The wave equation

for the electric field can be presented as:

22

2

d EE

d tµ ε∇ = (10)

Considering a y-polarized TE mode which propagates in the z-direction and � as a

propagation constant in longitudinal direction will then yield:

2 2

2

2 2

y y

y y

d E d EE E

dx dyβ ϖµε+ − =−

(11)

Taking 2k ϖ as the total propagation constant which combine the horizontal and

vertical part will then produce:

222 2

2 2( ) 0

y

y

d Ed Eyk E

dx dyβ+ + − =

(12)

Knowing that k is a multiplication of free space propagation constant, k0 and

refractive index, n for respective layer, Equation (12) can be written in the form of:

222 2 2

02 2( ) 0

y

y

d Ed Eyk n E

dx dyβ+ + − =

(13)

Equation (6) is the eigenfunction that need to be solved for determining the

eigenvalue of β and TE field distribution throughout the medium of interest.

26

In the application of finite difference method to solve Equation (6), the E

field and the refractive index, n, is considered to be a discrete value at respective x-

and y coordinate and bounded in a box, which represent the waveguide cross section.

The box is divided into smaller rectangular area with a dimension of x and y in

x- and y- directions respectively [8]. Brief description is given in Figure 1, where the

waveguide cross section area is divided into M × N grid lines, which corresponds to

the mesh size of x and y .

Considering the Ey having component in x and y direction E(x,y), Taylor’s expansion

is applied to Equation (13) where the differential components are obtained as

follows:

2

2 2

2

2 2

( 1, ) ( 1, ) 2 ( , )

( , 1) ( , 1) 2 ( , )

d E E i j E i j E i j

dx x

d E E i j E i j E i j

dy y

+ + − −=

∆

+ + − −=

∆

(14)

27

Combining Equations (6) and (7) will produce a basic equation for obtaining the

electric field:

2

2

2

22

2 2 2 2

0

( 1, ) ( 1, ) ( ( , 1) ( , 1))

( , )

2 1 ( ( , ) )

xE i j i j E i j E i j

yE i j

xx k n i j

yβ

� �∆+ + − + + + −� �

∆� �=� �� ∆� �+ − ∆ −� �� ∆� ��

(15)

Where i and j represent the mesh point corresponding to x and y directions

respectively. If Equation (13) is multiplied with y E and operating double integration

towards x and y, it will yield:

2 2

2 2

02 2

2

2

y y

y y

y

d E d EE k n E dxdy

dx dy

E dxdyβ

� �� + +� ��

� �� =

��

�� (16)

Equation (9) is called Rayleigh Quotient. Further application of finite difference

method and trapezoidal rule to Equation (16) shall then produce:

(17)

Equation (17) is obtained by applying Dirichlet boundary condition which states the

E (i, j) = 0 at the boundary. Initial value of E (i, j) = 1 is set for other points. In order

to speed up the process, a successive over relaxation (SOR) parameter [8, 9], C

introduced to Equation (15), which states that the iteration will converge faster for C

28

between 1 and 2. According to [9], taking SOR parameter into consideration will

modify Equation (15) to be:

(18) Alternate usage of Equations (17) and (18) for the decided tolerance will produce the

final value of and the TE field distribution for the entire waveguide cross section.

neff of the fundamental mode is related to the propagation constant by 2

βλ

π. Due to

difficulties in interpreting small differences of effective index values, a more

sensitive comparison is made by introducing a normalized propagation constant [4],

2 2

2 2

eff substrate

guide substrate

n nb

n n

−=

− (19)

This mathematical calculation will be developed into computer programming using

Matlab R2006a and the result can be used to plot graph.

CHAPTER 4

MATLAB AND GUI DEVELOPMENT

4.1 Introduction of MATLAB software

MATLAB was mainly designed to solve any type level of mathematical

problem for analysis purpose. Beside that, good capability of the software to deal

with various useful problems concerned with the modeling, evaluation and

optimization of the 3D waveguide structure performance. The Figure 4.1 shows that

how the MATLAB works to develop software for optical waveguide simulation and

the overall methodology of project will be given by flow chart in Figure 4.1.

4.1.1 Basic MATLAB features

MATLAB provides a logical solution to evaluate a number of commands or

wish to change value of one or more variables in one prompt. It allows placing

MATLAB commands in a simple text file and then telling MATLAB to open the file

and evaluate commands exactly. These files are called script files or simply M-files.

The term M-files recognizes the fact that script file name must end with the

extension.m example, amp1.m to create a script M-files on a personal computer,

choose New from the File menu and select M-File. This procedure brings up a text

editor window where you enter MATLB commands. On other platforms, it is

convenient to open a separate terminal window and use your favorite text editor in

that window to generate script M-File. Script files are also convenient for entering

30

large arrays that may, for example, come from laboratory measurements. By using a

text editor to enter one or more arrays, the editing capabilities of the editor make it is

easy to correct mistakes without having to type the whole array in again.

The utility of MATLAB comments is readily apparent when using script files

as show in M-file.m file. Comments allow you to document the command found in

script file so that they are not forgotten when viewed in future. After running script

files, the results of the command are displayed in the Command Window with

variable identified. The plotting result for responses of command script files will be

display on Figure. waveguides. An example of computational and software

development step is as shows in Figure 4.4.You can see the MATLAB source code

simulation propagation APPENDIX A.

31

Figure 4.1: The flow chart show that how MATLAB work

32

YES

NO

Figure 4.2: The flow chart of the programming process

Preliminary studies Topic research and

info gathering

Mathematical equations for derivation and

numerical method

TASK: Development program MATLAB

in 3 D and simulation-model waveguide

structure (buried)

Test and run

Developed with Graphical User Interface

(GUI)

Trouble-shoot and

reprogramming

Update and upgrade

End

Success?

33

4.2 Basic Graphic User Interface (GUI)

The MATLAB programming environment is flexible and there are many

ways to achieve the same functionality, especially in GUI programs. There are many

advantages when we use the GUI programs, as an example, we can develop a simple

graphical application, demogui. This application will display a window with an

editable text field containing a number (initially "1") and two buttons which will

allow us to increment or decrement this number by 1. The design of the user

interface and the functionality of the application are often the most difficult aspects

of GUI programming; the programming itself is not that hard. All functionality is

programmed into a single m-file with a single argument which serves as a function

selector. The various operations are to be implemented by calling this m-file with

different values for the selector. The initialization of the application is achieved by

calling demogui with no arguments. In Matlab, GUI can be designed using GUIDE.

GUIDE is the MATLAB graphical user interface development environment. It

provides a set of tools for creating graphical user interfaces (GUIs). It use to simplify

the process of designing and building GUIs.

4.2.1 User of GUIDE

1) Lay out the GUI

It can lay out a GUI easily by clicking and dragging GUI components such as

panels, buttons, text fields, sliders, menus and so on. The GUIDE stores the

GUI lay out in a FIG-file.

2) Program the GUI

GUIDE automatically generates an M-file that controls how the GUI

operates. M-file initializes the GUI and contains a framework for the most

commonly used callbacks for each component (the commands that execute

34

when a user clicks a GUI component). We can edit the code of callbacks in

M-file Editor.

4.2.2 Starting GUIDE

The GUIDE can be start by typing ‘guide’ at the MATLAB command

window. Then, GUIDE Quick Start dialog box will be displayed. In Matlab, there are

10 styles of Matlab Uicontrol objects. As example, Push Buttons, Toggle Buttons,

Check Box, Radio Button, Editable text, List Box, Pop-up Menu, Slider, Frame and

Static Text.

4.3 ‘My GUI’ Concept

‘My GUI’ name will be given of this project. From main page,user can

explore many section of Buried optical waveguide with just click the button. The

EXAMPLE section have 3 subsection which waveguide 3x3, waveguide 5x5,

waveguide 7x7.The objective to build this section to show the 3D figure of refractive

index, optical normalized power and e-field profile with influence of air and larger

thickness and width value.Next section is CALCULATION section, user just put the

parameter of core thickness and core width,the result of effective index and

normalized propagation constant will out. ANALYSIS section show the graph of

effective index and normalized propagation from CALCULATION section.Last

section is APPLICATION which it will give briefing and idea to the user about

generally application and data sheet of optical waveguide.In APPLICATION section

have 4 subsection such as optical concept, mathematical equation, material/substrate

application and optical devices (APD Preamplifier, PIN Photo Diode, Optical fiber,

Fiber Spec Corning, Laser Diode and Fabrication Process). Figure 4.3 shows the

overview plan of ‘My GUI’ concept and figure 4.4 – figure 4.33 shows the ‘My

GUI’ output and pop up with friendly user.

35

Figure 4.3: Overview plan of ‘My GUI’

36

Figure 4.4: Main Page of ‘My GUI’

37

Figure 4.5: Main page for EXAMPLE section- waveguide (3 x 3)

Figure 4.6: Refractive index profile button- n core (3.44),n cladding (3.34) and

n air (1)

38

Figure 4.7: Optical Normalized Power button - 0.7010

Figure 4.8: E-field profile button

39


Figure 4.10: Refractive index profile button- n core (3.44),n cladding (3.34) and

n air (1)

40



41


Figure 4.14: Refractive index profile button- n core (3.44), n cladding (3.34) and

n air (1)

42



43

Figure 4.17: Calculation part in ‘My GUI’

44

Figure 4.18: Analysis section in ‘My GUI’

Figure 4.19: neff graph (left) and b Graph (right)

45

Figure 4.20: Main page of application in ‘My GUI’

46

Figure 4.21: Optical concept button

Figure 4.22: Symmetry waveguide (left) and ray transmission (right) button

47

Figure 4.23: Mathematical Equation button

48

Figure 4.24: Material application button

Figure 4.25: figure 1 (left) and figure 2 (right) from material application button

49

Figure 4.26: Main pages of optical devices application button

50

Figure 4.27: APD Preamplifier application button

Figure 4.28: Photo diode application button

51

Figure 4.29: Optical fiber application button

Figure 4.30: Fiber Spec Corning application button

52

Figure 4.31: Laser diode application button

Figure 4.32: Fabrication Process button

CHAPTER 5

RESULT, ANALYSIS AND DISCUSSION

5.1 Result Process

Using MATLAB software it will be design 3D dimensional structure of

buried waveguide channel and it will be user friendly for waveguide analysis on

computer modeling. In This project to get the finally result must have two stage, first

stage is MATLAB M-file result and second stage is GUI result.

5.1.1 First stage

The software consists of three main components which are inputs parameters,

processing data and output. The input parameters for the software can be divided into

two categories as shown in table 4.1. First categories of inputs are required by the

algorithm of the Finite Difference Method. Second categories of inputs are used to

control the sequence of the application. Data from input parameters will be used for

calculating the output or to be transformed to other form of data.

54

Table 5.1: Categories of input

Categories Of Inputs

Types of Inputs Control Input

1)Rectangular waveguide dimension =

w x t

2)Refractive index , n core = 3.44,

n clad = 3.34

3)Mesh Size, dx = 0.01,dy =0.01

4)Wavelength = 1550 nm

Tolerance = 0.0001

Table 5.2: Processing Data

Input Processing data Output

1)Waveguide dimension:

thickness of cladding,

guiding and core

layer

2) Mesh size

Index = width / mesh size

Size of mesh index

Such as N x M

Table 5.3: Final Output

Input Output

1)Electric field distribution

2)Propagation constant,�

1)Effective Index, neff

2)Normalized Constant

3)Three Graph:

i) Refractive Index Distribution

ii) 3D field distribution

iii) Contour plot of field distribution

55

5.1.2 Second stage

After done with debugging and testing the code in M-file editor, graphical

user interface (GUI) was applied to the code.GUI Builder is used for this purpose.

The GUI has three sections as shown in the Figure 4.7.The Buried structure figure is

used as a reference for the user to put the input parameters for the simulation. The

input parameters are divided into three section; Waveguide dimension, Refractive

index and Analysis setting. CALCULATE button on the below right of the GUI need

to be pushed to start the simulation. The output for the simulation; Effective index

and Normalized Propagation Constant will be shown on the same GUI. A window

containing three figures; 3D plot contour, refractive index profile and field

distribution profile also will pop up after the simulation.

5.2 Calculation result and Buried optical waveguide figure presentation

Figure 5.1 - 5.9 shows the waveguide structure of buried waveguide

channel.n1 is the refractive index upper cladding, n2 is the refractive index core and

n3 is the refractive index lower cladding. Meanwhile t1 represent of upper cladding

thickness and w stand for core width. This project focused on buried square channel

that symmetrical and straight waveguide. Have a little bit assumption for the

calculation which assumes no air at the waveguide, t1 and t3 was fixed at 2

micrometer and assume n upper cladding (n1) and n lower cladding (n3) equal to

3.34. Beside that n core (n2) equal to 3.44 also assume lambda wavelength is 1.55

micrometer.

Meanwhile, the figure also shows the refractive Index profile, E-field contour

plot with difference thickness. The value of E-field profile not constant and not

proportional because the value depends on core thickness and core width. Its mean

difference thickness and width influencing the optical normalized power and light

propagation in the waveguide. Contour plot shows where light wave propagate and

E-field radiated in waveguide either in core region or outside core region. The small

56

difference refractive index among core and cladding can give better performance of

electromagnetic field pattern so electric field energy will radiate into core region and

the single mode can propagate inside the waveguide. It will make contour plot

located at the centre (core region) of waveguide which prove it is a buried channel.

n1 t1=2µm

10µm 10µm

t2 n2

w

n3 t3= 2µm

Figure 5.1: Buried optical waveguide structure plan view

57

Figure 5.2 (a): The result of effective index, neff and normalized propagation, b

at 3 x 3 waveguide

Figure 5.2 (b): The figure of refractive index profile, E-field profile and E-field

contour plot output at waveguide 3 x3 from calculation section

58


at 3.5 x 3.5 waveguide


contour plot output at waveguide 3.5 x 3.5 from calculation section

59


at 4 x 4 waveguide


contour plot output at waveguide 4 x4 from calculation section

60

Figure 5.5 (a): The result of effective index,neff and normalized propagation,b




61


at 5x5 waveguide


contour plot output at waveguide 5 x 5 from calculation section

62





63


at 6 x 6 waveguide



64





65


at 7 x 7 waveguide



66

5.3 Effective index, neff and Normalized propagation constant, b analysis:

In order to determine the accuracy light intensity trapped inside the core area

within the structure, the effective index profile, neff should be in range between core

refractive index, ncore (n2) and cladding refractive index, n cladding (n1 and n3) ,

ncladding �neff �ncore. neff of the fundamental mode is related to the propagation constant

by 2

βλ

π. From the table 1(a) have 9 sample data neff that calculate from GUI which

from 3µm thickness to 7 µm thickness with rectangular channel. The range

neff,3.4281�neff�3.4294. From the data show that the neff in range between n core

and n cladding and it suitable with theory. The increasing of thickness will produce

the increasing of neff (figure 5.10 (a)). Therefore the value of � also increase and it

make the propagation light within the structure fully trapped into core active region

also propagation loss was decreased.

Due to difficulties in interpreting small differences of effective index values,

a more sensitive comparison is made by introducing a normalize propagation

constant,

2 2

2 2

eff substra te

guide substrate

n nb

n n

−=

−

The range of b from 3µm to 7 µm thicknesses was 0.3776 � b � 0.0241 as

shown at table 5.4. From the graph 5.10 (b), b was decreasing when thickness

increasing.

Table 5.4: 9 samples of data from GUI calculation (refer section 5.2)

t2(µm) 3 3.5 4 4.5 5

neff 3.4281 3.4314 3.4337 3.4357 3.4365

b 0.3776 0.2720 0.1994 0.1474 0.1089

t2(µm) 5.5 6 6.5 7

neff 3.4375 3.4382 3.4387 3.4392

b 0.0796 0.0568 0.0387 0.0241

67

0 1 2 3 4 5 6 73.428

3.43

3.432

3.434

3.436

3.438

3.44

3.442Effective Index (neff) Graph

Eff

ective I

ndex x

(neff

)

Thickness(um)

Figure 5.11 (a): Effective Index, neff graph

0 1 2 3 4 5 6 70

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Normalized propagation constant Graph

Norm

aliz

ed p

ropagation c

onsta

nt

Thickness(um)

Figure 5.11 (b): Normalized propagation constant, b graph

68

5.4 Comparison with previous analysis

The analysis of Buried rectangular waveguide is similar to that of the

dielectric guide in air. We study in this case the effect of anisotropy by considering a

buried guide of the same aspect ratio as the dielectric guide studied (t x w ,with w =

2t).From reference [14], the core has an anisotropic relative permittivity tensor with

components nx2=nz

2=2.31 and ny

2=2.19 and buried in a cladding of permittivity n2

2 =

2.05.

Figure 5.11 shows the dispersion characteristics for the lowest four modes of

propagation in the waveguide. Computed results agree very well with those obtained

by Ohtaka [15], Using a variational method and cylindrical harmonic function

expansions. His results have been used frequently as a standard for comparison.

Similarly to what was observed for the former example of a microwave dielectric

guide with isotropic core, the use of finite elements rather than simple truncation

greatly improves the accuracy of the solution in the low frequency range (kot <

3.5).The aspect ratio of the region divided into finite elements, the relative extent of

finite elements outside the core and indeed the mesh quadrilaterals.

Compare with this project result, although use difference refractive index as a

sample, but consider from effective index graph (see figure 5.10(a)) look neff

proportional with thickness. When thickness increase cause neff increase and it is

same with reference [14] and Ohtaka [15]. These project results are agreeable with

theory.

69

kot

Figure 5.12: Dispersion characteristic for the lowest four modes of an anisotropic

Rectangular dielectric waveguide

70

5.5 DISCUSSION

From the point of view of the electromagnetic analysis, Buried optical

waveguides can be characterized for not having closed boundaries, allowing the

fields to extend to infinity in the transverse direction. The wave guiding effect is not

produced by the presence of metallic walls but instead, being dielectric waveguides,

this is produced only by differences in the refractive index of materials involved.

Metal can be present, and indeed they are used in some optical guides, but their

behavior differs substantially to that observed at microwave frequencies where the

assumption of perfect conductivity is usually made. At optical wavelengths metals

show strong absorption, this can be represented by a complex permittivity or

refractive index. A dielectric material used in these guides often anisotropic and

some degree of absorption (loss) is common and unavoidable. Additionally, optical

waveguide frequently include active regions, effectively introducing a distributed

gain in the structure which can be represented in the same form as losses are treated,

that is, by a complex value of permittivity over those regions, this time with a

positive imaginary part. Also, leakage into the substrate is not uncommon. This can

occur in some optical wave guiding structures where the substrate or surrounding

material has a high refractive index. Leaky modes do not show an evanescent

behavior in the exterior region. They have complex propagation constants due to the

radiation loss and consequently they need a special treatment for their calculation.

Although increasing core thickness is another option theoretically, on a

practical level changing the core thickness is not desirable. A thick core has a lot of

side effects, such as higher thresholds for lasers, and introduces poorer saturation

characteristics for a semiconductor optical amplifier (SOA)[12].

The outputs for the simulation waveguide are influences by several factors

such as mesh size which mesh size are important factor in determine the accuracy of

the simulation process. Smaller mesh size will increase the accuracy of the Effective

Index and Normalized Propagation Constant. The mesh size also determine the

sharpness of the plotting either more accurate or not. But if the mesh size is too

small, the simulating will take a longer computational time. Another factor is

71

tolerance where tolerance input will determine the number of iteration that will be

process by the program. It is also contributing to the accuracy of the simulation

because the � used to calculate Effective Index and Normalized Propagation

Constant need to be converging. The smaller value of the tolerance will also increase

computational time. To determine the accuracy of this program, comparison was

made to other existing method. Results were compared to Finite Element Method.

CHAPTER 6

CONCLUSION AND RECOMMENDATION

6.1 Conclusion

A good design of the buried optical waveguide is intended to limit

propagation loss and the transition losses. So, in the integrated optical circuit, the

optimum design of the buried channel waveguide should support with low loss and

strongly optical confinement for practical implementation.

The propagation loss on straight waveguide dependence on the declaration

value of refractive index used between core and cladding waveguide. Besides that, it

wills dependence on value changers of lateral refractive index different whether it

can propagates in fully energy or not within the structure waveguide. Therefore, the

performance of buried waveguide will performed when refractive index different is

high. This lateral index different is produced by the dispersion of material refractive

indices and the electromagnetic different. So, the increased or refractive index

difference will produces strong an optical confinement. Besides that, core thickness

and core width influence the value of E-field, effective index and normalized

propagation constant. In conclusion, the simulation software in this project can helps

application of designed modeling performance especially aims for educational field

and industries. It also economical to user with cheaper price than available optical

software for example software from oversea that money exchange requirement.

73

6.2 Recommendation

There are two suitable recommendations to purpose in future works. In this

project, the implement of waveguide simulation was used in a symmetrical planar

waveguide. Firstly, I will recommend investigating an asymmetrical buried bend

waveguide as a medium used to further my simulation programmed. In order to

determine the accuracy of modeling techniques for calculating the result of integrated

optical waveguides, we should compare for other techniques such as Finite Element

Method (FEM) and Effective Index Method (EIM). The others software can be used

beside MATLAB, such as AUTO CAD and Beam Propagation Method (BPM) and

Bitline software, JAVA programming and Visual Basic programming.

74

REFERENCES:

1) Abu Sahmah Mohd Supa’at, Abu Bakar Mohammad & Norazan Mohd

Kassim,2002.Modelling techniques for rectangular dielectric

waveguides-Rib waveguides. Jurnal Teknologi,36(1) 129-143.

2) Palais J.C 1992, Fiber Optic Communication. Prentice Hall, Inc. A

Simon& Schuster, Eaglewood Cliffs, New Jersey.

3) Ruth A.Jarvis, November 2002, Photosensitive optical waveguides

devices and materials. Research School of Physical Sciences and

engineering, Australia National University, Thesis.

4) E.A Marcatili, Dielectric rectangular waveguide and directional coupler

for integrated optics,the Bell System Technical Journal September 1969,

pp.2071-2101.

5) Koshiba Masanori 1992.Optical Waveguide analysis. Publisher: New

York .Mac Graw-Hill 1992.

6) P.Sewell T.M Benson, M.Reed, P.C Kendell, “Transcendental equation

for the vectorial modes of buried waveguide, IEEE photonics.

7) Miller,SE 1969,Integrated Optics: An introduction, Bell System

Technical Journal,U8(7) 2059-2069.

8) Wikimedia Foundation, Inca, US. Registered 501©(3) tax

deduction.www.wikipedia.com.

9) Matthew N.O Sadiku-2001. Numerical techniques in electromagnetic.

Second Edition .CRC Press, London, Washington DC.

10) Norazan Kassim, Abu Bakar Mohammad, Mohd Haniff Ibrahim, Optical

waveguide modeling based on scalar finite difference scheme. Journal

Teknologi,42(D) Jun 2005;41-54© Universiti Teknologi Malaysia.

11) J.B Davies, C.A.Muliwyk.1996.Numerical solution of uniform hollow

waveguides with boundaries of arbitrary shape.

75

12) M.S Stern.1998.Semivectorial polarized finite difference method for

optical waveguides with arbitrary index profiles.IEEE Proc Vol.135, Pt

J.pp.56-63.

13) K.Bierwitrth, N.Schulz, F.arndt.1986.Finite difference analysis of

rectangular dielectric waveguide structure.IEEE Trans.Microwave

Theory Tech.Vol.34,P.P 1104-1114.

14) F. Anibal Fernandez, Yilong Lu.1996 Microwave and optical waveguide

analysis.Research studies press LTD, Somerset, England.

15) M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric

rectangular waveguide, (in Japanese) Trans. Ins. Electron. Commun.

Eng.Japan, vol. J64-C, pp. 674-681, October 1981

APPENDIX A

Source Code for Buried waveguide modeling by

using MATLAB

77

function varargout = main page(varargin)

% main page M-file for main page.fig

% GUIJ, by itself, creates a new GUIJ or raises the existing

% singleton*.

%

% H = GUIJ returns the handle to a new GUIJ or the handle to

% the existing singleton*.

%

% GUIJ('CALLBACK',hObject,eventData,handles,...) calls the local

% function named CALLBACK in GUIJ.M with the given input arguments.

%

% GUIJ('Property','Value',...) creates a new GUIJ or raises the

% existing singleton*. Starting from the left, property value pairs

are

% applied to the GUI before guij_OpeningFunction gets called. An

% unrecognized property name or invalid value makes property

application

% stop. All inputs are passed to guij_OpeningFcn via varargin.

%

% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one

% instance to run (singleton)".

%

% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help guij

% Last Modified by GUIDE v2.5 18-Mar-2008 00:07:44

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name', mfilename, ...

'gui_Singleton', gui_Singleton, ...

'gui_OpeningFcn', @guij_OpeningFcn, ...

'gui_OutputFcn', @guij_OutputFcn, ...

'gui_LayoutFcn', [] , ...

'gui_Callback', []);

if nargin && ischar(varargin{1})

gui_State.gui_Callback = str2func(varargin{1});

end

if nargout

[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before guij is made visible.

function guij_OpeningFcn(hObject, eventdata, handles, varargin)

% This function has no output args, see OutputFcn.

% hObject handle to figure

% eventdata reserved - to be defined in a future version of MATLAB

% handles structure with handles and user data (see GUIDATA)

% varargin command line arguments to guij (see VARARGIN)

% Choose default command line output for guij

handles.output = hObject;

[x,map]=imread('officialutmslide.jpg');

image(x)

colormap(map)

axis off

% Update handles structure

guidata(hObject, handles);

% UIWAIT makes main page wait for user response (see UIRESUME)

% uiwait(handles.figure1);

78

% --- Outputs from this function are returned to the command line.

function varargout = main page_OutputFcn(hObject, eventdata, handles)

% varargout cell array for returning output args (see VARARGOUT);




% Get default command line output from handles structure

varargout{1} = handles.output;

% --- Executes on button press in pushbutton1.

function pushbutton1_Callback(hObject, eventdata, handles)

% hObject handle to pushbutton1 (see GCBO)



[pushbutton1]=wg3x3();


















[pushbutton4]=CALCULATION();

% --- Executes on selection change in popupmenu1.

function popupmenu1_Callback(hObject, eventdata, handles)

% hObject handle to popupmenu1 (see GCBO)



% Hints: contents = get(hObject,'String') returns popupmenu1 contents as

cell array

% contents{get(hObject,'Value')} returns selected item from

popupmenu1

% --- Executes during object creation, after setting all properties.

function popupmenu1_CreateFcn(hObject, eventdata, handles)



% handles empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.

% See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'),

get(0,'defaultUicontrolBackgroundColor'))

set(hObject,'BackgroundColor','white');

end





79



cell array


popupmenu3











end

function edit1_Callback(hObject, eventdata, handles)

% hObject handle to edit1 (see GCBO)



% Hints: get(hObject,'String') returns contents of edit1 as text

% str2double(get(hObject,'String')) returns contents of edit1 as a

double


function edit1_CreateFcn(hObject, eventdata, handles)




% Hint: edit controls usually have a white background on Windows.





end







cell array


popupmenu4










80


end






[pushbutton5]=aplication()






[pushbutton6]=ANALYSIS2()

CALCULATION PART

function varargout = CALCULATION(varargin)

% CALCULATION M-file for CALCULATION.fig

% CALCULATION, by itself, creates a new CALCULATION or raises the

existing

% singleton*.

%

% H = CALCULATION returns the handle to a new CALCULATION or the handle

to

% the existing singleton*.

%

% CALCULATION('CALLBACK',hObject,eventData,handles,...) calls the local

% function named CALLBACK in CALCULATION.M with the given input

arguments.

%

% CALCULATION('Property','Value',...) creates a new CALCULATION or

raises the

% existing singleton*. Starting from the left, property value pairs

are

% applied to the GUI before CALCULATION_OpeningFunction gets called.

An

% unrecognized property name or invalid value makes property

application

% stop. All inputs are passed to CALCULATION_OpeningFcn via varargin.

%

% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one

% instance to run (singleton)".

%

% See also: GUIDE, GUIDATA, GUIHANDLES

% Copyright 2002-2003 The MathWorks, Inc.

% Edit the above text to modify the response to help CALCULATION

% Last Modified by GUIDE v2.5 06-Apr-2008 15:02:22

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name', mfilename, ...

'gui_Singleton', gui_Singleton, ...

'gui_OpeningFcn', @CALCULATION_OpeningFcn, ...

'gui_OutputFcn', @CALCULATION_OutputFcn, ...

'gui_LayoutFcn', [] , ...

'gui_Callback', []);

if nargin && ischar(varargin{1})

gui_State.gui_Callback = str2func(varargin{1});

end

81

if nargout

[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before CALCULATION is made visible.

function CALCULATION_OpeningFcn(hObject, eventdata, handles, varargin)

% This function has no output args, see OutputFcn.




% varargin command line arguments to CALCULATION (see VARARGIN)

% Choose default command line output for CALCULATION

handles.output = hObject;



[x,map]=imread('structure.JPG');

image(x)

colormap(map)

axis off



% UIWAIT makes CALCULATION wait for user response (see UIRESUME)

% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.

function varargout = CALCULATION_OutputFcn(hObject, eventdata, handles)

% varargout cell array for returning output args (see VARARGOUT);




% Get default command line output from handles structure

varargout{1} = handles.output;

function t2_Callback(hObject, eventdata, handles)

% hObject handle to t2 (see GCBO)



% Hints: get(hObject,'String') returns contents of t2 as text

% str2double(get(hObject,'String')) returns contents of t2 as a

double

t2= str2double(get(hObject, 'String'));

if isnan(t2)

set(hObject, 'String', 0);

errordlg('Input must be a number','Error');

end

% Save the new volume value

handles.metricdata.t2=t2;

guidata(hObject,handles)


function t2_CreateFcn(hObject, eventdata, handles)

% hObject handle to t2 (see GCBO)


82







end

function W_Callback(hObject, eventdata, handles)

% hObject handle to W (see GCBO)



% Hints: get(hObject,'String') returns contents of W as text

% str2double(get(hObject,'String')) returns contents of W as a double

W= str2double(get(hObject, 'String'));

if isnan(W)



end


handles.metricdata.W=W;



function W_CreateFcn(hObject, eventdata, handles)

% hObject handle to W (see GCBO)








end

function n1_Callback(hObject, eventdata, handles)

% hObject handle to n1 (see GCBO)



% Hints: get(hObject,'String') returns contents of n1 as text

% str2double(get(hObject,'String')) returns contents of n1 as a

double

n1= str2double(get(hObject, 'String'));

if isnan(n1)



end


handles.metricdata.n1=n1;



function n1_CreateFcn(hObject, eventdata, handles)




83






end







double


if isnan(n2)



end














end







double


if isnan(n3)



end













84


end

% --- Executes on button press in CALCULATE.

function CALCULATE_Callback(hObject, eventdata, handles)

% hObject handle to CALCULATE (see GCBO)



dx1=0.1; %handles.metricdata.dx;

dy1=0.1; %handles.metricdata.dy;

t2=handles.metricdata.t2;

t3=2; %handles.metricdata.t3;

w=handles.metricdata.W;

h=2;%handles.metricdata.h;

lamda=1.55; %handles.metricdata.lamda;

a=10;%handles.metricdata.a;

n1=handles.metricdata.n1;



Iteration1=500; %handles.metricdata.Iteration;

lamda=lamda*10^(-6);

miu=4*pi*10^(-7);

heks=8.854*10^(-12);

C=3*10^8;

kiraan=1;

T=h+t2+t3;

L=a+a+w;

mT=round(T/dy1);

mh=round(h/dy1);

mt2=round(t2/dy1);

mt3=round(t3/dy1);

mL=round(L/dx1);

mw=round(w/dx1);

ma=round(a/dx1);

r=sqrt((dy1^2)/(dx1^2));

N=ones((mT+1),(mL+1));

%*****************************************

%Buried Optical waveguide modeling

%*****************************************

for i=(mT+1):-1:(mh+mt2+2)

for j=1:1:(mL+1)

N(i,j)=n4;

end

end

for i=(mh+mt2+1):-1:(mh+2)

for j=(ma+1):1:(ma+mw+2)

N(i,j)=n2;

end

end

for i=(mh+mt2+1):-1:(mh+2)

for j=1:1:ma

N(i,j)=n3;

end

end

for i=(mh+mt2+1):-1:(mh+2)

for j=(ma+mw+1):1:(mL+1)

N(i,j)=n3;

end

85

end

for i=mh:-1:1

for j=1:1:(mL+1)

N(i,j)=n1;

end

end

f=C/lamda;

omega=2*pi*f;

ko=sqrt((omega^2)*miu*heks);

beta=ko*n4;

ddx=dx1*10^(-6);

E=ones((mT+1),(mL+1));

E(:,1)=0;

E(:,(mL+1))=0;

E(1,:)=0;

E((mT+1),:)=0;

%******************************************

%calculation start

%*****************************************

while kiraan<Iteration1

for i=mT:-1:2

for j=2:1:mL

E(i,j)=(E((i+1),j) + E((i-1),j) + (E(i,(j+1)) + E(i,(j-

1)))*r^2)/(2*(1+r^2) - (ddx^2)*((ko^2)*(N(i,j)^2)-beta^2));

end

end

kiraan = kiraan + 1;

ddy=dy1*10^(-6);

%******************************************

% neff calculation

%******************************************

%Calculate num and den for Raleigh Equation

num=0; den=0;

for i=mT:-1:2

for j=2:1:mL

d2Ex=(E((i+1),j)+E((i-1),j)-2*E(i,j))/(ddx*ddx);

d2Ey=(E(i,(j+1))+E(i,(j-1))-2*E(i,j))/(ddy*ddy);

num=num+dy1*dx1*(E(i,j)*(d2Ex+d2Ey+E(i,j)*N(i,j)*N(i,j)*ko*ko));

den=den+dy1*dx1*E(i,j)*E(i,j);

%calculate new beta

beta=sqrt(num/den);

%effective index calculation

Neff=beta*lamda/(2*pi);

%normalized calculation constant calculation

b=((Neff*Neff-n2*n2)/(n3*n3-n2*n2))*pi;

end

end

%normalization equation

Etotal=0;

for j=1:1:mL

for i=1:1:mT

Etotal=Etotal + E(i,j);% Larger value E(i,j)

end

end

for j=1:1:mL

for i=1:1:mT

E(i,j)=E(i,j)/Etotal;% normalize equation

86

end

end

end

set(handles.Neff,'String',Neff);

set(handles.b,'String', b);

x=0:dx1:L;

y=T:-dy1:0;

figure

subplot(2,2,2);

mesh(x,y,E)

xlabel('X-axis,mikrometer')

ylabel('Y-axis,mikrometer')

zlabel('E distribution')

title('E-field Profile')

subplot(2,2,1);

mesh(x,y,N)

title('Refractive Index Profile')

subplot(2,2,3);

contour(x,y,E)

xlabel('Waveguide width (um)')

ylabel('Waveguide heigth (um)')

title('E-field Contour Plot')

hold on

x=[0 L L 0 0];

y=[0 0 T T 0];

line(x,y,'linewidth',1);

hold on

x=[0 L];

y=[t3 t3];


hold on

x=[0 a a a+w a+w L];

y=[t2+h t2+h t3 t3 t2+h t2+h];


hold on

% --- Executes on button press in MENU.

function MENU_Callback(hObject, eventdata, handles)

% hObject handle to MENU (see GCBO)



[MENU]=main page();

main

function edit11_Callback(hObject, eventdata, handles)




% Hints: get(hObject,'String') returns contents of edit11 as text

% str2double(get(hObject,'String')) returns contents of edit11 as a

double


function edit11_CreateFcn(hObject, eventdata, handles)




87






end

126_mohdmuzafarbinismail2008.pdf

Documents

modeling optical waveguide

abstract optical waveguides

allah s

blessing of allah

crucial process

accuracy of simulation

fabrication process

warm support