INVESTIGATION OF TEMPERATURE PROLIFE IN THE WAVEGUIDE

SHAFINI MOHD. SHAFIE

A project report submitted in partial fulfilment of the requirements for the award of

the degree of

Master of Electrical-Electronic& Telecommunications

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

May 2006

4

ACKNOWLEDGEMENT

I would like to thank my family, especially my dad for providing wisdom,

encouragement and support in good times and bad. No matter what, they have been

to keep me focused and on the path to success. I would not be where I am today

without their love. I must also thank my supervisor, Assoc. Prof. Dr. Abu Sahmah

bin Mohd Supa’at for his patience, advice and expertise. His mentorship style,

guiding rather than leading, has allowed me to strengthen my intellectual wings and

tackle problems on my own. When I needed it, he was always ready with a helpful

suggestion as well explanation. To all my friends thank a lot for all supporting.

7

ABSTRACT

The demand for data traffic has initiated the development of optical telecommunications. Due to explosive growth of optical network, has brought forward an increased need for guided-wave optical component. The purpose of this work is to investigate the temperature profile in the thermo-optic waveguide. Here, we use one and two dimensional model to analyze the thermal model. We focus on polymer waveguide since these technology is attractive for many advantages, including large thermo-optic coefficient (for Polyurethane (PUR): dn/dt ~ -3.3-4 K-1) and low thermal conductivity ( ~ 0.19 W m-1 K-1). The buried and rib waveguide structure is used for two dimensional model thermal analysis. We interested to see how heating the heater will change the refractive index and change the profile in the waveguide. Thermal coupling became next task of this project. We analyze the effect of heater to the nearby waveguide. To perform this analysis, we utilized a commercial finite element method (FEMLAB 2.0), which is a tool for PDE-based multiphysics modelling in an interactive environment-MATLAB. The simulated result will use one and two dimensional model respectively. Effective index change is dependency of heater size as well as distance between core to the heater. Increasing 1µm of heater width will reduce -0.1 of dneff/dt it also increasing the power consumption. Thermal coupling is related to waveguide spacing and depth. The coupling estimation is increase with the waveguide depth but decrease with the waveguide spacing. Apply trench structure can reduce the thermal coupling estimation, K .The temperature of heated waveguide decreases as the trench depth increases, therefore it requires less power in performing its function.

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ABSTRAK

Perkembangan terhadap komunikasi optik bermula dengan permintaan terhadap pengangkutan data. Peningkatan yang cepat memberi peluang terhadap penggunaan komponen gelombang pandu. Matlamat di sini adalah untuk mencari kesan suhu terhadap gelombang yang di panaskan. Oleh itu, penggunaan satu dan dua dimensi digunakan didalam analisis kesan haba ini. Analisis ini dilakukan menggunakan bahan polimer kerana ia mempunyai pemalar haba optik yang tinggi( dn/dt ~ -3.3-4 K-1) dan juga pengaliran arus elektrik yang rendah ( ~ 0.19 W m-1 K-1). Model haba menggunakan dua bentuk struktur gelombang yang berbeza iaitu penanaman (buried) dan juga melengkung (rib). Kami ingin melihat bagaimana haba memberi impak terhadap perubahan indek bias dan juga terhadap profil gelombang. Selepas itu, fokus terhadap perangkai haba (thermal coupling) di lakukan. Analisis pemanas terhadap gelombang yang bersebelahan dilakukan. Untuk melakukan semua analisis ini kami menggunakan komersial perisian iaitu FEMLAB 2.0 yang mana menggunakan asas fenomena fizik model dan juga persamaan matematik. Ia juga interaktif dengan perisian MATLAB. Simulasi akan menggunakan satu dan dua dimensi. Perubahan indek bias bergantung kepada saiz pemanas dan juga jarak di antara teras (core) kepada pemanas. Peningkatan sebanyak 1µm kelebaran pemanas akan mengurangkan -0.1 perubahan indek bias (dneff/dt) dan ini akan meningkatkan penggunaan kuasa. Manakala, perangkai haba (thermal coupling) amat bergantung kepada jarak di antara dua gelombang dan juga kedalaman teras. Nilai ini, K akan meningkat bergantung kepada jarak kedalaman gelombang dan mengurang sekiranya jarak di antara dua gelombang meningkat. Penggunaan kaedah perparitan (trench) akan mengurangkan nilai perangkai haba,K. Suhu gelombang yang di panaskan akan berkurang sekiranya kedalam parit (trench depth) meningkat. Oleh itu, ia akan menjimatkan penggunaan kuasa di dalam melakukan sesuatu fungsi.

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LIST OF CONTENTS

CHAPTER TITLE PAGE

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

1 INTRODUCTION 1

1.1 Statement of the Problem 2

1.2 Integrated Optics in Polymers 3

1.3 Scope of this Work 5

1.4 Overview of this Report 6

2 THERMAL WAVEGUIDE ANALYSIS 7

2.1 A Brief History of Integrated Optic 7

2.2 Literature Review 9

2.2.1 Thermal Analysis 12

2.2.2 Thermal Coupling 13

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3 OPTICAL WAVEGUIDE 14

3.1 Optical Waveguide Theory 14

3.1.1 Wave vector and propagation constant 15

3.1.2 Maxwell Equation 16

3.1.3 Wave Equation 17

3.2 Structure Waveguide Concepts 19

3.2.1 Rib waveguide 21

3.2.2 Buried waveguide 21

3.3 Waveguide Control 22

3.4 Polymer Waveguide 23

3.4.1 Material thermal properties 24

4 MODELING AND DESIGN OF WAVEGUIDE 26

4.1 Finite Element Method 26

4.2 Heat Transfer Equation 30

4.2.1 One dimensional model 31

4.2.2 Two-dimensional model 32

4.3 Thermal Model 33

4.4 Simulation Guide 35

4.4.1 Setting the model in FEMLAB 35

4.4.2 Option and Settings 37

4.4.3 Draw mode 39

4.4.4 Boundary Mode 40

4.4.5 Sub domain mode 41

4.4.6 Mesh Mode 42

5 RESULTS 44

5.1 Thermal Analysis 45

5.1.1 Two Dimensional 46

5.1.1.1 Rib Waveguide Structure 46

5.1.1.2 Buried Waveguide Structure 49

5.1.2 One Dimensional 54

5.2 Thermal Coupling 55

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6 DISCUSSION 61

6.1 Thermal Analysis 61

6.1.1 Rib waveguide structure 62

6.1.2 Buried waveguide structure 65

6.2 Thermal Coupling 69

6.2.1 Original waveguide structure 69

6.2.2 Trench structure 71

7 CONCLUSION & RECOMMENDATION 78

7.1 Thermal Analysis Model 78

7.2 Thermal Coupling Model 79

7.3 Future directions 80

REFERENCES 74

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LIST OF TABLES

TABLE NO. TITLE PAGE

1.1 Integrated optics market in 2001 by material type 2

1.2 Typical properties of waveguides in popular materials 4

used in integrated optic.

5.1 Opto-thermal parameters for utilized materials 44

5.2 Two types (A-B) of waveguide structure, shown together with

response times. 52

6.1 Waveguide Geometric Dimension 63

6.2 Thermo-optic coefficient, dneff/dT dependent on heater width. 68

6.3 Calculated Power for various trench depth structure 77

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Integration and cost reduction roadmap for 10

organic-inorganic hybrid integration platform.

2.2 Thermal distribution at heater temperature of 100°C and

(b) effective refractive index change versus heater temperature

for various distance H of the heater in structures of series 1. 12

3.1 Vector triangle describing the relationship between β, к and k. 15

3.2 Illustration of typical rib waveguide geometry and reference 17

coordinate geometry.

3.3 Simple waveguide structure 18

3.4 Typical dielectric waveguides 20

3.5 Schematic concept for control of guided modes. 22

4.1 (a) Finite different and (b) finite element method discretizations

geometry. 27

4.2 Divided the region (a) the rib waveguide is divided into sub-

domain region, which are triangles and (b) one dimensional is

divided into finite number of element. 28

4.3 Geometry of (a) cross section of rib waveguide with heater on

top of ridge and (b) buried waveguide structure used for

coupling analysis. 34

5.1 Schematic diagrams of the (a) rib and (b) buried waveguide

structure cross section. 45

5.2 2D thermal distribution with W= 1µm and H=0.5µm. 46

5.3 2D thermal model rib waveguide structure with H=0.2µm and

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heater temperature 300K. 47

5.4 Contour plot of heat lateral (a) heater width 20µm and (b) heater

width 10µm.The heater temperature apply is 350K. 48

5.5 Temperature distributions for buried waveguide structure with

core dimension 8µm×8µm at heater temperature 100K. 49

5.6 Temperature distributions for buried waveguide structure with

core dimension 6µm×6µm at heater temperature 100K. 50

5.7 Heat distributions for buried waveguide structure with

8µm×8µm at heater temperature 350K with different distance. 51

5.8 Calculated temperature distribution in (a) rib waveguide

structure (type B), and (b) a buried waveguide structure (type A). 53

5.9 1D thermal distribution with W= 0.5µm and H=1µm. 54

5.10 The cross section of a thermo-optic waveguide (a) original

waveguide with heater on top and (b) trench structure. 56

5.11 The temperature distribution of the original waveguide where

the waveguide dimension is 8µm× 8µm. 57

5.12 The temperature distribution of the trench waveguide. 58

5.13 Temperature distribution where (a) trench depth, h is 3µm and

trench width 2µm, (b) trench depth, h is 13µm and trench width

2µm, (c) trench depth, h 4µm and trench width 2µm and

(d) trench depth, h 4µm and trench width 1µm. 60

6.1 Effective index change versus heater temperature for various

distance H of the heater. 62

6.2 Thermo-optic coefficient dneff/dt and switching power versus

the waveguide rib width. 64

6.3 Core waveguide temperatures in the function of waveguide size. 65

6.4 Effective index change versus heater temperature for various

distance H of the heater. 67

6.5 Effective index change in the function of heater width with

H=7µm and core size 8µm× 8µm. 68

6.6 Coupling estimation, K versus spacing for original structure in the

function of waveguide depth, h. 70

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6.7 Coupling estimation, K versus spacing for trench structure in the

function of waveguide depth, h. 71

6.8 Comparison between the original and trench structure (a) coupling

estimation and (b) effective index change different waveguide 1

and waveguide 2. 73

6.9 The relationship between (a) the K and (b) effective index

different versus trench depth when waveguide spacing is 4µm. 75

6.10 The temperature rise of the heat waveguide and trench depth with

varies the waveguide depth. 77

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LIST OF SYMBOLS

A - contact area

C - heat capacity

d - trench depth

d - distance of heat flow

K - thermal coupling estimation

k - thermal conductivity

H - distance from heater to waveguide core

h - waveguide depth

L - heater lenght

n - refractive index

Q - rate of heat flow

s - waveguide spacing

t - thickness of the polymer bottom layer

W - heater width

β - propagation constant

ε - relative permittivity

µ - relative permeability

∆ - temperature ratio different

Φ - change in polarizability with temperature

ρ - density capacity

λ - wavelength

γ - coefficient of volume expansion

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CHAPTER 1

INTRODUCTION

Guided wave optics will play an increasing and important role in optical

communication networks and optical sensor systems. In particular, polymeric

waveguide devices are being developed; because the process can be low-cost, and

high manufacturing output can be achieved. The low temperature fabrication process

of polymer waveguide also gives the designer a large degree of freedom. Because

most polymer materials have a thermo-optic coefficient an order of magnitude larger

than that of silica, thus, they can be temperature tuned over a wider spectral range

(Edwin Y. B. Pun and W.H. Wong, 2002).

In general polymer has a temperature dependent refractive index which is

known as the thermo optic (TO) effect. Recently, the active optical glass waveguide

utilizing the TO effect such as modulators and switches has been demonstrated

(M.Haruna and J.Koyama ,1982). In 1989, there is published paper due to application

of TO which is using polymer waveguide to make a switch. The author demonstrated

that effective index changes at least one order higher than those obtained with the

electro optic effect in LiNbO3 are found (M.B.J. Diemeer, J.J. Brons and E.S.

Trommel, 1989). Two years ago, the researcher (H.P. Chan, C.K. Chow and Alok K.

Das 4, 2003), found that by using the polymer material in application of digital

optical switch (DOS), there can reduces the crosstalk value.

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Nowadays, there have a lot of research to find a robust material or versatile in

optic communication application. Figure 1 shows the material that used until 2001,

polymer contribute only few percentage.

Table 1.1: Integrated optics market in 2001 by material type (L. Gasman, 2001)

Material %

Lithium niobate 30

Indium phosphide 22

Gallium arsenide 20

Silica on silicon 11

Polymer 5

Silicon 3

Other 9

TOTAL 100

1.1 Statement of the Problem

The explosive growth of the Internet, and the emergence of a strong wireless

market are driving these changes, and optoelectronic components are fundamental

enablers of this transformation. This combination of optical and electrical

technologies allows data to be generated, transported and manipulated at high rates.

Today, optoelectronics are being integrated into existing networks. By 2007, all-

optical networks will most likely be needed (John Stafford, 2001).

Today’s components and packages are too costly as well as too cumbersome.

The industry will need to move to new technologies, such as flip chip instead of wire

bond, and multichip modules to reduce package size (John Stafford, 2001). Still need

a lot a research in this field due to demanding of optical communication.

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As the new technology trends to increase the speed and the bandwidth for

communications in wide area networks, the all optical network becomes a good

choice as a solution for that problem. New devices and materials using linear or non

linear effects of light are extremely useful for such networks because of their

compatible speed (Mario L and Jose A.M. Pereira, 1996). Our project use polymer

material to build optical waveguide. Recently, development on optical polymer

waveguide will used electro –optic to implement the device. Because polymer has

large TO coefficient, we will apply this effect to implement future device.

1.2 Integrated Optics in Polymers

Polymer materials are of great interest in integrated optics as they can be

tailored to meet specific applications. The thermo-optic effect is large in these

materials -1×10-4 K-1 to -4×10-4 K-1 which leads to power efficient dynamic

components. They are potentially low cost and rapidly processed by direct photo

patterning or reactive ion etching. Waveguide can be designed with very large or

very small index contrast between core and cladding (0% – 35%). Polymer can also

have very low optical loss <0.1dB/cm at the telecommunication wavelengths 1310

nm and 1550 nm (John M. Senior, 1992). Cross linked polymer systems operated

above the glass transition temperature even allow for waveguides free of stress

induced scattering and birefringence. Polymer material classes used in integrated

optics include acrylates, polyimides, polycarbonates and olefins (Robert Blum,

2003).

Realized polymer devices cover a wide range of optical applications like

switches, couplers, filters, attenuators, polarization controllers, dispersion

compensators, modulator, laser and amplifiers (R.T. Chan,1993).Even 3D multi layer

architectures of integrated circuits are possible as successive layers are deposited b

simple spin coating (S.M. Garner et all, 1999).Table 2 compares several typical

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materials used in integrated optics. In almost all categories polymers exhibit

excellent values. However, it is difficult to combine all these properties in single

material.

Table1.2: Typical properties of waveguides in popular materials used in integrated

optics. The refractive indices of the core and cladding materials are denoted by ncor

and nclad respectively.

Propagation

Loss

[dB/cm]

Refractive

Index

Index

Contrast

(ncornclad)/ncor

Birefringence T/O

Coef.dn/dt

[K-1]

Max.

Modulation

Freq.

Silica 0.1 1.5 0-1.5% 10-4-10-2 10-5 1kHz (TO)

Silicon 0.1 3.5 70% 10-4-10-2 1.8×10-4 1kHz (TO)

Polymers 0.1 1.3-1.7 0-35% 10-6-10-2 -1×10-4- -

4×10-4

1kHz (TO)

Lithium

Niobate

0.5 2.2 0-0.5% 10-2-10-1 10-5 40GHz

(EO)

Indium

Phospide

3 3.1 0-3% 10-3 0.8×10-4 40GHz

(EO)

Gallium

Arsenide

0.5 3.4 0-14% 10-3 2.5×10-4 20GHz

(EO)

Most serious problems in connection with polymers are environmental

stability (temperature, humidity) and commercial availability. Thermal aging due to

oxidation is often observed in organic materials as well as water incursion and the

associated optical absorption from the overtone bands of the OH stretch (Robert

Blum, 2003).However, these problems have been solved by many manufacturers

(e.g. AlliedSignal, JDS Uniphase, Du Pont, Dow Chemical) and some materials even

passed the Bellcore 1209 and 1221 test (R, Moosburger et all, 1996).

Unlike silicon, silica or InP, polymers are materials are designed by chemists

to meet specific needs. Their usage is often hindered by patents and they are seldom

sold or manufactured in small quantities as needed for integrated optics (J.D.

Plumber, M.D. Deal and P.B. Griffin, 2000). Therefore commercially available

polymers are usually built for other applications like microelectronics, display or

21

furniture coating. By chance, some of them also show desirable optical

characteristics like BCB (Cyclotene by Dow Chemical).

1.3 Scope of this Work

This project is about an investigation of temperature profile in the thermo-

optic waveguide due to the effect of having thin film heater on top of polymer

waveguide structure by using the one and two dimensional model. Here, we would

like to determine the effective index change from the change of temperature. By

heating the heater, it will distribute the heat in the surrounding area and cause

increasing the temperature in the waveguide structure.

In the way to analyze the TO effect, we will design thermal model based on

two different structure which is rib waveguide structure and buried waveguide

structure. The lateral heat diffusion distance in both structures will be studied. Two

phenomena will be studied seriously, which is the distance from heater to the core

waveguide (H) affect the effective index change. We also interested to investigate

how heater size would affect the key parameters in modelling waveguide structure.

Thermal coupling became an issue when we have two waveguides in parallel.

The structure will consists of two square waveguide. Due to thermal phenomena,

heat one of the waveguide will effects nearby waveguide. Actually, these are

unwanted phenomena and will degrade the devices performance. The relationship

between them is known as thermal coupling estimation. Here, we will determine

these values and try to figure out the way to reduce these effects. One method is by

applying the trench structure. All the simulation is done using software named

FEMLAB. The result can be obtained by GUI (Graphical User Interface). This

software apply finite element as a method to solve all the problems.

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1.4 Overview of this Report

This section outlines the organization of the work contained in this thesis.

Throughout this thesis we have seven chapters including the conclusion. A brief

history of integrated optic is discussed in Chapter 2. Follow with the literature review

of this project. Several papers are discussed under section 2.2 sub topics.

In Chapter 3, all the theory that applies for the project progress is explained

briefly. The discussion start with phenomena that cause light can travel in the

waveguide. Maxwell equation are introduces to get wave equation. Then, the types of

the structure are discussed following with several type of control waveguide. But for

this project, we focus on thermo-optic control. At the end of this chapter, the

subtopic is on polymer waveguide.

Chapter 4 is about the methodology of the project. Since we used the

numerical method in the way to get the result, a basic theory of finite element

method is discuss. Thermal analysis, which is the heat transfer equation are explain

due to the one and two dimension respectively. Thermal model including rib and

buried waveguide structure is explained under section 4.3. Lastly, a quick step on

simulation used FEMLAB software is shown.

The result section is divided into two sub topic which is thermal model and

thermal coupling. Under thermal model we show the result for rib and buried

structure. One dimensional is also shown under this sub topic. All the parameter that

will be influence the performance of effective index change is shown in this topic.

Discussion and analysis or data interpretation are shown in Chapter 6. A lot of issue

is discussed here. Last chapter is about the conclusion of the project throughout this

course.

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