SIMULATION OF DUAL FIBRE BRAGG GRATINGS AS A FABRY-PEROT

TUNABLE FILTER

SITI NAFISAH BINTI MD RASHID

UNIVERSITI TEKNOLOGI MALAYSIA

SIMULATION OF DUAL FIBRE BRAGG GRATINGS AS A FABRY-PEROT

TUNABLE FILTER

SITI NAFISAH BINTI MD RASHID

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Science (Physics)

Faculty of Science

Universiti Teknologi Malaysia

JUNE 2010

iii

This thesis is dedicated to my wonderful parents,

Md Rashid Md Said and Hanizah Abd Jalil.

iv

ACKNOWLEDGEMENT

First of all, thanks to Allah the Almighty for His guidance and giving me the

strength to complete this project. In particular, I would like to record my sincere

appreciation to my main supervisor, Prof. Dr. Jalil Ali, for his guidance, valuable advice,

constructive criticism, stimulating discussions and valuable suggestions during the

preparation of this project. I am also very thankful to my co-supervisors, Prof. Dr. Rosly

Abdul Rahman and Dr. Saktioto for their guidance, help, advice and motivation.

Without their continued support and interest, this thesis would not have materialized.

I am also indebted to Ministry of Science, Technology and Innovation (MOSTI)

for the National Science Fellowship (NSF) scholar, and to my parents for the initial

financial support the Master of Science study. Librarians at UTM and staffs also deserve

special thanks for their assistance in supplying the relevant literatures.

My sincere appreciation also goes to all my colleague, staff at the Faculty of

Science, Institute of Advanced Photonics Science (APSI), ESciNano Research Alliance,

who are always ready to give their helping hands. Last but not least, no words can be

used to express my deepest gratitude to my parent and family, for their encouragement

and love, which I am forever indebted.

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ABSTRACT

A Fabry-Perot Bragg Gratings (FP-BG) is developed by using two uniform fibre

Bragg gratings (FBG) system. The objective of this research is to simulate single, dual

FBGs and fabricate single FBG by using phase mask writing with a UV KrF excimer

laser. Three single FBGs with Bragg wavelength of 1551.09 nm, 1551.29 nm and

1551.66 nm have been fabricated with reflectivity values of 30.2%, 78.1% and 44.7%

respectively. FBG’s with reflectivity value of 78.1% are categorized as good and strong

FBG, since its reflectivity value is more than 50%. Some simulation works were also

executed in this research to generate the transmission spectrum of single and dual FBGs.

For single FBG, the transmission spectra for different values of grating lengths and

reflectivities have been studied. Results showed that the transmission spectra of single

FBG becomes wider if the grating produced is short, and longer when the reflectivity

value is increased. For dual FBGs, simulations were performed by varying the

separation distance between the two FBGs. The separation distance was varied from 0.5

cm to 5.5 cm, with an increment of 0.5 cm. The result showed that any increase of the

separation distance led to an increase in the number of maximum transmission peaks of

dual FBGs, due to the absorption phenomenon. Only selected wavelengths with certain

frequencies were allowed to transmit at the fibre’s end and the dual FBGs performed

acted as a Fabry-Perot filter. This new configuration of FP filter exhibited similar

behaviours as the conventional FP etalon, in which the parameters of free spectral range

(FSR), full-width-half-maximum (FWHM) and finesse can be obtained from the

transmission profiles.

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ABSTRAK

Satu Fabry-Perot telah dibina menggunakan dua parutan Bragg (FP-BG).

Objektif penyelidikan ini adalah untuk memfabrikasi satu dan dua parutan Bragg di

dalam teras gentian optik menggunakan kaedah topeng fasa, dan laser KrF sebagai

sumber tenaga UV. Tiga parutan Bragg dihasilkan, dengan panjang gelombang Bragg

1551.09 nm, 1551.29 nm dan 1551.66 nm, bersama nilai pantulan masing-masing

30.2%, 78.1% dan 44.7%. Parutan Bragg dengan nilai pantulan 78.1% dikategorikan

sebagai parutan Bragg yang kuat dan berkualiti kerana mempunyai nilai pantulan

melebihi 50%. Kerja-kerja simulasi turut dilakukan dalam kajian ini bagi menghasilkan

spektrum lepasan untuk satu dan dua parutan Bragg. Untuk satu parutan Bragg, kerja

simulasi melibatkan perubahan pada panjang parutan Bragg dan juga nilai pantulan.

Hasil yang diperoleh menunjukkan spektrum lepasan parutan Bragg menjadi semakin

lebar apabila panjang parutan adalah pendek, dan kelihatan panjang, sekiranya nilai

pantulan ditambah. Untuk dua parutan Bragg, kerja simulasi melibatkan perubahan pada

jarak pemisahan antara dua parutan, yang mana ia diubah dari nilai 0.5 cm hingga 5.5

cm, dengan pertambahan sebanyak 0.5 cm. Hasil simulasi menunjukkan apabila jarak

pemisahan ditambah, bilangan spektrum lepasan maksima akan bertambah, disebabkan

oleh fenomena serapan. Hanya panjang gelombang dengan frekuensi tertentu sahaja

dibenarkan untuk melepasi suatu gentian optik, menjadikannya berfungsi sebagai suatu

penapis Fabry-Perot. Sebagai satu konfigurasi Fabry-Perot, dua parutan Bragg ini turut

menghasilkan profil lepasan seperti FP etalon, di mana parameter-parameter seperti free

spectral range (FSR), full-width-half-maximum (FWHM) dan finesse dapat dilihat pada

spektrum lepasan yang terhasil.

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TABLE 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

LIST OF APPENDICES xvi

1 INTRODUCTION 1

1.1 Background of Study 1

1.2 Problem Statement 2

1.3 Objectives of Study 3

1.4 Scope of Study 3

1.5 Research Methodology 3

1.6 Significance of Study 4

1.7 Organization of the Study 4

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2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 Photosensitivity 7

2.3 Fibre Bragg Grating 8

2.4 Parameters of Fibre Bragg Grating 10

2.4.1 Grating Period 10

2.4.2 Effective Refractive Index 11

2.4.3 Grating Length 11

2.5 Fabrication Technique of Fibre Bragg Gratings 12

2.5.1 Internal Inscription of Bragg Gratings 13

2.5.2 External Inscription of Bragg Gratings 14

2.6 Fabry-Perot Bragg Gratings 19

3 SIMULATION OF FABRY-PEROT BRAGGGRATINGS

22

3.1 Introduction 22

3.2 Coupled Mode Theory 22

3.3 Transfer Matrix Method 25

4 RESEARCH METHODOLOGY 28

4.1 Introduction 28

4.2 Preparation of fibre 28

4.3 Fabrication of fibre Bragg grating 30

4.3.1 Excimer Laser Machine 31

4.3.2 Mask Aligner 33

4.3.3 Phase Mask 35

4.3.4 Tunable Laser Source 36

4.3.5 Optical Spectrum Analyzer 36

4.4 Modeling of single fibre Bragg grating 37

4.5 Modeling of dual fibre Bragg grating 40

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5 RESULTS AND DISCUSSIONS 42

5.1 Introduction 42

5.2 Results on Fabrication Process of Single Fibre Bragg

Grating

42

5.3 Result on Modeling of Fibre Bragg Grating 46

5.3.1 The Model of Single and Uniform Fibre Bragg

Grating

46

5.3.2 The Effect of Reflectivity and Grating Lengths

on Fibre Bragg Grating

50

5.3.3 The Model of Dual Fibre Bragg Gratings 54

5.4 Summary 58

6 CONCLUSION 60

6.1 Conclusion 60

6.2 Future Work 61

REFERENCES 62

APPENDICES 67

LIST OF PUBLICATIONS 82

x

LIST OF TABLES

TABLE NO. TITLE PAGE

4.1 Relevant setting of FBG’s parameters 37

4.2 Relevant setting used in simulation of dual FBGs 40

5.1 Data collected in the fabrication process of single FBG 44

5.2 Comparison values of Bragg wavelength after a period

five months

45

5.3 Relevant setting of single FBG with different

reflectivities, R

52

5.4 Relevant setting of single FBG with different grating

lengths, L

53

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Fabry-Perot interferometer system 1

2.1 An experimental arrangement of fibre photosensitivity 6

2.2 Illustration of fibre Bragg grating 8

2.3 Schematic diagram of fibre Bragg grating 9

2.4 Reflection spectrum of fibre Bragg grating 12

2.5 A typical setup used for generating self-induced Bragg

grating

13

2.6 An amplitude splitting interferometer 15

2.7 Interference fringes induced by two interfering UV

beams

15

2.8 Schematic of the UV radiation at normal incidence of

phase masks

17

2.9 Fabry-Perot etalon 19

2.10 Illustration of dual fibre Bragg gratings 19

3.1 The TMM applied to obtain spectral characteristics of a

fibre grating

25

4.1 Fibre polisher 29

4.2 The apparatus during preparation of fibre 29

4.3 The experimental setup of fabrication process 30

4.4 A COMPEX excimer laser 32

4.5 The inner part of the excimer laser 32

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4.6 A handheld keypad 33

4.7 Mask aligner 33

4.8 An illustration of the light propagation inside the mask

aligner

34

4.9 Phase mask 35

4.10 Tunable Laser Source 36

4.11 Optical Spectrum Analyzer 36

4.12 Flow chart of single FBG for different reflectivities 38

4.13 Flow chart of single FBG for different grating lengths 39

4.14 Flow chart of dual FBGs for different separation

distances

41

5.1 Transmission spectrum of fabricated fibre Bragg grating 43

5.2 Transmission spectrum of single and uniform fibre Bragg

grating

46

5.3 Transmission spectrum of FBG 1 from (a) experiment (b)

simulation

47

5.4 Transmission spectrum of FBG 2 from (a) experiment (b)

simulation

48

5.5 Transmission spectrum of FBG 3 from (a) experiment (b)

simulation

49

5.6 Minor peaks appeared on the transmission spectrum of

fabricated FBG.

50

5.7 FBG Reflection Experimental setup 51

5.8 Reflectance peak of single FBG 51

5.9 Transmission spectrum of FBG for different value of

reflectivities

52

5.10 Transmission spectrum of fibre Bragg grating for

different grating lengths

54

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5.11 Dual FBGs with a separation distance of 0.5 cm 55

5.12 Graph plotted when the separation distance between two

FBGs is varied

56

5.13 Profile of FSR and FWHM 57

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LIST OF SYMBOLS

)(ia - Amplitude of -ith mode traveling in +z directions

)(ia - Amplitude of -ith mode traveling in -z directions

A - Absorption

D - Dip power

d - Separation distance between two fibre Bragg gratings

dz - Length of the kth uniform section

)(zE - Electric field

Euv - UV pulse energy

ie - Modal field of the –ith mode

FBG - Fibre Bragg grating

FP - Fabry-Perot

FSR - Free spectral range

FWHM Full-width-half-maximum

k - Wave vector

K - Magnitude of the grating plane

L - Grating length

effn - Effective refractive index

),,( zyxn - Periodic refractive index perturbation of the grating

),,(20 zyxn - Index profile of waveguide

),,( zyxn - Grating index profile

OSA - Optical spectrum analyzer

xv

P - Phase shift matrix

R - Reflectivity

kT - Transfer matrix of fibre Bragg grating

T - Transmission

TLS - Tunable laser source

tuv - UV exposure time

i - Propagation constant of the –ith mode

- Local coupling coefficient

- “dc” self coefficient

- Detuning

n - Index perturbation - “ac” coupling coefficient

- Fringe visibility

- Wavelength

bragg - Bragg wavelength

uv - UV wavelength

- Grating period

pm - Phase mask period

g - Period of the fringes

- Bandwidth

- Angular frequency of propagation

xvi

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Transmission spectrum of fabricated FBGs 67

B Transmission spectrum of fabricated FBGs after a period of

five months

69

C Matlab coding for single fibre Bragg grating 71

D Matlab coding for single FBG with different reflectivity 72

E Matlab coding for single FBG with different grating length 75

F Matlab coding for dual fibre Bragg gratings 78

G Transmission spectrum of dual FBGs for different separation

distances between two FBGs

80

CHAPTER 1

INTRODUCTION

1.1 Background of Study

Fabry-Perot filter is an optical resonator that confines and stores light energy at

selected frequencies (K.Madingoane, 2009). In an optical transmission system which

incorporates a feedback mechanism, light is repeatedly reflected within the system and

thus circulates without escaping from the system. A simple Fabry-Perot (FP) filter

comprises of two parallel planar mirrors spaced at a fixed distance apart as shown in

Figure 1.1.

Figure 1.1 : Fabry-Perot interferometer system (K.Thyagarajan and A.Ghatak, 2007)

2

The rays travelling between the mirrors are kept perpendicular to the plane of the

mirrors via a two-lens system. The lenses are placed outside the mirrors in order to

establish parallel rays inside the resonance cavity between the mirrors, and to focus the

output light onto the detector following the Fabry-Perot filter.

A Fabry-Perot device can be used for measuring wavelengths with high

precision, for studying the fine structure of spectrum lines and as a high quality optical

resonator for a laser construction. Placing two identical Bragg gratings in series on a

single-mode fibre, results in a FP etalon within the fibre core. This is a novel way of

introducing a tunable filter. This filter allows specific wavelength to pass while rejecting

all other wavelengths.

This new configuration will offer different perspectives compared to the

conventional one. Thus, it can be applied to be used in both fibre laser and fibre sensing

field.

1.2 Problem Statement

The main motivation in this research is to fabricate two fibre Bragg gratings in a

single length of optical fibre. Towards this end, the research addresses a set of

interrelated questions such as which technique is suitable to use for fabricating the dual

FBG’s, what are the effects of grating length and reflectivity parameters to the FBG

transmission spectrum, how does the FBG transmission spectrum changes if the value of

separation length between two FBGs are varied?

3

1.3 Objectives of Study

The objective of this research is to fabricate a single and dual fibre Bragg

gratings in the core of an optical fibre by using the phase mask technique. The

characteristics of FBG will be studied and compared with the simulated result. A model

based on coupled mode theory is developed. The modelling part includes the

investigation of the transmission and reflection spectrum of single FBG for different

values of reflectivity and grating length. For dual FBGs, this study will investigate the

transmission spectrum produced by dual FBGs, when the separation distance between

two FBGs is varied.

1.4 Scope of Study

This research begins with the historical perspective of FBG, principles operation,

and its fabrication techniques. Secondly, we will identify the equipments, parameters

and requirement involve in the yielding of single and dual FBG. Thirdly, the fabrication

process of FBG will be conducted by using a phase mask technique using an excimer

laser. Finally, the performance of fabricated FBG will be assessed in different

experimental setups.

1.5 Research Methodology

Research methodology plays an important role in any type of research. The first

step in any research methodology is conducting a literature survey. The related topics

had been reviewed which consists of the historical aspects of FBG, the theory and

concepts been used, the parameters and characteristics of FBG, and also their

applications. Using the coupled mode theory (CMT) and transfer matrix method (TMM)

4

equations are first derived to describe the single and dual FBG’s. A model is then

developed to describe the transmission and reflection spectra of single and dual FBG’s

based on the variations of reflectivities, grating lengths and separation distance between

two FBG’s. The derived equations are solved using computational codes developed

based on the Matlab software.

For the experimental investigations, the single FBG’s are fabricated using a

phase mask technique. A KrF UV excimer laser is used to write the gratings inside the

core of the optical fibre. The transmission or reflection spectrum is monitored using the

OSA. A TLS is used to provide the broadband spectrum. The results achieved from both

works have been compared and discussed.

1.6 Significance of Study

This research will provide an understanding of single and dual FBG’s, its

fabrication process, its reliability and as a Fabry-Perot tunable filter using the novel idea

of two gratings inside the fibre core.

1.7 Organization of the Study

The thesis consists of six chapters. Chapter 1 provides the background of study,

problem statement, objectives, scope of study, research methodology, and also the

significance of study. The literature review is described in Chapter 2 including the

theory, principles, characteristics and properties, fabrication methods, and the review on

applications of dual FBGs. Chapter 3 provides the mathematical approach that has been

used in modelling work, which consists of the Coupled Mode Theory and Transfer

Matrix Method.

5

Chapter 4 discusses the experimental set-up, equipments needed, fabrication

process of single FBG using a phase mask technique, and the simulation of single and

dual FBGs respectively, using the Matlab software. The results from the experimental

work and simulation work are discussed and analyzed in Chapter 5. Finally, the

conclusion with some recommendations are made in Chapter 6.