SIMULATION OF DUAL FIBRE BRAGG GRATINGS AS A FABRY-PEROT TUNABLE FILTER
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
This thesis is dedicated to my wonderful parents,
Md Rashid Md Said and Hanizah Abd Jalil.
iii
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.
v
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.
vi
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.
vii
TABLE OF CONTENTS
CHAPTER
DECLARATION
DEDICATION
ACKNOWLEDGEMENT
TITLE
ABSTRACT
ABSTRAK
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF APPENDICES
1 INTRODUCTION
1.1 Background of Study
1.2 Problem Statement
1.3 Objectives of Study
1.4 Scope of Study
1.5 Research Methodology
1.6 Significance of Study
1.7 Organization of the Study
PAGE ii iii iv v vi vii x xi xiv xvi
4
4
3
3
2
3
1
1
2
3
4
LITERATURE REVIEW
2.1 Introduction
2.2 Photosensitivity
2.3 Fibre Bragg Grating
2.4 Parameters of Fibre Bragg Grating
2.4.1 Grating Period
2.4.2 Effective Refractive Index
2.4.3 Grating Length
2.5 Fabrication Technique of Fibre Bragg Gratings
2.5.1 Internal Inscription of Bragg Gratings
2.5.2 External Inscription of Bragg Gratings
2.6 Fabry-Perot Bragg Gratings
SIMULATION OF FABRY-PEROT BRAGG
GRATINGS
3.1 Introduction
3.2 Coupled Mode Theory
3.3 Transfer Matrix Method
RESEARCH METHODOLOGY
4.1 Introduction
4.2 Preparation of fibre
4.3 Fabrication of fibre Bragg grating
4.3.1 Excimer Laser Machine
4.3.2 Mask Aligner
4.3.3 Phase Mask
4.3.4 Tunable Laser Source
4.3.5 Optical Spectrum Analyzer
4.4 Modeling of single fibre Bragg grating
4.5 Modeling of dual fibre Bragg grating
22
22
22
25
31
33
35
36
28
28
28
30
36
37
40
10
10
11
11
12
13
7
8
6
6
14
19 viii
5
6
RESULTS AND DISCUSSIONS
5.1 Introduction
5.2 Results on Fabrication Process of Single Fibre Bragg
Grating
5.3 Result on Modeling of Fibre Bragg Grating
5.3.1 The Model of Single and Uniform Fibre Bragg
Grating
5.3.2 The Effect of Reflectivity and Grating Lengths
on Fibre Bragg Grating
5.3.3 The Model of Dual Fibre Bragg Gratings
5.4 Summary
CONCLUSION
6.1 Conclusion
6.2 Future Work
REFERENCES
APPENDICES
LIST OF PUBLICATIONS
62
67
82
54
58
60
60
61
46
46
50
42
42
42 ix
LIST OF TABLES
5.3
5.4
TABLE NO.
4.1
4.2
5.1
5.2
TITLE
Relevant setting of FBG’s parameters
Relevant setting used in simulation of dual FBGs
Data collected in the fabrication process of single FBG
Comparison values of Bragg wavelength after a period five months
Relevant setting of single FBG with different reflectivities, R
Relevant setting of single FBG with different grating lengths, L
PAGE
37
40
44
45
52
53 x
LIST OF FIGURES
2.6
2.7
2.8
4.1
4.2
4.3
4.4
4.5
2.9
2.10
3.1
FIGURE NO.
1.1
2.1
2.2
2.3
2.4
2.5
TITLE
Fabry-Perot interferometer system
An experimental arrangement of fibre photosensitivity
Illustration of fibre Bragg grating
Schematic diagram of fibre Bragg grating
Reflection spectrum of fibre Bragg grating
A typical setup used for generating self-induced Bragg grating
An amplitude splitting interferometer
Interference fringes induced by two interfering UV beams
Schematic of the UV radiation at normal incidence of phase masks
Fabry-Perot etalon
Illustration of dual fibre Bragg gratings
The TMM applied to obtain spectral characteristics of a fibre grating
Fibre polisher
The apparatus during preparation of fibre
The experimental setup of fabrication process
A COMPEX excimer laser
The inner part of the excimer laser
29
29
30
32
32
19
19
25
15
15
17
PAGE
1
6
8
9
12
13 xi
5.5
5.6
5.3
5.4
5.7
5.8
5.9
5.10
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
5.1
5.2
A handheld keypad
Mask aligner
An illustration of the light propagation inside the mask aligner
Phase mask
Tunable Laser Source
Optical Spectrum Analyzer
Flow chart of single FBG for different reflectivities
Flow chart of single FBG for different grating lengths
Flow chart of dual FBGs for different separation distances
Transmission spectrum of fabricated fibre Bragg grating
Transmission spectrum of single and uniform fibre Bragg grating
Transmission spectrum of FBG 1 from (a) experiment (b) simulation
Transmission spectrum of FBG 2 from (a) experiment (b) simulation
Transmission spectrum of FBG 3 from (a) experiment (b) simulation
Minor peaks appeared on the transmission spectrum of fabricated FBG.
FBG Reflection Experimental setup
Reflectance peak of single FBG
Transmission spectrum of FBG for different value of reflectivities
Transmission spectrum of fibre Bragg grating for different grating lengths
49
50
47
48
51
51
52
54
35
36
36
38
39
41
33
33
34
43
46 xii
5.11
5.12
5.13
Dual FBGs with a separation distance of 0.5 cm
Graph plotted when the separation distance between two
FBGs is varied
Profile of FSR and FWHM
55
56
57 xiii
LIST OF SYMBOLS
E e
uv i
FBG -
FP -
FSR -
FWHM k -
K n eff
L -
-
-
a i
( ) a i
( )
A -
D d dz -
( z ) -
-
n ( x , y , z ) n
0
2 ( x , y , z ) n ( x , y , z )
OSA -
-
-
-
Amplitude of i th mode traveling in +z directions
Amplitude of i th mode traveling in -z directions
Absorption
Dip power
Separation distance between two fibre Bragg gratings
Length of the k th uniform section
Electric field
UV pulse energy
Modal field of the – i th mode
Fibre Bragg grating
Fabry-Perot
Free spectral range
Full-width-half-maximum
Wave vector
Magnitude of the grating plane
Grating length
Effective refractive index
Periodic refractive index perturbation of the grating
Index profile of waveguide
Grating index profile
Optical spectrum analyzer xiv
-
-
-
n
-
-
-
-
bragg
-
T k
P -
R -
-
T -
TLS t uv
-
i
-
uv
pm
g
-
-
-
-
-
-
Phase shift matrix
Reflectivity
Transfer matrix of fibre Bragg grating
Transmission
Tunable laser source
UV exposure time
Propagation constant of the – i th mode
Local coupling coefficient
“dc” self coefficient
Detuning
Index perturbation
“ac” coupling coefficient
Fringe visibility
Wavelength
Bragg wavelength
UV wavelength
Grating period
Phase mask period
Period of the fringes
Bandwidth
Angular frequency of propagation xv
xvi
LIST OF APPENDICES
E
F
C
D
G
APPENDIX
A
B
TITLE
Transmission spectrum of fabricated FBGs
Transmission spectrum of fabricated FBGs after a period of five months
Matlab coding for single fibre Bragg grating
Matlab coding for single FBG with different reflectivity
Matlab coding for single FBG with different grating length
Matlab coding for dual fibre Bragg gratings
Transmission spectrum of dual FBGs for different separation distances between two FBGs
PAGE
67
69
71
72
75
78
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.
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
The term Bragg gratings originate from Bragg’s Law, which is used to create the spacing of the changes. This was inspired by Sir William Lawrence Bragg in his study of X-rays and crystal structures (S. Kurtaran et al., 2007). Fibre Bragg grating (FBG) was first introduced to the industry in the 1980s after Hill and his colleague discovered the phenomenon of photosensitivity in 1978 at the Communication Research Centre
(CRC) in Canada, during the non-linear effects’ experiments using a germanosilicate fibre and visible 488 nm Argon ion laser, as shown in Figure 2.1.
Figure 2.1: An experimental arrangement of fibre photosensitivity
(Othonos and Kalli, 1999)
7
During the experiment, a continuous wave of blue light from Argon ion laser is launched into the fibre core, and the intensity of the light reflected from the fibre has been monitored. Primarily, the intensity of reflected light is low, but after a few minutes, it grew in strength until almost all of the light launched is back-reflected (K.O. Hill and
G. Meltz, 1997).
2.2
Photosensitivity
Generally, the word of photosensitivity refers to a permanent change of the refractive index of the core of an optical fibre, when it is exposed to the light with characteristics wavelength and intensity, which depends on the core material itself.
Hence, the technique for inscribing or fabricating Bragg grating inside the fibre’s core has become emerged. Not only that, the FBG also creates renewed interest in diverse modern optoelectronics, optical fibre sensors and optical fibre communication system
(J.Hongzhi and L.Yulin, 2000), as they offer a number of inherent advantages, which include their ability to be lightweight, small size, passive, low power and resistant to electromagnetic interference, high sensitivity and environmental ruggedness (Shizhuo
Yin et.al
, 2008).
8
2.3
Fibre Bragg Grating
Fibre Bragg gratings are made from a simple ordinary single mode fibre. Figure
2.2 shows the diagram of fibre Bragg grating, where the grating is constructed in the fibre core by varying the index of refraction of the core along the fibre’s length (R.Hui
and M.O.Sullivan, 2009).
Figure 2.2: Illustration of fibre Bragg grating (R.Kashyap, 1998)
The FBG acts as a mirror, where the light guided along the fibre core are scattered by the regularly-spaced index variation, which then causes the waves to interfere with each other in the fibre (Al-Azzawi, 2007). A constructive interference occurs when the light at the wavelength hits each index peak at the same phase, and is selectively reflected back toward the source. These are called resonant waves. The spacing of the grating matches the resonant wavelength, b
2 n eff
, known as the
Bragg wavelength. Otherwise, light scattered at other wavelengths by the grating is out of phase and cancels out by destructive interference. The waves transmitted though the fibre is called non-resonant waves.
9
Basically, the Bragg gratings must satisfy both energy and momentum conservations (Othonos and Kalli, 1999). Figure 2.3 shows a diagram of the Bragg gratings inscribed in the core of an optical fibre.
Figure 2.3: Schematic diagram of FBG (K.O.Hill and G.Meltz, 1997)
In Figure 2.3, the frequency of the incident and reflected radiations are equal, that is
2
1 due to energy conservation. However, for momentum conservation, the wavevector of the scattered radiation, k
2 is the additional value of the incident wavevector, k
1 and the grating vector,
K .
This equation can be simplified as, k
2
k
1
(2.1)
The magnitude for both
k
1 and k
2 can defined as k n
2 n and the magnitude of the grating plane is K 2 , where known as the grating spacing. Since the photon frequencies are identical for the two propagating waves, hence, Equation (2.1) becomes
2
2 n eff
b
2
(2.2)
This, then, simplifies to the first-order Bragg condition
b
2 n eff
(2.3) where b is the Bragg grating wavelength, which is the free space centre wavelength of the input light that will be back-reflected from the Bragg gratings, and n eff is the effective refractive index of the fibre core at the free space centre wavelength, (Othonos and Kalli, 1999).
10
2.4
Parameters of fibre Bragg grating
The FBG performance is influenced by the centre wavelength, bandwidth and reflectance peak. The centre wavelength refers to the Bragg wavelength, which given in
Equation (2.3). The peak reflectivity, R and the bandwidth, of a FBG of length L are given approximately by (K.Thyagarajan and A.Ghatak, 2007)
R tanh 2 L (2.4) and
n
2 b eff
L
1
2 L 2
2
1 / 2
(2.5) where
nI
b
Here, n is the peak refractive index change within the grating and I is given by
(2.6)
I 1 exp
2 a w 2
2
(2.7) where a is the radius of fibre core and w represents the Gaussian spot size of the fundamental modes.
The FBG posses basic parameters that control the performance, namely, the grating period, the grating length, the modulation depth, the effective refractive index profile and the wavelength of the incoming light (Al-Azzawi, 2007). In this section, these parameters will be discussed and their relationships examined.
2.4.1 Grating period
Generally the gratings can be made in various shapes such as sinusoidal, square or triangle. The gratings can have uniform and non-uniform period. In this thesis, the uniform FBG is used. The uniform Bragg grating means that the grating period, , and
11 the refractive index change, n , are constant over the whole length of the gratings. The grating period, shown in Figure 2.2 is directly related to the phase mask period, given by equation
PM
2
(2.8) where Λ is the grating period and Λ
PM is the phase mask period. The grating period is only determined by the phase mask period and the grating strength is also directly related to the efficiency of the beams which diffracted by the phase mask in ±1 order.
The grating period, Λ is also related to the grating length L , and the index perturbation strength n . These important parameters are useful for fabricating FBGs.
2.4.2 Effective refractive index
The value of effective refractive index is different for each individual mode, and generally is defined as n eff
b
2
(2.9) where
B is the Bragg wavelength and Λ is the grating period. The effective refractive index has the similar meaning for the light propagation in a waveguide.
2.4.3 Grating Length
According to T.Erdogan (1997), K.Thyagarajan and A.Ghatak (2007), the grating length is related to the bandwidth in the reflection spectrum, where the peak reflectivity implies a value of L , as mentioned in Equation (2.8) and (2.9).
12
The bandwidth, as shown in Figure 2.4.
defined as the wavelength spacing between the first minima
Figure 2.4: Reflection spectrum of fibre Bragg gratings (Fuxi Gan and Lei Xu, 2006)
The bandwidth can be increased or decreased by increasing or decreasing the grating length while keeping the product nL constant. The equation of grating length expressed as
L
n
eff
2
B
tanh 1
2
2 (2.10)
2.5
Fabrication technique of fibre Bragg gratings
The fabrication of FBG typically involves the illumination of the core material with ultraviolet laser light which induces some structural changes and permanent modification of the refractive index. Consequently, a variety of different approaches to inscribe the Bragg gratings have been developed, which can be grouped into two main categories; internally and externally written gratings (Othonos and Kalli, 1999).
13
2.5.1 Internal inscription of Bragg gratings
According to I. Bennion et al.
(1996), internal inscription means that the grating is written directly into germanosilicate optical fibre as periodic perturbations of the refractive index along the fibre length. The grating which known as “Hill grating”
(R.Kashyap, 1999) was first achieved by interfering light that propagated in a forward direction along an optical fibre with light that was reflected from the fibre end and propagated in a backward direction (M. Bass, 2002). Figure 2.5 shows the experimental setup used for generating self-induced Bragg grating.
Figure 2.5: A typical setup used for generating self-induced Bragg grating
(Hill et al.
, 1978)
In this experiment, the grating was formed by the standing-wave interference pattern set up by counter propagating beams of light at 488 nm or 514.5 nm from an
Argon ion laser. Permanent and very narrowband Bragg reflection filters of order one meter in length were formed with reflectivity approaching 100%, following the exposure of several minutes’ duration (I. Bennion et al.
, 1995), with a refractive index change in the order of 10 -5 to 10 -6 and FWHM of 200 MHz (K.O. Hill et al.
, 1993). Unfortunately, the earliest internal writing method has some limitations which cause the development of Bragg gratings to become sluggish.
14
These are some of the disadvantages of internal writing of FBGs. For example, this experiment is not reproducible. It can only be functioned at light wavelengths in the visible close to the wavelength of the writing light (Hill and Meltz, 1997). At that time, only filters in the visible blue-green spectrum (488 nm and 514.5 nm) have been written.
This does not correspond to the spectrum for fibre optic communications ranged in the infrared region (700 nm to 1600 nm). Nevertheless, with the discovery of a new inscribing method by Meltz et al.
in 1989, those disadvantages have been overcome.
2.5.2 External inscription of Bragg gratings
The external writing method which require sub-micron resolution and stability, was first demonstrated in 1989 by Meltz and his friends, who recognized from the work of Lam and Garside (D.K.W.Lam
et al.
, 1981) that photosensitivity was a two photon process that could be made much more efficient if it were a one photon process at a wavelength in the 5 eV (245 nm) germania oxygen-vacancy defect band (K.O.Hill and
G.Meltz, 2000). As well the writing efficiency can be improved (I.Bennion
et al.
, 1996), the FBGs produced by this method are allowed to operate at wavelengths other than near the writing wavelengths (R.Kashyap, 1998). The externally inscribed Bragg grating is further divided into three main categories; interferometric, point-by-point and phase mask technique (Othonos and Kalli, 1999). The techniques differ in the principle of writing and consequently, in the equipment used in writing process.
The interferometric techniques introduced by Meltz et al.
(1989) exist in several various manifestations (B.A.Tahir
et al.
, 2007), and the most versatile one is called amplitude-splitting interferometric technique. In this technique, the incoming ultraviolet
(UV) laser beam is split into two or more beams and recombined at a certain angle, known as mutual angle, , to form an interferometric pattern inside the photosensitive fibre, inducing a permanent refractive index modulation (D.Basting and G.Marowsky,
2005).
15
The setup of amplitude-splitting interferometric is explained specifically in
Figure 2.6. An excimer-pumped dye laser with 486-500 nm wavelength operation was frequency doubled using a non-linear crystal, to supply a UV source in the 244 nm band with adequate coherence length. The UV laser light is divided into two equal intensity beams. Subsequently these beams recombine after having undergone a series of reflections in each optical path to form an interference pattern. A pair of cylindrical lens which placed outside the interferometer is used to focus the light onto the fibre, resulting higher intensities at the fibre core, thereby improving the grating inscription.
Figure 2.6: Amplitude-splitting interferometer (Othonos and Kalli, 1999)
Figure 2.7 : Interference fringes induced by two interfering UV beams
(I.Bennion
et al .
, 1996).
16
The grating is photoinduced as a spatial modulation of the core refractive index with a period uv
2 sin determined by the angle between the two writing beams of wavelength uv
(I.Bennion
et al .
, 1996). Thus, Equation (2.3) of Bragg wavelength can be simplified as b
uv n eff sin . It shows that the Bragg wavelength can be varied either by changing the wavelength of the basic laser beam, uv and/or . By changing the intersecting angle, having a Bragg wavelength equal to uv
, it is possible to write Bragg grating for almost any wavelength (K.T.V.Grattan and B.T.Meggit,
2000).
In 1993, Malo et al.
discovered another method of grating inscription known as point-by-point technique. This involves directing a tightly focused beam of UV light onto the core for a brief period, stepping the fibre along by the grating period and then repeating the process many times (D.A.Jackson and D.J. Webb, 2004). The major advantage of this technique is, it is flexible to alter the Bragg grating parameters. The structure of the grating is built up a point at a time so that variations in grating length, grating pitch, and spectral response can easily be incorporated. Therefore, it is suitable to fabricate spatial mode converters, polarisation mode converters or rocking filters that have a grating period, Λ, ranging from tens of micrometers to tens of millimeters (K.T.V
Grattan and B.T. Meggitt, 2000). Unfortunately, this technique is tedious and requires a longer processing time. Some error in the grating spacing may possibly occur resulting in a small variation in the fibre strain or thermal effects.
One of the common and most effective methods proposed for writing the Bragg gratings in photosensitive fibre is the phase mask technique, which was originally introduced by Hill and Anderson in 1993 (K.O.Hill
et al.
, 1993 and D.Z.Anderson
et al.
,
1993). In this method, an ultraviolet (UV) source will be focused through the 0 th order suppressed phase mask onto the fibre. The interference pattern formed by the phase mask in conjunction with UV light induces a refractive index modulation in the core of the fibre (B.Kouskousis
et al ., 2006). Phase mask is a one-dimensional surface relief grating. It usually has a square wave shape in profile and is binary phase grating. The
UV laser beam will pass through the phase mask to form a three-dimensional (3-D)
17 interference field, which is useful for photo-imprinting a refractive index modulation in a photosensitive optical fibre core (Y.Qiu
et al ., 1999). Phase mask may be formed either holographically or by electron beam lithography. However, the electron beam lithography method is more valuable because of its simpler writing setup and more reproducible characteristics (B.A.Tahir
et al ., 2006).
Figure 2.8 shows when the UV radiation at normal incident, the diffracted radiation is split into 0, +1, and -1 diffracted orders. However, the phase mask is designed to suppress the zero-order by controlling the depth of corrugations on the phase mask. The two ±1 diffracted order beams interfere to produce a periodic pattern that photoimprints a corresponding grating in the optical fibre (K.O.Hill and G.Meltz, 1997).
Figure 2.8: Schematic of the UV radiation at normal incidence of phase mask
(R.Kashyap, 1998).
18
The interference pattern has a period of grating related to the diffraction angle
m
/ 2 by
2 sin
uv m
/ 2
2 pm (2.11) where pm is the period of the phase mask, is the period of the fringes and uv is the
UV wavelength. The period of the grating etched in the mask is determined by the required Bragg wavelength
Bragg for the grating in the fibre, yielding
N
Bragg
2 n eff
2 pm where N 1 is an integer indicating the grating period (R.Kashyap, 1998).
(2.12)
The phase-mask technique is chosen because of its simplicity, suitability for mass production (N.Sayers
et al.
, 2005), reduced mechanical sensitivity (S.Suchat and
P.P.Yupapin, 2003), while yielding high performance gratings (M.Bass, 2002). The most well-known UV source, which is KrF excimer laser, is used to fabricate Bragg grating because of its low spatial and temporal coherence properties (E.E.Mayer
et al.
, 1999).
The low spatial coherence requires the fibre to be located in proximity to the grating corrugations on the phase mask, to induce maximum modulation in the index of refraction. The further away the fibre is placed from the phase mask, the lower will be the index modulation, resulting in low reflectivity Bragg gratings (S. Suchat and P.
Yupapin, 2003). Thus, it is clear that the separation of the fibre from the phase mask is an important parameter to produce good quality gratings that is relatively easy to fabricate. However, by placing the fibre in contact with the fine grating corrugations, it may damage the phase mask.
At the moment, the techniques used for fabricating Bragg gratings are still an active area of research interests, to enhance the performance of the photoimprinted gratings and diminish the manufacturing costs (K.O.Hill, 2000).
19
2.6
Fabry-Perot Bragg Gratings
The conventional Fabry-Perot (FP) interferometer shown in Figure 2.9 consists of two parallel flat semi-transparent mirrors separated by a fixed distance. This arrangement is called an etalon (Fabry and Perot, 1897). Light that enters the etalon undergoes multiple reflections and the interference of the light emerging from the etalon during each bounce causes a modulation in the transmitted and reflected beams.
Figure 2.9 : Fabry-Perot etalon
In recent times, a new configuration of FP interferometer has been introduced, by fabricating two Bragg gratings on a single mode optical fibre, where the Bragg gratings will be functioned as the mirrors. The gratings are placed separately at a certain distance, d , which then can create a cavity between the gratings. This new configuration illustrated in Figure 2.10 is recognized as Fabry-Perot Bragg gratings, which can be useful in diverse kinds of optoelectronics, photonics and sensing field.
Figure 2.10: Illustration of FP Bragg gratings (Y.O.Barmenkov
et al.
, 2006)
20
For example, it can be used on optical clock recovery, bandpass filter for WDM systems, dispersion slope compensation for WDM channels and sensors (L.P.Pellegrino
et al.
, 2005). It also offers several advantages compared with traditional FP. One of the advantages is focussed on the possibility to choose the free-spectral-range (FSR) and the resonant wavelength of the cavity simultaneously, without changing the dispersive material between gratings (A.Meloni
et al., 2002). In addition, this new configuration is very compact and suitable for high density integrated optics, due to higher refractive index of the cavity material.
A similar configuration to Figure 2.10 was proposed by Y.O. Barmenkov et al . in
2006. However, in their research, they focus to study the properties of Fabry-Perot cavity in terms of FBG’s effective length. They demonstrate that mode-spacing increases with an increase in the grating’s reflectivity, owing to the grating effective length shortening. Hence, this shows that the effective grating length is determined by the group delay of the grating, which depends on its diffraction efficiency and physical length.
Xu Ou et al.
(2008) have theoretically analyzed and modelled the characteristics of transmission spectrum for the all fibre multi-cavity Fabry-Perot filters configuration based on fibre Bragg gratings. In this study, the transmission peaks of single-cavity and two-cavity FP structures are compared, and the results show that by introducing another one more cavity, the flatness of the top and steepness at the edge of the transmission peak can be improved, as compared to the single-cavity FP structure. Furthermore, they also found that the steepness of peak slope can be improved by increase of FBG reflectivities, and these kinds of filter can be used as narrow-band single-channel selectors and multi-channel wavelength de-multiplexing by properly choose the length of cavities and reflectivities of FBGs.
The usage of Fabry-Perot device is ever increasing, as it can be used as a sensor due to the advantages of simple structure, low modulated voltage and cost effectiveness
(W.Wui
et.al
, 2008).
21
Historically, the first use of the fibre Fabry-Perot structure as a sensor was proposed by Kist and Soehler (S.F.O.Silva
et al., 2008); thereafter, extensive studies have been continued on the intrinsic and extrinsic types of optical fibre sensors.
Commonly, the Bragg grating sensors are used for temperature and axial strain measurement (S.V.Miridonov
et al ., 2001); however, C.Lan
et al.
(2008) reported that the FP Bragg grating can also be used as a liquid pressure sensor and blood pressure manometer, due to strain measurement resulting from blood pressure applied to the walls of an artery situated near the patient’s skin (A.V.Brakel
et al., 2005).
Therefore, it is predicted that the usage of FP Bragg grating will growth rapidly in the becoming of five years, to monitor physical, chemical, and biological parameters in industrial processes, medical treatment and ecosystem protection in our modern society (Sang X.Z.
et al., 2006).
In this research, the coupled mode theory and transfer matrix method were used to simulate the FP Bragg gratings. The value of separation distance between two FBGs, d , was varied to see the effects of transmission and reflection spectra produced by FP
Bragg gratings theoretically.
CHAPTER 3
SIMULATION OF FABRY-PEROT BRAGG GRATINGS
3.1
Introduction
In this chapter, a Matlab programme is used to model the FBG theoretically. The coupled mode theory (CMT) and transfer matrix method (TMM) will provide the mathematical basis in the numerical simulations. Only the TMM will be applied in this research in order to generate the transmission and reflection spectra of single FBG and dual FBGs respectively.
3.2
Coupled Mode Theory
The characteristics of fibre Bragg grating can be analysed using CMT which are derived from Maxwell equations. According to T.Erdogan (1997), CMT is a good tool for obtaining quantitative information about the diffraction efficiency and spectral dependence of fibre gratings, due to its simplicity, intuitively and accuracy. It also has been successfully applied to many different analyses of the uniform gratings, nonuniform gratings, tilted gratings and phase-shifted gratings (S.Shaari and M.C.Shong,
2000).
23
The fibre phase grating is produced by exposing an optical fibre to a spatially varying pattern of ultraviolet intensity. Thus, the effective refractive index, n eff of the guided modes can be simplified as (T. Erdogan, 1997)
n eff
( z ) n eff
( z ) 1 cos
2
z ( z )
(3.1) where n eff is the “dc” index change spatially averaged over a grating period, v is the fringe visibility of the index change, Λ is the nominal period, and Φ(z) describes grating chirp.
In the ideal-mode approximation of coupled mode theory, the transverse component of the electric field is assume as a superposition of the ideal modes labelled j
(the modes in an ideal waveguide with no grating perturbation), and thus can be written as t
( x , y , z , t ) j
A j
( z ) exp( i j z ) B j
( z ) exp( i j z )
jt
( x , y ) exp( i t ) (3.2) where A j
(z) and B j
(z) are slowly varying amplitudes of the j th mode travelling in the +z and –z directions, respectively. The transverse mode field jt
( x , y ) describes either the bound-core or radiation LP modes or cladding modes.
When the modes are orthogonal in an ideal waveguide, the presence of a dielectric perturbations causes the modes to be coupled such that the amplitudes A j
(z) and B j
(z) of the j th mode evolve along the z axis according to (T.Erdogan, 1997) dA j dz
i k
A k
( K t kj
K z kj
) exp[ i ( k
j
) z ] i k
B k
( K t kj
K z kj
) exp[ i ( k
j
) z ] (3.3) dB j dz
i k
A k
( K t kj
K z kj
) exp[ i ( k
j
) z ] i k
B k
( K t kj
K z kj
) exp[ i ( k
j
) z ] (3.4)
24
In Equation (3.3) and (3.4), K t kj
( z ) is the transverse coupling coefficient between modes j and k given by
K t kj
( z )
4
dxdy ( x , y , z ) e
kt
( x , y ) * jt
( x , y ) (3.5) where is the perturbation to the permittivity, approximately 2n n when n n.
The longitudinal coefficient K z kj
( z ) is analogous to K t kj
( z ) , but generally K z kj
( z )
K t kj
( z ) for fibre modes, and thus this coefficient is usually neglected. Hence, the coupled mode equations (3.3) and (3.4) can be written as (J.Bao
et al.
, 2001) dA j dz
i k
A k
K t kj exp[ i ( k
j
) z ] i k
B k
K t kj exp[ i ( k
j
) z ] dB dz j i k
A k
K t kj exp[ i ( k
j
) z ] i k
B k
K t kj exp[ i ( k
j
) z ]
(3.6)
(3.7)
In most fibre gratings, the induced index change n(x,y,z) is approximately uniform across the core and nonexistent outside the core. The core index can be describe as Equation (3.1), but n eff
( z ) have to be replaced by n co
( z ) .Two new coefficients are defined as
kj
( z )
n
2 co n co
( z ) core dxdy
kt
( x , y )
* jt
( x , y ) (3.8)
kj
( z ) v
2
kj
( z ) where coefficient. Thus, the general coupling coefficient can be written as
(3.9)
is a “dc” (period average) coupling coefficient and is an “ac” coupling
K t kj
( z ) kj
( z ) 2 kj
( z ) cos
2
z ( z )
(3.10)
25
3.3
Transfer Matrix Method (TMM)
The TMM approached developed by Yamada and Sakuda (1987) is a very powerful tool to investigate the characteristics of periodic structures (S.Pachnicke,
2007). It is also used to solve the coupled mode equations and to obtain the spectral response of fibre Bragg gratings (J.C.C. Carvalho et al.
, 2006).
In this approach, the grating is divided into uniform sections, where each section is represented by a 2 2 matrix. By multiplying these matrices, a global matrix that describes the whole grating is achieved. The refractive index inside an i th uniform section of a Bragg grating can be assume as n ( z ) n eff
n i cos
2 z
i
(3.11) where n eff is the effective refractive index of fibre core, amplitude modulation, and Λ i is the section grating period.
n i is the refractive index
Figure 3.1 shows a non-uniform fibre grating of length, L , which is divided into
M uniform gratings.
Figure 3.1: The TMM applied to obtain the spectral characteristics of a fibre grating
(K.T.V.Grattan and B.T.Meggitt, 2000).
26
The propagation through each uniform section i is described by a matrix T i defined as
R i
S i
T i
R
S i 1 i 1
(3.12)
Thus, the matrix T i for one section of the Bragg grating is defined by
T i
cosh
i dz i
j
i i
j sinh
i i sinh
i dz i
i dz i
cosh
j
i i
i dz i
sinh j
i i
i dz i
sinh
i dz i
(3.13)
Here, j 1 , S i is the slowly varying amplitudes of the fundamental mode travelling in the +z and –z directions, dz is the length of the i th uniform section, and are the local coupling coefficients for the i th section, and self coefficient given by
1
2 d dz with the derivative
1
2 d dz
2 2 .
is the general “dc”
(3.14) describes the possible chirp in the grating, while the detuning describes as
2 n eff
1
1
Bragg
(3.15) where
Bragg is known as the Bragg wavelength and is “dc” coupling coefficient. It is then related to the “ac” coupling coefficient where
2
(3.16) with is a fringe visibility. Once all the matrices for each individual sections is known, the output amplitude becomes
R
M
S
M
T
R
0
S
0
; T T
M
T
M 1
...
T i
...
T
1
(3.17)
27
Equation (3.13) to Equation (3.16) are also valid for dual FBGs. However, the output amplitude produced by the dual FBGs, are different as compared to the output amplitude of a single FBG. This is due to the existence of a phase shift matrix equation which is represented by
P
exp
0 i
2 k exp
0 i
2 k
(3.18) where
2 k
2 n
eff d
, with d is the separation distance between two FBGs.
Thus, the equation of dual FBGs transmission spectrum becomes
T T
M
P T
M 1
(3.19)
CHAPTER 4
RESEARCH METHODOLOGY
4.1
Introduction
This chapter will describe the experimental work that have been done, which includes the fibre’s preparation, the fabrication process of a single FBG, as well as the modeling and simulation work of single FBG. For dual FBGs, this research will mainly focus on the modelling and simulation work.
4.2
Preparation of fibre
In fibre’s preparation, a cleaver is used to cut a one meter of 1550 nm photosensitive fibre and removed the jacket of small section at fibre ends. The alcohol is used to make sure that the cladding is fully clean from the small pieces cut of the jacket, before the fibre’s core is put into a bare adapter for cleaning process. The fibre’s core is polished by using a lapping film, clean water and a polisher.
A portable microscope is used to check the cleanness of the fibre core. If the core is still dirty, then the process is kept repeated until the dust has been removed. This is
29 important since the clean core will make the light source easier to enter and propagate along the fibre.
Figure 4.1 shows the fibre polisher, and Figure 4.2 shows the equipments needed for fibre preparation. It consists of an alcohol, a portable microscope, a bare adapter, and a cleaver.
Figure 4.1 : Fibre Polisher
Figure 4.2 : The apparatus during preparation of fibre
30
4.3
Fabrication of fibre Bragg grating
A phase mask technique is used to inscribe the Bragg gratings inside the fibre’s core. The equipments needed in the fabrication system consists of an excimer laser machine, a mask aligner, a tunable laser source (TLS), an optical spectrum analyzer
(OSA), and also a phase mask. Figure 4.3 shows the experimental setup during the inscription process.
Figure 4.3 : The experimental setup of fabrication process
Before the fibre was placed on top of the phase mask holder, a cleaver is used to remove 5 cm of fibre’s jacket at the centre of photosensitive fibre. It is necessary to clean all the optical elements in mask aligner such as reflecting mirror, cylindrical lens, a phase mask and quartz plate by using a compressed nitrogen gas, to remove all dust which then will affect the efficiency of the process. The excimer laser needs to be warm up in 8 minutes before the process can be started. Several laser pulses in the range of
100-130 mJ at 20-30kV voltage supply were tested in a closed tube, to ensure the energy status of the excimer laser was in the right condition. If not, a new gas need to be refill
31 into the machine, with a fine tune on the optical alignment of the laser pulses was required after every new fill (H.S.Phing, 2008).
As illustrated in Figure 4.3, the fibre was placed on the phase mask holder, with a pair of magnet is used as a clamp. Then, the phase mask holder together with the fibre has been put in the mask aligner, and both of the fibre ends were connected to the TLS and the OSA. The TLS provides a light source which passes through the optical fibre, while the OSA will capture the reflection or transmission spectra of fabricated FBG. The process is started by running the excimer laser machine while at the same time; the readings of UV laser pulse energy could be taken by using a power meter. Instead of that, the initial time of the process should also be recorded. During the fabrication process, the UV laser beam was directed into the phase mask and focused with a cylindrical lens onto the fibre. The transmission spectrum of FBG has been monitored through the OSA until the very minimum dip transmission spectrum is appeared. At this time, the writing process has to be stopped, and the final time will be recorded. The details of the equipments being used in this experiment will be discussed in the next subchapter.
4.3.1 Excimer Laser Machine
An excimer laser is a form of ultraviolet laser which is typically use as a combination of an inert gas (argon, krypton or xenon) and a reactive gas (fluorine or chlorine). The UV light from the excimer laser will be absorbed by the molecule of the atom and finally will destroy the fibre through ablation process. This research used a
COMPEX excimer laser machine from Germany, made by a company named Lambda
Physik AG. This machine is designed to emit the laser light in pulses (Lambda Physik,
2003), with a krypton fluoride (KrF) gas has been chosen as a writing source.
32
Figure 4.4 shows the picture of COMPEX excimer laser used in this study, while
Figure 4.5 shows the inner part of the excimer laser, which consists of a laser tube, high voltage power supply, thyratron, capacitor array, communication interface, energy monitor and vacuum pump.
.
Figure 4.4: A COMPEX excimer laser
Figure 4.5: The inner part of the excimer laser (Noor Azura, 2007)
According to Figure 4.5, a high voltage power supply will provide the electrical energy for each laser pulse, whereby this energy will be stored by a capacitor array.
When a laser pulse is needed, a thyratron as an electronic switch, will enabled the capacitors to be discharged. The energy is then transferred to the laser-active medium and thus stimulates the laser pulse. In order to monitor the components of the excimer
33 laser, the communication interface is used, whereby a handheld keypad was functioned as a remote control of the system, as shown in Figure 4.6.
Figure 4.6: A handheld keypad
4.3.2 Mask aligner
A mask aligner shown in Figure 4.7 is design to align the laser beam before it irradiates the photosensitive fibre.
Figure 4.7 : Mask aligner
34
The system consists of an exposure unit, which contains a manual beam attenuator, plano-concave cylindrical lens, two plano-concave spherical lenses, a mask holder and CCD camera, as illustrated in Figure 4.8.
Figure 4.8: An illustration of the light propagation inside the mask aligner
The optical system in the mask aligner will transport the beam from the laser onto a phase mask, which is held in a removable holder. The fibre which placed inside the mask aligner need to be aligns to produce a good grating, and this can be monitored through the CCD camera. After the override key at the control panel switched ON, the attenuator unit control was turned into minimum transmission, and thus the front panel of the exposure unit is removed. The laser is started at the low power with the repetition rate of 1 Hz, and the shutter on the control panel is opened. After that, the laser beam will pass centrally through the shutter and hits the first turning mirror in centre, which then will initially aligned.
35
Then, the beam using the second turning mirror was adjusted to centre beam on the third turning mirror. The fibre jig was placed on its three point mounting and the third turning mirror is used to align the laser beam to be central on the aperture plate. In the last stage, the position of the cylindrical lens was adjusted, so that the beam is centred and focused to the aperture plate.
4.3.3 Phase Mask
A phase mask shown in Figure 4.9 is a one-dimensional surface relief grating and made from a fused silica. This phase mask is used to spatially modulate and diffract the UV laser beam onto the fibre core to produce the gratings. Each phase mask has its own value of grating pitch on their surface. In this research, the phase mask used has the value of grating pitch of 1070.22 nm, thus it is suitable for an operating wavelength at
248 nm like KrF excimer laser.
phase mask
Figure 4.9: Phase mask
36
4.3.4 Tunable Laser Source (TLS)
A TLS model MG9637A from Anritsu Corporation in Figure 4.10 was used to manipulate the input power of laser source. The TLS provide a wavelength in the range of 1498.764 nm up to 1581.294 nm. The TLS also need to be warmed up before it could be used. Generally, it took an hour to warm-up this TLS.
Figure 4.10 : Tunable Laser Source
4.3.5 Optical Spectrum Analyzer (OSA)
In this research, an OSA model MS9710B was used to monitor and capture the transmission or reflection spectra of FBG. The MS9710B OSA as shown in Figure 4.11
provides excellent wavelength accuracy and waveform shape.
Figure 4.11: Optical Spectrum Analyzer
37
It covers a wide wavelength range from 600 nm to 1750 nm. It is necessary to warm up the OSA in 15 to 30 minutes, before it can be used. One of the advantages using the OSA, the measured data can be stored or saved in the floppy disk in the format of bitmap, so that it is easier to recall or recheck the data if it is needed.
4.4
Modelling of single fibre Bragg grating
In the simulation of single FBG, the initial FBG’s parameters have been set as shown in Table 4.1. The Bragg wavelength is modelled in the range of 1551 nm to
1551.6 nm. Equations (3.13) to (3.16) have been used to generate the transmission and reflection spectrum produced by the single FBG.
Table 4.1 : Relevant setting of FBG’s parameters
Parameters Settings
1551.29 nm Bragg wavelength,
Bragg
Reflectivity, R
Effective refractive index, n eff
Grating length, L
Section of phase mask, M
Grating period, Λ
0.718
1.4495
1.458 cm
100
L/M
The simulation work of single FBG is extended for different values of reflectivities and grating lengths in order to study the effects of the FBG transmission spectrum.
38
The computational flow chart of single FBG for different value of reflectivities is depicted in Figure 4.12.
Start
Initial parameters are Bragg wavelength, index, n eff
Bragg
, effective refractive
, and grating length, L.
T i
cosh
i dz i
j
i i
Main equations involved: j
i i sinh
i dz i
j
i i sinh
i dz
i
cosh
1
2 d dz
i dz i
sinh j
i i
i dz sinh i
i dz i
2 n eff
1
1
Bragg
2
Reflectivity, R = 0.318, 0.718,
0.918
Plot graph of FBG transmission spectrum
Finish
Figure 4.12 : Flow chart of a single FBG for different reflectivities
39
While Figure 4.13 shows the computational flow chart of single FBG for different value of grating lengths.
Start
Initial parameters are Bragg wavelength, index, n eff
Bragg
, effective refractive
, and reflectivity, R.
T i
cosh
i dz i
j
i i
Main equations involved: j sinh
i i
i sinh dz
i
i dz i
cosh
1
2 d dz
i j dz
i i i
sinh j
i i
i dz sinh i
i dz i
2 n eff
1
1
Bragg
2
Grating length, L = 0.458 cm,
1.458 cm, 5.458 cm
Plot graph of FBG transmission spectrum
Finish
Figure 4.13 : Flow chart of a single FBG for different grating lengths.
40
4.5
Modelling of dual fibre Bragg grating
In dual FBGs, two Bragg gratings are written in the fibre’s core, in which the gratings are placed separately with a certain value of separation distance, d.
In the simulation of dual FBGs, the initial FBG’s parameters have been set as shown in Table
4.2. The Bragg wavelength is modelled in the range of 1551 nm to 1551.6 nm. Equations
(3.13) to (3.16) and Equation (3.18) have been used to generate the transmission and reflection spectrum of the dual FBGs
Table 4.2 : Relevant setting used in simulation of dual FBGs.
Parameters Settings
1551.29 nm Bragg wavelength,
Bragg
Reflectivity, R
Effective refractive index, n eff
Grating length, L
Section of phase mask, M
Grating period, Λ
Separation distance, d
0.718
1.4495
1.458 cm
100
L/M
0.5 cm
The simulation work of dual FBGs is extended for different values of separation distance between two FBGs in order to observe the effects of the FBG transmission spectrum.
41
The computational flow chart of dual FBGs for different separation distances between two FBG is depicted in Figure 4.14.
Start
Initial parameters are Bragg wavelength,
Bragg
, effective refractive index, n eff reflectivity, R and grating length, L.
,
T i
cosh
i dz i
P
j
i i
Main equations involved : j
i i sinh
i dz i
j
i i sinh
i dz i
cosh
i dz i
1
2 d dz
exp
0
, i
2 k
2 n eff exp
0 i
2 k
1
,
1
Bragg
2 k
sinh j
i i
i dz i
sinh
i dz i
,
2 n eff
d
2
0.5 cm < d < 5.5 cm
Plot graph of FBG transmission spectrum
Finish
Figure 4.14 : Flow chart of dual FBGs for different separation distance
CHAPTER 5
RESULTS AND DISCUSSIONS
5.1
Introduction
In this chapter, the results obtained from the experimental and modelling studies will be discussed. The experimental data are obtained during the fabrication process of single FBG, while the simulation data of single FBG and dual FBGs are taken from the modelling work by using Matlab programming..
5.2
Results on Fabrication Process of Single Fibre Bragg Grating
In this research, fibre Bragg grating is produced by using a phase mask technique, whereby the KrF excimer laser was used with the phase mask, to write the gratings inside the fibre core. The transmission or reflection spectra are monitored through the optical spectrum analyzer (OSA), where the process will then be stopped when the minimum dip value of transmission spectrum has been achieved.
43
Figure 5.1 shows a typical transmission spectrum of the fabricated FBG. The value of Bragg wavelength, dip power and bandwidth can be obtained directly from the
OSA.
(ii) Bandwidth
(iii) Dip power
(i) Bragg wavelength
Dip power
Figure 5.1 : Transmission spectrum of fabricated FBG
A clear single transmission dip is observed at 1551.29 nm with a dip power value of 6.6 dB, and the bandwidth of 0.12 nm. The reflectivity can be calculated using
Equation (5.1)
R
1 10
D
10 100 % (5.1) where, D is the dip power in decibel. Hence, from calculation, the reflectivity for the sample FBG was 78.1%. From Figure 5.1, there are other small peaks in the FBG which might be due to other fibre modes (S.P.Yam
et al.
, 2009).
44
Table 5.1 : Data collected in the fabrication process of single FBG
FBG
FBG 1
FBG 2
FBG 3
UV pulse energy
( E uv
± 0.1) mJ
70.0
78.1
130.0
UV exposure time
( t uv
± 1) min
20
20
15
Dip power
( D ± 0.001) dB
Reflectivity
( R ± 0.1) %
Bragg wavelength
(
B
± 0.01) nm
Bandwidth
( ± 0.01) nm
1.560
6.600
2.575
30.2
78.1
44.7
1551.09
1551.29
1551.66
0.15
0.12
0.14
Table 5.1 summarizes the analysis of three fabricated FBG, named as FBG 1,
FBG 2 and FBG 3. Results clearly show that the UV exposure time depends on the UV pulse energy. The higher UV pulse energy, the shorter exposure time is needed, in order to achieve the highest reflectivity. The quality of fibre Bragg grating can also be determined by knowing its reflectivity value. A higher reflectivity indicates that the FBG is of good quality. FBG 2 shows the highest reflectivity value as compared to FBG 1 and
FBG 3. The reflectivity of nearly 100% will produce a stronger grating, while for reflectivity less than 50%, it will produce a weak grating (Othonos and Kalli, 1999).
Hence, from this experiment, FBG 2 is categorized as a good quality grating.
During the fabrication process, there are some parameters which cannot be controlled, such as the effective refractive index and the grating length of FBG. The refractive index depends on the exposure time of UV light to the photosensitive fibre.
The effective refractive index can be determined by using Equation (2.4) and (2.5) where the calculated value of grating period is 535.11 nm and with the given value of phase mask period from the manufacturer is 1070.22 nm. From these calculations, the effective refractive indexes of the three FBGs are 1.4493, 1.4495 and 1.4498
respectively. This means that the average value of effective refractive index of every fabricated FBG in this research is slightly near to 1.45. This is almost as equal to refractive index of the cladding.
45
Another important parameter that is affected during the fabrication process is the grating length, L . From Equation (2.10), it is found that the grating length is inversely proportional to the full bandwidth. For the three fabricated FBGs, the grating lengths are
1.112 cm, 1.458 cm and 1.200 cm respectively.
The reading of fabricated FBGs is measured again after a period of five months to check whether there is any change to the Bragg wavelength. Table 5.2 shows the comparison of Bragg wavelength’s readings before and after a period of five months.
Table 5.2 : Comparison values of Bragg wavelength after a period five months
FBG Initial
Bragg
Bragg after 5 months Difference
(
B
± 0.001) nm (
B
± 0.001) nm (nm)
FBG 1
FBG 2
FBG 3
1551.090
1551.290
1551.660
1550.001
1549.972
1551.019
-1.089
-1.318
-0.641
From Table 5.2, the value of Bragg wavelength for three fabricated FBGs shows negative value of differences. This means that the value of Bragg wavelength produced by all fabricated FBGs becomes smaller, after it has been kept for a period of five months. This phenomenon will not occur if the annealing process is taken into account, since it insures the stability during the lifetime of the device (P.Lefebvre
et al ., 2006).
46
5.3
Result on Modelling of Fibre Bragg Grating
5.3.1 The Model of Single and Uniform Fibre Bragg Grating
Various kind of methods can be used to model the fibre Bragg gratings. In this research, the Matlab software is chosen, since it is user friendly. The transfer matrix function equations are applied in the Matlab coding, to generate the transmission spectrum of single and uniform FBG as depicted in Figure 5.2.
Figure 5.2: Transmission spectrum of single and uniform fibre Bragg grating
The spectrum is plotted for wavelength ranging from 1551 nm to 1551.6 nm, with the value of Bragg wavelength,
Bragg
= 1551.29 nm, effective refractive index, n eff
= 1.4495, grating length, L = 1.458 cm and reflectivity, R = 78.1% which are taken from the experimental data of FBG 2.
47
The results obtained from simulation are compared with the FBG transmission spectrum captured by the OSA as depicted in Figure 5.3 to Figure 5.5. In Figure 5.3, the transmission spectrum of FBG 1 is plotted in the range of wavelength 1550 nm to 1555 nm, with the Bragg wavelength,
B = effective refractive index, n eff
= 1.4493.
1551.09 nm, grating length, L =1.112 cm. and
(a)
(b)
Figure 5.3 : Transmission spectrum of FBG 1 from (a) experiment (b) simulation
48
In Figure 5.4, the transmission spectrum of FBG 2 is plotted in the range of wavelength 1550 nm to 1555 nm, with Bragg wavelength,
B = length, L =1.458 cm. and effective refractive index, n eff
= 1.4495.
1551.29 nm, grating
(a)
(b)
Figure 5.4: Transmission spectrum of FBG 2 from (a) experiment (b) simulation
49
In Figure 5.5, the transmission spectrum of FBG 3 is plotted in the range of wavelength
1550 nm to 1555 nm, with Bragg wavelength,
B =
1551.66 nm, grating length, L =1.2
cm. and effective refractive index, n eff
= 1.4498.
(a)
(b)
Figure 5.5: Transmission spectrum of FBG 3 from (a) experiment (b) simulation
From Figure 5.3 to Figure 5.5, it can be clearly observed that similar transmission spectrum profiles of single FBG are obtained for both experimental and simulation investigations.
50
When the size of FBG transmission spectrum is enlarged, a minor or small peak can be seen clearly on the spectrum, as shown in Figure 5.6. This may probably be due to the fabrication process when using the phase mask technique. However, in the simulation work, the FBG will produce a smooth line of transmission spectrum.
Figure 5.6 : Minor peak appears on the transmission spectrum of fabricated FBG.
5.3.2 The effect of reflectivity and grating lengths on Fibre Bragg Grating
Reflectivity is an important parameter which can be used to explain the fibre
Bragg grating characteristics. For example during the fabrication process, the reflectivity of Bragg wavelength is monitored through the OSA until the maximum reflection’s reading has been achieved. At the same time, the excimer laser machine must be stopped and the similar processes are repeated in order to make another FBG.
51
The reflection spectrum of FBG can be obtained by connected the FBG to TLS and OSA through a 2 2 coupler, as illustrated in Figure 5.7. The coupler is used to
52
This study will also investigate the effects of FBG transmission spectrum due to the changes of reflectivity value, R.
Table 5.3 shows the relevant setting used to simulate the FBG spectrum with three different values of reflectivity, R1 , R2 and R3 .
Table 5.3 : Relevant settings of single FBG with different value of reflectivity
Parameters
Bragg wavelength,
Bragg
Settings
1551.29 nm
Effective refractive index, n eff
Grating length, L
Section of phase mask, M
Grating period, Λ
Reflectivity 1, R1
Reflectivity 2, R2
Reflectivity 3, R3
1.4495
1.458 cm
100
L/M
0.318
0.718
0.918
Figure 5.9 shows that any changes in the FBG reflectivity will lead to a change in the transmission spectrum.
Figure 5.9: Transmission spectrum of FBG for different value of reflectivity
53
Any increase in reflectivity values will increase the dip power, and thus producing a deeper transmission spectrum. Theoretically, to prepare a good FBG, it is necessary to have reflectivity larger than 50%, in order to produce a strong grating.
However, in practical, the reflectivity is not easy to control, due to other factors, such as the lifetime of KrF gas excimer laser, the UV pulse energy and also the UV exposure time, which will affect the quality of grating created.
Another important parameter involved in the fabrication process is the grating length, L . The fabricated FBGs have similar value of L . Thus, the L value of FBG 2 is taken as a reference since FBG 2 produces a good quality Bragg grating. FBG 2 has a grating length of 1.458 cm, and thus, in simulation, the transmission spectrum of single
FBG is plotted for the values of L less and more than the reference grating length. Table
5.4 a summary of the parameters that have been set to model the FBG transmission spectrum for different value of grating length.
Table 5.4 : Relevant settings of single FBG with different value of grating length
Parameters Settings
1551.29 nm Bragg wavelength,
Bragg
Effective refractive index, n eff
Section of phase mask, M
Grating period, Λ
Reflectivity, R
Grating length 1, L1
Grating length 2, L2
Grating length 3, L3
1.4495
100
L/M
0.718
0.458 cm
1.458 cm
5.458 cm
54
Figure 5.10 shows the transmission spectrum produced when the value of grating length is varied. From the simulation work, the result clearly shows that the width of the transmission spectrum is increased when the value of grating length is decreased.
Practically, the grating length is difficult to monitor, due to the exposure length of the phase mask. Since the phase mask used in this study has an exposure length of 1.0 cm, each fabricated FBG will produce a grating length in the range of 1.0 cm to 1.5 cm.
Figure 5.10: Transmission spectrum of fibre Bragg grating for different grating length
5.3.3 The Model of dual fibre Bragg grating
The transfer matrix equations are used to simulate the dual fibre Bragg gratings.
In this study, the separation distance, d , between two Bragg gratings is varied, and thus their effect to the transmission spectrum of dual FBGs will be investigated. The relevant settings as shown in Table 4.2 in Chapter 4 are made, and the spectrums are plotted for wavelengths ranging from 1551 nm to 1551.6 nm.
55
Figure 5.11 shows the reflection and transmission spectrum of dual FBGs with separation distance, d , of 0.5 cm. Since this research only focuses on the simulation of dual FBGs transmission spectrum, the dual FBGs will produce a single reflection pattern similar with a reflection profile produced by a single FBG. Moreover, the matrix introduced in Equation (3.13) is only related to the transmission spectrum of FBG and not the reflection spectrum. On the basis of this, the dual FBGs in this research produces only a single reflectance peak compared to the transmission spectrum.
Maximum small peak
Figure 5.11: Dual FBGs with a separation distance of 0.5 cm
In addition, from Figure 5.11, there is a maximum small peak produced by dual
FBGs with a separation distance of 0.5 cm. The existence of this small peak may be attributed to the absorption process which occurs in the fibre’s core. Energy conservation requires that
T + R + A = 1 (5.2)
T is the transmission coefficient, R is the reflection coefficient and A is the absorption coefficient.
56
The light guided along the fibre’s core is absorbed at a certain value of the wavelength. This will only allow light waves with frequency that is equal to the resonant frequency of dual Bragg gratings to transmit, while blocking the other wavelength. This shows that dual FBGs can act as filter. For example, the dual FBGs with a separation distance of 0.5 cm, produces only one maximum small peak, meaning that there is only one light frequency that can be transmitted along the fibre length.
The simulation work has been extended into eleven different values of separation distance between two FBGs, which ranges from 0.5 cm to 5.5 cm, with an increment of
0.5 cm. The simulation results of dual FBGs are as attached in Appendix G. Figure 5.12
shows the numbers of maximum small peaks appearing at the transmission spectrum against the separation distance between two FBGs.
Number of maximum small peaks vs Separation distance between two FBGs
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4
Separation distance between two FBGs, d (cm)
5 6
Figure 5.12 : Graph plotted when the separation distance between two FBGs is varied.
Figure 5.12 shows that there is a linear relationship between the number of maximum small peaks observed and the separation distance between two FBGs. As the value of separation distance is increased, the number of maximum small peaks appearing at the transmission spectrum of dual FBGs will also be increased.
57
In other words, as the value of separation distance is increased, the number of filtered frequency for dual FBGs is also increased. Therefore, only selected wavelengths with certain value of frequencies are allowed to transmit at the fibre’s end.
One of the factors that may contribute to the existence of the maximum small peaks can be described in terms of the phase shift using Equation (3.18). The phase shift is related to the separation distance between two FBGs. The phase shift is the shift experience between directly transmitted beam and the beam which is transmitted after one roundtrip in the cavity.
Theoretically, light is transmitted when there is constructive interference and is reflected back when there is destructive interference. Hence, in this simulation of dual
FBGs, the constructive interference is created only if the separation distance of dual
FBGs is an integer number of specific wavelength, which d = m . Thus, for a specific separation distance, there is only discrete number of wavelength that fulfils this condition (S. Doric and J. L. Neron, 2007).
In the region of maximum transmission, similar behaviours of conventional FP etalon are produced in which the value of free spectral range (FSR) and full-width-halfmaximum can be obtained from the transmission profile, as shown in Figure 5.13.
Figure 5.13 : Profile of FSR and FWHM
58
The FSR is defined as spacing between two resonance peaks in frequency domain. It is related to the separation distance of dual FBGs, as follows:
FSR c
2 nd
(5.3) where, n is the refractive index of the gap material, c is the speed of light in vacuum, and d is the distance of two FBGs. In addition, the FSR is also related to the FWHM, which determines the finesse of the transmission line produced by dual FBGs. The finesse, F of the FP Bragg grating is defined as the ratio of FSR and FWHM where
F
FSR
FWHM
(5.4)
Theoretically, a higher finesse will show sharper transmission peaks with lower minimum transmission coefficient. Since all the transmission spectrum of dual FBGs for different value of separation distance in the simulation work produced sharper transmission peaks, it shows that this dual FBG configuration has a higher finesse.
5.4
Summary
Based on the results of this study, it can be summarized that to fabricate a strong
Bragg grating, the highest value of dip power is needed to produce the maximum reflectivity. During the experiment, the value of Bragg wavelength,
Bragg
, dip power, D, and bandwidth, be determined.
are captured from the OSA. Hence, by doing some mathematical calculations, the reflectivity, R , grating length, L , and effective refractive index, n eff can
This study also shows that some parameters cannot be controlled simultaneously during the fabrication process, such as the reflectivity and the grating length. Therefore, a simulation work is developed to see or monitor their effects to the transmission spectrum of FBG. From the simulation, the transmission spectrum of FBG becomes
59 wider if the grating produced is short, and looks longer when the reflectivity value is increased.
A coupled mode theory and transfer matrix equations are used for investigating the characteristics of single and dual fibre Bragg grating. The equations are applied in
Matlab, and the results produced were compared with the experimental work. In the simulation of dual FBGs, a linear relationship is observed between the number of maximum transmission peaks and the separation distance between two FBGs. Thus, the number of filtered frequency for dual FBGs is also increased. In addition, the profile shown by transmission spectrum of dual FBGs has produced similar characteristics as conventional FP, where the parameters of FSR, FWHM and finesse can be obtained from the profile.
CHAPTER 6
CONCLUSION
6.1
Conclusion
In this study, three fibre Bragg gratings defined as FBG1, FBG2 and FBG3 are fabricated using the phase mask technique. A KrF gas is chosen as a writing source, with
UV pulse energy of 78.1 mJ and UV exposure time of 20 minutes is used to produce the
Bragg grating. FBG1 produced a Bragg wavelength of 1551.09 nm with 30.2% of reflectivity. FBG2 produced a Bragg wavelength of 1551.29 nm with 78.1% of reflectivity. FBG3 produced a Bragg wavelength of 1551.66 nm with 44.7% reflectivity.
Hence, from mathematical calculation, the grating lengths for the three fabricated FBGs are 1.112 cm, 1.458 cm and 1.200 cm respectively. Results obtained indicate that FBGs with reflectivities of more than 50% produces a good quality and strong FBG.
In this study, we also found that there are some parameters that cannot be control simultaneously during the fabrication process such as the reflectivity, R , the grating length, L , and the effective refractive index, n eff
. The transfer matrix equations are applied in Matlab to simulate the transmission and reflection spectrum of single FBG as well as observed their effects. Results obtained from modelling shows that the FBG transmission spectrum becomes wider if the grating length, L produced is short, and it will become longer when the reflectivity, R value is increased.
61
This study also investigates the transmission spectrum of dual FBGs.for different value of separation distance, d . Two Bragg gratings are modelled in a single length of an optical fibre, with certain values of d . The parameter d is varied from 0.5 cm to 5.5 cm, with an increment of 0.5 cm. Results show that as the value of separation distance between two FBGs is increased, the number of maximum small peaks appearing at the transmission spectrum of dual FBGs is also increased. The maximum small peaks represent the filtered frequency for dual FBGs. Only selected wavelengths with certain value of frequencies are allowed to transmit at the fibre’s end, while others are blocked.
In this simulation studies, it can be shown that dual FBGs produces similar behaviour and characteristics as conventional Fabry-Perot filter, where the parameters of FSR,
FWHM and finesse can be obtained from the transmission’s profile.
6.2
Future Work
Dual FBGs are important for multiplexing and sensing purposes. The model can be further enhanced based on the FBG nonlinear effects, for predicting the parametric variations during fabrication process. Another important aspect is to develop an accelerated method to determine the reliability of these FBG’s over a period of time. It is recommended that experimental studies on dual FBG’s fabrication be conducted and the results obtained can be compared with the simulated studies. The study on transmission profiles produced by dual FBG sin terms of the FWHM, FSR and finesse characteristics, as these parameters will give more information on possible applications in communications.
62
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APPENDIX A
Transmission spectrum of fabricated FBGs
FBG 1
67
FBG 2
FBG 3
68
APPENDIX B
Transmission spectrum of fabricated FBGs after a period of five months
69
FBG 1
FBG 2
FBG 3
70
APPENDIX C
Matlab coding for single FBG
Braggwave=1551.29e-9; w1=1551e-9; w2=1551.6e-9; step=1000; wa1=[w1:(w2-w1)/step:w2];
%Bragg wavelength
%start wavelength
%stop wavelength
%Reflectivity
Rmax=0.718; rmax=sqrt(Rmax); kL=atanh(rmax); %coupling coefficient
%Transfer matrix function neff=1.4495;
L=1.458e-2;
M=100; dz=L/M; kac=kL/L;
%grating length in metre
%ac coupling coefficient v=10; kdc=2*kac/v;
%fringe visibility
%dc coupling coefficient for (r=1:step+1) w=wa1(r);
F=[1 0;0 1]; for (s=1:M) detuning=2*pi*neff*(1/w-1/Braggwave); selfdc=detuning+kdc; b1=sqrt(kac^2-selfdc^2); end f11=cosh(b1*dz)-i*(selfdc/b1)*sinh(b1*dz); f12=-i*(kac/b1)*sinh(b1*dz); f21=i*(kac/b1)*sinh(b1*dz); f22=cosh(b1*dz)+i*(selfdc/b1)*sinh(b1*dz); ff=[f11 f12; f21 f22];
F=ff*F; r3(r)=F(2,1)/F(1,1);
R3(r)=(abs(r3(r)))^2; end t3(r)=1/F(1,1);
T3(r)=(abs(t3(r)))^2; figure plot (wa1*1e9,T3, '-b' , 'Linewidth' ,2) grid axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel( 'Wavelength (nm)' ) ylabel( 'Power (p.u)' )
71
APPENDIX D
Matlab coding for single FBG with different reflectivity
Braggwave=1551.29e-9; w1=1551e-9; w2=1551.6e-9; step=1000; wa1=[w1:(w2-w1)/step:w2];
%Bragg wavelength
%start wavelength
%stop wavelength
%Reflectivity
Rmax=0.318; rmax=sqrt(Rmax); kL=atanh(rmax); %coupling coefficient
%Transfer matrix function neff=1.4495;
L=1.458e-2;
M=100; dz=L/M; kac=kL/L; v=10; kdc=2*kac/v;
%grating length in metre
%ac coupling coefficient
%fringe visibility
%dc coupling coefficient for (r=1:step+1) w=wa1(r);
F=[1 0;0 1]; for (s=1:M) detuning=2*pi*neff*(1/w-1/Braggwave); selfdc=detuning+kdc; b1=sqrt(kac^2-selfdc^2); end f11=cosh(b1*dz)-i*(selfdc/b1)*sinh(b1*dz); f12=-i*(kac/b1)*sinh(b1*dz); f21=i*(kac/b1)*sinh(b1*dz); f22=cosh(b1*dz)+i*(selfdc/b1)*sinh(b1*dz); ff=[f11 f12; f21 f22];
F=ff*F; r3(r)=F(2,1)/F(1,1);
R3(r)=(abs(r3(r)))^2; end t3(r)=1/F(1,1);
T3(r)=(abs(t3(r)))^2;
R1max=0.718; r1max=sqrt(R1max); kL1=atanh(r1max); kac1=kL1/L; kdc1=2*kac1/v;
%coupling coefficient
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for (s=1:step+1) w1=wa1(s);
G=[1 0;0 1]; for (t=1:M) detuning1=2*pi*neff*(1/w1-1/Braggwave); selfdc1=detuning1+kdc1; b12=sqrt(kac1^2-selfdc1^2); end g11=cosh(b12*dz)-i*(selfdc1/b12)*sinh(b12*dz); g12=-i*(kac1/b12)*sinh(b12*dz); g21=i*(kac1/b12)*sinh(b12*dz); g22=cosh(b12*dz)+i*(selfdc1/b12)*sinh(b12*dz); gg=[g11 g12; g21 g22];
G=gg*G; r4(s)=G(2,1)/G(1,1);
R4(s)=(abs(r4(s)))^2; end t4(s)=1/G(1,1);
T4(s)=(abs(t4(s)))^2;
R2max=0.918; r2max=sqrt(R2max); kL2=atanh(r2max); kac2=kL2/L; kdc2=2*kac2/v; for (a=1:step+1) w2=wa1(a);
H=[1 0;0 1];
%coupling coefficient for (u=1:M) detuning2=2*pi*neff*(1/w2-1/Braggwave); selfdc2=detuning2+kdc2; b13=sqrt(kac2^2-selfdc2^2); end h11=cosh(b13*dz)-i*(selfdc2/b13)*sinh(b13*dz); h12=-i*(kac2/b13)*sinh(b13*dz); h21=i*(kac2/b13)*sinh(b13*dz); h22=cosh(b13*dz)+i*(selfdc2/b13)*sinh(b13*dz); hh=[h11 h12; h21 h22];
H=hh*H; r5(a)=H(2,1)/H(1,1);
R5(a)=(abs(r5(a)))^2; end t5(a)=1/H(1,1);
T5(a)=(abs(t5(a)))^2; figure plot (wa1*1e9,T3, '-b' , 'Linewidth' ,2)
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grid axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' ) hold on box on plot (wa1*1e9,T4, '-r' , 'Linewidth' ,2) grid on axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' ) hold on box on plot (wa1*1e9,T5, '-g' , 'Linewidth' ,2) grid on axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' )
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APPENDIX E
Matlab coding for single FBG with different grating length
Braggwave=1551.29e-9; w1=1551e-9; w2=1551.6e-9; step=1000; wa1=[w1:(w2-w1)/step:w2];
%Bragg wavelength
%start wavelength
%stop wavelength
%Reflectivity
Rmax=0.718; rmax=sqrt(Rmax); kL=atanh(rmax); %coupling coefficient
%Transfer matrix function neff=1.4495;
L=0.458e-2;
M=100; dz=L/M; kac=kL/L;
%grating length in metre
%ac coupling coefficient v=10; kdc=2*kac/v;
%fringe visibility
%dc coupling coefficient for (r=1:step+1) w=wa1(r);
F=[1 0;0 1]; for (s=1:M) detuning=2*pi*neff*(1/w-1/Braggwave); selfdc=detuning+kdc; b1=sqrt(kac^2-selfdc^2); end f11=cosh(b1*dz)-i*(selfdc/b1)*sinh(b1*dz); f12=-i*(kac/b1)*sinh(b1*dz); f21=i*(kac/b1)*sinh(b1*dz); f22=cosh(b1*dz)+i*(selfdc/b1)*sinh(b1*dz); ff=[f11 f12; f21 f22];
F=ff*F; r3(r)=F(2,1)/F(1,1);
R3(r)=(abs(r3(r)))^2; end t3(r)=1/F(1,1);
T3(r)=(abs(t3(r)))^2;
L1=1.458e-2;
M=100; dz=L1/M;
%grating length in metre
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kac2=kL/L1; kdc2=2*kac2/v;
%ac coupling coefficient
%dc coupling coefficient for (s=1:step+1) w1=wa1(s);
G=[1 0;0 1]; for (t=1:M) detuning2=2*pi*neff*(1/w1-1/Braggwave); selfdc2=detuning2+kdc2; b12=sqrt(kac2^2-selfdc2^2); end g11=cosh(b12*dz)-i*(selfdc2/b12)*sinh(b12*dz); g12=-i*(kac2/b12)*sinh(b12*dz); g21=i*(kac2/b12)*sinh(b12*dz); g22=cosh(b12*dz)+i*(selfdc2/b12)*sinh(b12*dz); gg=[g11 g12; g21 g22];
G=gg*G; r4(s)=G(2,1)/G(1,1);
R4(s)=(abs(r4(s)))^2; end t4(s)=1/G(1,1);
T4(s)=(abs(t4(s)))^2;
L2=5.458e-2;
M=100; dz=L2/M; kac3=kL/L2; kdc3=2*kac3/v;
%grating length in metre for (a=1:step+1) w2=wa1(a);
H=[1 0;0 1];
%ac coupling coefficient
%dc coupling coefficient for (u=1:M) detuning3=2*pi*neff*(1/w2-1/Braggwave); selfdc3=detuning3+kdc3; b13=sqrt(kac3^2-selfdc3^2); end h11=cosh(b13*dz)-i*(selfdc3/b13)*sinh(b13*dz); h12=-i*(kac3/b13)*sinh(b13*dz); h21=i*(kac3/b13)*sinh(b13*dz); h22=cosh(b13*dz)+i*(selfdc3/b13)*sinh(b13*dz); hh=[h11 h12; h21 h22];
H=hh*H; r5(a)=H(2,1)/H(1,1);
R5(a)=(abs(r5(a)))^2; t5(a)=1/H(1,1);
T5(a)=(abs(t5(a)))^2;
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end figure plot (wa1*1e9,T3, '-b' , 'Linewidth' ,2) grid axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' ) hold on box on plot (wa1*1e9,T4, '-r' , 'Linewidth' ,2) grid on axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' ) hold on box on plot (wa1*1e9,T5, '-g' , 'Linewidth' ,2) grid on axis ([1551 1551.6 0 1]) title ( 'Transmission spectrum of single FBG' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Power (p.u)' )
77
APPENDIX F
Matlab coding for dual fibre Bragg gratings
Bragg=1551.29e-9; w1=1551e-9; w2=1551.6e-9; step=1000;
%design wavelength wa1=[w1:(w2-w1)/step:w2];
R=0.718; r=sqrt(R); k=atanh(r); v=1;
%required maximum reflectivity nef=1.4495; %effective RI
L=1.458e-2; %grating length
M=100; dz=L/M; dL=0.5e-2; kac=k/L;
%distance between gratings
%AC coupling coefficient kdc=2*kac/v; %DC coupling coefficient for (r=1:step+1) w=wa1(r);
F=[1 0; 0 1]; for (s=1:M) d=2*pi*nef*(1/w-1/Bragg); %detuning selfdc=d+kdc; b1=sqrt(kac^2-selfdc^2);
%dc self coupling f11=cosh(b1*dz)-i*(selfdc/b1)*sinh(b1*dz); f12=-i*(kac/b1)*sinh(b1*dz); f21=i*(kac/b1)*sinh(b1*dz); f22=cosh(b1*dz)+i*(selfdc/b1)*sinh(b1*dz); ff=[f11 f12; f21 f22];
F=ff*F; end r3(r)=F(2,1)/F(1,1);
R3(r)=(abs(r3(r)))^2;
%amplitude reflection coefficient
%power reflection coefficient
PHI=2*pi*nef*dL/w; %phase different btween gratings
Fp=[exp(-i*PHI) 0; 0 exp(i*PHI)];
Ffp=F*Fp*F; t3(r)=1/Ffp(1,1); %amplitude transmission coefficient
T3(r)=(abs(t3(r)))^2; %power transmission coefficient FP filter end figure(1)
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plot(wa1*1e9, T3, 'r' , 'Linewidth' ,2) grid on axis([1551 1551.6 0 1]) title ( 'Reflection and Transmission Spectrum of Dual FBGs' ) xlabel ( 'Wavelength (nm)' ) ylabel ( 'Reflection/Transmission' )
79
APPENDIX G
Transmission spectrum of dual FBGs for different separation distances between two FBGs
80 d = 0.5 cm d = 1.5 cm d = 2.5 cm d = 1.0 cm d = 2.0 cm d = 3.0 cm
d = 3.5 cm d = 4.5 cm d = 4.0 cm d = 5.0 cm d = 5.5 cm
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82
LIST OF PUBLICATIONS
S.Nafisah
, H.M.Hairi, Saktioto, J.Ali and P.P.Yupapin (2010). Novel design of multiplexed sensors using a dual FBGs scheme.
Microwave and Optical Technology
Letters, Vol.52(5) : 1218-1221.
S.Nafisah
, Saktioto, M.Fadhali, R.A.Rahman, P.P.Yupapin and J.Ali (2010). An investigation of transmission spectrum of a fiber Bragg grating fabricated by a phase mask method.
Optik-International Journal for Light and Electron Optics.
(In press).
S.Nafisah
, H.M.Hairi, Saktioto, J.Ali and P.P.Yupapin (2010). Optical multiplexed sensors using FBG with classical and quantum measurement self calibration.
Microwave and Optical Technology Letters.
(In press).
S.Nafisah
, Saktioto, M.Fadhali, P.P.Yupapin and J.Ali (2010). Effect of separation length on dual fibre Bragg gratings.
Proc. SPIE , 4 th International Conference on
Experimental Mechanics (ICEM 2009).
Vol. 7522, 75524V 18-20 November 2009.
Singapore.
H.M.Hairi, Saktioto, S.Nafisah
, M.Fadhali, B.A.Tahir, P.P.Yupapin and J.Ali (2010).
Multi photons squeezing control within fiber Bragg grating for quantum bits parallel processing operation. Journal of Electromagnetic Waves & Applications, PIERS &
JEMWA.
H.M.Hairi, Saktioto, S.Nafisah
, M.Fadhali, Rabia Qindeel, P.P.Yupapin and J.Ali
(2010). Multi photons trapping stability within a fiber Bragg grating for quantum sensor use.
PIERS Proceedings, 1698-1703, 22-26 March 2010. Xi’an, China.
S.Nafisah
, Saktioto, M.Fadhali, P.P.Yupapin and J.Ali (2009). Transmission spectrum of fibre Bragg grating for different grating lengths and reflectivities.
IEEE Regional
Symposium on Micro and Nanoelectronics (RSM 2009).
10-12 August 2009. Kota
Bharu, Malaysia.
83
N.F.Hanim, S.Nafisah
, H.M.Hairi, Saktioto, F.H.Suhailin, J.Ali, P.P.Yupapin (2009).
An experimental investigation of multisoliton generation using erbium doped fiber amplifier and a fiber optic ring resonator.
Microwave and Optical Technology Letters.
Vol.51.
Rosly A. Rahman, H.M. Hairi, Saktioto, S. Nafisah , M. Fadhali, P.P. Yupapin and J.Ali
(2009). Motion of Photon Parametric for Bragg Resonance Condition.
ESciNano
Annual Symposium 2009 , November 30 – December 1, 2009. The Zon Regency
Hotel, Johor Bahru, Malaysia.
Bashir A. Tahir, H.M. Hairi, Saktioto, M. Fadhali, S.Nafisah
, Preecha P. Yupapin and
Jalil Ali (2009). Photon Trapping in a Fiber Bragg Grating.
ESciNano Annual
Symposium 2009 , November 30 – December 1, 2009. The Zon Regency Hotel, Johor
Bahru, Malaysia.
