A NOVEL IDEA OF USING SOLITON IN FIBER BRAGG GRATING HARYANA BINTI MOHD HAIRI UNIVERSITI TEKNOLOGI MALAYSIA

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1 A NOVEL IDEA OF USING SOLITON IN FIBER BRAGG GRATING HARYANA BINTI MOHD HAIRI UNIVERSITI TEKNOLOGI MALAYSIA

2 A NOVEL IDEA OF USING SOLITON IN FIBER BRAGG GRATING HARYANA BINTI MOHD HAIRI A thesis submitted in fulfillment of the requirements for the award of the degree of Master of Science (Physics) Faculty of Science Universiti Teknologi Malaysia AUGUST 2010

3 iii To all the beloved person in life especially Mom, Dad and My Lovely Siblings No Love can cross the path of our destiny without leaving some mark on it forever... To my dearest friends: There are no limits to our possibilities. At any moment, we have more possibilities that we can act upon. When we imagine the possibilities, our vision expands, We capture our friends and our life is meaningful. We can reach out and touch the limits of our being.

4 iv ACKNOWLEDGEMENTS First and foremost, I would like to express my deepest gratitude to Allah S.W.T for giving the strength to complete my research successfully. Secondly, without their guidance, I would be nowhere. I would like to convey my deepest appreciation to my supervisors, Prof. Dr. Jalil Ali, Prof. Dr. Rosly Abd. Rahman, Dr. Saktioto and Prof. Dr. Preecha Yupapin (KMITL, Thailand) for all their guidance and support throughout the duration of this research and thesis writing. I am greatly indebted to them for the knowledge imparted and the precious time they allocated to guide me. Prof. Dr. Jalil Ali provided the overall framework of this studies. Together with Prof. Dr. Preecha Yupapin, they guided me on how to produce good results and publish papers. Prof. Dr. Rosly Abdul Rahman provided the FBG research facilities and Dr. Saktioto assisted in modeling work. I would like to extend my sincere appreciation to my family especially mom and dad for their tender support, morally and financially. During the final stage of my thesis writing, my dad had a severe stroke, I am thankful to my supervisors for being understanding during this point of time. I would also like to convey many thanks to members of the Institute of Advanced Photonics and Sciences (APSI) for their assistance. They had provided me with ample information, cooperation and help during the process of conducting my research. Last but not least, I would like to thanks my constant companions, Asiah, Nafisah and Hanim who had given me a lot of support as well as fruitful ideas and comments which had helped me a lot in completing this research.

5 v ABSTRACT With the rapid development in sensing and optical telecommunication, fiber optic plays an important role in transmission systems as a low-loss and wide-bandwidth medium. In this study, three fiber Bragg gratings (FBGs) are fabricated using conventional method known as the phase mask technique. Bragg s wavelength of nm, nm and nm and reflectivities values of 30.18%, 78.12% and 44.73% respectively are obtained. For soliton writing, the equations based on the coupled mode theory have been derived. A Matlab coding has been developed in order to solve some of these equations. The simulation of potential energy distribution throughout the grating is examined by varying the value of nonlinear parameters of α, β, γ, and a new element known as θ is added in the equations. The results show that the nonlinear parameters affect the motion of photon in the FBG and under certain condition, it is possible to trap the photon and hence obtain the optical soliton. The fabrication results show that the FBG with reflectivity of 78.12% can be classified as good FBG compared to the other two FBGs. The simulation studies show that amongst those nonlinear parameters, α significantly affects the potential well due to its ability of this parameter in order of photon trapping. This study thus shows that is plausible to use soliton for FBG writing and the properties of soliton for such purpose can be controlled by manipulating α, β, γ and θ.

6 vi ABSTRAK Sejajar dengan perkembangan pesat dalam bidang penderia dan teknologi komunikasi, gentian optik memainkan peranan penting dalam sistem pancaran sebagai medium yang mempunyai daya kehilangan yang rendah dan jalur lebar yang luas. Dalam kajian ini, tiga gentian parutan Bragg (FBG) telah berjaya difabrikasi menggunakan teknik topeng fasa dengan panjang gelombang masing-masing ialah nm, nm dan nm bersama darjah pantulan masing-masing sebanyak 30.18%, 78.12% dan 44.73%. Teknik penghasilan parutan Bragg menggunakan soliton telah diterbitkan dalam beberapa persamaan yang diperolehi daripada Teori Mod Pengganding. Kod Matlab juga telah dihasilkan dalam menyelesaikan persamaan-persamaan yang telah diterbitkan. Simulasi taburan tenaga keupayaan sepanjang parutan telah dibuat dengan mengubah nilai-nilai parameter tak linear iaitu nilai-nilai α, β dan γ. Selain itu, satu parameter yang baru telah ditambah dalam persamaan tenaga keupayaan untuk mengkaji kesannya terhadap taburan tenaga keupayaan. Hasil keputusan kajian fabrikasi menunjukkan FBG dengan darjah pantulan 78.12% adalah yang terbaik berbanding FBG yang lain dan dari simulasi pula jelas menunjukkan α memberi impak yang paling besar terhadap pola pergerakan foton dalam telaga keupayaan berbanding parameter-paramater tak linear yang lain. Ini menyumbang terhadap penangkapan foton sekaligus kewujudan elemen yang dikenali sebagai soliton optik. Ini menunjukkan bahawa adalah mungkin penggunaan soliton untuk fabrikasi FBG dan ciri-ciri soliton untuk tujuan berkenaan boleh dikawal dengan memanipulasi α, β, γ dan θ.

7 vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS LIST OF APPENDICES ii iii iv v vi vii x xii xiii xvi 1 INTRODUCTION Introduction Background of the Study Problem Statement Aims and Objectives Scope of the Study Research Methodology Significance of the Study Organization of the Study 7

8 viii 2 LITERATURE REVIEW Optical Soliton Coupled-Mode Theory for FBG Soliton in Fiber Bragg Grating Pulse propagation in FBG Properties of Fiber Bragg Grating Bragg condition Uniform Bragg grating reflectivity Photosensitivity in Optical Fiber Fabrication Technique for Fiber Bragg Grating Internal Inscription of Bragg Gratings External Inscription of Bragg Gratings Point-by-point Writing Technique The Phase Mask Technique 26 3 EXPERIMENTAL SETUP Introduction Experimental Setup of Fiber Bragg Grating Fabrication KrF Excimer Laser Overview Mask Aligner Overview Phase mask Tunable Laser Source Optical Spectrum Analyzer 37 4 FIBER BRAGG GRATING MODEL OF POTENTIAL ENERGY DISTRIBUTION Coupled Mode Theory Derivation of Nonlinear Coupled Mode Equation (NLCM) Derivation of Potential Energy Distribution in Fiber Bragg Grating Modelling of Optical Soliton using NLCM 50

9 ix 4.5 Modelling of Potential Energy Distribution in Fiber Bragg Grating structures Multi Perturbation of Potential Energy Photon in Fiber Bragg Grating External Perturbation of Potential Energy Flowchart for computational modelling 55 5 RESULTS AND DISCUSSION Introduction Results of Fiber Bragg Grating Fabrication Results for Simulation of Soliton in Fiber Bragg Grating Nonlinear Parametric Studies of Photon in Fiber Bragg Grating External Disturbance of Potential Energy Photon in Fiber Bragg Grating Motion of Photon due to External Energy Perturbation in Potential Well Summary 72 6 CONCLUSION Introduction Conclusions Future Work 75 7 REFERENCES 76 8 APPENDICES 79 9 PUBLISHED PAPERS 93

10 x LIST OF TABLES TABLE NO. TITLE PAGE 5.1 Summary of the data collected for fabrication 62

11 xi LIST OF FIGURES FIGURE NO. TITLE PAGE 1.1 Illustration of Fiber Bragg Grating The flow chart for the research methodology on the 6 novel idea of using optical soliton in FBG. 2.1 Cross-section of an optical fiber with the corresponding 11 refractive index profile. 2.2 A basic diagram of Fiber Bragg Grating Oxygen-deficient germania defects thought to be 20 responsible for the photosensitive effect in germania-doped silica. 2.4 Schematic of original apparatus used for recording Bragg 22 Gratings in optical fibers. A position sensor monitored the Amount of strectching of the Bragg gratings as it was strain-tuned to measure its very narrow-band response. 2.5 Schematic design of the diffraction of an incident beam 27 from a phase mask. 3.1 Schematic diagram of Fiber Bragg Grating fabrication 29 experimental setup. 3.2 KrF Excimer Laser Functional design of the COMPex laser system Optical components of mask aligner Schematic diagram on propagation of light in mask aligner Phase Mask Holder Tunable Laser Source Overview 37

12 xii 3.8 The Optical Spectrum Analyzer Flow chart in the case where there is no energy disturbance Flow chart of simulation with potential energy disturbance factor Flow chart of potential energy under multi-perturbation condition The transmission spectrum to monitor the growth of fiber 60 grating in FBG1 5.2 Results of fabricated FBG The motion of photon in double well for different values of α The optimized point of the double well potential for 63 different values of α 5.5 Under Bragg resonance condition the system possesses 64 double well potential for γ = 0.13 to The optimized point of the double well potential when 65 γ = 0.1 to The motion of photon in potential well for α = 0.9, β = 0.3, 66 θ = 0.09 and γ is varies from 0.3 to The effect of theta,θ to γ and shape of the potential well of 67 the photon. 5.9 The disturbance to the potential energy by β factor The motion of photon in potential well for α = 0.9, β = 0.3, 69 θ = 0.09 and γ is varies from 0.3 to The disturbance factor that affect the shape of the 71 potential well of the motion of photon.

13 xiii LIST OF SYMBOLS λ B - Bragg wavelength Λ - Spatial period (or pitch) of the periodic variation N eff - Effective index for light propagating in a single mode fiber A(z) - Forward propagating modes B(z) - Backward propagating modes ( x, y) ψ - Transverse modal field distribution ω - Frequency β - Propagation constant of the mode ( x, y z) 2 n g, - Refractive index variation along the fiber K - Spatial frequency of the grating 2 Δ n - Index modulation of the grating Γ - Coupling coefficient r - Radius of the core of FBG a - Radius of the cladding of FBG l - Length of the grating R - Reflectivity of the grating n 2 - Kerr coefficient δn g (z) - Periodic index variation inside the grating n 2 I - Nonlinear index change n - Average refractive index of the medium ε(z) - ( z t) E f, b, - Perturbed permittivity Forward and backward propagating waves

14 xiv κ - Coupling between the forward and backward propagating waves in the FBG k i - Incident wavevector K - Grating wavevector k f - Wavevector of the scattered radiation n eff - Effective refractive index of the fiber core at free space center wavelength Δn - Amplitude of the induced refractive index perturbation formed in the core of the fiber z - Distance along the fiber in longitudinal axis R( l,λ) - Reflectivity λ - Wavelength Ω - Coupling coefficient Δ k - Detuning wavevector K - Propagation constant M p - Fraction of the fiber mode power contained by the fiber core V - Normalized frequency of the fiber n co - Core radius n cl - Cladding radius λ w - Irradiation wavelength ϕ - Intersecting beams Λ g - Period of the grating Λ pm - Period of the phase mask Λ g - Period of fringes λ uv - UV wavelength N - Number of grating P unperturbed - Unperturbed polarization P grating - Perturbed polarization μ - Transverse mode number ê z δ μυ - - Unit vector along the propagation direction z Kronecker s delta

15 xv E r - Electric field vectors H r - Magnetic field vectors D r - Displacement vectors B v - Flux density c - Speed of light r E ( z, t) - Electric field ω 0 - Central frequency k 0 - Wavenumber P 0 - Total power inside the grating e f - Forward propagating modes e b - Backward propagating modes Γ s - Self Phase Modulation Γ x - Cross-phase modulation effects C - Constant of integration δˆ - Detuning parameter V(A 0 ) - Potential energy distribution in a FBG structures while the light propagating through the grating structures

16 xvi LIST OF APPENDICES APPENDIX TITLE PAGE A The transmission spectrum to monitor the growth of 79 fiber grating during FBG fabrication using phase mask technique B Characteristics of fabricated FBGs based on the 81 transmission spectrum C MatLab coding of potential energy distribution in 83 Bragg grating D MatLab coding for optimizing photon trapping under the 85 effects of nonlinear parameters, α, β, γ and θ in an FBG E Matlab coding of potential well insertion of θ factor 87 when soliton propagates in FBG F MatLab coding for higher order disturbance factor under 89 multi-perturbation factor

17 CHAPTER 1 INTRODUCTION 1.1 Introduction A Fiber Bragg Grating (FBG) is a periodic variation of the refractive index of the core in the fiber optic along the length of the fiber as shown in Figure 1.1. The principal property of FBGs is that they reflect light in a narrow bandwidth that is centered abour the Bragg wavelength, λ B which is given as (A. Orthonos and K. Kalli, 1999) Figure 1.1: Illustration of Fiber Bragg Grating (R. Kashyap, 1999)

18 2 λ B = 2Neff Λ (1.1.) where Λ is the spatial period (or pitch) of the periodic variation and N eff is the effective index for light propagating in a single mode fiber. FBGs are simple intrinsic devices that are made in the fibre core by imaging an interference pattern through the side of the fibre (Meltz et. al, 1989). FBGs have all the advantages of an optical fibre, such as electrically passive operation, lightweight, high sensitivity with also unique features for self-referencing and multiplexing capabilities. This gives them a distinct edge over conventional devices (Nahar Singh et. al, 2006). Therefore, FBGs in optical fibers have a wide range of applications, such as for sensors, dispersion compensators, optical fibre filters, and all-optical switching and routing (T. Sun et. al,2002). An UV laser source is used to form FBG s in fiber optics either through internal writing (Hill et. al, 1978) or external writing technique (A. Orthonos and K. Kalli, 1999). In this study, the novel idea of using soliton is introduced for FBG. Solitons are particle-like waves that propagate in dispersive or absorptive media without changing their pulse shapes and can survive after collisions. Various types of optical soliton phenomenon have been studied extensively in the area of nonlinear optical physics. These includes the nonlinear Schredinger solitons in dispersive optical fibers, spatial and vortex solitons in photorefractive material, waveguides and cavity solitons in resonators (Y. S. Kivshar and G. P. Agrawal, 2003). The first step in this study is to fabricate FBGs using conventional method. Then the novel method of writing the gratings on FBG using soliton is introduced. This will be studied numerically. Mathematical modelling is developed through the first principle of derivation. Simulated result obtain will be able to characterize the soliton waves and FBG s. Further details about FBG and soliton history,

19 3 development, theory, fabrication, simulation, testing and evaluation are expounded in this thesis. 1.2 Background of the Study Over the last decade fiber Bragg gratings(fbg) have become the key components for optical communications systems and sensor applications. They are used as flexible and low cost in-line components to manipulate any part of the optical transmission and reflection spectrum. FBG is formed by the periodic variations of the refractive index in the fiber core. Several techniques have been established to inscribe them with UV-lasers (R. Kashyap, 1999). However, these technologies are limited to photosensitive fiber core material, which are unsuitable for high power applications. Only recently modifications have been demonstrated in a non photosensitive fiber but at the expense of longer exposure times (K. W. Chow et. al, 2008). 1.3 Problem Statement The main motivation of this research is to pursue the novel idea of using optical soliton writing in Fiber Bragg Gratings. First, the FBGs are fabricated using the Excimer UV Laser conventional method. For the soliton writing, distribution of potential energy equations has been derived based on coupled-mode theory. Simulation has shown the trend of photon movement along the grating in order to obtained optical soliton. Current method of using UV laser source could be enhanced by introducing soliton since we know that lasers are expensive and bulky in size. Usage of solitons gives less external interference since it only consists of

20 4 minimal amount of losses along the propagation regarding the properties of soliton itself. Based on this study, the optimized parameters will be identified for inscribing grating to fiber optics using optical soliton. 1.4 Aims and Objectives This research aims to introduce new soliton writing in FBG. The principal objective of this study is to investigate the novel idea of using soliton in FBG. A mathematical model on soliton FBG writing will be developed. The equations will be derived based on the coupled mode theory. A MatLab coding will be developed to solve these equations. 1.5 Scope of the Study This research starts with a literature review of FBG s. Next the FBG s principle of operation, and fabrication techniques are discussed. The theory involved in the modelling of soliton will be developed. It is based on the coupled-mode theory including the Kerr nonlinearity, group velocity dispersion (GVD) and self phase modulation (SPM) and simulation on soliton writing of FBG will be performed. The conventional method of FBG fabrication process will be conducted using the phase mask technique using Excimer UV laser source at a wavelength of 248 nm. Results obtained from experiments, modelling and simulation will be analysed in terms of Bragg wavelength, reflectivity and the bandwidth.

21 5 1.6 Research Methodology This study covers two main areas, namely, experimental setup of FBG fabrication, evaluation, modelling and simulation on the existence of optical soliton in grating structure in FBG. Phase mask technique is utilized to fabricate the FBGs in this research. The motion of a particle moving in FBG represents the pulse propagation in the grating structure of fiber optics exhibiting the existence of optical fiber. In order to describe the photon motion, the function of potential energy is depicted via modelling and the simulation. Figure 1.2 shows the flow and steps undertaken to conduct this research.

22 6 Literature Review on FBG s Fabrication of FBGs by phase mask technique FBG experiments The measurements of FBG transmission spectrum while inscribing the gratings The measurement of fabricated Fiber Bragg Gratings Modelling of optical soliton Derive equations using the Coupled-Mode Theory (CMT) Develop and write the MatLab coding for solving equations Run the MatLab coding by setting several parameters such as the value of α, β, γ and θ Results, Analysis and Discussion Conclusions Figure 1.2: The flow chart for the research methodology on using optical soliton writing in FBG.

23 7 1.7 Significance of the Study This research will contribute towards the research areas of nanophotonics and optical solitons especially in FBG writing. These lasers are complicated devices, and additionally their use restricts significantly the possibilities to adjust pulse parameters like its duration and shape. Furthermore it may overcome the disadvantages of the bulky lasers and high power requirements. The novel idea of using soliton writing in Fiber Bragg Grating will be plausible. 1.8 Organization of the Study Chapter 1 provides a brief introduction on the overall review of the research background, work undertaken including the problem statement, objectives, scope,significance of the study and the research outline. The literature review is introduced in Chapter 2. Chapter 3 describes the simulations related to the modelling of FBG according to the certain properties and characteristics. In Chapter 4, the mathematical modelling of soliton will be shown numerically. Chapter 5 describes the fabrication technique used and the results of the FBG experiments. Chapter 6 presents the results and discusses the parameters obtained from the fabricated FBG through experiment and simulation. Finally, the thesis is summed up as Chapter 6 and recommendations for future work are suggested.

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