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研究生: 朱柏翰
論文名稱: 一維光子晶體光電特性之研究
指導教授: 吳謙讓
學位類別: 碩士
Master
系所名稱: 光電工程研究所
Graduate Institute of Electro-Optical Engineering
論文出版年: 2009
畢業學年度: 97
語文別: 英文
論文頁數: 38
中文關鍵詞: 光子晶體布拉格反射器啁啾結構左手材料傳輸矩陣法Fabry-Perot 共振器
英文關鍵詞: photonic crystal, DBR, chirped, LHM, transfer matrix method (TMM), Fabry-Perot resonator (FPR)
論文種類: 學術論文
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  • Abstract
    Photonic crystals (PCs) are periodic structures made of materials with different refractive indices. With their interesting and amazing electromagnetic properties, research on PCs continues to be a hot issue in photonics in recent years.
    The main feature of PCs is that they can prohibit the propagation of electromagnetic waves within a certain frequency range called photonic band gap (PBG). The materials containing PBG have many potential applications in optoelectronics and optical communication. For instance, a dielectric layered structure can be used to design as a Fabry-Perot interferometer, dielectric reflectors, and antireflection coating.
    In this thesis, we study the electromagnetic and optical properties of PCs by using the transfer matrix method (TMM).The thesis consists of six chapters. The first chapter is to give a brief review of PCs. The second describes the theoretical background that will be used in our calculation. Some topics under study are given in chapter 3, 4, 5. The conclusion is summarized in chapter 6.
    In our considered topics, we first give a theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR). The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio. We demonstrate how a chirped structure can affect the photonic bandgaps (PBGs). In the second one, we shall design a multilayer Fabry-Perot resonator (FPR) which is formed by taking the left-handed material (LHM) as the structure defect in a one-dimensional PC. We find some useful design rules for a FPR made by the quarter-wave stacks. In the third topic, we theoretically studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructures.

    Abstract
    Photonic crystals (PCs) are periodic structures made of materials with different refractive indices. With their interesting and amazing electromagnetic properties, research on PCs continues to be a hot issue in photonics in recent years.
    The main feature of PCs is that they can prohibit the propagation of electromagnetic waves within a certain frequency range called photonic band gap (PBG). The materials containing PBG have many potential applications in optoelectronics and optical communication. For instance, a dielectric layered structure can be used to design as a Fabry-Perot interferometer, dielectric reflectors, and antireflection coating.
    In this thesis, we study the electromagnetic and optical properties of PCs by using the transfer matrix method (TMM).The thesis consists of six chapters. The first chapter is to give a brief review of PCs. The second describes the theoretical background that will be used in our calculation. Some topics under study are given in chapter 3, 4, 5. The conclusion is summarized in chapter 6.
    In our considered topics, we first give a theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR). The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio. We demonstrate how a chirped structure can affect the photonic bandgaps (PBGs). In the second one, we shall design a multilayer Fabry-Perot resonator (FPR) which is formed by taking the left-handed material (LHM) as the structure defect in a one-dimensional PC. We find some useful design rules for a FPR made by the quarter-wave stacks. In the third topic, we theoretically studied the omnidirectional total reflection frequency range of a multilayered dielectric heterostructures.

    Abstract i Acknowledgement ii Contents iii Chapter 1 Introduction 1-1 Literature Review 1 1-2 Motivations and Applications of PCs 3 1-3 Thesis Overview 4 Chapter 2 Theoretical Methods 2-0 Transfer Matrix Method (TMM) 5 2-1 Dynamical Matrix of a Medium ----A Single-Boundary Problem 5 2-2 A Single Slab---Two-Boundary Problem 8 2-3 Matrix Formulation for Multilayer System 10 2-4 Periodic Structure Containing DPS and DNG Media 12 Chapter 3 Optical Reflection in a Chirped DBR 3-1 Basic Studies of DBR 15 3-2 Summary 22 Chapter 4 Design of Multilayer Fabry-Perot Resonator Using Left-Handed Defect 4-1 Multilayer FPR using left-handed defect 23 4-2 Numerical results and discussion 25 4-3 Summary 28 Chapter 5 Omnidirectional Reflection in Photonic Crystal Heterostructures 5-1 Introduction 29 5-2 Numerical results and discussion 29 5-3 Conclusion 33 Chapter 6 Conclusions 35 References 37

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