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Author: 吳聲志
Sheng-Chih Wu
Thesis Title: 單負材料光子晶體光學性質之研究
Optical Properties of Photonic Crystals Containing Single-Negative Materials
Advisor: 吳謙讓
Wu, Chien-Jang
Degree: 碩士
Master
Department: 光電工程研究所
Graduate Institute of Electro-Optical Engineering
Thesis Publication Year: 2011
Academic Year: 99
Language: 英文
Number of pages: 50
Keywords (in Chinese): 光子晶體
Keywords (in English): Photonic Crystals
Thesis Type: Academic thesis/ dissertation
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In this thesis, we shall study the optical properties for the one-dimensional photonic crystals (PCs) containing the single-negative (SNG) materials. Three main topics are involved. In the first part, we consider a PC that has a period of ENG-MNG bilayer, where ENG means the epsilon-negative material and MNG is the mu-negative material. We investigate the photonic stop band and passband structure based on the transfer matrix method. In the second part, we study the optical properties for a SNG Fibonacci PC. With this quasi-periodic structure, we show that the photonic band structure is strongly dependent on the number of Fibonacci sequence. The third topic is to study the transmission properties in a defective SNG. The resonant tunneling spectrum will be investigated in the symmetric and asymmetric structure. The defect modes are closely related to the thickness of the SNG layer in addition to the thickness of the defect layer.

In this thesis, we shall study the optical properties for the one-dimensional photonic crystals (PCs) containing the single-negative (SNG) materials. Three main topics are involved. In the first part, we consider a PC that has a period of ENG-MNG bilayer, where ENG means the epsilon-negative material and MNG is the mu-negative material. We investigate the photonic stop band and passband structure based on the transfer matrix method. In the second part, we study the optical properties for a SNG Fibonacci PC. With this quasi-periodic structure, we show that the photonic band structure is strongly dependent on the number of Fibonacci sequence. The third topic is to study the transmission properties in a defective SNG. The resonant tunneling spectrum will be investigated in the symmetric and asymmetric structure. The defect modes are closely related to the thickness of the SNG layer in addition to the thickness of the defect layer.

Abstract i Acknowledgement ii Contents iii Chapter 1 Introduction 1-1 Metamaterials(Mtms) 1 1-2 Photonic Crystals (PCs) 2 1-3 Thesis Format 3 Chapter 2 Theoretical Methods 2-1 Transfer Matrix Method (TMM) 5 2-2 Dynamical Matrix of a Medium ----A Single-Boundary Problem 5 2-3 A Single Slab---Two-Boundary Problem 8 2-4 Matrix Formulation for Multilayer System 11 2-5 Transmittance and reflectance 12 2-6 Electromagnetic Metamaterials (MTMs) and Left-handed Materials (LHMs) 13 2-7 Fibonacci Sequence 14 Chapter 3 Photonic Reflection Spectra in an MNG-ENG Photonic Crystal 3-1 Introduction 17 3-2 Results and Analysis 17 3-3 Conclusion 29 Chapter 4 Transmission Properties of Fibonacci Quasi-Periodic One-dimensional Photonic Crystals Containing Single-Negative Materials 4-1 introduction 31 4-2 Fibonacci Quasiperiodic Layered Structure 32 4-3 Numerical Results and Discussion 33 4-4 Conclusion 36 Chapter 5 Resonant Tunneling Properties of Photonic Crystals Containing Single-Negative Materials 5-1 introduction 38 5-2 Structures of Interest 40 5-3 Numerical Results and Discussion 42 5-4 Conclusion 47 Chapter 6 Conclusion 49

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[3] H. Rahimi & A. Namdar, “Photonic Transmission Spectrain in One-Dimensional Fibonacci Multilayer Structures Containing Single-Negative Metamaterials”, Electromagnetics Research, PIER 102, 15-30, 2010.

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[5] Liwei Zhang, Kai Fang, Guiqiang Du, Haitao Jiang, Junfang Zhao, “Transmission Properties of Fibonacci Quasi-periodic One-dimensional Photonic Crystals Containing Indefinite Metamaterials”, Optics Communications 284 703–706, (2011).

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[7] F.F. de Medeiros, E.L. Albuquerque, M.S. Vasconcelos, “Transmission Spectra in Photonic Band-gap Fibonacci Nanostructures”, Surface Science 601 4492–4496, 2007.

[8] Deng XinHua, LIU NianHua, “Resonant Tunneling Properties of Photonic Crystals Consisting of Single-Negative Materials”, Sci. In China Press, 2008.

[9] Haitao Jiang, Hong Chen, Hongqiang Li, Yewen Zhang,Jian Zi, and Shiyao Zhu, “Properties of One-dimensional Photonic Crystals Containing Single-Negative Materials”, Phys. Rev. E, 69, 066607 (2004).

[10] Li-Gang Wang, Hong Chen, and Shi-Yao Zhu, “Omnidirectional Gap and Defect Mode of One-dimensional Photonic Crystals with Single-Negative Materials”, Phys. Rev. B 70, 245102 (2004).

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