在本博士論文中，全波時域有限差分法(Finite-Difference Time-Domain Method)結合細線以及細狹縫近似方法被提出來並使用於分析由週期性蘑菇型結構所組成的超穎物質(Metamaterial)，該方法適用於分析大尺寸且局部具有細微變化的結構。此外，蘑菇型結構的週期性分析可以藉由計算單一蘑菇型結構並利用週期性的邊界條件產生近似於無限週期性的電磁場分佈，然後得到該結構的色散曲線。混合型的右/左手(Composite Right-/Left-Handed)傳輸線方法藉由使用等效的集總電路模型可以被用於近似CRLH Metamaterial。一個平面型左手微波透鏡與一個由410個蘑菇型結構所組成的拋物線型左手微波透鏡在本論文被提出，並以實驗及全波模擬的方法證明該透鏡具有負的折射係數。

A full wave finite-difference time-domain method (FDTD) combined with thin-wire and thin-slot algorithms to analyze a metamaterial fabricated with periodic mushroom structures, is proposed in this dissertation. This proposed method is suitable for analyzing problems involving large structures with fine structural details. A periodic analysis for mushroom structures is presented. Only a single unit mushroom cell is required to present the phenomena of infinite periodicity with the help of periodic boundary conditions (PBCs).
The composite right-/left-handed (CRLH) transmission line (TL) approach is introduced and used to approximate CRLH metamaterial through lumped L and C. Finally, several CRLH metamaterial mushroom-based structures are investigated. A 19 by 8 flat microwave lens and a parabolic microwave lens structure composed of 410 unit mushroom cells are investigated. These structures demonstrate negative refractive index (NRI) characteristics while operate in the left-hand (LH) region. The simulation and measurement results of one- and two-dimensional CRLH mushroom-based structures are compared.

1 Introduction 1
1.1 Left-Handed Material 1
1.2 Finite-Difference Time-Domain Analysis of Mushroom Structures 2
1.3 Overview 3
2 Finite-Difference Time-Domain Method 4
2.1 FDTD Method 4
2.2 Stability Condition 10
2.3 Algorithms for Handling Fine Geometrical Features in FDTD Method 12
2.3.1 Thin Wire Algorithm 13
2.3.2 Thin Slot Algorithm 15
2.3.3 Coaxial Line Algorithm 16
2.4 Periodic Boundary Conditions 19
2.5 Convolution Perfectly Matched Layer 26
3 Composite Right-/Left-Handed Metamaterials 28
3.1 Left-Handed Materials 28
3.2 Composite Right-/Left-Handed Transmission Line 29
3.3 Practical Implementation of CRLH TL 35
3.3.1 One-dimensional CRLH TL 36
3.3.2 Two-dimensional CRLH TL 41
4 The Analysis of Left-Handed Mushroom Structures by FDTD Method 43
4.1 1-D Linear Four-cell Mushroom Structure 43
4.2 Dispersion Diagram of Mushroom Structure 48
4.2.1 Dispersion Diagram Calculation using Periodic Boundary Condition 48
4.2.2 Dispersion Diagram Calculation using S-parameters 51
4.3 17 by 17-cell Square Mushroom Structure 52
4.4 Left-Handed Microwave Lens 59
4.4.1 Interface between RH and LH Media 59
4.4.2 Flat Lens 61
4.4.3 Parabolic Lens 63
5 Conclusions 68
Bibliography 69
Appendix A: FDTD Updating Equations 74
Appendix B: CPML Updating Equations 77
Vita 82

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