在論文的第一部分，我們利用有限時域差分法來數值分析各種光學反應，並著重探討螺旋結構的光學掌性，其中包含圓二色性質。我們建立一個系統模型來模擬不同材料、幾何參數和入射方向的圓二色效果。最終藉由合適的材料及幾何參數選擇來調整光學掌性的性質。此外也系統性探討電漿共振以及入射方向對圓二色性質的影響。

在論文的第二部分，主要探討非晶螺旋二十四面體網絡的光學性質。我們採用兩種不同的模型來建立此種網絡並呈現兩者的幾何特徵和能隙形成的關聯。並提出藉由亂度及幾何特徵來定義能隙性質的判斷標準，用來建立一個能隙地圖來對照能隙出現位置。結論上，這些模型能提供高反射非晶結構的設計方針並在光學應用上有重要意義。

In the first part of the study, we presented chiroptical properties of helix structures. We used FDTD method to numerically analyze various optical responses, including circular dichroism (CD). We constructed a model system to simulate the CD effect of helix structure and examined the optical responses based on different materials, geometrical parameters, and orientation. With proper choice of materials and geometric parameters, we showed that chiroptical responses can be tailored and manipulated. The plasmon resonances were also systematically analyzed and orientation-dependent CD effects were studied and discussed.
In the second part of the study, we presented the investigation on the optical properties for amorphous gyroid networks. We employed two models for constructing amorphous gyroid networks and showed that the correlation between geometric characteristics and bandgap formation. In addition, we proposed criteria for bandgap by the randomness and geometric characteristics. A gap map was constructed to examine the emergence of bandgaps with respect to geometric characteristics. Consequently, our models and results provide guidelines toward various designs of highly reflective amorphous structure, which may be of a great importance for optical applications.

致謝 2
摘要 3
Abstract 4
List of figure 9
Chapter 1 Introduction 17
1.1 Chiral plasmonics in metallic structure 17
1.2 Optical properties of amorphous structure 21
1.3 Motivations 24
Chapter 2 Methods 25
2.1 Analysis method of chirality and simulation setup 25
2.1.1 Chirality: FOM 25
2.1.2 Circular dichroism and g factor 28
2.1.3 Geometry of helix structure 29
2.1.4 Random orientation 30
2.2 Analysis method and model construction of tripod network 30
2.2.1 Bandstructure 30
2.2.1.1 Finite-Difference Time-Domain method (FDTD) 30
2.2.1.2 Plane Wave Expansion Method (PWEM) 32
2.2.1.3 Brillouin Zone 33
2.2.2 Reflectance spectra 34
2.2.3 Density of state (DOS) 35
2.2.4 Analysis for networks 36
2.2.4.1 Basic statistics 36
2.2.4.2 Similarities 38
2.2.4.3 Ring length 42
2.2.5 Amorphous structure generated by random relocation of vertices (RRV) 43
2.2.5.1 Vertices and edges in ordered gyroid 43
2.2.5.2 Random relocation of vertices 44
2.2.5.3 Periodic boundary condition 47
2.2.6 Amorphous structure generated by CRNs 48
2.2.6.1 Randomly generate vertices and edges 48
2.2.6.2 Simulated annealing 52
2.2.6.3 Stone-Wales defect and bond transposition 55
2.2.6.4 Keating potential 57
2.2.7 Reconnected RRV networks 59
Chapter 3 Chirality of metallic helix structure 60
3.1 Chiroptical properties with different materials 60
3.2 Chiroptical properties with different geometrical parameters of helix 62
3.2.1 Pitch length p 63
3.2.2 Helix radius R 65
3.2.3 Fiber radius r 67
3.2.4 Number of period n 69
3.3 Orientation dependence 71
3.4 Discussion 79
Chapter 4 Analysis of amorphous gyroid network 82
4.1 Bandgap analysis of amorphous structure generated by random relocation of vertices (RRV) 82
4.2 Bandgap analysis of amorphous structure generated by CRNs 88
4.3 Ring length effects on photonic bandgap 94
4.4 Photonic bandgap map and its improvement 100
Chapter 5 Conclusions 103
Bibliography 105

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