高反射材料近年來因其能應用於各式各樣的領域而受到廣大的注意，高反射材料的光學性質主要是受到其組成材料、結構特徵以及材料排列方式的影響，不論是有序結構或無序結構的高反射材料，均已被科學家們發現於生物界中實際存在著。科學家們亦透過生物自組裝的方式，成功製造出可調控光學性質的有序結構高反射材料，然而相較於有序結構，無序結構的可調控性無論是在理論基礎或是實驗製造上，目前仍然是一大挑戰。在本研究中，我們利用了有限時域差分法的數值模擬針對有序結構以及無序結構進行高反射材料的研究。有序結構方面，我們採用螺旋二十四面體結構當作模型，並透過系統化的結構位移及結構拉伸去探討其對於光子能隙以及材料反射的影響。根據模擬結果，我們發現螺旋二十四面體網狀結構的殼聚醣有望成為能應用於紫外光波段的高反射材料。此外，我們亦發現可調控反射波段從可見光到紅外光的高反射嵌段共聚物材料可透過對螺旋二十四面體的結構進行拉伸來達成，而且模擬結果也與實驗結果互相符合。無序結構方面，我們發展了一種方法，能夠有效率地建造出可調控亂度的無序三叉模型；透過系統化的分析，我們探討了結構亂度與能隙特性之間的關聯以及材料能產生全方向能隙的關鍵因素。我們的模擬結果為各種無序結構高反射材料提供了設計的理論基礎以及方法，或許未來將能使用在各式各樣先進的光學應用上。

Highly reflective materials have drawn considerable attention owing to broad applications in various fields. The optical properties are governed by the constituent materials as well as structural features and arrangements. Both ordered and amorphous structures exhibiting high reflection have been found in nature. While techniques based on self‐assembly have been well developed to construct ordered structures with controlled optical properties, manipulation of amorphous structures remains a challenge, both theoretically and experimentally.In this study, we carry out numerical calculations based on finite‐difference time-domain method to investigate the ordered and amorphous structures for highly reflective materials. For the ordered structures, we employ the gyroid networks as a model system to study the effect of structural arrangement on reflections. A systematic analysis is conducted to examine properties of band gap and reflection while the gyroid networks undergo relative shifting or stretching. Based on the results, we demonstrate that a gyroid-structured and chitosan‐based highly reflective material is promising to be operated in the UV regime. In addition, we show that a highly reflective material of block copolymer with a broad tunable range from the visible to infrared can be realized by stretching of gyroid networks, which is consistent with the experiment result. For amorphous structures, we develop an efficient approach to construct connected tripod structures with controlled randomness. The correlation between the structural randomness and band gap properties is systematically studied, and the critical factors that may be relevant to the emergence of complete band gaps are discussed. Our results provide guidelines and strategies toward versatile designs of highly reflective materials with amorphous structures, which may be of great use for a variety of advanced optical applications.

Abstract.........................................................Ⅰ
Contents.........................................................Ⅲ
List of Figures..................................................Ⅴ
List of Tables...................................................Ⅹ
Chapter 1 Introduction...........................................1
1.1 Introduction to metamaterials................................1
1.2 Photonic crystals............................................4
1.3 Chiral structures............................................6
1.4 Amorphous structures.........................................8
1.5 Motivation..................................................10
Chapter 2 Methods...............................................12
2.1 Band structure..............................................12
2.1.1 Finite-difference time-domain method......................12
2.1.2 Plane wave expansion method...............................13
2.1.3 Brillouin zone............................................14
2.2 Simulation of reflection spectra............................15
2.3 Experimental measurement....................................15
2.3.1 Transmittance.............................................15
2.3.2 Extinction coefficient and refractive index (Ellipsometry) ................................................................16
2.4 Effective medium model......................................18
Chapter 3 Design and analysis of gyroid photonic crystals.......22
3.1 Model construction..........................................22
3.1.1 Gyroid structure morphology...............................22
3.1.2 Orientation of gyroid photonic crystal....................22
3.1.3 Shifting of intertwined gyroid-structured networks........24
3.2 High reflection of gyroid-structured chitosan...............28
3.2.1 Shifting of gyroid-structured chitosan....................28
3.2.2 Optical properties of chitosan............................30
3.2.3 Band structure and reflection spectra of gyroid-structured chitosan........................................................31
3.3 Swelling of gyroid photonic crystals........................36
3.3.1 Trapping of structural coloration.........................36
3.3.2 Swelling method of simulation.............................38
3.3.3 Reflection spectra of swelling gyroid.....................40
Chapter 4 Design and analysis of amorphous photonic crystals....43
4.1 Model construction of porous amorphous photonic crystal.....43
4.1.1 Random close packing......................................43
4.1.2 Spinodal decomposition....................................44
4.2 Model construction of rod-connected amorphous photonic crystal ................................................................45
4.2.1 Rod-connected amorphous tetrahedral networks..............46
4.2.2 Rod-connected amorphous trihedral networks................53
4.3 Analysis of polyhedral photonic crystal.....................60
4.3.1 Structure order parameter.................................60
4.3.2 Similarity................................................61
4.4 A novel method of construction of amorphous gyroid photonic crystal.........................................................64
4.4.1 Ordered nodes arrangement of gyroid photonic crystal......64
4.4.2 Random relocation of nodes................................65
4.4.3 Periodic boundary condition...............................67
4.5 Band gap of amorphous gyroid photonic crystal...............69
Chapter 5 Conclusions and prospectives..........................75
References......................................................77

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