掌性介質超穎材料近年來為應用於奈米光學元件裡的指標性結構，其強響應光學性以及二色性吸引了許多關注，其中尤其螺旋結構更是與旋性光交互作用的最佳的系統。過去的研究專注於二維或半二維的掌性結構上，但隨著製程技術進步，三維掌性結構的探索也隨之發展，而其中螺旋結構因其與旋性光的相似性成為適合研究旋性光與掌性介質互動的模板。
本論文以方格排列的螺旋結構作為模型分析旋性光在三維介電質週期性結構中的特性。以時域有限差分法分析後，結果發現螺旋結構無論從光子晶體或表面材料的面向都能得到令人驚豔的結果。從光子晶體的的方面分析，能夠發現一個有別於布拉格散射的產生光子能隙機制。此機制產生的混成能隙對於光子晶體的橫向週期較為敏感，與傳統的布拉格能隙對縱向週期較敏感有很大的不同。深入研究之後發現混成能隙產生的原因是波導共振模態，而其中共振的部分是源於沒有旋性的柱狀週期性結構。另一方面，當螺旋介質的縱向週期變為僅一週的時候則能夠形成類似超穎介面的效果，在旋性光照射下能夠產生法諾共振。在特定的結構參數下，能量甚至能在相反旋性的模態之間轉移，進而產生頻寬甚小的電磁感應透明效果。

Chiral nanostructure has attracted great interests in recent years owing to fascinating properties such as negative refraction, strong optical activity, and circular dichroism, which can be applied in many optoelectronic devices. Past studies mainly focus on two-dimensional or layered two-dimensional structures; however, with the advance of fabrication techniques, the exploration of three dimensional nanostructures also rises. Among all, helix is especially suitable for studying chiral responses as its geometry well resembles the feature of circularly polarized light.
In the thesis, we study the general response of a dielectric three-dimensional helix structure to circularly polarized light. The optical characterization is performed based on finite-difference time-domain method, and the results show that the helix structure arranged in square exhibits fascinating properties in both crystal-like and surface-like form. In multiple pitch helix arrays, the nanostructure displays a band gap mechanism other than typically observed Bragg resonance, the hybridization gap, which is rather sensitive to lateral period instead of longitudinal period. Further analysis shows that the gap emerged due to the coupling of guided mode resonance, in which the resonance can be traced down to the local resonance of rod array. On the other hand, the structure resembles a metasurface when reduced to a single pitch. Fano resonance occurs upon incidence of CP light, and energy conversion between modes with opposite handedness can be observed under certain configurations. When the structural parameters are altered, electrically induced transparency can be induced. The two features discussed in the thesis provide examples for versatile characteristics of helix array and more are expected in future research.

致謝 I
摘要 III
Abstract IV
List of figure VIII
1 Chapter 1 Introduction 1
1.1 Photonic crystal 1
1.2 Metamaterial 3
1.3 Chiral structure 4
1.3.1 Helix photonic metamaterial 6
1.4 Hybridization gap 8
1.5 Fano resonance 10
1.6 Motivations 11
2 Chapter 2 Methods 13
2.1 Numerical Methods 13
2.1.1 Finite-Difference Time-Domain method (FDTD) 13
2.1.2 Plane Wave Expansion Method (PWEM) 15
2.1.3 Finite Difference Eigenmode solver (FDE) 16
2.2 Photonic bandstructure 17
2.2.1 The irreducible Brillouin Zone 17
2.2.2 Dispersion surface and Equi-Frequency Contours (EFCs) 18
2.2.3 Circular Dichroism (CD) 20
2.3 Simulation structure 21
3 Chapter 3 Hybridization gap in 3D dielectric helix structure 24
3.1 Evolution of band gaps in a dielectric helix structure 24
3.2 Guided mode resonance 27
3.3 Collimation and negative refraction 33
4 Chapter 4 Fano resonance in dielectric helix metasurface 35
4.1 Fano resonance in case I helix metasurface 35
4.2 Fano resonance in case III helix metasurface 38
4.3 Possible applications 42
5 Chapter 5 Conclusions 44
Bibliography 45

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