旋性光會與掌性結構有很強的交互作用，因而產生出許多極性相關的特性，例如圓二色性。在這論文中，我們使用了完整與非完整的介電質螺旋結構作為一個系統模型，去檢驗旋性光與螺旋結構之間的交互作用。介電質螺旋陣列會產生出不只跟結構同旋性的能隙之外，也會產生出反旋性的能隙，而這個反旋性的能隙是來自於兩個螺旋結構之間產生出的另一旋性的等效結構。可以藉由調整結構參數，去調控這兩個旋性極化能隙的特性，不同的光學性質可以用於許多光電的元件與應用。
　　雙曲超穎材料因為它奇特的光學性質引起了許多注意，其中之一的特性為藉由雙曲色散的性質來增益自發性輻射。然而，因為高波數模態特性的關係，將光從雙曲超穎材料給耦合出來是很困難的。在這論文中，我們會先檢驗加上增益結構的雙曲超穎材料之光學性質。結果顯示增益結構可以減少系統的損耗並且將高波數模態給耦合出雙曲超穎材料，發光增益可以在紅外光區域達到7.2。另外我們也會分析在柱狀雙曲超穎材料內的共振，來檢驗增益光的機制。這些分析結果對於使用雙曲超穎材料來製成高效率的光學元件是非常重要的。

Chiral structures exhibit strong interactions with circularly polarized light, and have been demonstrated to show many polarization dependent properties, such as circular dichroism. In this study, we use a complete and incomplete dielectric helix array as a model system to examine the interactions of circularly polarized light with helical structures. A dielectric helix array produces the circular polarization band gaps having not only the same handedness with the structure but also the opposite handedness. The gap with the opposite handedness results from additional chiral motifs induced by the adjacent helices. Dual polarization band gaps can thus be tailored by varying the geometrical parameters, and circular-polarization dependent properties can be manipulated for optoelectronic devices and applications.
Hyperbolic metamaterial (HMM) has attracted considerable attention owing to several exotic optical properties. One of these is the enhanced spontaneous emission, resulting from the hyperbolic dispersion of HMM. However, the out-coupling of light from HMMs is difficult due to the evanescent character of the high-k modes at the surface. In this study, the optical properties of nanowire HMMs with the enhanced structure are characterized. The results show the loss in the system is reduced, and the high-k modes of HMM is coupled out by virtue of the enhanced structure. The radiative enhancement can reach the value of 7.2 in the infrared region. The resonances inside the nanowire HMM are also analyzed to examine the mechanism of the enhancement of light. The analysis results are important toward engineering highly-efficient photonic devices based on HMMs.

Abstract i
Contents ii
1 Introduction 1
1.1 Introduction of Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Chiral Photonic Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Helix Photonic Metamaterials . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Hyperbolic Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Methods 11
2.1 Finite-Difference Time-domain Method . . . . . . . . . . . . . . . . . . . . . 11
2.2 Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 CD Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Coupling Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Effective Medium Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Purcell Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Radiative Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Simulation Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 Helix Photonic Metamaterial . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.2 Hyperbolic Metamaterial . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Dual Polarization Band Gap in Helix Photonic Metamaterials 19
3.1 Complete Helix Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1.1 Band Structure and Reflectance Spectrum . . . . . . . . . . 19
3.1.1.2 Resonance of CP Modes in RH Helices . . . . . . . . . . . . 21
3.1.2 Effect of Geometry Parameters . . . . . . . . . . . . . . . . . . . . . 23
3.1.2.1 Helix Radius R . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2.2 Wire Radius r . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.2.3 Phase Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Incomplete Helix Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2.1 Band Structure and Reflectance Spectrum . . . . . . . . . . 30
3.2.2.2 Conversion between RH and LH Modes . . . . . . . . . . . 32
3.2.3 Tailoring Fractional Helix . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.3.1 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3.2 Perfection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Enhancement of Light Extraction Based on Nanowire Hyperbolic Metamaterials
39
4.1 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.1 Effective permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.2 Purcell Factor and Radiative Enhancement . . . . . . . . . . . . . . . 40
4.1.3 Mode profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Enhanced structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 1D Grating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 Reflection Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.3 Flat Layer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 The resonances inside HMM . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Conclusions 55
Bibliography 56

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