臺灣博碩士論文加值系統

螺旋二十四面體是一種三維旋性結構，在許多昆蟲物種可發現。因為其週期性與具有旋性的結構，螺旋二十四面體已被證明具有光子能隙及圓偏振相關特性。在之前的結果顯示雙螺旋二十四面體的光學特性可以透過結構的折射率及體積分率調控。但是雙螺旋二十四面體主要是基於介電質或是金屬的一種單一材料進行研究。由不同材料組成的雙螺旋二十四面體的光學性質的影響尚未探討。
在本研究，建立在有限差分時域法，我們研究金屬及介電質所組成的雙螺旋二十四面體的旋性相關特性。我們計算能帶結構、穿透頻譜、圓二色性指標、耦合係數確認旋性能隙及完全能隙在金屬/介電質雙螺旋二十四面體的存在。對應不同參數的變化也發表其中。除此之外，我們利用色散曲面及等頻線圖分析金屬/介電質雙螺旋二十四面體，因為其特殊的色散性質，我們探討包括負折射、自準直效應在內的異常折射。這些結果對於基於混合金屬/電介質雙陀螺結構的圓偏振元件的功能設計可能是非常有意義的。

Gyroid is a type of three-dimensional chiral structure that has been found in many insect species. Due to the periodic and chiral structure, the gyroid has been shown to exhibit photonic band gap and circular polarization dependent characteristics. Previous results show that the optical properties of the double gyroid can be tuned by refractive index contrast of the constituent materials or the volume fraction. However, double gyroid structures are mainly studied based on one constituent material, either dielectric or metal. The influence of different materials on the optical properties of double gyroid has not been explored.
In this work, we investigate the polarization-dependent characteristics of a hybrid metal/dielectric double gyroid based on finite-difference time domain (FDTD) method. The corresponding band structure, transmission spectra, CD indices and coupling indices are calculated to examine the existence of polarization band gap and complete band gap in a metal/dielectric double gyroid. The evolution of band gaps with respect to different fractions of the hybrid system are presented. Furthermore, the dispersion surfaces and equifrequency contours (EFCs) are analyzed in the hybrid double gyroid. Based on the dispersion characteristics, anomalous guiding characteristics including negative refraction and collimation effect are discussed. These results could be of great interests for the design of function of circular-polarization devices based on hybrid metal/dielectric double gyroid structures.

第一章 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 光子晶體介紹 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 手性結構中的螺旋二十四面體介紹 . . . . . . . . . . . . . . . . 2
1.2.1 單螺旋二十四面體介紹 . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 雙螺旋二十四面體 . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 螺旋二十四面體光學特性 . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 完全光子能隙 . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 旋性能隙. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 負折射 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 論文動機. . . . . . . . .. . . . .. . . . . . . . . . . . . . . 11

第二章 實驗方法 . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 光子能帶. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 時域有限差分法 (Finite-Difference Time-domain Method) . . . . 13
2.1.2 約化布里淵區 (The irreducible Brillouin Zone) . . . . . . . . 14
2.1.3 色散曲面及等頻率線圖(EFCs) . . . . . . . . . . . . . . . . . . 15
2.2 圓二色性 (Circular Dichroism , CD) . . . . . . . . . . . . 17
2.2.1 左右旋判定方式 . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 圓二色性指數 (CD index) . . . . . . . . .. . . . .. . . . . . 17
2.2.3 耦合係數 (Coupling index). . . . . . . . .. . . . .. . . . . . 18
2.3 模擬設定. . . . . .. . . . . . . . .. . . . .. . . . . . . . . 19
2.3.1 雙螺旋二十四面體(Double Gyroid, DG) . . . . . . . . . . . . . 19

第三章 金屬/介電質 混成雙螺旋二十四面體的旋性能隙 . . . . . . . . . . 20
3.1 金屬/介電質 混成雙螺旋二十四面體 . . . . . . . . . . . . 20
3.1.1 金屬單螺旋二十四面體 . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 能帶圖及穿透頻譜分析 . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 結構參數與材料參數之影響 . . . . . . .. . . . . . . . . . . . . 27
3.1.3.1 整體體積分率 . . . . . . . . . . . . . . . . . . .. . . . . 27
3.1.3.2 完美導體的體積分率 . . . . . . . . . . . . . . . . . . . . . 29
3.1.3.3 介電質折射率 . . . . . . . . . . . . . . . . . . . . . . . . 30

第四章 金屬/介電質 混成雙螺旋二十四面體之模態演變 . . . . . . . . . . 34
4.1 等頻率線分析 . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 等頻率線預測與驗證 . . . . . . . . . . . . . . . . . . . . . . 37
4.3 電磁場輪廓 . . . . . . . . . . . . . . . . . . . . . . . . . . 41

第五章 結果與未來展望 . . . . . . . . . . . . . . . . . . . . . . . . 49

參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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