邱奕鵬臺灣大學：光電工程學研究所朱詠聯Chu, Yung-LienYung-LienChu2007-11-252018-07-052007-11-252018-07-052004http://ntur.lib.ntu.edu.tw//handle/246246/50769我們將討論光子晶體超稜鏡和光子晶體蜂窩結構光纖的應用，一個可以充光與放光的微共振腔，以及可調Y-shape液晶波導。最後提出光子晶體結構高分子液晶薄膜的想法。 在超稜鏡方面，我們用平面波展開法求出光子晶體頻帶結構，進而求出光子晶體的色散曲面，再求出光波在光子晶體的傳播方向，然後利用時域有限差分法來模擬光在光子晶體中偏折的方向，進而驗證平面波展開法中的結果。 在光子晶體蜂窩結構光纖方面，我們求出在平面內頻帶結構並畫出出平面傳播相對頻帶大小，來說明當我們適當的調變基本蜂窩狀晶胞時，的確能增大頻隙大小，最後畫出導波模態。 在可以充光與放光的可調的微共振腔方面，首先我們先求出橢圓柱的光子晶體頻帶結構，利用橢圓柱旋轉所造的缺陷，我們可以充光和放光。 接著我們實際研究液晶元件，由液晶的各向異性特性與光子晶體頻隙中導波模態截止頻率，產生了可調的截止頻率。這使得液晶缺陷變成了開關，我們將成功的展示Y-shape液晶波導的模擬。液晶缺陷開關的概念，使得電場控制微共振腔充放光成為可能。In the thesis, we study photonic crystal superprism devices and honeycomb photonic crystal fibers. Then we investigate tunable microcavities which can fill light and release light. The concept of tunable microcavities imitates the concept of the capacitances in circuits. We also analyze tunable Y-shape liquid crystal waveguides, and bring up an idea of polymer dispersed liquid crystal films with photonic crystal structures. In the study of photonic crystal superprism devices, photonic crystal band structures are obtained by the plane wave expansion method. Then, photonic crystal dispersion surfaces are calculated. Propagation characteristics in the photonic crystal structures are determined. The deflections of light in photonic crystals are simulated by finite-difference time-domain method and the results are verified by the plane wave expansion method. In the study of honeycomb photonic crystal fibers, in-plane band structures are solved and out of plane propagation relative bandgap sizes are plotted. The bandgap sizes can be enlarged with appropriate modification of honeycomb cells. Then, a guided mode pattern of the honeycomb photonic crystal fiber is plotted. In the study of tunable microcavities, the photonic crystal band structures for the ellipse-rod-defects waveguides are calculated. The ellipse rods are rotated to switch the tunable microcavities. In addition, liquid crystal devices are studied. The anisotropy of liquid crystals makes the cutoff frequency of guided modes in the photonic bandgap tunable. Liquid crystal defects become switches of light. Tunable Y-shape liquid crystal waveguides are simulated successfully. The concept of liquid crystal switches makes it possible to control the tunable microcavities by electric fields. We develop the extended plane wave expansion method and the extended finite-difference time-domain method for the anisotropic materials. Finally, polymer dispersed liquid crystal films with photonic crystal structures are proposed.Contents(內容) 第一章介紹 1 1.1光子晶體的觀念 1 1.2數值分析方法:平面波展開法 3 1.3數值分析方法:有限差分時域法 4 1.4本論文主題的觀念 4 1.5研究動機 5 第二章平面波展開法 10 2.1平面波展開法的理論 10 2.2任意週期性結構的平面波展開法 15 2.3相關的模擬 16 第三章有限差分時域法 21 3.1有限差分時域法的基本觀念 21 3.2完美相配層吸收邊界條件 26 3.3相關的模擬 32 第四章光子晶體超稜鏡與光子晶體光纖 38 4.1光子晶體超稜鏡 38 4.2光子晶體頻隙光纖 41 第五章可調光子晶體元件 62 5.1橢圓柱可調微共振腔 62 5.2可調Y-shape液晶波導 63 5.3光子晶體結構的高分子分散液晶薄膜 69 第六章 結論 85 參考資料 86en-US超稜鏡光纖光子晶體液晶photonic crystalsliquid crystalsuperprismfiberthesis