本篇論文是利用平面波展開法以及有限元素法 (COMSOL Multiphysics 3.5a軟體) 模擬與分析各種填入液晶材料的光子晶體結構的光學特性，並設計有用的光電元件。含液晶的光子晶體是利用外加電場影響液晶主軸角度以達到光子晶體能帶調變的效果，並從光子晶體能帶色散關係曲線圖中找出極大而且有用的光子晶體能隙，即可設計出可調變的光電元件。如此方便的調變特性使得含液晶的光子晶體在積體光學的應用上有相當大的發揮空間。
本論文中我們設計並模擬分析一種在交叉點處有一個填入液晶的共振腔的Y型分支波導的特性。此種結構中的共振腔可篩選特定之共振頻率，並利用外加電場來調變控制TE mode在共振腔中的模態方向以決定導波的傳播走向。與此類似的結構在未來或許可以推廣應用在篩選頻率的分光器上面，或是做為積體光路中的開關元件。

In this thesis we use the plane wave expansion method together with the finite element method (COMSOL Multiphysics 3.5a) to investigate the optical properties of some silicon based two-dimensional photonic crystals infiltrated with liquid crystals. We show that the photonic band gaps can be tuned by changing the orientation of the director of the liquid crystal (the direction of preferred orientation of liquid crystal molecules in the neighborhood of any point), which is controlled by the externally applied electric field. Large and useful photonic band gaps can be found from the calculations of the photonic band structures. Such a mechanism of controlling light waves should be useful in designing components in photonic integrated circuits.
As an example of application, we design a Y-shaped photonic crystal waveguide and study its properties. The waveguide contains a photonic crystal cavity located at the branch point, which is infiltrated with liquid crystal material. With this cavity inside, only those guided modes within a frequency range near the specific resonance frequencies of the cavity can be propagated. We found that the propagating direction of the guided waves are determined by the orientation of the cavity mode patterns, which can be controlled by changing the direction of the applied external electric field since the cavity is infiltrated with liquid crystal material. We expect that similar devices can be developed to be used as frequency-selective or switching devices in optical circuits.

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