在本研究中，主要是進行偏平面光子晶體的能帶研究，利用兩種數值模擬方法:純量平面波展開法與向量平面波展開法來進行分析。我們以理論數值模擬各種晶格的二維與三維光子晶體，並改變其結構參數(填充率、介電質介電常數、介質柱形) 以觀察H偏振、E偏振和偏平面的能帶變化情形，試圖找出全方位完全能隙，並比較兩種數值模擬方法在研究偏平面二維光子晶體上的差異。 In this thesis, we study the Off-Plane Band Gap of Photonic Crystals. We use two numerical simulation methods, Scalar Plane Wave Expansion Method and Vector Plane Wave Expansion Method, to calculate photonic crystal band structure. We change many parameters, which include lattice structure, filling faction, dielectric constant, and shape of rods, to calculate and analyze Band Structure of H polarization, E polarization and Off-plane, and try to find out omni-directional absolute band gaps. At last, we compare the results obtained by these two methods.
