Ge基二维正方晶格光子晶体带隙优化设计

采用平面波展开法模拟二维光子晶体在E极化和H极化下的能带结构，研究Ge基二维正方晶格光子晶体的填充比以及晶格排列结构对最大禁带宽度的影响。结果表明：在空气背景材料中填充Ge柱的介质柱结构中，可产生TE、TM带隙，且各方向完全带隙出现在r/a=0.19~0.47范围内，最大完全帯隙禁带宽度可以达到0.064（归一化频率）；在选取Ge为背景材料的空气孔型结构中，同样可产生TE、TM带隙，且各方向完全带隙出现在r/a=0.46~0.49范围内，最大完全帯隙禁带宽度可以达到0.051（归一化频率）。同时，不论在介质柱型还是空气孔型结构中，带隙宽度都随着r/a的增大呈先增大后减小的趋势。

Optimal Design of Photonic Band Gap in Ge-based Tetragonal Lattice 2D Photonic Crystal

Using the plane wave expansion method, the band structure of two-dimensional photonic crystal was calculated under E polarization and H polarization. The influence of Ge-based tetragonal lattice photonic crystal filling ratio and the lattice structure on the maximum photonic band gap were analyzed. When Ge cylinders are placed in the air background, the TE band and TM band generate and the maximum complete band gap appears in the range of r/a=0.19~0.47, the maximum photonic band gap width can reach 0.064(normalized frequency). When air holes are placed in the Ge background, the TE and TM band also generate, and the maximum complete band gap appears in the range of r/a=0.46~0.49, the maximum photonic band gap width can reach 0.051(normalized frequency). Meanwhile, in both of the cylinder and air holes structure, along with the rising of r/a, the band gap width increases at first, and then decreases.