修正的频域有限差分法在二维金属光子晶体分析中的应用

与介质光子晶体相比，金属光子晶体的带隙特性在毫米波和亚毫米波波段有着重要的应用价值.基于Yee网格的频域有限差分法推导得出的本征模方程，求解后能方便而又可靠地得出介质光子晶体的带隙图和场分布.但由于金属与介质的本质差异，该方法不能直接应用于金属光子晶体.文中引入了金属表面边界条件，推导了二维金属周期结构的光子带隙本征模方程.通过数值计算，得出了不同晶格结构（正方/三角格子）下两种模式（TE/TM）的全禁带特性，并与介质周期结构的禁带特性进行对比，分析了金属周期结构在模式选择和器件集成方面的优点.

Modified finite-difference frequency-domain method for two-dimensional metallic photonic crystal analysis

In contrast to dielectric photonic crystals, the propagation characteristics of metallic photonic crystals are of great importance in millimeter wave and submillimeter wave applications. It is convenient and reliable to get the band diagrams and field distributions of photonic crystals after solutions of the eigenmode equations, which is derived from the Yee-mesh-based finite-difference frequency-domain method. However, this method cannot be used for the analysis of metallic photonic crystals because of the essential distinctions between metal and dielectric. Based on this method, we derive eigenmode equations for two-dimensional metallic photonic crystals by introducing the metal surface boundary conditions. And then, after some numerical calculations, the transverse electric mode and the transverse magnetic mode global band gaps of different lattice structures are obtained, including both square lattice and triangular lattice. Finally, we discuss the advantages of metallic periodic structures in mode selection and device integration by the comparison between metallic photonic band gap and dielectric photonic band gap.