二维金属光子晶体的带结构研究

采用一种新的平面波展开法研究金属光子晶体的带结构，即在传统平面波展开法的基础上，将“原问题”拓展，引入一个“新问题”，通过求解“新问题”得到“原问题”的带结构，并论证了它们之间的关系.为了准确求解“新问题”，引入辅助函数，将其色散关系等价为一个积分微分本征方程，求解这个本征方程得到“新问题”的带结构，从而由此导出“原问题”的带结构.最后，以正方晶格二维金属光子晶体为例，进行数值计算，得到了满意的结果. 关键词： 金属光子晶体 平面波展开法 带结构 正方晶格

Study of 2D metallic photonic band gap structures

In order to study 2D metallic photonic crystal, a new plane-wave expansion method was proposed. Based on traditional plane wave expansion method, the “original problem” to be solved was extended to a “new problem”. First, the relation between them were given, second, the “new problem” was transformed to an integral-differential eigen equation through an auxiliary function. The eigen equation was solved to obtain the band gap structures of the “new problem”. The band gap structures of the “original problem” were deduced according to “new problem”. Finally, numerical computations were done for 2D square-lattice square metallic rods photonic crystal, and excellent results were achieved.