基于Dirichlet-to-Neumann映射计算半无限二维光子晶体的表面模式

Computing surface modes of semi-infinite two dimensional photonic crystals by Dirichlet-to-Neumann maps

介绍了一种基于Dirichlet-toNeumann(DtN)映射的计算半无限二维光子晶体表面模式的有效数值方法.首先利用三种不同单元晶格的DtN算子构造出超级晶胞的DtN映射,然后在超级晶胞的两条边界上建立特征值问题来计算光子晶体表面模式,建立的特征值问题是线性的,而且其中的矩阵比较小.最后用两个数值算例验证了数值方法的有效性.

An efficient numerical method is developed for calculating surface modes of a semi-infinite two dimensional photonic crystals by Dirichlet-to-Neumann( DtN) maps. Using the DtN maps of three different unit cells to construct the DtN map of the supercell,the surface modes are solved from a linear eigenvalue problem on two boundaries of the supercell,leading to relatively small matrices.Finally we use two numerical examples to verify the effectiveness of the method.