薄板光子晶体表面模式的分析及算法优化

Algorithm optimization for computing surface modes in photonic crystal slabs

薄板光子晶体的表面模式在设计制造性能更加优异的光子元件领域发挥了重要的作用.本文扩展了Dirichlet-to-Neumann(DtN)映射方法,将其用于计算二维薄板光子晶体的表面模式.这种方法以单元晶格的DtN映射为基础,利用标准与非标准单元晶格的DtN映射,构造出超级晶格的DtN映射,然后在超级晶格的边界上建立起特征值问题来进行求解.由于只需要在区域的边界上进行离散,所以特征值问题涉及到的矩阵是比较小的.在文章的算例部分验证了这种方法的有效性,并且应用这种方法在薄板光子晶体与完美磁导体(Perfect Magnetic Conductor)的交界面上发现了一种新的表面模式.

Surface modes in photonic crystal slabs play an important role in designing photonic crystal devices.In this paper,we extended the Dirichlet-to-Neumann (DtN) map method to analyze surface modes in two-dimensional photonic crystal (PhC) slabs.This method is based on the DtN maps of unit cells.By using the DtN maps of standard and non-standard unit cells,we can construct the DtN map of a supercell.Then,eigenvalue problems are established on the boundaries of the supercell.Since we only need to discretize on the boundaries,the matrices of the eigenvalue problems are relatively small.Finally,some numerical examples are used to verify our method.And as an application of this method,we found a new kind of surface mode which exists on the boundary between a PhC slab and a perfect magnetic conductor (PMC).