旋磁光子晶体元件的高效数值模拟

Efficient numerical modeling of gyromagnetic photonic crystal devices

针对分析、设计与优化旋磁光子晶体元件需要有效数值方法的现状,扩展了Dirichlet-to-Neumann(DtN)映射方法,将其用于计算二维旋磁光子晶体元件的传输和反射光谱。由于DtN映射方法避免了单元晶格内部的离散,只需在单元晶格的边界上进行离散,极大减少了未知数的总量,从而得到一个规模非常小的线性方程组,提升了计算速度。采用四端口旋磁光子晶体环形器和波导交叉结构的数值算例验证了该方法的有效性。

In recent years, gyromagnetic photonic crystals(GPCs) have attracted more and more attention due to their unique controllability.The GPC devices fabricated by GPCs are research hotspot in the fields of optical integrated chips, optical communication, and optical signal processing.Efficient numerical methods are needed to analyze, design, and optimize GPC devices.We extend the Dirichlet-to-Neumann(DtN) map method to calculate the transmission and reflection spectra of two-dimensional GPC devices.Since the DtN map method can avoid discretization inside the unit cells and only need to discretize on the edges of the unit cells, the total number of unknowns can be significantly reduced.Therefore, the coefficient matrix of the linear system is relatively small.Numerical examples are used to illustrate the method, including a four-port circulator and the waveguide cross structure.