An Exponential Time Differencing Algorithm for the FDTD-PML Analysis of Nonlinear Photonic Bandgap Structures

An exponential time differencing (ETD) algorithm is presented for the analysis of photonic crystal structures comprising the third-order nonlinear materials. Compared with the well known Z-transform method and auxiliary differential equation method for incorporating the nonlinearity, the proposed ETD algorithm has the least memory requirement and shows the same accuracy. The stretched coordinates perfectly matched layer (PML) with the complex frequency shifted variable implemented using the ETD algorithm is applied to terminate nonlinear photonic bandgap structures. Compared with the conventional PML and the convolutional PML, the proposed implementation can improve the absorbing performance significantly with similar memory requirement.