Title :
An Exponential Time Differencing Algorithm for the FDTD-PML Analysis of Nonlinear Photonic Bandgap Structures
Author :
Xu Zhuansun ; Xikui Ma ; Qi Liu
Author_Institution :
State Key Lab. of Electr. Insulation & Power Equip., Xi´an Jiaotong Univ., Xi´an, China
Abstract :
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.
Keywords :
finite difference time-domain analysis; nonlinear optics; optical materials; photonic band gap; ETD algorithm; FDTD-PML analysis; Z-transform method; auxiliary differential equation method; complex frequency shifted variable; exponential time differencing algorithm; finite difference time-domain analysis; memory requirement; nonlinear photonic bandgap structures; perfectly matched layer; third-order nonlinear materials; Algorithm design and analysis; Equations; Finite difference methods; Media; Memory management; Photonic band gap; Time-domain analysis; Boundary conditions; finite difference methods; nonlinear optics;
Journal_Title :
Magnetics, IEEE Transactions on
DOI :
10.1109/TMAG.2013.2283227
