一种高稳定的复杂色散介质分析FDTD方法

针对复杂色散介质电磁特性分析问题，提出一种新的、高稳定通用时域有限差分法．该方法从二阶复有理函数形式的极化率函数入手，将纽马克算法同时作用于极化矢量与电场的时域关系式两边，得到显式时域有限差分时域递推公式，并从理论和数值两方面对该算法的稳定性进行了分析．该方法不仅可作为处理包括复共轭极点-留数、临界点、修正洛伦兹以及二阶复有理函数等复杂色散介质问题的通用时域有限差分方法，而且具有更高的稳定性．

Highly stable FDTD method for complicated dispersive medium

A novel finite-difference time-domain (FDTD) approach for analyzing a complicated dispersion model is presented. Starting from the susceptibility in the quadratic rational function form, the explicit FDTD time-step formula is obtained by applying the Newmark algorithm to both sides of the relation equation with the polarization vector and electric field in the time domain. Then, the stability of the presented algorithm is investigated from two aspects of theory and numerical computation. It is observed that this method has the advantages of generality and high stability and can thus be applied to the treatment of many complicated dispersion models, including the complex conjugate pole residue model, the critical point model, the modified Lorentz model, the complex quadratic rational function, etc.