高阶色散介质的改进移位算子时域有限差分方法

Improved shift operator FDTD method for high order dispersive media

提出一种适用于高阶Debye,Drude,Lorentz及其混合模型的改进移位算子的时域有限差分(SO-FDTD)方法。从介质极化率函数出发,将其写成一阶或二阶有理分式求和的形式,并在随时间步推进计算的过程中,通过引入中间变量和设置临时变量,克服了常规SO-FDTD将高阶模型直接转化为有理分式所导致的计算复杂性和内存占用量大的问题。同时,改进SO-FDTD方法的时域推进计算步骤具有通用性,克服了常规递归卷积(RC-FDTD)方法对各种高阶模型具有不同计算公式,因而不能形成通用计算程序的问题。最后,通过空气-高阶色散介质界面的反射系数计算验证了算法的有效性和通用性。

An improved shift operator finite-difference time-domain（SO-FDTD） method for the high order Debye,Drude,Lorentz and hybrid model dispersive media is presented.The susceptibility function of dispersive media is firstly represented as the sum of rational fractions.The computational complexity and large storage requirement in the conventional SO-FDTD method for the high order dispersive model is solved by introducing an intermediate variable and setting a temporary variable.Meanwhile,the generality of updated formulation in the improved SO-FDTD method is superior to that of the conventional recursive convolution FDTD（RC-FDTD） method,in which different formulations are required for different dispersive models.Finally,the generality and feasibility of the presented scheme are validated by the calculation of reflection coefficients for high order Debye,high order Lorentz,and Drude-Lorentz hybrid dispersive dielectric slabs.