A Generally Optimized FDTD Model for Simulating Arbitrary Dispersion Based on the Maclaurin Series Expansion

An optimized solution to the discrete numerical model for simulating arbitrary dispersion by the finite-difference time-domain (FDTD) method is derived for both the single-pole and two-pole frequency responses of dispersive media. Based on the method of Maclaurin series expansion, the derivation is aimed to suppress the redundant truncation errors into minimum levels by eliminating the first several series terms of difference between the numerical and theoretical solutions to a modeled susceptibility. The accuracy of numerical approximation to theoretical dielectric functions based on our proposed approach is shown to be exactly equivalent to the bilinear transformation model for the single-pole dispersion response of the modeled dispersive material, but higher than those of other two previously reported models for a two-pole dispersion response of a modeled dispersive material. The explicit coefficients of the proposed model for several classical types of dispersive materials are derived and their corresponding dominant truncation errors are given as well. Both the analytical and simulation results obtained from the FDTD modeling of an exemplified material, silver, demonstrate that the new model outperforms the other models when they are incorporated into the fourth-order accurate FDTD algorithm with small numerical dispersion error rather than in the second-order one with large numerical dispersion error.