A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method

Two novel methods for implementing recursively the convolution betweenthe electric field and a time dependent electric susceptibility function inthe finite-difference time domain (FDTD) method are presented. Both resultingalgorithms are straightforward to implement and employ an inclusive susceptibilityfunction which holds as special cases the Lorentz, Debye, and Drude mediarelaxations. The accuracy of the new proposed algorithms is found to be systematicallyimproved when compared to existing standard piecewise linear recursive convolution(PLRC) approaches, it is conjectured that the reason for this improvementis that the new proposed algorithms do not make any assumptions about thetime variation of the polarization density in each time interval; no finitedifference or semi-implicit schemes are used for the calculation of the polarizationdensity. The only assumption that these two new methods make is that the firsttime derivative of the electric field is constant within each FDTD time interval.