On the Stability of the FDTD Implementation of High Order Rational Constitutive Relations

The stability of the finite difference time domain (FDTD) implementation of high order rational constitutive relations is studied by means of the root-locus method. The proposal equally is applicable to electrically and/or magnetically dispersive models. It is shown that by adopting the bilinear transformation into the constitutive relation FDTD implementation, the conventional non-dispersive Courant-Friedrichs-Lewy stability limit will be retained. Numerical simulations carried out for a four-pole complex rational function are included to validate both the stability and the accuracy of the derived equations.