Fractional-calculus-based FDTD method for solving pulse propagation problems

In this paper, an accurate finite-difference time-domain (FDTD) scheme for modeling the electromagnetic pulse propagation in arbitrary dispersive media is presented. The main mathematical drawbacks encountered while solving this class of problems by means of the FDTD technique is the approximation of the fractional derivatives appearing in the time-domain permittivity response pertaining such materials. In order to overcome this issue, the proposed scheme solves the Maxwell's equations directly in the time-domain by using the Riemann-Liouville fractional derivative operator. The feasibility of the proposed method is demonstrated by simulating the ultra-wideband wave propagation in general stratified Raicu dispersive media displaying multiple relaxation times response.