A novel FDTD formulation based on fractional derivatives for dispersive Havriliak-Negami media

A novel finite-difference time-domain (FDTD) scheme modeling the electromagnetic pulse propagation in Havriliak–Negami dispersive media is proposed. In traditional FDTD methods, the main drawback occurring in the evaluation of the electromagnetic propagation is the approximation of the fractional derivatives appearing in the Havriliak– Negami model equation. In order to overcome this problem, we have developed a novel FDTD scheme based on the direct solution of the time-domain Maxwell equations by using the Riemann–Liouville operator for fractional differentiation.The scheme can be easily applied to other dispersive material models such as Debye, Cole–Cole and Cole– Davidson. Different examples relevant to plane wave propagation in a variety of dispersive media are analyzed. The numerical results obtained by means of the proposed FDTD scheme are found to be in good accordance with those obtained implementing analytical method based on Fourier transformation over a wide frequency range. Moreover, the feasibility of the proposed method is demonstrated by simulating the transient wave propagation in slabs of dispersive materials.