FDTD method for wave propagation in Havriliak-Negami media based on fractional derivative approximation

A finite-difference time-domain (FDTD) method for simulating wave propagation in Havriliak-Negami (HN) dispersive media is presented. In an HN medium, the polarization relation is a fractional differential equation, whose numerical treatment results in significant memory storage demands due to the nonlocality of the fractional differential operator. However, by an appropriate approximation of the fractional differential operator, an FDTD scheme with reasonable memory requirements is feasible.