A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media

A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data.