A frequency-dependent finite-difference time-domain formulation for general dispersive media

A weakness of the finite-difference-time-domain (FDTD) method is that dispersion of the dielectric properties of the scattering/absorbing body is often ignored and frequency-independent properties are generally taken. While this is not a disadvantage for CW or narrowband irradiation, the results thus obtained may be highly erroneous for short pulses where ultrawide bandwidths are involved. In some recent publications, procedures based on a convolution integral describing D(t) in terms of E(t) are given for media for which the complex permittivity ∈*(ω) may be described by a single-order Debye relaxation equation or a modified version thereof. Procedures are, however, needed for general dispersive media for which ∈*(ω) and μ*(ω) may be expressible in terms of rational functions, or for human tissues for which multiterm Debye relaxation equations must generally be used. The authors describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) in terms of E(t) by means of a differential equation involving E, and their time derivatives. The method is illustrated for several examples