FDTD formulation for frequency dependent permittivity

Current finite-difference time-domain (FDTD) formulations require the permittivity, permeability, and conductivity to be constant. However, for many real materials of interest these parameters vary significantly with frequency. The effects of constitutive parameters which vary with frequency are included in a frequency dependent FDTD formulation, (FD)/sup 2/TD, by extending the traditional Yee formulation to include discrete time-domain convolution. To apply (FD)/sup 2/TD all of the frequency domain information (in the complex permittivity function) is Fourier-transformed to a time-domain susceptibility function. To demonstrate (FD)/sup 2/TD computation of wideband reflections at an air-water interface the authors consider a one-dimensional problem space consisting of 1000 cells: 499 cells were used to model free space (air) and 501 cells were used for water. They compare (FD)/sup 2/TD results after 1200 time steps and FDTD results (with 20-GHz permittivity and conductivity values constant) after 8000 time steps with the exact analytical frequency domain result. The (FD)/sup 2/TD formulation is clearly much more accurate than traditional FDTD.<>