Dispersion analyses of FDTD schemes associated with dispersive media

Researchers have been extending the finite difference time domain algorithm to account for frequency-dependent media. These algorithms have been devised for cold plasma (isotropic and anisotropic), Debye, Lorentz media, etc. Essentially, the methodologies are either convolution based, which discretizes the constitutive convolution integral, or direct integration based, which discretizes an auxiliary set of equations. Although all schemes have been shown to yield good results, for a certain selection of numerical discretization parameters, it is not clear which method leads to more accurate solutions, all other things being equal. We present various analyses that highlight the dispersive and dissipation errors created by each of the discretization schemes, namely, those of Luebbers et al. (1990, 1992), Joseph et al. (1991) and Young (see IEEE Trans. Ant. and Prop., Nov. 1994). This is accomplished by considering the dispersive relationship of each method with Debye and Lorentz media in mind.