Analysis and compensation of numerical dispersion in the FDTD method for layered, anisotropic media

In this work, we investigate the effects of numerical dispersion in the finite-difference time-domain (FDTD) algorithm for layered, anisotropic media. We first derive numerical dispersion relations for diagonally anisotropic media (corresponding to an FDTD reference frame coinciding with the principal axes of a biaxial media). In addition, we incorporate the discretization effects on the reflection and transmission coefficients in layered media. We then apply this analysis to minimize the numerical dispersion error of Huygens' plane-wave sources in layered, uniaxial media. For usual discretization sizes, a typical reduction of the scattered field error on the order of 30 dB is demonstrated.