Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM

A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into finite-difference time-domain (FDTD) simulations. For fields which are traveling obliquely to the grid axes, there is no simple way to account fully for the effects of the inherent numerical artifacts associated with plane-wave propagation in the FDTD grid. Failure to account for these artifacts causes erroneous fields to leak across the TFSF boundary. Recent publications have proposed ways to use the dispersion relation to describe precisely plane-wave propagation in the FDTD grid thus permitting the realization of a nearly perfect TFSF boundary. However, these publications did not cover certain implementations details (such as the type of Fourier transform which is needed) or their scope was so broad as to mask the relative simplicity with which the approach can be applied to problems involving planar interfaces. This work considers the Fourier transforms needed in order for the implementation to be exact. Reflection and transmission coefficients for a planar interface are derived. Implementation for planar perfect electric conductors is also presented.