Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary

The total-field/scattered-field (TFSF) boundary has been successfully used for a number of years to introduce energy into finite-difference time-domain (FDTD) grids. If the propagation of the incident field is grid-aligned, a perfect TFSF implementation can be realized by using an auxiliary one-dimensional FDTD simulation which models propagation of the incident field. Here "perfect" implies the incident field propagation exactly matches the way in which the field propagates in the FDTD grid. However, for propagation which is not grid-aligned, no similarly perfect implementation has previously been presented. This work provides a framework for a perfect TFSF boundary for pulsed plane waves which do not propagate in a grid-aligned fashion. To achieve this, homogeneous plane-wave propagation is rigorously quantified. Using this knowledge and a specification of the desired incident field, the dispersion relation is used to ascertain the incident field at any point in the grid. It is required to account for, unlike in the continuous world, the electric field, the magnetic field, and the wavenumber vector not forming a mutually orthogonal set. Group velocity is also considered because of its relevance to the implementation.