Perfectly matched plane wave source in FDTD via efficient and true time-domain update equations

The FDTD Total Field Scattered Field (TF/SF) formulation presented in [1] is a powerful tool for simulating scattered fields reflected from objects with extremely complex geometries and heterogeneities. Unfortunately, accurate TF/SF for general modes at present is only limited to a 2D application since the present Analytic Field Propagator (AFP) of [2] when applied to a 3D problem consumes a large amount of storage. With the help of discrete signal techniques, it is possible to significantly improve the memory constraint and the accuracy of the present AFP so that the technique is practical for any dimensions. However, one may still wonder if a true time-domain propagator directly derived from the FDTD update equations can be constructed. In other words, the FDTD scheme is a true time-domain technique and why should the TF/SF be solved via the frequency domain? In this paper, we show that a true FDTD planewave exists and its solution is fairly straightforward.