Analytical Expression for the Time-Domain Green’s Function of a Discrete Plane Wave Propagating in a 3-D FDTD Grid

In this paper, a closed-form expression for the time-domain dyadic Green's function of a discrete plane wave (DPW) propagating in a 3-D finite-difference time-domain (FDTD) grid is derived. In order to verify our findings, the time-domain implementation of the DPW-injection technique is developed with the use of the derived expression for 3-D total-field/scattered-field (TFSF) FDTD simulations. This implementation requires computations of the time-domain Green's function of DPW with the use of multiple-precision arithmetic. Then, excitations at the TFSF interface can be computed as a time-domain convolution of a source function with Green's function of DPW. The developed time-domain implementation of the DPW-injection technique demonstrates the leakage error across the TFSF interface around the numerical noise level that verifies the correctness of the derivation.