Analytical Expression for the Time-Domain Discrete Green´s Function of a Plane Wave Propagating in the 2-D FDTD Grid

In this letter, a new closed-form expression for the time-domain discrete Green´s function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of AFP requires computations of time-domain DGF for the plane wave 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 DGF. The developed time-domain implementation of AFP demonstrates the leakage error across the TFSF interface around the numerical noise level that validates the correctness of the DGF derivation.