A compact wave source condition for the pseudospectral time-domain method [EM wave propagation applications]

An incident wave source condition that specifies the field at a single grid point is problematic for the pseudospectral time-domain (PSTD) method because of the spatial Fourier transforms inherent in the algorithm. Previously, it had been suggested in the literature that a spatially smoothed source spanning several grid cells in each direction was required to avoid aliasing errors, referred to as Gibbs phenomena. Here, we show that a spatially compact wave source condition, spanning only two spatial grid cells in each direction, eliminates the numerical artifacts induced by this aliasing/Gibbs effect. We demonstrate the successful implementation of this source condition in two practical PSTD modeling examples: fundamental mode excitation in a dielectric slab waveguide and cylindrical wave excitation via an infinite electric line source in a two-dimensional grid.