The Optimal Spatially-Smoothed Source Patterns for the Pseudospectral Time-Domain Method

Spatially-smoothed sources are often utilized in the pseudospectral time-domain (PSTD) method to suppress the associated aliasing errors to levels as low as possible. In this work, the explicit conditions of the optimal source patterns for these spanning sources are presented based on the fact that the aliasing errors are mainly attributed to the high spatial-frequency parts of the time-stepped source items and the source patterns are thereafter demonstrated to be exactly corresponding to the normalized rows of the Pascal's triangle. The excellent performance of these optimal sources is verified by the practical 1-D, 2-D and 3-D PSTD simulations and also compared with that of non-optimal sources.