  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 subsequently demonstrated to be exactly
corresponding to the normalized rows of Pascal's triangle. The outstanding
performance of these optimal sources is verified by the practical 1-D, 2-D and
3-D PSTD simulations and compared with that of non-optimal sources.
