The $(n+1)/2$ Rule for Dealiasing in the Split-Step Fourier Methods for $n$-Wave Interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (
n
+1)/2, where
n
is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(
n
+1) fraction of each spectral dimension.