A Space-Time Split-Step Algorithm for Pulse Propagation in Refracting Media

A simple, time-domain split-step algorithm for pulse propagation in a refracting medium is derived from the time-dependent wave equation (TDWE). The derivation is similar in form and spirit to the factored Helmholtz equation methods used in finding generalized parabolic equations. Like the Helmholtz equation analyses, the factored TDWE involves non- local pseudo-differential operators and a commutator term. Making use of causality and considering media in which the index-of-refraction changes only slowly over a typical acoustic wavelength, the commutator term can be neglected and the TDWE reduces to a Schrodinger-like equation in space-time.