A Numerical and Analytical Approach for Pulse Propagation in Refracting and Random Media

By considering the time-dependent wave equation, an approximate solution for a narrow-band, forward-traveling pulse is derived as a split-step algorithm. The required approximations are similar to those of the familiar Tappert-Hardin split-step algorithm for the parabolic wave equation. This leads to an evolution operator analogous to the standard parabolic propagator. Consideration of the physical meaning of the resulting parabolic evolution operator reveals a simple improvement leading to another evolution operator analogous to the Thomson-Chapman propagator.