Propagation Technique for Ultrashort Pulses II: Numerical Methods to Solve the Pulse Propagation Equation

Abstract

We presented the numerical technique to approximately solve the pulse propagation equation. Two efficient methods for this problem, the Split-Step Fourier and the fourth order Runge-Kutta methods are considered. Their high accuracy are shown by comparison with analytical solutions in some particular situations. Our numerical experiments are implemented for soliton propagation and interacting high order solitons. We also numerically investigate an important technique to create ultrashort pulses, which is known as the pulse compression. It is based on high order soliton propagation in Kerr media when the effect of stimulated Raman scattering is taken into account.