Split Step Fourier Transform: A Comparison Between Single and Multiple Envelope Formalisms

We describe a modified version of the split step Fourier transform algorithm used to analyze the propagation of multi-channel optical pulses. The modified algorithm divides the signal spectrum into separate envelopes, one for each channel, and computes the evolution of a set of nonlinear Schrödinger equations which accounts for the dispersion of both linear and nonlinear propagating parameters. We choose four exemplary cases for which the performances of the modified and standard split-step methods are compared in terms of computation cost versus global error of the solutions. We show that the modified technique is inferior when the spectrum is dense but it has a significant advantage for sparsely occupied spectra and for cases when the linear and nonlinear propagation parameters are dispersive.