Modelling optical pulse propagation in nonlinear media using wavelets

A wavelet based model for propagation of optical pulses in nonlinear media is presented. We obtain an O(N) algorithm for linear propagation by replacing the wavelet-domain propagation operator by its Taylor series approximation. Nonlinear propagation is then achieved by adding the nonlinear term in mid-step in a method analogous to the split-step Fourier method. Using wavelets offers the advantage of O(N) computational complexity compared with O(N log N) for fast Fourier transform methods. Using a wavelet basis also leads naturally to the time-resolved spectrum of the signal. Another advantage is that the local properties of wavelets will allow locally adaptive algorithms to be implemented