Wavelet operators for nonlinear optical pulse propagation

A method that uses discrete wavelet transforms for the solution of evolutio n equations that describe optical pulse propogation in nonlinear media is p resented. The theory of orthogonal wavelet transforms is outlined and appli ed to the representation of optical pulses. Wavelet transform representatio ns of propagation operators are presented and applied to the nonlinear Schr odinger equation, yielding results that are indistinguishable from traditio nal Fourier-based simulations. The compression properties of wavelet repres entations of optical pulses permit significant improvement in execution spe ed compared with that of the split-step Fourier method. (C) 2000 Optical So ciety of America [S0740-3232(00)03012-X] OCIS codes: 190.0140, 190.4370.