Modeling propagation in optical fibers using wavelets

A new model for the linear and nonlinear propagation of arbitrary optical waveforms through monomode fiber is presented. The basis of the method is the representation of the in-phase and quadrature components of the propagating electric field by their wavelet transform coefficients. For certain wavelet functions, a closed-form solution of the dispersive wave equation can be obtained, thereby allowing an analytic description of the propagating waveform in linear fiber. Nonlinear propagation is modeled using a split-step wavelet method that proceeds in a manner analogous to the split-step Fourier method. Arbitrarily shaped pulses or pulse sequences, with or without frequency chirping of the source, are accommodated with ease. A particular feature of the method is its inherent ability to provide time-resolved power spectra of the propagating waveforms