Schrödinger equation description for cross-phase modulation in grating structures

We present a simple approximate description of systems involving cross-phase modulation in highly dispersive media. Optical pulses in such systems suffer large frequency shifts and correspondingly experience large variations in group velocity dispersion so that a simple nonlinear Schr\"odinger equation description is not valid. We take the frequency shift into account in a moments based model that extends the standard Schr\"odinger description, and apply the model to the particular case of optical pulse compression in nonlinear Bragg gratings. The model is tested against full numerical simulations. Finally, we consider some of the difficulties involved in observing the pulse-compression effect.