Parametric amplification of short pulses in optical fiber Bragg gratings

We study chi((3)) parametric amplification of a weak signal pulse tuned to a Bragg grating; through a series of numerical simulations. These simulations demonstrate that gratings permit strong signal amplification for large wave vector mismatches between pump, signal, and idler, even though gain would be prohibited in the corresponding uniform medium. The enhanced gain is explained in terms of a shift in the signal wave vector due to the strong dispersion induced by the grating, an effect which is; well known from other frequency conversion processes. For chi((3)) Parametric amplification, the pulsed regime introduces several new effects, many of which are explained by simple arguments based on the cw dispersion relation of the grating. Notably, the gain exhibits a ''self-locking'' behavior, in that there is considerable freedom in the input frequency of the signal.