From parametric gap solitons to chaos by means of second-harmonic generation in Bragg gratings

We review the theory of light localization due to the combined action of single or double Bragg coupling between dichromatic counterpropagating envelopes and parametric mixing nonlinearities. We discuss existence, stability, and excitation of such localized envelopes. We also investigate the link between stationary gap solitons and input-output response of nonlinear quadratic Bragg gratings. Frustrated transmission and multistable switching is expected to occur under suitable integrable (cascading) limits. Substantial deviations from these conditions lead to the onset of spatial chaos. (c) 2000 American Institute of Physics.