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 si ngle or double Bragg coupling between dichromatic counterpropagating envelo pes and parametric mixing nonlinearities. We discuss existence, stability, and excitation of such localized envelopes. We also investigate the link be tween stationary gap solitons and input-output response of nonlinear quadra tic Bragg gratings. Frustrated transmission and multistable switching is ex pected to occur under suitable integrable (cascading) limits. Substantial d eviations from these conditions lead to the onset of spatial chaos. (C) 200 0 American Institute of Physics. [S1054-1500(00)00903-4].