Solitons in Bragg gratings with saturable nonlinearities

Abstract

We introduce two different systems of coupled-mode equations to describethe interaction of two waves coupled by the Bragg reflection in thepresence of saturable nonlinearity. The basic model assumes the ordinarylinear coupling between the modes. It may be realized as a photorefractivewaveguide, with a Bragg lattice permanently written in its cladding.We demonstrate the presence of a cutoff point in the system's bandgap,with gap solitons existing only on one side of it. Close to thispoint, the soliton's norm diverges with power -3/2. The soliton familybetween the cutoff point and the edge of the bandgap is stable. Inthis model, stationary bound states of two in-phase solitons arefound too, but they are unstable, transforming themselves into breathers.Another model assumes a photoinduced longitudinal bulk grating, withthe corresponding intermode coupling subject to saturation alongwith the nonlinearity. In that model, another cutoff point is found,with the soliton's norm diverging near it with power -2. Solitonsare stable in this model too (while it does not give rise to two-solitonbound states). Collisions between moving solitons are always quasi-elastic,in either model. (c) 2007 Optical Society of America.