Solitons in Bragg gratings with saturable nonlinearities

We introduce two different systems of coupled-mode equations to describe the interaction of two waves coupled by the Bragg reflection in the presence of saturable nonlinearity. The basic model assumes the ordinary linear coupling between the modes. It may be realized as a photorefractive waveguide, 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 this point, the soliton's norm diverges with power -3/2. The soliton family between the cutoff point and the edge of the bandgap is stable. In this model, stationary bound states of two in-phase solitons. are found too, but they are unstable, transforming themselves into breathers. Another model assumes a photoinduced longitudinal bulk grating, with the corresponding intermode coupling subject to saturation along with the nonlinearity. In that model, another cutoff point is found, with the soliton's norm diverging near it with power -2. Solitons are stable in this model too (while it does not give rise to two-soliton bound states). Collisions between moving solitons are always quasi-elastic, in either model.