Abstract
We consider a model of a nonlinear planar waveguide with a sinusoidal modulation of the refractive index in the transverse direction, which gives rise to a system of parallel troughs that may serve as channels that trap solitary beams (spatial solitons). The model can also be considered as an asymptotic one describing a dense planar array of parallel nonlinear optical fibers, with the modulation representing the corresponding effective Peierls–Nabarro potential. By means of the variational approximation and by direct simulations we demonstrate that the one-soliton state trapped in a channel has no existence threshold and is always stable. In contrast with this a stationary state of two beams trapped in two adjacent troughs has an existence border, which is found numerically. Depending on the values of the parameters, the two-soliton states are found to be dynamically stable over an indefinitely long or a finite but large distance. We consider the possibility of switching the beam from a channel where it was trapped into an adjacent one by a localized spot attracting the beam through the cross-phase modulation. The spot can be created between the troughs by a focused laser beam shone transversely to the waveguide. By means of the perturbation theory and numerical method we demonstrate that the switching is possible, provided that the spot’s strength exceeds a certain threshold value.