Bragg diffraction of a plane wave by a standing spatial soliton

Diffraction of a plane wave by a grating induced in a cubic nonlinear medium by counterpropagating solitons is considered. A two-wave diffraction problem is solved in the approximation of slowly varying amplitudes. The Bragg phase matching is assumed in determination of the exact solution for a probe wave propagating at a grazing angle relative to the direction of propagation of the solitons. The conditions for the amplitudes of the scattered waves to be comparable with the incident-wave amplitude are found.