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Nonlinear interaction of optical beams in gradient waveguides

We investigate the interaction of two optical beams at different frequencies in an optical gradient waveguide. The index has a parabolic profile, and the nonlinearity belongs to a defocusing type. The total reflection of a tilted signal beam from a negative inhomogeneity induced by pump-beam occurs while both beams are trapped in the refractive index trough is considered. We derive the equation for the rays, taking into account cubic nonlinearity and transverse inhomogeneity. Trajectories of the signal beam at different ratios of the values of the nonlinearity, heterogeneity and the initial angle of inclination are plotted. The critical angle of total reflection in a gradient waveguide with negative nonlinearity is found. The interaction of co-axis beams is also discussed. The waveguiding propagation of a pump beam under the balance between defocusing with negative nonlinearity and focusing with parabolic inhomogeneity is presented. The wide signal beam can split by narrow pump beam.