Elastic Collisions and Scattering of Optical Beams with Three-Wave Parametric Interactions

The theory of optical beam spatial switching with three-wave vector interaction is first elaborated. The main idea is that due to mismatched noncollinear parametric interaction power pump beam along with excited sum wave induce an inhomogeneity to the weak signal beam. The induced refractive index replicates the pump intensity distribution. It results in a signal beam path curvature. Under certain conditions the pump beam totally reflects the signal beam. We have derived the trajectory equations by geometric optics approximation and variational method. The parametric reflection occurs for tilt angles less than the critical value proportionate to pump intensity. We found the simple expression for the critical angle. A larger tilted wave passes through the pump beam with no reflection. To enlarge the critical angle it is profitably to use focused pump wave and to reflect narrow signal beam from the pump waist. Such method also enables decreasing required pump intensity. The analytical estimates are in a good agreement with the numerical simulation results.