Parametric reflection upon cascade interaction of focused optical beams

The parametric reflection of a signal beam in the waist of the reference pump beam upon mismatched three-frequency interaction in a quadratically nonlinear medium is discussed. The critical angle of total internal reflection from the induced defocusing channel is found as a function of the beam waist parameters. It is shown that when the reference beam is focused, this angle increases and some distortions are introduced into the reflected wave due to a finite length of the waist. The modification of the cross section of a wave reflected from a convex parametric mirror is analysed. The optimal beam focusing geometry is found at which the distortions of the shape and divergence of the reflected wave are minimal. Under certain conditions, the signal wave also flows around a cylindrical inhomogeneity produced by the axially symmetric pump beam. The results of theoretical analysis and numerical simulation are in good agreement.