Elliptic focusing of Gaussian beams in parametric frequency conversion in a nonlinear crystal

A theoretical analysis is given of two-dimensional focusing of light beams with Gaussian distributions of the amplitudes. The influence of the anisotropy as a method for increasing the efficiency of conversion of radiation in a nonlinear crystal is considered. The conversion at the sum and difference frequencies is discussed. An optimal ratio of the focal radii of the pump and signal beams is obtained for the axis along which rays are displaced because of the anisotropy. An estimate is made of the efficiency of conversion from λ = 10.6 μ to the visible range in a proustite crystal.