The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization

Abstract

The index matching technique of Giordmaine and Maker has been extended to include the more general three-wave interaction. Two fundamentally different experimental arrangements may be considered; one has the two low frequency waves in parallel polarizations and the other has these waves in orthogonal polarizations. The equations relating the phase matching angle in uniaxial crystals to the crystal birefringence, dispersion, and the frequencies of the three waves are given. These equations allow a cone of phase matched directions to be generated about the crystal optic axis. The effect of the symmetry properties of the second-order polarizability tensor on the strength of the phase matched output signal at particular azimuthal angles is discussed for all non-centro-symmetrical uniaxial crystal classes. The particular form of the second-order polarizability tensor for each of the uniaxial crystals is tabulated assuming that Kleinman's symmetry conjecture is valid.