THE CONDITION OF PHASE MATCHING IN LIGHT-WAVE FREQUENCY CONVERSION,

From a continuation of an earlier paper DAN BSSR v, 8, no. 11, 713, 1964, the report gives a general solution for the problem of light-wave frequency conversion by crystals and shows that in general, 14 polarization waves are produced when two waves are incident on a nonlinear crystal. The present paper considers the possibility of phase matching of all these waves, wherein the vector of the polarization-wave refraction coincides with the vector of the generated-wave refraction. The necessary condition for the phase matching is derived and is shown to be related with the ratio of the birefringence and the dispersion. The analysis shows that phase matching is possible for nine different polarization waves, and the wave with the higher frequency polarization or pumping waves should have a lower refractive index. The possibility of phase matching in a uniaxial crystal is further considered, and it is shown that in the case when the ordinary beam from a ruby laser operating at 6934 A is mixed with the extraordinary beam from a CaWO4Nd3 laser 10582 A in a KDP crystal, phase matching takes place at an angle of 54.6 degrees, whereas in the case when only the ordinary beams of these lasers are mixed the matching takes place at 42.6 degrees. Author