Influence of a transverse inhomogeneity of the refractive index of a nonlinear crystal on second-harmonic generation

A regular transverse inhomogeneity of the refractive index of a nonlinear crystalline medium is shown to have an influence on the generation of a second harmonic. In general, the dependence of the second-harmonic power on the inhomogeneity cannot be represented by elementary functions, and numerical calculations are essential. Expressions giving the second-harmonic power are obtained for different degrees of transverse inhomogeneity, and the conditions of validity of these expressions are derived. The results of the calculations are in agreement with the experimental data obtained in the generation of a second harmonic in a crystal of lithium niobate.