Abstract

We analyze a three-dimensional problem of propagation of beams in a quadratically nonlinear medium. It is shown how the results of a one dimensional model are modified because of the initially Gaussian transverse profile of the fundamental and because of the presence of diffraction. The effect of anisotropy is also studied, and it is shown to result in both linear and nonlinear walk-off between the beams. The resulting coupled parabolic equations are studied numerically with the help of a parallel algorithm for the split-step beam propagation method. Optimum focussing conditions are discussed.

© 1992 Optical Society of America