Reflection and refraction of a three-dimensional Gaussian beam at a nonlinear interface

Calculations are performed that show the nature of finite, scalar optical beam reflection and refraction from a three-dimensional Kerr nonlinear optical interface. The numerical technique, comments on its accuracy and stability, and preliminary results are presented. At least four qualitatively different behaviors have been observed, depending on the intensity of the incident beam. These behaviors are different from previously published results for two-dimensional treatments.