Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation

Abstract

The process of two input electromagnetic waves at different frequencies overlapping in a nonlinear medium is a typical phenomenon of nonlinear optics. The traditional method of dealing with such a problem is to use the coupled-wave equations. In this paper, sum- and difference-frequency generation of cylindrical electromagnetic waves in a nonlinear medium is investigated in a different way. We use exact solutions of Maxwell's equations to describe the propagation of cylindrical electromagnetic waves in a nonlinear medium and show that sum- and difference-frequency generation comes out quite naturally from such exact solutions. For comparison, the traditional method of utilizing the coupled-wave equations is also discussed, and we find that the results obtained from the two different approaches are consistent with each other.