Gaussian Beam-Propagation Theory for Nonlinear Optics - Featuring an Exact Treatment of Orbital Angular Momentum Transfer

We present a general, Gaussian spatial mode propagation formalism for describing the generation of higher order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical angular momentum transfer interactions, and show how one can optimize the interaction to reduce the undesired modes. Past theoretical treatments of this problem have often been phenomenological, at best. Here we present an exact solution for the single-pass no-cavity regime, in which the the nonlinear interaction is not overly strong. We apply our theory to two experiments, with very good agreement, and give examples of several more configurations, easily tested in the laboratory.