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

## TL;DR

This paper introduces an exact Gaussian mode propagation formalism for nonlinear optics that accurately models orbital angular momentum transfer, enabling optimization and better understanding of multi-mode beam generation.

## Contribution

It provides the first exact solution for Gaussian beam propagation in nonlinear optics with orbital angular momentum transfer, improving upon previous phenomenological models.

## Key findings

- Excellent agreement with two experimental cases
- Method enables optimization of nonlinear interactions
- Applicable to various laboratory configurations

## Abstract

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.