Orbital angular momentum mixing in type II second harmonic generation

TL;DR

This paper explores how orbital angular momentum modes interact and mix during type II second harmonic generation, revealing new selection rules for mode combinations and confirming them through experiments.

Contribution

It derives the selection rules for orbital angular momentum mixing in nonlinear interactions and experimentally confirms the less intuitive radial order rule.

Findings

Conservation of topological charge in mode interactions

Identification of a new radial order selection rule

Experimental validation of the theoretical predictions

Abstract

We investigate the non linear mixing of orbital angular momentum in type II second harmonic generation with arbitrary topological charges imprinted on two orthogonally polarized beams. Starting from the basic nonlinear equations for the interacting fields, we derive the selection rules determining the set of paraxial modes taking part in the interaction. Conservation of orbital angular momentum naturally appears as the topological charge selection rule. However, a less intuitive rule applies to the radial orders when modes carrying opposite helicities are combined in the nonlinear crystal, an intriguing feature confirmed by experimental measurements.