Poincar\'e sphere symmetries in four-wave mixing with orbital angular momentum

TL;DR

This paper investigates how orbital angular momentum Poincaré sphere modes influence four-wave mixing in rubidium vapor, revealing symmetry relations, mode transfer rules, and complex field structures validated by experiments.

Contribution

It introduces a framework linking Poincaré sphere modes to four-wave mixing signals, demonstrating mode transfer rules and intricate field structures in nonlinear optical interactions.

Findings

Output fields also belong to Poincaré spheres with related angles.

Experimental results match theoretical predictions.

Transition of transverse profiles between near- and far-field regions.

Abstract

We explore a degenerate four-wave mixing process induced by transversely structured light beams in a rubidium vapor cell. In particular, we consider the nonlinear interaction driven by optical modes contained in the orbital angular momentum Poincar\'e sphere, which can be parametrized in terms of a polar and an azimuthal angle. In this context we investigate the transfer of spatial structure to two distinct four-wave mixing signals, possessing different propagation directions in space. We show that under usual assumptions, the output fields can also be described by modes belonging to Poincar\'e spheres, and that the angles describing the input and output modes are related according to well-defined rules. Our experimental results show good agreement with the calculations, which predict intricate field structures and a transition of the FWM transverse profile between the near- and far-field regions.