Gouy phase-matched angular and radial mode conversion in four-wave mixing

TL;DR

This paper investigates how Gouy phase matching enables conversion between azimuthal and radial light modes in four-wave mixing within heated rubidium vapor, revealing new insights into mode interactions in nonlinear media.

Contribution

It demonstrates the role of Gouy phase in mode conversion and bridges the understanding between thick atomic media and nonlinear crystals.

Findings

Gouy phase is crucial for mode conversion understanding.

Systematic demonstration of radial-azimuthal mode transfer.

Different behaviors observed in thick versus thin media regimes.

Abstract

Studying the conversion between transverse light modes via four-wave mixing in a heated rubidium vapour, we demonstrate and explain a transfer between azimuthal and radial mode numbers. These relate to orthogonal modal dimensions, which one would not normally expect to interact. While angular momentum conservation in this nonlinear process dictates the selection rules for the angular mode number, the role of the radial mode number is more esoteric. We demonstrate systematically that the Gouy phase is the key to understanding this conversion, leading to strikingly different conversion behaviour in the thick and thin medium regime. Our experimental investigation of the transition between these regimes bridges the gap between previous experiments in atomic thick media and work in nonlinear crystals. Our work sets a clear starting point to explore new territory in the thick medium regime, allowing efficient radial-to-azimuthal and radial-to-radial mode conversion.