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

Rachel F. Offer, Andrew Daffurn, Erling Riis, Paul F. Griffin, Aidan S. Arnold, Sonja Franke-Arnold

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)
38 Downloads (Pure)


Studying the conversion between transverse light modes via four-wave mixing in a heated rubidium vapor, we demonstrate and explain a transfer between azimuthal and radial mode numbers. They 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 behavior in the thick- and thin-medium regimes. 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 the thick-medium regime, allowing efficient radial-to-azimuthal and radial-to-radial mode conversion.

Original languageEnglish
Article numberL021502
Number of pages7
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 26 Feb 2021


  • atomic physics
  • optics
  • Gouy phase


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