Experimental results on the phase transfer from structured beams to parametric light, generated by inducing four-wave mixing in an atomic gas, are reported. Near-infrared, Mathieu, and Gaussian pump beams yield a blue coherent Mathieu electromagnetic field and an infrared beam. Two complementary techniques enable full characterization of the up-converted modes. The unambiguous and efficient phase heritage of these complex quasipropagation invariant modes to up-converted photons is demonstrated. The presented data enable a quantitative study of dynamical variables related to Mathieu beams. These include elliptic angular momentum, a generalization of the orbital angular momentum of light, which is also up-converted through the nonlinear process.

• Received 22 February 2021
• Accepted 3 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033170

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Published by the American Physical Society