Under the Collins transformation, the orthonormal set of Hermite-Gaussian modes maps into an orthonormal set of beams with a Gaussian envelope. Among them are the Laguerre-Gaussian beams and the recently introduced Hermite-Laguerre-Gaussian beams. Compact expressions for the complex field amplitude and the Wigner distribution of these modes are derived. The obtained results are useful for the solution of the phase retrieval problem and the design of mode converters and imaging systems.
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