Laguerre-Gaussian Modes and the Wigner Transform

Details Laguerre-Gaussian Modes and the Wigner Transform Laguerre-Gaussian Modes and the Wigner Transform

2008-05-07

arxiv.org/abs/0805.0816v3

Journal of Modern Optics. Volume 55, Issue 21, 3535--3547 (2008).

Physics

Quantum Physics

12 pages, minor corrections; submitted, Journal of Modern Optics

Scientific paper

10.1080/09500340802322434

Recent developments in laser physics have called renewed attention to Laguerre-Gaussian (LG) beams of paraxial light. In this paper we consider the corresponding LG modes for the two-dimensional harmonic oscillator, which appear in the transversal plane at the laser beam's waist. We see how they arise as Wigner transforms of Hermite-Gaussian modes, and we proceed to find a closed form for their own Wigner transforms, providing an alternative to the methods of Simon and Agarwal. Our main observation is that the Wigner transform intertwines the creation and annihilation operators for the two classes of modes.

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