A phase-space description of the Laguerre–Gaussian modes is presented that points out the connection between these modes and the Hermite–Gaussian modes. We exploit the underlying phase-space symmetries to derive a closed-form expression for the Wigner distribution function of Laguerre–Gaussian modes. This expression is as compact as the one for the Hermite–Gaussian modes.
© 2000 Optical Society of America
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(080.2720) Geometric optics : Mathematical methods (general)
(260.0260) Physical optics : Physical optics
(350.5500) Other areas of optics : Propagation
R. Simon and G. S. Agarwal, "Wigner representation of Laguerre--Gaussian beams," Opt. Lett. 25, 1313-1315 (2000)