Wigner representation of Laguerre--Gaussian beams

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