Representation of Laguerre-Gaussian modes by the Wigner distribution function

The Wigner distribution function (WDF) of the general helical Laguerre-Gaussian modes are calculated in an analytical form. The propagation law of the WDF of the corresponding beams leads to the concept of generalized rays, 2-D subspaces of the 4-D phase-space are introduced in the form of sagittal and tangential planes. In these planes the WDF provides an intuitive picture of the focusing and twisting of the beam. The WDF´s of the lowest helical mode in sagittal and tangential subspaces are depicted graphically in the phase-space and generalized ray representation, respectively. A global twist angle is introduced and discussed