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.<
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