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We investigate polynomial Gaussian beams with rotationally symmetric Gaussian envelops and complex bivariate polynomial prefactors of finite order. A formalism for the propagation of such beams is developed, which expresses how the coefficients of the polynomial transform during propagation. This formalism is used to proof that global topological charge is conserved for this class of polynomial Gaussian...
The morphology (i.e. the anisotropy and its orientation) of optical vortices in general changes during propagation. Here we investigate the spatial evolution of the morphology of a canonically launched optical vortex dipole, propagating in a Gaussian beam. Expressions for the anisotropy and the orientation as a function of the propagation distance are derived and discussed. These expressions are used...
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