Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes

Abstract

Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index $n$ associated with the orbital angular momentum carried by the beam, and $\chi$ related to the dilation of the beam. It is shown that, from these modes, by choosing appropriate weighting factors, it is possible to create a number of well- and less-known solutions of the paraxial equation: Gaussian (shifted and non-shifted) beam, $\gamma$ beam, Kummer-Gaussian beam, special hyperbolic Bessel-Gaussian beam, a certain special Laguerre-Gaussian beam, and generalized paraxial beams in hyperbolic and regular versions.

11 pages, 2 figures, ReVTeX

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• Hypergeometric-Gaussian Modes
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Cited by in corpus (1)

• Paraxial Dirac equation