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 $\ensuremath{\chi}$ 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: a Gaussian (shifted and nonshifted) beam, a $\ensuremath{\gamma}$ beam, Kummer-Gaussian beam, a special hyperbolic Bessel-Gaussian beam, a certain special Laguerre-Gaussian beam, and generalized paraxial beams in hyperbolic and regular versions.