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

TL;DR

This paper explores superpositions of Bessel-Gaussian and modified Bessel-Gaussian beams, demonstrating how to generate various known and novel paraxial beam solutions by adjusting parameters and weights.

Contribution

It introduces a method to construct multiple paraxial beam solutions from superpositions of Bessel-Gaussian modes using two key parameters, expanding the toolkit for beam shaping.

Findings

Able to generate Gaussian, γ, Kummer-Gaussian, hyperbolic Bessel-Gaussian, and Laguerre-Gaussian beams

Demonstrates flexibility in creating generalized paraxial beams

Shows how parameter choices influence beam properties

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.