Bessel beams revisited: a generalized scheme to derive optical vortices

TL;DR

This paper compares different derivation methods for optical vortices, revealing differences in electromagnetic field contributions, and introduces a generalized approach that restores symmetry and extends the spectrum of solutions.

Contribution

It presents a unified scheme for deriving optical vortex fields, highlighting differences between Lorenz and Coulomb gauge methods, and introduces a generalized solution spectrum.

Findings

Lorenz gauge derivation restores field symmetry in Bessel beams

Different derivation procedures affect electric and magnetic field contributions

A proposed experiment can test the new theoretical findings

Abstract

The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial solutions with Laguerre-Gauss radial profiles, while the latter procedure has been used to derive full solutions of the wave equation with Bessel radial profiles. We investigate the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles. We show that the electromagnetic fields thus derived differ in the relative strength of electric and magnetic contributions. The new solution that arises from the Lorenz procedure in the case of Bessel beams restores a field symmetry that previous work failed to resolve. Our procedure is further generalized and we find a spectrum of fields beyond the Lorenz and Coulomb gauge types. Finally, we describe a possible experiment to test our findings.