Mapping of focused Laguerre-Gauss beams: The interplay between spin and orbital angular momentum and its dependence on detector characteristics

TL;DR

This paper investigates the detailed electromagnetic structure of focused Laguerre-Gauss beams, revealing how detector characteristics influence the mapping of spin and orbital angular momentum, especially beyond the paraxial approximation.

Contribution

It provides a comprehensive analysis of the electromagnetic field variations in focused Laguerre-Gauss beams and how detector orientation affects the observed angular momentum properties.

Findings

On-axis magnetic and electric field gradients exist for |l|=2 beams.

Detector orientation significantly influences beam mapping.

Polarization and topological charge interplay affects beam symmetry.

Abstract

We show that propagating optical fields bearing an axial symmetry are not truly hollow in spite of a null electric field on-axis. The result, obtained by general arguments based upon the vectorial nature of electromagnetic fields, is of particular significance in the situation of an extreme focusing, when the paraxial approximation no longer holds. The rapid spatial variations of fields with a "complicated" spatial structure are extensively analyzed in the general case and for a Laguerre-Gauss beam 2 as well, notably for beams bearing a |l| = 2 orbital angular momentum for which a magnetic field and a gradient of the electric field are present on-axis. We thus analyze the behavior of a atomic size light-detector, sensitive as well to quadrupole electric transitions and to magnetic dipole transitions, and apply it to the case of Laguerre-Gauss beam. We detail how the mapping of such a beam depends on the nature and on the specific orientation of the detector. We show also that the interplay of mixing of polarization and topological charge, respectively associated to spin and orbital momentum when the paraxial approximation holds, modifies the apparent size of the beam in the focal plane. This even leads to a breaking of the cylindrical symmetry in the case of a linearly polarized transverse electric field.