Relevance of Longitudinal Fields of Paraxial Optical Vortices

TL;DR

This paper investigates the significance of longitudinal electromagnetic fields in paraxial optical vortex beams, revealing their impact on angular momentum, light-matter interactions, and the limits of the paraxial approximation.

Contribution

It derives and numerically analyzes first-order longitudinal components of Laguerre-Gaussian modes, highlighting their role in optical vortex properties and interactions.

Findings

Longitudinal fields are significant in paraxial vortex beams.

Longitudinal components influence angular momentum and spin-orbit interactions.

Restrictions on paraxial approximation validity are identified for light-matter interactions.

Abstract

Longitudinal electromagnetic fields generally become comparable with the usually dominant transverse components in strongly-focussed, non-paraxial beams. For optical vortex modes it is highlighted here how their angular momentum properties produce longitudinal fields that in general must be accounted for, even within the paraxial regime. First-order longitudinal components of quantized Laguerre-Gaussian modes are derived and numerically studied with respect to the paraxial parameter, highlighting light-matter and spin-orbit interactions that stem from longitudinal fields of weakly-focussed, paraxial beams in free space. New restrictions are cast on the validity of the paraxial approximation for optical vortices interacting with atoms, molecules and other nanostructures.