Chirality and helicity of optical vortices of small beam waists

TL;DR

This paper investigates how small-beam-waist Laguerre-Gaussian beams exhibit non-zero chirality and helicity due to their longitudinal fields, revealing how these properties vary with propagation and beam parameters.

Contribution

It demonstrates the presence and evolution of chirality and helicity in small-waist LG beams, highlighting their dependence on propagation and beam structure.

Findings

Chirality and helicity are non-zero in small-waist LG beams.

Different distributions of chirality and helicity are observed at the focal plane.

Beam convergence affects the evolution of chirality and helicity patterns.

Abstract

The chirality and helicity of linearly polarised Laguerre-Gaussian (LG) beams are examined. Such a type of light possesses a substantial longitudinal field when its beam waist is sufficiently small and so gives rise to non-zero chirality and helicity. In the simplest case of a doughnut beam of winding number $\ell=1$ and another identical to it but has $\ell= -1$, we obtain different chirality and helicity distributions at the focal plane $z=0$. We also show that this chiral behaviour persists and the patterns evolve so that on planes at $z<0$ and $z>0$ the beam convergence contributes differently to the changes in the chirality and helicity distributions.