Angular momentum of a strongly focussed Gaussian beam

TL;DR

This paper explains how a focused Gaussian laser beam's spin angular momentum converts into orbital angular momentum, demonstrating that rotationally symmetric optics can generate optical orbital angular momentum while conserving total angular momentum.

Contribution

It reveals the conversion mechanism of spin to orbital angular momentum in focused beams using rotationally symmetric systems, preserving total angular momentum.

Findings

Focusing reduces spin angular momentum per photon

Longitudinal optical vortex appears at focus

Total angular momentum remains conserved

Abstract

A circularly polarized rotationally symmetric paraxial laser beams carries hbar angular momentum per photon as spin. Focussing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focussed beam must have spin less than hbar per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitudinal optical vortex at the focus. This demonstrates that optical orbital angular momentum can be generated by a rotationally symmetric optical system which preserves the total angular momentum of the beam.