Angular momentum of focused beams: beyond the paraxial approximation

TL;DR

This paper explores the complex behavior of focused Laguerre-Gaussian laser beams with orbital angular momentum, revealing unexpected properties due to non-paraxial effects and demonstrating conservation of total angular momentum despite changes in spin and orbital components.

Contribution

It provides a detailed analysis of the angular momentum distribution in non-paraxial focused beams, highlighting phenomena beyond the traditional paraxial approximation.

Findings

Energy can locally counter-propagate near the beam axis for certain conditions.

The total angular momentum flux per unit power remains conserved after focusing.

Spin and orbital angular momentum contributions change, despite overall conservation.

Abstract

We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam ($\hbar \ell$ orbital angular momentum per photon; $\sigma=1/-1$ for left/right-handed polarization) by a high numerical aperture objective. The diffraction-limited focused beam has unexpected properties, resulting from a strong interplay between the angular spatial structure and the local polarization in the non-paraxial regime. In the region near the beam axis, and provided that $|\ell|\ge 2$ and $\ell$ and $\sigma$ have opposite signs, the energy locally counter-propagates and the projection of the electric field onto the focal plane counter-rotates with respect to the circular polarization of the incident beam. We explicitly show that the total angular momentum flux per unit power is conserved after focusing, as expected by rotational symmetry, but the spin and orbital separate contributions change.