Transverse angular momentum of photons

TL;DR

This paper develops a quantum theory for the transverse angular momentum of light beams, accurately describing energy flow and photon angular momentum, including spin and orbital contributions, in paraxial and quasi-paraxial regimes.

Contribution

It introduces a comprehensive quantum framework for transverse angular momentum of light, incorporating first-order derivatives and clarifying the behavior of orbital angular momentum operators.

Findings

Orbital angular momentum operators do not satisfy standard commutation rules for collimated beams.

The theory reproduces classical results when applied to coherent states.

It provides a detailed description of energy flow and photon angular momentum in light beams.

Abstract

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasi-paraxial photon beams in vacuum, and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.