Surface angular momentum of light beams

TL;DR

This paper introduces a new surface term in the calculation of optical angular momentum for light beams, ensuring gauge invariance and providing more accurate descriptions for practical beam configurations.

Contribution

It reveals the necessity of an extra surface term in angular momentum calculations for light beams, extending the traditional wave packet approach to more realistic beam geometries.

Findings

Extra surface term is essential for gauge invariance.

Application to Laguerre-Gaussian and Bessel beams.

Improved understanding of angular momentum in realistic optical beams.

Abstract

Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded transversely and longitudinally while a beam has, in principle, an infinite extent along the direction of propagation, renders incomplete the textbook calculation of the spin/orbital separation of the angular momentum of a light beam. In this work we demonstrate that a novel, extra surface part must be added in order to preserve the gauge invariance of the optical angular momentum per unit length. The impact of this extra term is quantified by means of two examples: a Laguerre-Gaussian and a Bessel beam, both circularly polarized.