Optical angular momentum in dispersive media

TL;DR

This paper derives the angular momentum density and flux of light in dispersive media, revealing complex relationships between optical angular and linear momentum, and confirming that circular polarization carries quantized spin angular momentum even in dispersive environments.

Contribution

It provides a theoretical derivation of optical angular momentum in dispersive media from Noether's theorem, highlighting the non-trivial interplay with energy and linear momentum.

Findings

Optical angular momentum in dispersive media is not simply related to linear momentum.

A circularly polarized monochromatic beam carries b1ar{ ext{ extmu}}h per b5ar{ ext{ extmu}}h energy.

The derivation clarifies the role of dispersion in optical angular momentum.

Abstract

The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum of $\pm\hbar$ per energy $\hbar\omega$, as in vacuum. This result demonstrates the non-trivial interplay of dispersive contributions to optical angular momentum and energy.