Total helicity of electromagnetic fields and matter

TL;DR

This paper unifies the concepts of electromagnetic helicity in free fields and matter, showing they are different aspects of a single total helicity, which has implications for light-matter interactions.

Contribution

It introduces a unified framework for total helicity, combining free electromagnetic field helicity and static magnetic helicity into a single physical quantity.

Findings

Total helicity comprises photon chirality and magnetization screwiness.

Different frequency regimes reveal different manifestations of total helicity.

The framework enables studying helicity conversion during light-matter interactions.

Abstract

The electromagnetic helicity of the free electromagnetic field and the static magnetic helicity are shown to be two different embodiments of the same physical quantity, the total helicity. The total helicity is the sum of two terms: a term that measures the difference between the number of left-handed and right-handed photons of the free field, and another term that measures the screwiness of the static magnetization density in matter. Each term is the manifestation of the total helicity in different frequency regimes: $\omega$ > 0 and $\omega$ = 0, respectively. This unification establishes the theoretical basis for studying the conversion between the two embodiments of total helicity upon light-matter interaction.