One more time on the helicity decomposition of spin and orbital optical currents

TL;DR

This paper extends the helicity decomposition of optical currents to nonmonochromatic fields, revealing that the separation into right- and left-handed components is approximate and dependent on averaging, unlike the monochromatic case.

Contribution

It generalizes the helicity representation of optical momentum to nonmonochromatic fields, highlighting differences from the monochromatic case and the conditions for approximate separation.

Findings

Linear momentum density does not separate into helicity components for nonmonochromatic light.

Time-averaging approximately restores helicity separation in quasimonochromatic fields.

The work clarifies the helicity decomposition in more general optical regimes.

Abstract

The helicity representation of the linear momentum density of a light wave is well understood for monochromatic optical fields in both paraxial and non-paraxial regimes of propagation. In this note we generalize such representation to nonmonochromatic optical fields. We find that, differently from the monochromatic case, the linear momentum density, aka the Poynting vector divided by $c^2$, does not separate into the sum of right-handed and left-handed terms, even when the so-called electric-magnetic democracy in enforced by averaging the electric and magnetic contributions. However, for quasimonochromatic light, such a separation is approximately restored after time-averaging. This paper is dedicated to Sir Michael Berry on the occasion of his $80$th birthday.