Note on the helicity decomposition of spin and orbital optical currents

TL;DR

This paper clarifies how the helicity representation separates optical currents into right- and left-handed components, showing that electric-magnetic averaging restores this separation for orbital and spin contributions.

Contribution

It demonstrates that electric-magnetic averaging cancels cross-helicity terms, ensuring a clear helicity-based separation of optical currents for both orbital and spin parts.

Findings

Electric-magnetic averaging cancels cross-helicity terms.

Helicity decomposition separates optical currents into pure right- and left-handed parts.

The approach clarifies the physical interpretation of optical currents in helicity representation.

Abstract

In the helicity representation, the Poynting vector (current) for a monochromatic optical field, when calculated using either the electric or the magnetic field, separates into right-handed and left-handed contributions, with no cross-helicity contributions. Cross-helicity terms do appear in the orbital and spin contributions to the current. But when the electric and magnetic formulas are averaged ('electric-magnetic democracy'), these terms cancel, restoring the separation into right-handed and left-handed currents for orbital and spin separately.