Characterizing optical chirality

TL;DR

This paper analyzes an optical chirality measure using momentum and helicity bases, clarifying its physical meaning and relation to other optical properties, and deriving simple operator forms.

Contribution

It introduces a detailed analysis of optical chirality measure, linking it to polarization helicity, spin angular momentum, and energy flow, with new operator derivations in the helicity basis.

Findings

Clarifies the physical meaning of optical chirality measure.

Unveils the relation between chirality, helicity, and energy flow.

Derives simple forms of chirality operators in the helicity basis.

Abstract

We examine the recently introduced measure of chirality of a monochromatic optical field [Y. Tang and A. E. Cohen, Phys. Rev. Lett. 104, 163901 (2010)] using the momentum (plane-wave) representation and helicity basis. Our analysis clarifies the physical meaning of the measure of chirality and unveils its close relation to the polarization helicity, spin angular momentum, energy density, and Poynting energy flow. We derive the operators of the optical chirality and of the corresponding chiral momentum, which acquire remarkably simple forms in the helicity representation.