# On the conservation of helicity in a chiral medium

## TL;DR

This paper introduces a new form of helicity density for circularly polarized light in lossless chiral media, ensuring consistency with dual symmetry and accurately representing photon helicity.

## Contribution

It proposes a first-order helicity density expression for chiral media that aligns with photon helicity and extends to arbitrary order in the chirality parameter.

## Key findings

- Helicity density of ±ħ per photon for circular polarization.
- Modified helicity density form is necessary for dual symmetry.
- Derived exact energy-helicity relationship in chiral media.

## Abstract

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $\beta$. A form for the helicity density is introduced, valid to first order in $\beta$, that produces a helicity of $\pm\hbar$ per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of ${\epsilon}/{\mu}$. Extending the results to arbitrary order in $\beta$ establishes an exact relationship between the energy and helicity densities in a chiral medium.