Optical chirality in gyrotropic media: symmetry approach

TL;DR

This paper explores optical chirality in gyrotropic media using a symmetry-based formalism, revealing how different symmetries influence conservation laws and the definition of optical chirality in various crystal types.

Contribution

It introduces a symmetry approach to analyze optical chirality in gyrotropic media, clarifying the roles of duality and helicity symmetries in different material contexts.

Findings

Optical chirality is conserved in isotropic chiral media due to duality and helicity symmetries.

In gyrotropic crystals, either duality or helicity symmetry can be preserved, affecting optical chirality.

Some low-symmetry media do not support a well-defined optical chirality.

Abstract

We discuss optical chirality in different types of gyrotropic media. Our analysis is based on the formalism of nongeometric symmetries of Maxwell's equations in vacuum generalized to material media with given constituent relations. This approach enables us to derive directly conservation laws related to the nongeometric symmetries. For isotropic chiral media, we demonstrate that likewise free electromagnetic field, both duality and helicity generators belong to the basis set of nongeometric symmetries that guarantees the conservation of optical chirality. In gyrotropic crystals, which exhibit natural optical activity, the situation is quite different from the case of isotropic media. For light propagating along certain crystallographic direction, there arise two distinct cases, i.~e., (1) the duality is broken but the helicity is preserved, or (2) only the duality symmetry survives. We show that the existence of one of these symmetries (duality or helicity) is enough to define optical chirality. In addition, we present examples of low-symmetry media, where optical chirality can not be defined.