Necessary symmetry conditions for the rotation of light

TL;DR

This paper identifies necessary symmetry conditions, including lack of mirror symmetry and duality symmetry, for systems to rotate light polarization, with implications for molecular optical activity and nanoscale polarization devices.

Contribution

It establishes the fundamental symmetry conditions required for light polarization rotation, linking helicity preservation to particle properties and scattering direction.

Findings

Helicity preservation occurs only if the particle preserves helicity, except in forward scattering.

Lack of mirror symmetry (chirality) is necessary for polarization rotation.

Random molecular orientation can induce effective rotational symmetry in forward scattering.

Abstract

Two conditions on symmetries are identified as necessary for a linear scattering system to be able to rotate the linear polarisation of light: Lack of at least one mirror plane of symmetry and electromagnetic duality symmetry. Duality symmetry is equivalent to the conservation of the helicity of light in the same way that rotational symmetry is equivalent to the conservation of angular momentum. When the system is a solution of a single species of particles, the lack of at least one mirror plane of symmetry leads to the familiar requirement of chirality of the individual particle. With respect to helicity preservation, according to the analytical and numerical evidence presented in this paper, the solution preserves helicity if and only if the individual particle itself preserves helicity. However, only in the particular case of forward scattering the helicity preservation condition on the particle is relaxed: We show that the random orientation of the molecules endows the solution with an effective rotational symmetry; at its turn, this leads to helicity preservation in the forward scattering direction independently of any property of the particle. This is not the case for a general scattering direction. These results advance the current understanding of the phenomena of molecular optical activity and provide insight for the design of polarisation control devices at the nanoscale.