Necessary symmetry conditions for the rotation of light

Two conditions on symmetries are identified as necessary for a general 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, which is equivalent to the conservation of the helicity of light. When the system is a solution of a single species of particles, the lack of at least one mirror symmetry leads to the familiar requirement of chirality of the individual particle, and, 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, in forward scattering the helicity preservation condition on the particle is relaxed: We show that the effective rotational symmetry of such system leads to helicity preservation in the forward scattering direction independently of any property of the particle. 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.