  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.

Optics