Spatial dispersion and rotatory power of short-pitch periodic dielectric media

By a Bloch-wave decomposition, we deduce a general expression for the effective optical dielectric tensor of a short-pitch periodic dielectric medium. The effective dielectric tensor describes an equivalent homogeneous medium presenting spatial dispersion. We consider in derail the case of a cholesteric liquid crystal, deformed by a flexoelectric torque induced by an electric field orthogonal to the helical axis. The distorted structure displays a true rotatory power that scales as the ratio between the pitch of the cholesteric and the vacuum light wavelength. The approximate analytical results are compared with exact numerical calculations, showing a good agreement even far from the limits of validity of the theory. Possible generalizations of these results are discussed.