Form birefringence in helical liquid crystals

(Received 23 July 1993, accepted in final form 8 November 1993)

Abstract
The optical properties of cholesteric and chiral smectic liquid crystals are studied, in the limit of pitch smaller than the wavelength of visible light, by means of a formalism borrowing techniques developed to explain form birefringence effects in particulate media. The behaviour of actual stratified anisotropic substances is shown to be accurately approximated, in this limit, by an effective homogeneous uniaxial crystal, whose dielectric tensor elements are easily obtained from the exact values corresponding to the stratified medium. In two notable cases, i.e., for normal incidence of light and in smectic-C liquid crystals with a critical value of the tilt angle, the optical properties of the stratified material may only be accounted for by introducing an effective medium suitably characterized by optical activity. In all the examined cases, the periodic media appear to be completely equivalent to homogeneous crystals displaying optical activity, up to pitch values corresponding to one half of the first Bragg diffraction band. The model's results having higher relevance both in fundamental studies and applications are described and discussed.