Optic models for short-pitch cholesteric and chiral smectic liquid crystals

Abstract

The optical properties of cholesteric and chiral smectic-$C$ liquid crystals having a pitch shorter than the light wavelength are studied, both theoretically and experimentally. A particular emphasis is placed on the optical activity. For smectics, the optical rotation is maximum for a tilt angle of $45°$ and for light propagating orthogonally to the helix axis; for short-pitch cholesterics, the optical activity is, in any case, very small. The limits of validity of a recently proposed macroscopic model for such media are discussed, in the framework of a more general discussion on optical models for gyrotropic media. It is shown that the macroscopic models generally work well for the bulk properties. However, for chiral smectics with the smectic planes parallel or nearly parallel to the boundary planes, no homogeneous model is able to account for the gyrotropic properties, independently of how small the pitch is and for any sample thickness. Our experimental data are in agreement with these theoretical findings.