The cholesteric liquid crystal as a spatially dispersive medium

Abstract

A medium with periodic variation of the dielectric tensor is considered. It is assumed to have helical symmetry. The response to external fields is described by the most general linear law-that is, by the methods of spatial dispersion theory. The propagation of a wave is described by a mutually consistent electric field and polarisation. It is shown that the presence of the medium produces changes in the polarisation and wave vector of the electric field, and the selection rules governing these changes are derived from symmetry. The results generalise previous work on the Oseen model for a cholesteric liquid crystal to the case when the molecules are not perpendicular to the helical axis. This can arise in an external magnetic field applied along this axis.