Optical rotatory power of liquid crystals

A theory of the very high rotatory power exhibited by cholesteric liquid crystals is developed by the use of the Jones calculus for optical systems. The calculations are based on the model proposed by de Vries in which the liquid crystal is regarded as built up of a large number of thin birefringent layers arranged helically. When light is incident normal to the layers, i.e. along the screw axis, selective reflexion of one of the circularly polarized components takes place and the rotatory dispersion in the neighbourhood of the region of reflexion is anomalous. The reflexion curve and the amplitude attenuation factor, exp (−ξ), for circularly polarized light at normal incidence are derived as functions of wavelength by setting up difference equations closely similar to those formulated by Darwin in his dynamical theory of X-ray diffraction. Within the range of total reflexion, ξ is real, primary extinction occurs and the medium is highly circularly dichroic. The spectral width of the reflexion and the primary extinction coefficient predicted by theory compare favourably with the experimental values. Outside the region of total reflexion, ξ is imaginary and opposite in sign on opposite sides of the reflected band. This is responsible for the reversal of the sign of the rotation on crossing the band. The anomalous part of the rotation is a direct measure of the phase of the primary wave given by the dynamical theory.