Optical rotatory power of liquid crystals

A theory of the very high rotatory power exhibited by cholesteric liq. crystals is developed by the use of the Jones calculus for optical systems. The calcns. are based on the model proposed by de Vries in which the liq. crystal is regarded as built up of a large no. of thin birefringent layers arranged helically. When light is incident normal to the layers, i.e. along the screw axis, selective reflection of one of circularly polarized components takes place and the rotatory dispersion in the neighborhood of the region of reflection is anomalous. The reflection curve and the amplitude attenuation factor, exp(-I¾), 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 reflection, I¾ is real, primary extinction occurs, and the medium is highly circularly dichroic. The spectral width of the reflection and the primary extinction coeff. predicted by theory compare favorably with the exptl. values. Outside the region of total reflection, I¾ 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. [on SciFinder(R)]