Reflection and Transmission by Single-Domain Cholesteric Liquid Crystal Films: Theory and Verification

Abstract

We have developed a fast and essentially exact numerical technique for computing propagation, reflection and transmission of light by a flat layer of any linear optical medium in which the dielectric tensor varies only in a direction normal to the surfaces. Using this technique with Oseen's spiraling-dielectric-tensor model of a single domain in a cholesteric liquid crystal, we predicted triplet Bragg reflection bands of both first and higher orders for light incident obliquely on thin films, similar to the triplet bands that Taupin predicted by a different technique for semi-infinite samples. We have observed the first and second order Bragg reflection bands for light incident at 45 degrees on single-domain cholesteric films between two glass prisms. The films used were mixtures of 4,4′-Bis(n-hexyloxy)azoxybenzene, which is nematic at about 100°C, and dextro-4,4′-Bis(2-methylbutoxy)azoxybenzene which is asymmetric and causes the cholesteric spiral twist in the mixture. Adjustment of parameters in a general spiraling ellipsoid model to fit the data shows that the dielectric ellipsoids of such films are approximately prolate spheroids with the major axis normal to the spiral axis, as hypothesized by Oseen and Taupin. In mixtures having a pitch of 0.764 microns, for example, the two unlike principal values of the dielectric tensor are approximately 3.060 and 2.430 for blue light around the second order triplet. Additional Bragg reflection bands, which we predicted if no major axis of the dielectric ellipsoid were parallel to the spiral axis, were not observed.