Optical Properties of Cholesteric Liquid Crystals

Abstract

A general theory of wave propagation in helical structures is developed. It is shown that this problem is quite similar to the well-known wave propagation in solid crystal lattices. If energy dissipation is neglected there are shown to exist frequency bands for wave propagation without attenuation separated by frequency bands where waves are damped out and cannot propagate. Formally, the waves have the form of Bloch waves ${e}^{i\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}.\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, having the character of plane waves modulated by a function $u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ which is periodic with the structure. Based on this theory, for reflection of light by homogeneously ordered cholesteric liquid crystals the following results are obtained: For incident light parallel to the helical axis there exists only one band of selective reflection. For obliquely incident light, however, an infinite series of higher-order reflection bands occur. Each reflection band is split into two branches. The angular dependence of the reflection bands and the sequence of the higher-order reflections on the wavelength scale bear a certain analogy to Bragg reflection.