Conoscopy of chiral smectic liquid crystal cells

The conoscopic method for investigating the optical properties of a liquid crystal cell is studied with the aim of determining the effects of the approximations used in the calculation on the results. We confirm that the chiral liquid crystal cell forming a helical structure can be regarded as a single biaxial plate for analyzing the conoscopic image only if the helical pitch is less than several multiples of the wavelength of light. This approximation implies that the square of the refractive index along a direction is averaged over all the layers. An incorrectly chosen value for one of the principal refractive indices to be used in the analysis of the conoscopic data can lead to an incorrect conclusion, especially for the case when the wavelength dispersion of the refractive index is neglected. A thicker cell and a longer wavelength of the incident light can minimize these limitations of the conoscopic method. We propose a novel simulation method to find the molecular distribution in a liquid crystal cell based on the average-refractive-index approximation and the conoscopic data. This is shown to be a fast, more efficient, and useful method for estimating the director distributions.