Optics in smoothly varying anisotropic planar structures: Application to liquid-crystal twist cells*

TLDR

Optical transmittance and reflectance of continuously varying anisotropic planar media, such as nematic liquid crystals in Schadt–Helfrich twist cells or cholesterics between parallel rubbed surfaces, have previously been computed with a 4 × 4 matrix method by discretizing the medium into many thin parallel layers treated as homogeneous anisotropic. This study demonstrates that numerical computations of twist‑cell optics can be performed accurately with much thicker layers, providing better insight into oblique‑ray behavior and suggesting elastic‑constant measurement via transmittance comparison. The authors use a matrix‑multiplication framework with truncated power‑series approximations, treating each layer—potentially several wavelengths thick—as homogeneous anisotropic material, and present two strategies for rapid convergence. The method yields improved understanding of twist‑cell optical properties for oblique incidence, showing how thicker layers influence transmittance and reflectance.

Abstract

Optical transmittance and reflectance of continuously varying anisotropic planar media, such as nematic liquid crystals in Schadt–Helfrich twist cells or cholesterics between parallel rubbed surfaces, have previously been computed with a 4 × 4 matrix method by considering the medium as broken up into many thin parallel layers and treating each as if it had homogeneous anisotropic optical parameters. A matrix multiplication was done for each layer, and unless each layer was much less than one wavelength thick, several more multiplications were done within each layer. Here we show how to do numerical computations with equal accuracy using much thicker layers. We use a truncated power series to approximate the variation of optical parameters through each layer. We also show two ways to obtain fast convergence of numerical computations with layers of homogeneous anisotropic material that are several wavelengths thick. We use the method to get a better understanding of the optical properties of twist cells, particularly for oblique rays. The possibility of measuring elastic constants by comparing measured with computed transmittance of twist cells is suggested.