The geometrical optics approach for multidimensional liquid crystal cells

Abstract

We present an approach based on the geometrical optics approximation (GOA) for analysis of liquid crystal cells whose director varies in more than one spatial dimension (multidimensional liquid crystal cells). The GOA is applied to calculate light transmittance and far field diffraction patterns for two- and three-dimensional nematic liquid crystal films. Important features of the GOA, such as a method of eliminating non-convergence problems that can occur during the iterative numerical solution of the equations for the amplitudes of the electromagnetic field, are described. We compare the results obtained from the GOA with those produced by the quasi-one-dimensional Jones calculus and the beam propagation method, where the latter is applicable. It was found that the refraction (or ray bending) effects, produced by the GOA, are more important than effects of diffraction and light scattering, which means that the GOA (unlike the Jones calculus) is accurate for the considered type of liquid crystal cells, whose director varies on the micron scale. The GOA is about as fast as the Jones method and is applicable for calculating optical properties of liquid crystal cells with any number of dimensions of director variations.