Dwight W. Berreman

Optics in Stratified and Anisotropic Media: 4×4-Matrix Formulation

A 4×4-matrix technique was recently introduced by Teitler and Henvis for finding propagation and reflection by stratified anisotropic media. It is more general than the 2×2-matrix technique developed by Jones and by Abeles and is applicable to problems involving media of low optical symmetry. A little later, we developed a 4×4 differential-matrix technique in order to solve the problem of reflection and transmission by cholesteric liquid crystals and other liquid crystals with continuously varying but planar ordering. Our technique is mathematically equivalent to that of Teitler and Henvis, but we used a somewhat different approach. We start with a 6×6-matrix representation of Maxwell’s equations that can include Faraday rotation and optical activity. From this, we derive expressions for 16 differential-matrix elements so that a wide variety of specific problems can be attacked without repeating a large amount of tedious algebra. The 4×4-matrix technique is particularly well suited for solving complicated reflection and transmission problems on a computer. It also serves as an illuminating alternative way to rederive closed solutions to a number of less-complicated classical problems. Teitler and Henvis described a method of solving some of these problems, briefly in their paper. We give solutions to several such problems and add a solution to the Oseen–DeVries optical model of a cholesteric liquid crystal, to illustrate the power and simplicity of the 4×4-matrix technique.

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

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.

Alignment of Liquid Crystals by Grooved Surfaces

Abstract We have observed alignment of nematic, cholesteric and smectic liquid crystals in directions depending on the orientation of submicroscopic, parallel grooves in adjacent glass and fused quartz surfaces. The alignment can be explained on the basis of elastic strain energy in the bulk of the liquid crystal that would be increased if the long axes of the molecules were aligned by the surface but were not approximately parallel to the groove direction. We have also observed alignment parallel to grooved surfaces but skewed with respect to the grooves, apparently when long molecules become attached to the surface in a direction that causes a competing torque on the director of adjacent liquid crystal molecules.

Liquid‐crystal twist cell dynamics with backflow

We describe and present results of a numerical method we have used to solve the hydrodynamic equations with negligible rates of change of momentum and angular momentum, but without other approximations, in a liquid‐crystal twist cell. We verify that the ’’bounce’’ in transmission of normally incident light that is observed when the electric potential across the cell is turned off is an effect of shear flow (backflow) which causes temporary reverse rotation of directors in the middle of the cell. It is not an inertial effect. Inertial effects would have transient times much shorter than the times associated with the optical bounce. When fluid flow is omitted, as in our previous papers, molecules do not tilt backward and the ’’optical bounce’’ occurs only for light that is obliquely incident in one quadrant. A qualitative explanation of the optics of the bounce is given, in addition to numerical results.

New bistable liquid‐crystal twist cell

We have shown experimentally that some cholesteric liquid crystals in cells with parallel or skew director orientations at the two surfaces may be made to have two bistable laminar states that can be switched either way by applying temporary electric potentials between the surfaces. Numerical solutions of the Oseen‐Frank equations in the laminar case, augmented with cholesteric twist and electric field terms, confirm the bistability. Numerical solutions of the Leslie‐Ericksen hydrodynamic equations in the laminar case, similarly augmented, describe the switching mechanism. We have made and operated several such cells.

New bistable cholesteric liquid‐crystal display

We have made a new type of cholesteric liquid‐crystal display device that is bistable in the absence of an applied field. One of the two stable states has 360° of twist between the two surfaces. The other is an untwisted state, like an unstrained nematic with all directors parallel. One method of switching is to apply a pulse of about 3 V or more between the cell surfaces, to obtain the twisted state or a pulse of about 1.5–2 V to obtain the untwisted state. Lesser pulses have no lasting effect. These switching characteristics have promise for displays with large numbers of characters.

Dynamics of liquid‐crystal twist cells

This paper describes a numerical method by which we have computed the change in molecular orientation with time in liquid‐crystal twist cells when the applied field is changed. No small‐angle approximation is made but backflow is neglected for simplicity. The general features of the results are illustrated with computations using typical elastic and viscous constants in doped MBBA, without and with a cholesteric twist term.

Twisted Smectic C Phase: Unique Optical Properties

Abstract Single-domain samples of cholesteric liquid crystals and of the recently reported twisted smectic C phase may have identical optical properties for light incident in the direction of the axis of twist. A single Bragg-reflection band exists for either type of liquid crystal in that case. However, with obliquely incident light the twisted smectic C sample would show additional Bragg-reflection bands at optical frequencies intermediate between the bands that would appear in both samples. Examples of computed spectra are given showing the differences that appear as the angle of incidence departs from normal.

Boundary‐layer model of field effects in a bistable liquid‐crystal geometry

Electric‐field‐induced switching between equilibrium configurations in certain bistable liquid‐crystal geometries is governed by the motion of disclinations, propelled by elastic distortions of the equilibrium states subjected to applied fields. In this paper and the next (paper II), we describe the distortions and energies of bistable planar horizontal and vertical states, and nonplanar twist states in a tilted geometry, using exact numerical solutions of the equilibrium equations as well as a ’’boundary‐layer’’ approximation in the high‐field limit. The calculations illustrate the manner in which the distortions become concentrated in boundary layers within a coherence length from the surface, and show the convergence of the planar and nonplanar vertical states at relatively low fields. Implications for the switching mechanism are discussed. In paper II, the boundary‐layer model is used to describe the forces governing the movement of disclinations in bistable switching, producing a quantitative descrip...

Liquid crystal alignment on surfactant treated obliquely evaporated surfaces

We report observations on the alignment of nematic liquid crystals on surfaces of obliquely deposited silicon monoxide, with and without additional treatment with surfactant. The liquid crystals reported on are 4.4‐dihexylazoxybenzene and 4‐heptyl‐4’‐cyanobipheny. The surfactants used are N,N‐dimethyl‐N‐octadecyl‐3‐aminopropyltrimethoxysilyl chloride and plasma polymerized tetrafluoroethylene. While untreated silicon monoxide surfaces produce inclined alignment, with the liquid crystal director oriented in the same quadrant as the direction of deposition, it was found that treatment with surfactant can result in an inclined alignment away from the direction of deposition, with the director now oriented nearly perpendicular to the direction obtained in the absence of surfactant. A simple model to explain these observations is presented.