The modelling of nematic liquid crystal phase devices

Abstract

The implementation of nematic liquid crystal optical devices, which exploit the voltage dependent, optical path length modification of the electrical Freedrichsz transition, is presented. By combining refractive elements in a diffractive zone structure, efficient and flexible devices with relatively high refractive powers can be constructed. Continuously variable optical properties can be achieved by scaling the optical profile of the refractive elements and applying a phase correction to ensure that the transition between adjacent zones is an integral number of wavelength, hence a continuous optical profile is constructed. Two such devices are postulated; a variable deflection angle prism and a variable focal length lens, though the approach may be extended to other devices. The zones are addressed through combed electrode structures. The required voltage profile is produced by dropping the applied voltages across a shaped conductive strip. A sampling of the profile is transported along the length of the zone via discrete electrodes. In order to produce the required scalability and independent phase correction of the optical profile, it is necessary to restrict the design and operation of the electrodes to the approximately linear region of the response curve. Two-dimensional optical structures can either be achieved through the use of planar earth plates, to mask connections to the centre of the device, or by cascading devices with electrode structures open to connection at the edges. In order to predict the optical profiles of these and other devices, a model was constructed which describes the director orientation through a two-dimensioned electrode structure. The variational finite element method was employed to minimize the electrical Gibbs free energy of a liquid crystal cell, in order to find the equilibrium director orientation. A preliminary version of this model is presented which is restricted to rotation of the liquid crystal to within the plane of the solution.