Periodically Aligned Liquid Crystal Cell For Projection Displays

We consider a nematic liquid crystal (NLC) cell with planar structure of director sinusoidally modulated in transverse direction in the cell plane. If thickness of the cell is such that it locally acts as a half-wave plate, thin screen approximation predicts complete diffraction of normally incident light into +1st and -1st diffraction orders. We numerically study the case when this periodically aligned structure is made using anchoring at surfaces. Proper direction of anchoring can be achieved by illumination of photosensitive polymer coating by interference pattern of pair of circularly polarized waves. We found that the structure is unstable when its thickness exceeds a certain critical thickness. Calculations show that for a number of commonly used NLC\u27s this critical thickness lies between 0.66 and 0.86 of the physical period. Such thickness allows for diffraction angles up to 21°. Friedericksz transition voltage of this structure depends on its thickness. This dependence can be well described by an ellipse in the voltage-thickness coordinates. Propagation of a plane wave through the periodically aligned NLC is described using coupled-mode approach. We estimate the contrast ratio versus the influence of walk-off effects and deviation of equilibrium structure from perfectly sinusoidal. Estimations for reasonable set of NLC\u27s parameters show that contrast ratio can be 1000:1 and higher. As a result of this analysis, the transverse size of the cell can be estimated to be less or about 0.25 mm, which suggests it for use as a pixel in projection displays