Abstract

We develop the mathematical procedures for quantitatively describing the optical performance of a liquid-crystal image transducer as a function of transducer parameters and operating conditions. These procedures are based on a 4 × 4 matrix formalism which provides an exact numerical solution of Maxwell’s equations. Our calculations include interference effects arising from the multilayer structure of the transducer and we realistically treat reflection and transmission at isotropic-anisotropic layer boundaries. We compute the off-state optical properties of a twisted nematic reflection-mode transducer developed at Hughes Research Laboratories. We show that the dependence of output light intensity on liquid-crystal thickness is strongly influenced by the optically isotropic layers in the transducer, especially the electrodes. If the liquid-crystal thickness varies across the transducer aperture, these layers can produce a sharp fringe pattern in the output intensity. We also analyze the effect of varying the angle between the input polarization and the director at the entrance face of the liquid-crystal layer. For a given liquid-crystal thickness, there always exists an angle for which the off-state intensity is zero. The sensitivity of off-state intensity to rotation varies with liquid-crystal thickness. Off-state behavior is independent of liquid-crystal pretilt for the range of pretilt angles used in typical transducers.

© 1980 Optical Society of America

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