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We have developed a numerical method for the calculation of the two-dimensional director distribution of nematic liquid crystals in inhomogeneous electric fields which is able to handle solutions with disclinations. As an application we firstly study the formation of disclinations in liquid crystal displays with small pixel electrodes due to the inhomogeneous electric field near the edges of the electrodes. Secondly we analyze in detail the director structure and the optical properties of a cylindrical liquid crystal microlens consisting of a liquid crystal cell with a slit patterned electrode in order to create an inhomogeneous electric field. Results for the focal length and the focussing quality as a function of the applied voltage and the width of the slit are given.
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Haas et al. (1991) studied this question.
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