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Simple analytic solutions to the equations governing the nematic liquid crystal director profiles under an external voltage and arbitrary anchoring energy, taking into consideration the non-uniform field distribution, are presented. Exact numerical results are compared to the analytic solutions showing good agreement particularly for the case of strong anchoring. The usefulness of the approximate analytic solutions is remarkable for the quick design of liquid crystal devices and understanding the dependence of the optical response on voltage and material parameters.
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Abdulhalim et al. (2010) studied this question.
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