A composite scheme based on the finite-difference time-domain method and a plane-wave expansion method is developed and applied to the optics of periodic liquid-crystal microstructures. This is used to investigate three-dimensional light-wave propagation in grating-induced bistable nematic devices with double periodicity. Detailed models of realistic devices are analyzed with emphasis on two different underlying surface-relief grating structures: a smooth bisinusoidal grating and a square-post array. The influence of the grating feature size is quantified. Device performance is examined in conjunction with an appropriate compensation layer, and the optimum layer thickness is determined for the different grating geometries.
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