We present a two-dimensional optical analysis of small pixels in reflective liquid-crystal-on-silicon microdisplay. The optical analysis is divided into two parts. In the first part, the two-dimensional (2D) director configuration of the liquid crystal display (LCD) in rectangular mesh was calculated by simultaneously solving the 2D Poisson and continuum theory equations. In the second part, generalized Jones matrix was used to simulate for optical reflectance through the LCD with the 2D director configuration obtained from the first part. This optical modeling was applied to analyze optical reflectance of small pixels in reflective mixed-mode twisted nematic and birefrigence (MTB) cells on silicon substrate. Both the simulated and experimental data of the MTB cells under frame and column inversions were presented. It was found that the frame inversion could give rise to a higher contrast ratio than the column inversion at the same driving voltage. It was also found that the optical reflectance decreased as the pixel size decreased due to the lateral electric field between the small pixels.

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One of the two classes of non-diverging algebraically special left-flat spaces found by Fette, Janis and Newman is generalised by allowing the (self-dual part of the) Weyl tensor to become algebraically general. Penrose's conformal approach is used, thereby allowing the desired asymptotic behaviour of the solutions to be prescribed from the outset. The 'solutions' are, however, still subject to some 'reduced equations'. For a specific choice of initial data at conformal null infinity these reduced equations simplify to Plebanski's second heavenly equation.