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Appl Opt. 1987 May 1;26(9):1714-21. doi: 10.1364/AO.26.001714.

Geometrical optics approach to the nematic liquid crystal grating: numerical results.


The problem of the grating action of a periodically distorted nematic liquid crystal layer, in the geometrical optics ray approximation is considered, and a theory for the calculation of the fringe powers is proposed. A nonabsorbing nematic phase is assumed, and the direction of incidence is taken to be normal to the layer. The powers of the resulting diffraction fringes are related to the spatial and angular deviation of the rays propagating across the layer and to the perturbation of the phase of the wave associated with the ray. The theory is applied to the simple case of a harmonically distorted nematic layer. In the case of a weakly distorted nematic layer the results agree with the predictions of Carroll's model, where only even-order fringes are important. As the distortion becomes larger, odd-order fringes (with the exception of the first order) become equally important, and particularly those at relatively large orders (e.g., seven and nine) exhibit maxima greater than that of the even-order neighbors. Finally, the dependence of the powers of odd-order fringes on the distortion angle is quite different from that of the even-order fringes.

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