Nematic cells with defect-patterned alignment layers.

Using Monte Carlo simulations of the Lebwohl-Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of +/-1 point topological defects of lattice spacing a . As expected on general physical grounds we find that the nematic order depends on the ratio of the height of the cell H to a . For thick cells (Ha > or = 0.9) we find that the system is very well ordered and the frustration induced by the lattice of defects is relieved in a novel way by a network of half-integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When Ha < or = 0.9 the system has zero nematic order parameter and the half-integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures in the presence of crossed polarizers.