Topological defect array in nematic liquid crystal

Topological defects arise when the symmetry of order in liquid crystal is broken during phase transitions or under specified boundary conditions. Fascinating applications, such as, optical vortex and optical memories, will be realized only if the type and position of defects can be precisely controlled. Topological defects were generated in nematic liquid crystal cell with homeotropic surface alignment when voltage is applied. The defects were precisely placed on designed positions using electric field. The topological charge and shape of the defect were assigned by the delicately designed pattern of the pixelated electrodes. The point defects with topological charges of +1 (hedgehog) and -1 (hyperbolic hedgehog) were arranged in square or hexagonal lattices as two dimensional crystals. Topological rules in the stable defect array were discovered. The topological charge of a bulk defect was equal to the Euler number of the pixel in two-dimensional space. The number of the hyperbolic hedgehogs was determined by the folds of rotational symmetry of the defect array. The transmission and scattering of light through the defect were characterized, and the visual effect of large array of defects were demonstrated. Scattering, diffraction, and lensing effects from the defect array renders hazy, watery, and glittering images, which is artistic like impressionist paintings.