Theoretical Prediction of Umbilics Creation in Nematic Liquid Crystals with Positive Dielectric Anisotropy.

Optically assisted electrical generation of umbilic defects, arising in homeotropically aligned nematic liquid crystal cells and known as topological templates for the generation of optical vortices, are reported in nematic liquid crystals with positive dielectric anisotropy in detail. It is shown that nematic liquid crystals with positive dielectric anisotropy can serve as a stable and efficient medium for the optical vortex generation from both linearly and circularly polarized input Gaussian beams. Hybrid cells made from a thin layer of nematic liquid crystal confined between a photoresponsive slab of iron-doped lithium niobate and a glass plate coated with an active material, i.e., indium tin oxide, were studied. Exposure to a laser beam locally induces a photovoltaic field in the iron-doped lithium niobate substrate, which can penetrate into the liquid crystal film and induce realignment of molecules. The photovoltaic field drives charge carrier accumulation at the interface of indium tin oxide with the liquid crystal, which effectively modifies the shape and symmetry of the electric field. The photovoltaic field has a continuous radial distribution in the transverse -plane, weakening with increasing distance from the light irradiation center, where the electric field is normal to the cell plane. Umbilics are created as a result of the liquid crystal tendency to realign parallel to the electric field. Numerical studies of the transmitted intensity profiles in between linear polarizers reveal optical vortex pattern (of four and eight brushes) characteristics for the umbilical defects. The application of crossed circular polarizers results in annular-shaped intensity patterns as a result of spin-to-orbital angular momentum conversions, which give rise to the optical vortices.