Shaping and positioning of topological defects in nematic liquid crystal cells equipped with patterned electrodes

Generation of topological defect that has a particular type (topological charge) and specific shape (radial, spiral, or circular) on a designed position is a crucial step in producing q plates and defect-mediated self-assembled micro structures. Shaping and positioning of topological defects can be achieved by applying delicately designed electric field on nematic liquid crystal (NLC). The guidelines for the electrode design are provided in this paper. The following are the three frequently asked questions: 1) What kinds of defects can exist in NLC? Points, lines, or walls? 2) How to generate a defect with a particular topological charge by setting proper boundary condition? 3) How to control the orientation of liquid crystal to have a defect with desired vorticity? The three questions can be answered by the three theories in physics: 1) Symmetry breaking in ordered material, 2) Euler characteristic and vectors in closed confinement, and 3) Minimization of free energy of NLC in electric field. Topological defects in spherical and toroidal confinements were generated in NLC cell and examined under polarized microscope. Radial and circular hedgehog defects were successfully created by fishbone- and coil-shaped patterned electrodes, respectively. By applying the three physical theories in NLC cell design, topological defects were successfully arranged in square and hexagonal arrays. They are large, stable, and re-configurable, and the applications in optics are demonstrated.