Array and alignment of topological defects in liquid crystal

Topological defects in liquid crystal diffract light, scatter light, and switch the photon angular momentum. Electric field can switch the defects on and off, since the liquid crystal is fluid and highly operatable. When the combination and the arrangement satisfy the topological conservation laws, the defects assemble into ordered structure by themselves. The new order is topologically protected, self-retained, and self-healing. Our research focus on the rules of the right combination, and if the topological defects drive the formation of natural patterns and optical texture. In the first part of this talk, a new model for 2D defect array is demonstrated. The model has been under construction based on our experimental results. Topological defects are arranged in rectangular, triangular, square, pentagonal, and hexagonal lattices like atoms in crystals and quasicrystals. By solving the Euler-Lagrange equation of the director field of a unit cell and by integrating the topological rules into the boundary conditions, the director field of a defect crystal are easily obtained. A large variety of topological defect crystals and quasicrystals are derived. The defects are radial or vortex-like. Both nematic and vector orders are considered. The second part of the talk is about the generation of topological defect arrays. The pads, crossed-strips, and pores on the electrode grab the defects to put them in order. Unexpectedly, the pore generates a pair of radial (+1) and hyperbolic (-1) defects, just in analogy to electric dipoles. The dipoles spontaneously align in parallel order, forming domains. In unit cells smaller than 10 um x 10 um, the defect dipoles still align in a large range, without relying on lithography and surface treatment. The spontaneous dipole aliment breaks through the technical limit. Following the natural self-assembly of topological defects, photonic crystals or artificial tissues simply grow and form.