On the origin of the optical vortex lattices in a nematic liquid crystal light valve

Abstract

Optical vortices and lattices of these are attracting the attention of the scientific community because of their applications in various fields of optical processing, communications, enhanced imaging systems, and bio-inspired devices. Programmable optical vortices lattices with arbitrary distributions have been achieved using illuminated liquid crystals with photosensitive walls. Using an amplitude equation that describes these optical valves close to the Freédericksz transition allows us to characterize analytically the vortices and the lattices they form. The numerical simulations of the amplitude equation, analytical solutions, and experimental observations show good agreement.

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

“…In the recent work by Calisto and co-workers, 66 the theoretical studies indicate the possibility of generation of optical vortices in a LC media with positive elastic anisotropy (δ > 0), defined as δ = ( K 1 – K 2 )/( K 1 + K 2 ). In another work, 67 it was shown that in the liquid crystal light valves (LCLVs), competition between the forcing of the external electric field induced by the inhomogeneous light profile and the elastic anisotropy can result in the swirling of the vortex arms.…”

“…As seen in Figures 8 and 9, the output intensity patterns exhibited a residual hexagonal symmetry because of the numerical calculations in the Cartesian coordinate system, and this issue can be simply avoided by simulating the LC cell in a cylindrical coordinate system. In the recent work by Calisto and co-workers, 66 the theoretical studies indicate the possibility of generation of optical vortices in a LC media with positive elastic anisotropy (δ > 0), defined as δ = (K 1 − K 2 )/(K 1 + K 2 ). In another work, 67 it was shown that in the liquid crystal light valves (LCLVs), competition between the forcing of the external electric field induced by the inhomogeneous light profile and the elastic anisotropy can result in the swirling of the vortex arms.…”

Umbilical defect dynamics in an inhomogeneous nematic liquid crystal layer

“…Indeed, vortices are topological defects since these solutions are created or destroyed by pairs with their respective opposite charge. Also, vortices can be induced by an external topological forcing [9][10][11].…”

“…Due to the complexity of the elastic theory of liquid crystals, the analytical study of the umbilical defects is inaccessible [12,13]. Weak nonlinear analysis, valid close to the orientational instability of the molecules, allows describing the dynamics of a nematic liquid crystal layer by the Ginzburg-Landau equation with real coefficients [10,11,[20][21][22][23]. This amplitude equation has gathered a great interest by describing several physical systems such as fluids, superfluids, superconductors, liquid crystals, magnetic media, and optical cavities, to mention a few (see the textbook [8] and reference therein).…”