In this thesis we have developed an anisotropic lattice Boltzmann (LB) model that recovers the incompressible isentropic Ericksen-Leslie-Parodi (ELP) equations of continuum nemato-dynamics in two dimensions with the director confined to the plane. Suitable validations of the developed model against known solutions of the continuum theory are undertaken as. well as investigations into nematic flow in interesting geometries. The model is based upon two coupled LBE schemes, the standard momentum density distribution and a new link angle distribution. To achieve evolution, the link angle distribution undergoes a Bhatnagar-Gross-Krook (BGK) collision step and advects (propagates) in unit time with the momentum densities. Anisotropy is introduced into the momentum density evolution scheme through a linearized Lattice Boltzmann (1LB) collision process which is made anisotropic. Correctly to capture the macroscopic dynamics, 6th order isotropy of the underlying lattice structure is required, accordingly we introduce a new variant on the standard 1LB scheme : a two-dimensional thirteen link (D2Q13) model. Chapmann-Enskog expansions of the momentum and angle evolution schemes are shown, through a suitable selection of equilibrium distribution functions and forcing terms, correctly to map onto the target macroscopic ELP equations of continuum nemato-dynamics. Results are presented which validate the new scheme against known analytical solutions of the governing equations to a high degree of accuracy. The validated scheme is subsequently applied to nemato-dynamic behavior in an applied magnetic field, i.e the Freedericksz transition and velocity back-flow with director kick-back. Finally we simulate the geometrically complex Zenithly Bi-stable Display (ZBD) device to illustrate some of the advantages of the LB schemes.

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We propose to develop a voltage-controllable multi-guide directional coupler in a planar nematic liquid crystal cell. The ITO grating-like electrodes are fabricated by the etching technique, and the director of liquid crystals will be aligned to the direction of applied electric field. Owing to the uniaxial property of liquid crystals, the difference of refractive index between two neighboring channels is increased with the applied voltage. Therefore, the coupling efficiency among grating-like multi-guide is also increased with the applied voltage. By using the combination of microscope and CCD system, the dynamic coupling can be observed under the distribution of grating-like electric field. The propagation of light in each channel can be selected by the controllable voltage between the electrodes of the individual channel. The intensity distribution of coupling in the transverse direction can be obtained by analyzing the image captured from the microscope and CCD system.

In this thesis, we report the study of two-dimensional spatial solitons observing in planar nematic liquid crystal cells with applied AC voltage. Two 2-D spatial solitons can be produced in one channel. They will attract or repulse each other, if we make the media with non-uniform reflection index. We study their interacting phenomena and expect the two solitons can make a spiral structure.

Abstract There are three parts in this paper. The first, we study the mechanism of soliton in nematic liquid crystal (NLC), molecules of NLC will be rotated easily by optical field while we apply an external electric field. Then the effective refraction index is changed. The light beam in NLC will create spatial soliton by producing the effect of self-focusing to balance the diffraction. Second, we study the interaction between solitons. One soliton will create a potential well of refraction index. The other one will be attracted in the potential well. These two solitons propagate in the form of spiral, if the separated distance and the angle are suitable. And the third, we observe the phenomenon with probe beam in the path of soliton. The path of the soliton forms a channel like a wave guide. The probe beam insert into the path of the soliton with different angles. The probe beam collides with the soliton in the proper range of angles will follow its path.

Compounds which exhibit liquid crystal phases have been widely used in display technology. The majority of display applications utilize the nematic liquid crystal phase, which is a liquid-like phase which has partial orientational order at the molecular level. The nematic phase exhibits birifringence which can be manipulated through the application of an external field. Subsequently, all liquid crystal-based display technology utilizes the application of an external field to ???switch??? or tune the optical properties of a nematic domain into a desired optical state. In addition to an external field, the geometry and surface interactions of the liquid crystal domain must be precisely controlled in order for the display to operate properly. Liquid crystal displays (LCDs) utilize a rectangular domain, or pixel, within which the nematic domain is exposed to surface anchoring conditions that result in a twist of the nematic alignment through the thickness of the domain. In this work, a different type of liquid crystal domain that is elliptic is studied which is formed through ???bottom-up??? techniques, such as phase separation of a liquid crystal/polymer mixture to form a polymer-dispersed liquid crystal (PDLC) composite. Nematic domains within PDLCs are spheroidal, as opposed to rectangular for a pixel, and thus exhibit substantially different behaviour in the presence of an external field. The fundamental difference between spheroidal and rectangular nematic domains is that the former requires the presence of defects in nematic order while the latter does not. The overall objective of this work is to study, for a simplified elliptic cylinder domain, the formation of the nematic domain, the resulting domain texture in the presence of an external field, and the domain texture following release of the external field. These three states are directly related to applications of PDLC films as optical functional materials, where an external (electric) field is used to manipulate the optical properties of the film. The effects of geometry (aspect ratio), surface anchoring, and external field strength are studied through a simulation-based approach using the Landau-de Gennes theory of the nematic phase.

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