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.

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.

In this study, a high power Q-switch pulse laser has been used as the writing beams. The laser-induced holographic gratings in the DR1-doped liquid crystal samples and the DR1-PMMA polymer thin films were investigated by changing the temperature of samples and the angles of two writing beams. The He-Ne cw laser has been used as a real-time probe beam to detect the first order diffraction signals. Without external field, the gratings are the results of concentrations and diffusions of azo dye isomers. The diffusion model has been utilized to analyze the first order diffraction signals in order to understand the mechanics of gratings and the effect of temperature and angle.

Nonlinear, nonlocal optical media has emerged as an ideal setting for experimentally observing and studying spatial optical solitary waves which otherwise cannot occur in Kerr media. Of particular interest is the eventual application to all-optical circuits. However, there is considerable work left to do on the theoretical end before this is a possibility. In this thesis we consider three problems. The first is how to solve the governing equations for optical beam propagation in the particular medium of the nematic liquid crystal (NLC), which is used as a prototypical example, exactly and approximately. In this respect we provide the first known, explicit solutions to the model as well as a comprehensive assessment on how to use variational, or modulation theory, in this context. This leads to the discovery of a novel form of bistability in the system, which shows there are two stable solitary wave solutions for a fixed power or L2 norm. We then consider how to approximate solutions for optical solitary waves propagating in a more general class of nonlocal nonlinear media using asymptotic methods. This is a long open problem and is resolved in the form of a simple to implement method with excellent accuracy and general applicability to previously intractable models. We conclude with the discovery and characterization of an instability mechanism in a coupled, defocussing nonlinear Schrodinger system. We show there is no stable, coupled, localized solution. This result is compared with the more well-studied bright solitary wave system and physical and mathematical explanations are offered.

Visualization and exploration of nematic liquid crystal (NLC) data is a challenging task due to the multidimensional and multivariate nature of the data. Simulation study of an NLC consists of multiple timesteps, where each timestep computes scalar, vector, and tensor parameters on a geometrical mesh. Scientists developing an understanding of liquid crystal interaction and physics require tools and techniques for effective exploration, visualization, and analysis of these data sets. Traditionally, scientists have used a combination of different tools and techniques like 2D plots, histograms, cut views, etc. for data visualization and analysis. However, such an environment does not provide the required insight into NLC datasets. This thesis addresses two areas of the study of NLC data---understanding of the tensor order field (the Q-tensor) and defect detection in this field. Tensor field understanding is enhanced by using a new glyph (NLCGlyph) based on a new design metric which is closely related to the underlying physical properties of an NLC, described using the Q-tensor. A new defect detection algorithm for 3D unstructured grids based on the orientation change of the director is developed. This method has been used successfully in detecting defects for both structured and unstructured models with varying grid complexity.

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This manuscript demonstrates the regularity and uniqueness of some geometric heat flows with critical nonlinearity. First, under the assumption of smallness of renormalized energy, several issues of the regularity and uniqueness of heat flow of harmonic maps into a unit sphere or a compact Riemannian homogeneous manifold without boundary are established. For a class of heat flow of harmonic maps to any compact Riemannian manifold without boundary, satisfying the Serrin's condition, the regularity and uniqueness is also established. As an application, the hydrodynamic flow of nematic liquid crystals in Serrin's class is proved to be regular and unique. The natural extension of all the results to the heat flow of biharmonic maps is also presented in this manuscript.

Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.

The laser-induced holographic gratings in the Azo dye-doped PMMA thin films with liquid crystal were investigated by changing the temperature of the sample, the angle of two writing beams and the rubbing. The high power Q-switch pulse laser has been used as the writing beams and the He-Ne cw laser has been used as a real-time probe beam to detect the first order diffraction singals. The grating are the results of photo-isomerization of azo dye and diffusions of liquid crystal. The model has been established to analyze the first order diffraction signals in order to understand the mechanism of grating and the effect of temperature and angle.

The process of forcibly dewetting a solid substrate from a bulk liquid so as to leave a thin residual layer on the surface is referred to as forced dewetting. This novel experimental approach helps to investigate interfacial species by minimizing the interference of the bulk liquid when coupled with spectroscopy. In this work, the scope of liquids investigating using this approach has been expanded from simple fluids to one type of complex fluid, a nematic liquid crystal, 4-n-pentyl-4'-cyanobiphenyl (5CB).In order to better understand the interfacial behavior of the simple fluids, water, chloroform, and n-pentane vapors were adsorbed onto omega-terminated SAM-modifed Ag (11-mercaptoundecanoic acid, 11-mercaptoundenanol, and undecanethiol) surfaces under vapor-saturated conditions. The kinetics of solvent adsorption on each of these surfaces were investigated and the thicknesses of the adsorbed layer were compared to predictions from Lifshitz theory of long-range van der Waals interactions. Although the predicted thicknesses do not match the experimental values for adsorbed films, the predicted thicknesses do match those observed experimentally using forced dewetting. The correlation between these predicted and observed thicknesses implies that residual film formation under the conditions of forced dewetting used in this laboratory is dictated by interfacial forces alone.The surface adsorption behavior of 5CB was investigated using surface-enhanced Raman spectroscopy with the aid of localized surface plasmon resonances-surface plasmon polaritron coupling. The results clearly indicate that 5CB is adsorbed to smooth Ag surface in a facial orientation with pi-d orbital interaction suggested.Finally, forced dewetting studies of bare, -NH2-temintaed SAM, and -CH3-temintaed SAM modified-SiO2 substrates from 5CB were undertaken. Residual layer thicknesses were monitored as a function of substrate velocity. The transition from the regime in which interfacial forces dictate residual layer thickness to the regime in which fluid dynamic forces dictate thickness was observed for the first time and was evaluated in terms of the average 5CB director orientation. Unlike simple fluids, 5CB has strong interfacial interactions from surface anchoring depending on the chemical nature of the substrate, which makes the residual layer thicknesses at least 100 times larger than observed in simple fluids.