Stability of an optical vortex in a circular nematic cell

The stability of an optical vortex in a cell with a circular cross section containing a nematic liquid crystal is studied. A modulation theory based on an averaged Lagrangian formulation is developed to study this stability. It is found that the vortex is stable unless the radius of the cell is very small, nearly the width of the vortex itself. Based on the analysis of a stationary vortex, the stability of a low-amplitude vortex in a large cell under the influence of its orbital angular momentum and the repelling effect of the cell boundary are studied. The predictions of this modulation theory are found to be in excellent agreement with numerical simulations

Optical solitary waves escaping a wide trapping potential in nematic liquid crystals:Modulation theory

A nonlinear extension of geometric optics is used to derive a modulation theory solution for the trajectory of an optical solitary wave in a nematic liquid crystal-i.e., a nematicon-in which a wide waveguide has been defined by an externally applied static electric field. This solution is used to find the power threshold for the solitary wave to escape the trapping waveguide. This threshold is found to be in excellent agreement with experimental results

Vector vortex solitons in nematic liquid crystals

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.Comment: 4 pages, 4 figures, submitted for publicatio

Stabilization of vortex-soliton beams in nematic liquid crystals

We study the interaction of two optical beams of different wavelengths (colors) in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave (nematicon) instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions

Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells

The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal—a nematicon—is mathematically modelled. In order to overcome the Freédricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the (2+1)-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results

Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays

We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely