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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 Freedricksz 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.

We demonstrate power-dependent steering of self-confined light beams propagating in the nonparaxial regime in a guest-host nonlinear medium. Exploiting the Janossy enhancement in dye-doped liquid crystals with reorientational response, we observe sub-mW spatial soliton self-steering as large as 39 degrees, accompanied by trapping of the light spontaneously emitted by the excited dye. The self-turning is modeled in terms of an effective transverse force stemming from the longitudinal electric field in the tightly confined beams, with good agreement between data and simulations.

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.

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.

The propagation and interaction of two solitary waves with angular momentum in bulk nematic liquid crystals, termed nematicons, have been studied in the nonlocal limit. These two spinning solitary waves are based on two different wavelengths of light and so are referred to as two-color nematicons. Under suitable boundary conditions, the two nematicons can form a bound state in which they spin about each other. This bound state is found to be stable to the emission of diffractive radiation as the nematicons evolve. In addition this bound state shows walk-off due to dispersion. Using an approximate method based on the use of suitable trial functions in an averaged Lagrangian of the two-color nematicon equations, modulation equations for the evolution of the individual nematicons are derived. These modulation equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found between solutions of the modulation equations and full numerical solutions of the nematicon equations. The shed diffractive radiation is found to play a much lesser role in the nonlocal limit than in the local limit.

The propagation and interaction of two bulk solitary waves, termed nematicons, in a nematic liquid crystal are studied in the local limit. These two nematicons are based on light of two different wavelengths, and so are referred to as two color nematicons. Under suitable boundary conditions the two nematicon beams of different wavelengths can couple, creating a self-localized vector solitary wave. Due to the different diffraction coefficients and indices of refraction for each wavelength, the vector solitary wave shows walk-off. Using a suitable trial function in an averaged Lagrangian formulation of the two color nematicon equations, approximate equations governing the evolution of the two color nematicons are derived. These approximate equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found for the walk-off as given by these approximate equations and by full numerical solutions of the nematicon equations. It is shown that the inclusion of the effect of the shed diffractive radiation is vital in order to obtain this excellent agreement.

We investigate the interaction between two beams differing in wavelength and the properties of dual-frequency spatial solitons in nonlocal birefringent reorientational media. We report the first experimental observations of anisotropic nonlocal vector solitons in unbiased nematic liquid crystals. Model and simulations, based on the paraxiality along the Poynting vectors, include joint walk-off and breathing.