The propagation of solitary waves, so-called nematicons, in a nonlinear nematic liquid crystal is considered in the nonlocal regime. Approximate modulation equations governing the evolution of input beams into steady nematicons are derived by using suitable trial functions in a Lagrangian formulation of the equations for a nematic liquid crystal. The variational equations are then extended to include the effect of diffractive loss as the beam evolves. It is found that the nonlocal nature of the interaction between the light and the nematic has a significant effect on the form of this diffractive radiation. Furthermore, it is this shed radiation that allows the input beam to evolve to a steady nematicon. Finally, excellent agreement is found between solutions of the modulation equations and numerical solutions of the nematic liquid-crystal equations. Disciplines Physical Sciences and Mathematics Publication DetailsMinzoni, A., Smyth, N. The propagation of solitary waves, so-called nematicons, in a nonlinear nematic liquid crystal is considered in the nonlocal regime. Approximate modulation equations governing the evolution of input beams into steady nematicons are derived by using suitable trial functions in a Lagrangian formulation of the equations for a nematic liquid crystal. The variational equations are then extended to include the effect of diffractive loss as the beam evolves. It is found that the nonlocal nature of the interaction between the light and the nematic has a significant effect on the form of this diffractive radiation. Furthermore, it is this shed radiation that allows the input beam to evolve to a steady nematicon. Finally, excellent agreement is found between solutions of the modulation equations and numerical solutions of the nematic liquid-crystal equations.

We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only. Disciplines Physical Sciences and Mathematics Publication DetailsMinzoni, A., Smyth, N. We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only.

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.

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We review the mathematical modelling of propagation and specific interactions of solitary beams in nematic liquid crystals - so-called nematicons. The theory is first developed for the evolution of a single nematicon; then it is extended to the interaction of two nematicons of different wavelengths, employing linear momentum conservation equations to predict that two colour nematicons can form a vector bound state. Considering optical vortices, we show that the nonlocal response of liquid crystals stabilises a single vortex, unstable in local media. Moreover, the interaction with a nematicon in another colour can stabilise a vortex for nonlocalities far below those at which an isolated vortex remains unstable. When multiple nematicons of the same wavelength interact, the radiation they shed can join them together, still resulting in a vortex. Finally, we discuss the escape of a nematicon from a nonlinear waveguide, using simple modulation theory based on momentum conservation to model the effect and get excellent agreement with the experimental results

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

Large amplitude nematicon propagation in a liquid crystal with local response Large amplitude nematicon propagation in a liquid crystal with local response Abstract AbstractThe evolution of polarized light in a nematic liquid crystal whose directors have a local response to reorienta-tion by the light is analyzed for arbitrary input light power. Approximate equations describing this evolution are derived based on a suitable trial function in a Lagrangian formulation of the basic equations governing the electric fields involved. It is shown that the nonlinearity of the material response is responsible for the forma-tion of solitons, so-called nematicons, by saturating the nonlinearity of the governing nonlinear Schrödinger equation. Therefore in the local material response limit, solitons are formed due to the nonlinear saturation behavior. It is finally shown that the solutions of the derived approximate equations for nematicon evolution are in excellent agreement with numerical solutions of the full nematicon equations in the local regime.

273The excitation of standing edge waves of frequency iw by a normally incident wave train of frequency w has been discussed previously (Guza & Davis 1974;Guza & Inman 1975;Guza & Bowen 1976) on the basis of shallow-water theory. Here the problem is formulated in the full water-wave theory without making the shallow-water approximation and solved for beach angles f3 = 7Tf2N, where N is an integer. The work confirms the shallow-water results in the limit N ~ 1, shows the effect of larger beach angles and allows a more complete discussion of some aspects of the problem.