Refraction of nonlinear light beams in nematic liquid crystals

Optical spatial solitons in nematic liquid crystals, termed nematicons, have become an excellent test bed for nonlinear optics, ranging from fundamental effects to potential uses, such as designing and demonstrating all-optical switching and routing circuits in reconfigurable settings and guided-wave formats. Following their demonstration in planar voltage-assisted nematic liquid crystal cells, the spatial routing of nematicons and associated waveguides have been successfully pursued by exploiting birefringent walkoff, interactions between solitons, electro-optic controlling, lensing effects, boundary effects, solitons in twisted arrangements, refraction and total internal reflection and dark solitons. Refraction and total internal reflection, relying on an interface between two dielectric regions in nematic liquid crystals, provides the most striking results in terms of angular steering. In this thesis, the refraction and total internal reflection of self-trapped optical beams in nematic liquid crystals in the case of a planar cell with two separate regions defined by independently applied bias voltages have been investigated with the aim of achieving a broader understanding of the nematicons and their control. The study of the refraction of nematicons is then extended to the equivalent refraction of optical vortices. The equations governing nonlinear optical beam propagation in nematic liquid crystals are a system consisting of a nonlinear Schr¨odinger-type equation for the optical beam and an elliptic Poisson equation for the medium response. This system of equations has no exact solitary wave solution or any other exact solutions. Although numerical solutions of the governing equations can be found, it has been found that modulation theories give insight into the mechanisms behind nonlinear optical beam evolution, while giving approximate solutions in good to excellent agreement with full numerical solutions and experimental results. The modulation theory reduces the infinite-dimensional partial differential equation problem to a finite dynamical system of comparatively simple ordinary differential equations which are, then easily solved numerically. The modulation theory results on the refraction and total internal reflection of nematicons are in excellent agreement with experimental data and numerical simulations, even when accounting for the birefringent walkoff. The modulation theory also gives excellent results for the refraction of optical vortices of +1 topological charge. The modulation theory predicts that the vortices can become unstable on interaction with the nematic interface, which is verified in quantitative detail by full numerical solutions. This prediction of their azimuthal instability and their break-up into bright beams still awaits an experimental demonstration, but the previously obtained agreement of modulation theory models with the behaviour of actual nematicons leads us to expect the forthcoming observation of the predicted effects with vortices as well