In this thesis we study the dynamics of dark solitons, vortices and Josephson effects, in trapped atomic Bose-Einstein condensates. We firstly demonstrate a novel, sound mediated, long-range interaction mechanism between dark solitons using the Gross-Pitaevskii equation. Then we present the effect of finite temperatures on the dynamics of vortices and Josephson effects using a generalised form of this equation, which additionally includes a source term modelling the coupling of the condensate to a fully dynamical thermal cloud, described by a quantum Boltzmann equation. The latter formalism is known as the Zaremba-Nikuni-Griffin scheme (ZNG). The sound-mediated interaction between dark solitons is such that the speed and trajectory of one soliton in a condensate confined by a harmonic trap can be significantly modified by the presence of a second soliton in the same trap. By confining the two solitons to spatially separated subregions of a double well trap, we show how this effect can be magnified. In particular we find it can be large, and therefore detectable, in experimentally relevant geometries, including high-periodicity optical lattices in which the ability of solitons to act as both absorbers and emitters of energy becomes apparent. At finite temperatures, we model the dynamics via the ZNG scheme. Firstly, we give a detailed description of the scheme for numerically solving these coupled equations including all collisional terms. Then we study the effect of a dynamical thermal cloud on vortex dynamics, in particular, focussing on the experimentally-relevant quantities of precession frequencies, decay rates and vortex core brightness. The changes in these are found to increase with increasing temperature for a pancake-shaped geometry, in particular for trapping parameters of a recent experiment of Freilich et al. (Science 329, 1182 (2010)). Particle exchanging collisions between the condensate and thermal cloud are found to be crucial in determining the rate of decay of a precessing vortex. We further show that, rotation of the thermal cloud can be a mechanism for radially translating the position of a vortex, a scenario under current investigation. Finally, we analyse the effect of finite temperatures on population dynamics in a double well atom chip experiment by LeBlanc et al. (Phys. Rev. Lett. 106, 025302 (2011)). Focussing on the coupled evolution in the absence of collisions, we find that it generates significant damping which is, however, less than that observed in the experiment. A detailed comparison in the presence of collisions is beyond the scope of this thesis.

Orbital angular momentum of light is a new field of research which is concerned with the mechanical and optical effects of light with a helical phase structure. In this thesis we ask fundamental questions on the properties of light carrying orbital angular momentum. We discuss the uncertainty relation for angle and angular momentum on the example of orbital angular momentum of light. The lower bound in the angular uncertainty relation is state dependent, which requires a distinction between states satisfying the equality in the uncertainty relation and states giving a minimum in the uncertainty product. We examine these special states and their uncertainty product. We show that for both kinds of states, the uncertainty product can be surprisingly large. We propose an experimentally testable criterion for an EPR paradox for orbital angular momentum and azimuthal angle. The criterion is designed for an experimental demonstration using orbital angular momentum of light. For the interpretation of future experimental results from the proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. We show how angular apertures can be used to determine the angle, and we discuss the effects of this measurement on the proposed criterion. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected. The quantum theory of rotation angles is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientation of a phase discontinuity associated with fractional values of the orbital angular momentum. We apply our formalism to the propagation of light modes with fractional orbital angular momentum in the paraxial and non-paraxial regime.

The work presented in this thesis concerns the design and synthesis of organic and metallo-organic chromophores for use in non-linear optics. The non-linear optical (NLO) properties have been quantified using hyper-Rayleigh scattering (HRS) studies to measure β, and using the two-state model βο values have been determined. Stark spectroscopy has also been used to derive βο values indirectly. Twenty four X-ray crystal structures have been solved, with six of these showing non-centrosymmetric (NCS) packing arrangements. HRS measurements have also been applied to two series of known co-ordination complexes in order to probe structure-activity relationships.

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