Vortex and texture defects in radiation and matter wavefields

In this thesis the features that arise from the interference of simple coherent waves are described, namely the topological defects of phase known as phase vortices permeating such wavefields. Phase vortices are associated with the rotation of energy and mass and arise naturally in regions containing coherent light and/or matter. The simplest possible system exhibiting these defects is that of three linearly interfering plane waves, described using the classical theory of monochromatic complex scalar wavefields. We explore the related case of three outgoing waves produced by point sources, such as a laser-illuminated screen that has been punctured by three pinholes. We develop a description of the resulting vortex structure in the optical far-field, and relate this to the source arrangement and parameters. This allows an estimate of the number and positions of the vortices, and leads to connections to particular results from information theory and number theory. Numerical simulations of the near-field defect structure are also presented. Findings from this study are then applied to the time evolution of a nonlinear Bose-Einstein condensate of atoms, which shares the property of coherence that enables its description by a related model of interfering Gaussian wavepackets. Numerical modelling of the nonlinear system is performed for both trapped and untrapped Bose-Einstein condensates (BECs) in two and three spatial dimensions, for BEC pieces initially positioned at the three corners of an equilateral triangle. We demonstrate the production of a distorted honeycomb vortex-antivortex lattice, due to wavepacket interference. The wavepacket expansion is halted by the presence of a magnetic trap, causing the lattice to melt and providing a population of mobile vortices and antivortices. The addition of nonlinearity in this system over the linear case leads to the formation of vortex clusters, whose dynamics we investigate. A model of a Laguerre-Gauss (LG) laser beam, which carries a phase vortex along its axis, is studied following its interaction with a ground-glass plate. We present preliminary results showing that the beam acquires interference-generated vortices whose number density evolves as a function of propagation distance and beam topological charge, due to interaction with the roughened glass. Beyond the nonlinear coherent wavefields applied to the description of Bose-condensed gases, a pseudo-spinor system described as a nonlinear coupled system of two complex scalar fields is studied. Such systems admit the existence of texture defects similar to those that exist in ferromagnetic systems. We numerically model a pseudo-spinor system that we arrange to generate carefully aligned honeycomb vortex-antivortex lattices in the coupled components. We find that this corresponds to a texture defect lattice and identify its constituent texture defects as merons and a type of planar defect. Following the analogy with the single component BEC, we also study texture defects and clusters in the trapped pseudo-spinor system.