The field of plasmonics investigates how electromagnetic fields can be confined into sub- wavelength dimensions. This discipline constitutes a major subset of nano-photonics, and is enabled by the rich physics of light-matter interactions at the nano-scale. However, at the lower end of the length scales involved in plasmonic devices, metals are often shaped to have dimensions that approach the thickness of only a few atomic layers, which makes classical local electrodynamics insufficient due to the emergence of nonlocal and quantum effects that are not included in the model. In this thesis we focus specifically on nonlocal effects, investigating their impact in experimentally relevant plasmonic nanostructures. In order to describe the spatial dispersion in the metal permittivity, we develop a full three-dimensional nonlocal hydrodynamic solution of Maxwell's equations in frequency domain, complementing it with analytical closed form solutions where possible. In this way, effects of nonlocal electron-electron interactions in the dielectric response of metals are taken into account in a phenomenological fashion, offering deep insights into the way spatial dispersion modifies the electromagnetic response of plasmonic nano- structures. The geometries we investigate are driven by both plane wave and electron beam sources, mimicking experimental conditions. We use our numerical approach to perform an exhaustive analysis of the impact of nonlocality in the plasmonic response of five ex- perimentally relevant plasmonic structures: plasmonic hourglass metal-insulator-metal waveguides, kissing metallic nanowires, nanofocusing metallic tips, three-dimensional nanocrescent light harvesters, and coupled metallic nanoprisms under electron beam excitation. Our results demonstrate the complexity of the interplay between nonlocal and geometric effects taking place in the structures under investigation. We discuss the different sens- itivities to both effects of the various plasmonic modes supported by these structures.

Three different types of liquid crystal have been studied under confinement within two novel sample environments. The thermotropic cyanobiphenyls 5CB and 8CB were also doped with both a core deuterated, fluorinated version of 110CB (F17) and the fully deuterated terphenyl d-5CT; their adsorption was measured using neutron reflectometry (NR). At the air/5CB interface, the adsorbed amount ofF17 decreased with increasing temperature within the nematic phase, it then remained constant in the isotropic with a small increase owing to nematic wetting at the surface. At the solid / nematic interface there was strong adsorption of F17 (4.9 ±0.9 mg m-2 ) with a fluorinated silane (PFDS) coating. There was negligible adsorption (0.4±0.2 mg m-2) for the hydrogenous (OTS) coated surface. In 8CB the F17 enhanced the surface smectic wetting at the fluorinated surface. NR was also used with a novel confinement cell. Both 8CB and 10CB were confined but showed no change in their structures and it appeared the 8CB nematic phase was squeezed out of the contact area. A surfactant, alcohol and D20 lyotropic system was also squeezed out under 1 bar of confinement for 80% water content, however, with 75% water the lyotropic remained in place with 1 bar of confinement. Phosphatidyl choline lipid bilayer stacks were the third liquid crystalline system to be confined. Despite the repeat distance, d, increasing for bilayers of DSPC and DPPC confined from the fluid (Lα phase and decreasing overall from the gel (Lβ1) phase, the same d was reached at 5 bar of confinement in both cases. Model fitting showed; for all lipid chain lengths, the lipid component increased in thickness and the water decreased, suggesting that the phase had changed. A confinement cell for use with X-ray reflection (XRR) and small angle X-ray scattering (SAXS) was designed and commissioned, through experiments on lipids and cyanobiphenyls. The reflectivity results were consistent with the NR results. SAXS was applied to a pair of planar aligned surfaces with a twist between the alignment directions. The decrease in thickness with applied confinement induced the twist grain boundary phase for angles between 68°and 90°. Hybrid alignment conditions showed a conversion from non-scattering to planar alignment with confinement

Colloidal dispersions in a nematic liquid crystal host are an emerging system in soft matter. They are of fundamental interest due to the long range interactions that the liquid crystal mediates between the colloidal particles. It has been shown that these interactions can result in self-assembly of colloidal crystal structures, which has great potential in the creation of a new class of metamaterials. Although nematic liquid crystals are a mature field of research, there is still a great deal that remains unknown regarding their role in governing the interaction between colloidal particles. Analytical solutions can only predict the behaviour of the system in the most simple of cases. In order to understand experimental observations and predict the behaviour of novel systems, numerical simulations are an essential tool. As the complexity of the system increases, so too does the computational expense of modelling it. Previous numerical studies have often focused on a very specific problem, relying on the ability to reduce it to a more simple one via symmetry arguments. While this is a useful means of analysing a given case, it leads to a model that is inflexible. If one is to develop a more general-purpose tool to study a wider variety of systems, a crucial consideration is the performance. In order to harness the full potential of modern computers, it is essential to expose the maximum degree of parallelism in a given problem. In this work, an existing algorithm used to model nematic liquid crystals has been ported to a platform that is capable of fully exploiting the levels of parallelism in modern computing systems. This has facilitated the study of systems much larger than could previously be simulated within reasonable time frames.

The study of frustrated magnetism sits at the frontier of modern condensed matter physics, offering the possibility to discover new states of matter with exotic excitations. A textbook example of this is seen in the rare earth pyrochlore oxides H02Ti20 7 and DY2Ti207, better known as "spin ice". These magnets exhibit a classical spin liquid state with emergent magnetic monopole excitations. Inspired by this, we explore in this thesis a wide landscape of possibilities for novel magnetic behaviour on the pyrochlore lattice. Starting from the most general model for anisotropic nearest neighbour exchange interactions we show that the full zero temperature classical phase diagram can be obtained simply by considering the symmetries of a tetralledron. In the process of doing this we obtain an exact rewriting of the model in terms of a set of local order parameter fields defined on tetrahedra. After classifying and describing the ordered phases of this model we turn to give consideration to the novel physics which may be found near the boundaries where phases with different symmetry meet. We find that interesting properties of several materials can be traced back to the "accidental" degeneracies which arise on these boundaries. These include the "order by disorder" in Er2Ti207, the "dimensional-reduction" observed in Yb2Ti207, and the suppression of The observation that the physics of the phase boundaries manifests itself throughout the nearby regions of the phase diagram leads us to a systematic analysis of all of the phase boundaries of the model. In several cases dipole order persists at the phase boundary, stabilised by fluctuations. By constructing the ground state manifolds in each case we identify those configurations which are favoured by fluctuations. We also identify two limits of the phase diagram in which dipolar order vanishes to be replaced by spin nematic order. At certain phase boundaries we find that magnetic order vanishes entirely. This leads to the discovery of a new classical spin liquid on the pyrochlore lattice- the anisotropic Coulomb liquid. This spin liquid, like the Coulomb phase observed in spin ice, possesses algebraic correlations and conserved fluxes but also presents several new features including an anisotropic Coulomb interaction between its excitations. A long-wavelength theory of this spin liquid is derived from the microscopic model by coarse graining the fluctuations of the local order-parameter fields. Homing in on a different limit of the phase diagram, we move on to consider the effects of quantum fluctuations on a spin ice material and in particular how these effects would manifest themselves in neutron scattering experiments. We explore the correlations of the U(I) spin liquid which arises in this limit by explicitly constructing a basis of photon operators on the pyrochlore lattice and calculating the associated dispersion relation and correlation functions. This enables us to quantitatively describe how these unusual excitations would manifest themselves in neutron scattering experiments. We find that "pinch points," which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its quantum spin liquid ground state.