Coherent radiation by an ensemble of scatterers can dramatically modify the ensemble's optical response. This can include, for example, enhanced and suppressed decay rates (superradiance and subradiance respectively), energy level shifts, and highly directional scattering. This behaviour is referred to as cooperative, since the scatterers in the ensemble behave as a collective rather than independently. In this Thesis, we investigate the cooperative behaviour of one- and two-dimensional arrays of interacting atoms. We calculate the extinction cross-section of these arrays, analysing how the cooperative eigenmodes of the ensemble contribute to the overall extinction. Typically, the dominant eigenmode if the atoms are driven by a uniform or Gaussian light beam is the mode in which the atomic dipoles oscillate in phase together and with the same polarisation as the driving field. The eigenvalues of this mode become strongly resonant as the atom number is increased. For a one-dimensional array, the location of these resonances occurs when the atomic spacing is an integer or half integer multiple of the wavelength, thus behaving analogously to a single atom in a cavity. The interference between this mode and additional eigenmodes can result in Fano-like asymmetric lineshapes in the extinction. We find that the kagome lattice in particular exhibits an exceptionally strong interference lineshape, like a cooperative analog of electromagnetically induced transparency. Triangular, square and hexagonal lattices however are typically dominated by one single mode which, for lattice spacings of the order of a wavelength, can be highly subradiant. This can result in near-perfect extinction of a resonant driving field, signifying a significant increase in the atom-light coupling efficiency. We show that this extinction is robust to possible experimental imperfections.

This thesis is divided into two distinct parts. Part I, consisting of chapters 1 to 3, deals with the determination of the far field when an E-polarised electromagnetic plane wave is incident on an imperfectly conducting rectangular cylinder. In chapter 1 the field is determined when an E-polarised plane wave is incident on an imperfectly conducting right-angle wedge. In chapter 2, the results of chapter 1 and Keller's method of geometrical diffraction are used to determine the far field when an E-polarised plane wave is incident on an imperfectly conducting rectangular cylinder. Chapter 3 deals with certain singular directions for which the results of chapter 2 are no longer valid. Part II, consisting of chapters 4 to 7, deals with the determination of the electromagnetic field when an electromagnetic wave is incident on a dielectric wedge. In chapter 4 a basic integral equation and an iteration scheme for its solution, subject to certain restrictions on the refractive index of the wedge, is derived for incidence by an E or H-polarised field on an arbitrary angle dielectric wedge. Chapter 5 determines the electromagnetic field when an E-polarised plane wave is incident on a right-angle dielectric wedge whose refractive index (= n) is such that 1 < |n| < &radic;2. In chapter 6 the electromagnetic far field is determined, when an arbitrary angle dielectric wedge whose refractive index is such that n &ap; 1, is illuminated by an E-polarised plane wave. The method of approach is different to that used in chapters 4 and 5, uses Kontorovich-Lebedev transforms In chapter 7 the field near to the tip of an arbitrary angle dielectric wedge of arbitrary refractive index, when illuminated by a line source of E or H-polarisation, is determined.

A theoretical study of the electronic properties of silicon quantum dots (QDs) in applied electric and magnetic fields is presented in this work. To obtain the electronic states inside the quantum dots, a new finite-element method based technique is proposed within the effective mass approximation, in order to solve the time independent Schrodinger equation. The method allows for arbitrary shaped QDs in any material. Applied magnetic fields have been included in the most general way, such that 2-spinor wavefunctions may be obtained, which may be of more use in further work when considering many body effects within the framework of density functional theory. Applied electric fields using metal gates surrounding the QD have also been included in a new way, allowing for more realistic gate geometries. The new methods derived by the author allowed two studies to be performed. Firstly, a study of charge polarisation (localisation) inside Si double quantum dots (DQDs) in an applied magnetic field is presented, with varying DQD geometry. It is shown that the magnitude of the charge polarisation in the DQD is strongly related to the asymmetry of the DQD, and to the coupling strength between the two dots making the DQD, as well as its overall size. The applied magnetic field however, can be used to control the charge polarisation, as is demonstrated. Secondly, a study of a realistic gated Si DQD structure examined in experiments by Ferrus et al. It is demonstrated that the electric fields generated by gate potentials of the order used in the experiments have a strong ability to induce charge polarisation within the dot. The prospects for further development of the model are highlighted, to obtain more realistic simulations of electronic Si-based quantum structures.

This thesis describes the potential of relaxor ferroelectrics for solid state cooling based on the electrocaloric effect. The core of this investigation is to identify the reliable methods to correctly evaluate the electrocaloric effect and develop materials with the properties required for commercial electrocaloric cooling. A thorough review of the state-of-the-art electrocaloric research reveals that too many research groups still rely on the indirect evaluation of the electrocaloric effect (ECE) from polarization measurements and highlights the need for direct ECE measurements. A direct electrocaloric effect measurement set-up based on a modified-differential scanning calorimeter, allowing the acquisition of both ther- mal (ECE, heat capacity) and electrical (P-E loops, leakage current) information simultaneously, has successfully been constructed and benchmarked. Direct ECE measurements have been performed on normal ferroelectrics, such as barium titanate, but also well-known relaxor ferroelectrics, such as the PMN- PT system, for fundamental understanding of the electrocaloric effect. These results highlight the importance of the polar direction of the electrocaloric mate- rials with regard to the direction of applied electric field. A region with negative ECE, which could be exploited to increase the efficiency of electrocaloric cooling cycles, has been identified for < 001 > -oriented PMN-30PT by both direct and indirect measurements. This negative ECE is observed in the vicinity of the low temperature field-induced structural phase transition, which forms intermediate lower-symmetry monoclinic phases. The occurrence of this phenomenon requires the combination of several parameters related to the direction of application of the electric field. The results on PMN-PT also show how the chemical disorder in ferroelectric relaxors provides important entropy changes over the ferroelectric to paraelectric transition which enables an extended cooling regime as the ECE maximum can be extended over several tens of degrees. Direct ECE measurements have therefore been performed on novel relaxor fer- roelectrics, including perovskite, Aurivillius phase and tungsten bronze structures, with a focus on lead-free, for environmental purposes, highly disordered materi- als. For most of these systems, the direct ECE measurement presented here are the first ever reported. The presence of a dual electrocaloric peak, sometimes far above the ferroelectric to paraelectric transition, is confirmed in all the studied relaxor ferroelectrics. This peak was attributed to the extra contribution to the field-induced entropy change by the polar nanodomains. The presence of this ex- tra ECE peak confirms the great potential of relaxor ferroelectrics for solid-state electrocaloric cooling over a range of temperature broad enough for commercial applications. Comparisons between direct and indirect measurements are performed on nu- merous systems throughout this thesis, in order to identify the domain of validity of the indirect method still overly used in the literature. It is shown that the indi- rect ECE method, although it gives satisfactory results for normal ferroelectrics, is unreliable for strong relaxor ferroelectrics above the ferroelectric to paraelectric phase transition, where the dual peak is observed by direct measurements. These limitations are attributed to the inability of the indirect method to account for the field-induced entropy contribution of the polar nanodomains to the electrocaloric effect.

This thesis describes experimental work on the interaction of the drifting charge carriers with the piezoelectric lattice modes in highly resistive CdS crystals. In these experiments the specimens were fitted with evaporated metal electrodes on opposite faces, and a fast electron or light pulse generated electron-hole pairs in a narrow region below the top electrode. The crystals were mounted on a silica buffer rod with a quartz transducer on its opposite end. A synchronized field pulse drew a thin space charge layer out of this region and the transit time and drift velocity were obtained directly. The new feature of this work is the simultaneous detection of the generated piezoelectric wave in a frequency range from 3 to 75 Mc/s. The results show a close correlation between the ultrasonic measurements and those features of the drift velocity experiments associated with the transient acoustoelectric interaction. The amplitude of the piezoelectric wave has been studied as a function of the applied field, temperature, excitation pulse length, electron beam current and beam energy (5-35 keV) and also as a function of steady, highly absorbed light incident on the specimen top surface. From the measurements it has been possible to estimate the value of the piezoelectric field. This is sufficient to explain the non-ohmic behaviour of the drift velocity versus applied field curves. On the basis of the above results a microscopic model is proposed. A single incident electron is considered which simultaneously generates an elementary piezoelectric wavelet and a distribution of free electrons within a few microns of the surface. The local interaction of the electrons with the wavelet leads to ultrasonic amplification in accordance with the White theory. The significance of the surface barrier in connection with the amplification is discussed. A quantitative estimate is made of the local density of the bunched carriers which, on the basis of the White theory, leads to a build-up time of the interaction of less than 10 nsec. The results of this analysis resolve one of the main difficulties in the understanding of the transient acoustoelectric interaction.

No description available.

This thesis presents a mixture of theoretical work and experimental results relating to the generation and transport of relativistic electrons in fast ignition inertial confinement fusion. First the theoretical work is presented, which focuses on the effect that a fast electron beam has on a background plasma. The fast electron beam drives a resistive return current in the plasma, which causes Ohmic heating, leading to a pressure gradient, and a $J \times B$ force. Both of these would be expected to cause cavitation in the background plasma. In this work an analytic model has been developed which shows that the pressure gradient is the dominant force, and predicts the significance of cavitation over a range of parameters relevant to fast ignition fusion. In addition to this the timescale on which shocks can form is considered. This work was verified by the development of a one dimensional fluid code which included the effects of a resistive return current, and was used to model shock formation when the cavitation in the plasma is strong. Some results from a two dimensional version of the code are also presented. The experimental work in this thesis focuses on an experiment which looked at the interaction of a high-powered laser with gold cone targets, similar to those that would be used in cone-guided fast ignition schemes. In this experiment, the effect of defocusing the laser upon the production of hot electrons was investigated. A copper wire was attached to the cones to act as a diagnostic for the hot electrons. A ray-tracing code was developed to better understand the change in intensity inside the cone when the laser is defocused. The results of this experiment demonstrate that the energy coupling of the laser into hot electrons is maintained when defocusing, while the spectrum of the hot electrons softens.

Magnetic fields play a very important role in the dynamics of plasmas. Through interactions with the ions and electrons within plasmas, their behaviour and evolution can be drastically influenced. It is the Zeeman effect that is responsible for the splitting of radiative lines observed. Zeeman spectroscopy is a tool used for the diagnosis of these magnetic fields within plasmas when the extent of this line splitting is observable. Aluminium is chosen as an element to model as it is easy to place within a pinch plasma. It is also relatively easy to ionise Aluminium into being Hydrogen-like within the conditions of pinch plasmas. The calculation of Lyman Alpha and Lyman Beta spectral lineshapes for a Hydrogen-like Aluminium plasma is presented from a fundamental standpoint. The Stark and Zeeman effects are explored and modelled. Modelling of the former is aided by an adapted version of the APEX code by R. Lee in order to calculate the probability distribution of electric fields around a radiator ion in the plasma. Both effects are calculated together as a quantum perturbation to the π = 1, 2, 3 atomic energy levels including fine structure. The lineshapes resulting from this calculation are compared with H-Line’s models (a code also by R. Lee) and shown to be significantly more detailed, including visible Zeeman splitting for test external magnetic fields of B = 100 T and B = 1000 T. Natural and Doppler broadening are also modelled. These extra broadening effects (in particular Doppler) are shown to be destructive to discernable lineshape detail, largely preventing magnetic field diagnosis through Zeeman spectroscopy. Lastly, Lyman Alpha and Lyman Beta are modelled for plasmas with Z-pinch and X-pinch conditions in order to determine the viability of visible Zeeman line splitting.

The free surface mixing properties of a scalar advected by a quasi-steady or unsteady electromagnetically forced flow are investigated. The scalar statistics are related with the topology of the velocity fields stirring them. The benefits and consequences of topologically folding a scalar to enhance homogenization are discussed, identifying how this process may lead to the attenuation of diffusion in vortical and chaotic flows. A pair of magnets, whose attitude is controlled during the experiment, is employed to generate a wide range of velocity fields in a shallow layer of conductive stratified brine. The simplicity of the system makes it possible to analyze the basic properties of the flows generated, relating them with more complex geometries found in literature. The concentration measurements characterizing the scalar field are based on LIF, for which a novel experimental procedure (including calibration, error management and statistical estimators) is presented. Special attention is paid to the relation between the variance decay rate and the mean gradient square, identifying several mechanisms that reduce the fidelity of Q2D experiments in reproducing some features of the transport equation. Evidence of the scalar spiral range is presented in the wavenumber and physical spaces for particular quasi-steady samples. When required, the system unsteadiness is generated by modifying the body forcing geometry throughout the experiment, producing chaotic advection regardless of the flow Re. The periodic nature of the forcing oscillations leads to an exponential variance decay dominated by a strange eigenmode. It is shown that such a system contains recurring temporal patterns and becomes independent of the scalar initial condition.

Lately, transformation optics (TO) has driven the development of metamaterial science, providing a direct link between a desired electromagnetic phenomenon and the material response required for its occurrence. However, this powerful framework is not restricted to the metamaterial design, and it has recently been exploited to study surface plasmon assisted phenomena. In this thesis, we mainly focus on the general strategy based on TO to design and study analytically plasmonic devices capable of efficiently harvesting light over a broadband spectrum and achieving considerable field confinement and enhancement. Using TO, we show that a finite nanoparticle with sharp geometrical features can behave like an infinite plasmonic system, thereby allowing simultaneously a broadband interaction with the incoming light as well as a spectacular nanofocusing of its energy. Various plasmonic structures are designed and studied, such as 2D crescents, groove/wedge like nanostructures, overlapping nanowires, and rough metal surfaces. Comprehensive discussions are also provided on practical issues of this problem. First, we discuss how the edge rounding at the sharp boundary affects the local field enhancement as well as the energy and bandwidth of each plasmonic resonance. In particular, the necessary conditions for achieving broadband light harvesting with blunt structures are highlighted. The TO approach is then applied to study the interaction between plasmonic nanoparticles. We demonstrate that the energy and spectral shape of the localized surface plasmon resonances can be precisely controlled by tuning the separation between the nanoparticles. Finally, we consider the extension of the TO framework to 3D geometries, and show that the 3D structure is more robust to radiative loss than its 2D counterpart. The physical insights into sharp and blunt plasmonic nanostructures presented in this thesis may be of great interest for the design of broadband light-harvesting devices, invisible and non-invasive biosensors, and slowing-light devices.