The nature and causes of variations in the atmospheric electric field as measured at the earth's surface at Durham are investigated. Determinations of the horizontal velocity of travel of variations of periods less than one hour, are made from simultaneous field measurements, using two rotating electrostatic fluxmetera, at two points approximately 100m apart. In fair weather the horizontal speed of the variations is about 1.2 times that of the wind at 10m, suggesting that they are due primarily to the motion of windborne space charges contained in the first 100m of atmosphere. In general the magnitude of the field variations appears to be dependent on the vertical stability of the lower atmosphere. Certain distinctive variations are believed to originate from charged locomotive steam while others appear related to atmospheric convective motion. Measurements in mist and fog support the view that the undulatory nature of the field is due to the horizontal drift of fog of varying thickness or density. Frequently fields below layer clouds show wave-like variations, these are shown to be due to the horizontal motion of cloud layers which contain a periodic spatial distribution of charges. This charge distribution appears to be closely related to visible structural variations in cloud thickness or density. Reasons are given for suggesting that, in stratus cloud, charge is separated by the Wilson process. It is shown that the field disturbances below shower clouds are due mainly to the horizontal drift of the charge system associated with the cloud. Such systems may be complex for appreciable charges appear to exist outside the cloud bounderies. Examples are given of the modification of surface fields by space charges liberated by point discharge processes and it is shown that surface measurements may be critically dependent on the location of the measuring instruments relative to discharging points.

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The problem of using the α,0 and the α, β-quasi periodic transformations within a finite element method in studying electromagnetic waves in a periodic space is addressed. We investigate an a priori error estimate for both transformations which allows us to solve our problem numerically on a uniform mesh. We also analyse the Dual Weighted Residual (DWR) method with the α,0-quasi periodic transformation to derive an a posteriori error estimate. This error estimate is later used to compute efficiently the numerical solution using an adaptive method. We then implement the above finite element methods. It is shown numerically that our numerical results are in good agreement with those in the literature, the α, β-quasi periodic method converges at a far lower number of degrees of freedom than the α,0-quasi periodic method and the DWR method converges faster and requires fewer degrees of freedom than the global a posteriori error estimate or the uniform mesh. We also explore the geometrical freedom given by the finite element method and examine wave scattering by the Morpho butterfly wing.

This thesis investigates the excitation of surface plasmon polaritons (SPPs) on a one dimensional (ID) grating etched in a gold film on a (high-index) gallium phosphide (GaP) substrate. The experimental component of the work addresses the design and building of an optical set-up for the far-field characterization of the spatially confined (-20 x 20μm) gratings in transmission, with better than 2° angular resolution, and the commissioning and use of a WiTec scanning near-field optical microscope (with bespoke modification) for near-field analysis. The purpose of the latter is to track the propagation of SPPs on the planar gold film region beyond the grating launch site. Both the far- and near-field experimental data are interpreted with reference to modelled results generated by using COMSOL, a commercial, finite-element analysis software package. Coupling efficiency of the incident light to the SPP is studied as a function of slit width where the grating periodicity and the (optimized) gold thickness remain constant. Defining a simple and convenient measure of the coupling efficiency the optimum slit width is found to be between 1/3 and 1/2 of the grating period. Such grating devices support only the fundamental mode and offer less radiative scattering of SPPs. The experimental results are in agreement with the far-field modelling results and the optimum slit-width range in the grating devices is close to that suggested by near-field analysis. The (maximum) propagation length, Lspp, just outside the grating device is found to be -13.33 ± 0.13μm under excitation by laser light of 785 nm wavelength. The Lspp is associated with the full width at half maximum (FWHM) of the SPP resonance. The grating on high refractive index substrate described above has intended application in heat assisted magnetic recording where it is envisaged that the focussing of optical energy to nanoscale dimensions will take place using SPPs generated by using a grating coupler integrated on a semiconductor laser chip. In addition, an optimal 1 D grating was designed and fabricated on a 50 nm Au film on a (low-index) glass substrate for application as a highly sensitive biosensor. The sensitivity was found to be 524 nm per refractive index unit (RIU) which is highly competitive with many other plasmon-based biosensors while being of simpler geometrical structure and more economical design.

On sub-wavelength scales, photon-matter interactions are limited by diffraction. Electromagnetic radiation propagating in free space - or far-field radiation - can be coupled into the surface plasmonpolaritons of nanostructured metallic surfaces in order to overcome this limitation. The distribution of electromagnetic energy in the near-field of these structures can be controlled by altering their geometry, dielectric environment and composition. Hence, surface plasmon polaritons allow electromagnetic radiation to be effectively utilized and controlled on the nanoscale. In this thesis a detailed study of the complex relationship between the electromagnetic near-field and far-field responses of 'real' nanostructured metallic surfaces is presented. The near-field and far-field responses are specified in terms of surface enhanced Raman scattering enhancement factor (SERS EF) spectra and optical extinction respectively. First, it is shown that in the far-field gold nanorod and nanotube array substrates exhibit two distinct localized surface plasmon-polariton resonances (LSPRs): a longitudinal and transverse mode. These modes are demonstrated both experimentally and theoretically, and a potential application of gold nanorod substrates as ultrathin absorbers is outlined. The near-field properties of these arrays are then studied, revealing the existence of a third type of LSPR: the cavity mode. The presence of this mode is confirmed using a combination of SERS EF spectra, electron microscopy and electromagnetic modelling. The cavity mode simultaneously has the largest impact on the near-field behaviour (as observed through the SERS EF) and the weakest optical interaction: it has a "near-field type" character. Conversely, the transverse and longitudinal modes have a significant impact on the far-field behaviour, but very little impact on SERS: they have a "far-field type" character. Based on this understanding of the contrasting character of the three LSPRs there follows a clear illustration and explanation of the non-correlation between the SERS EF spectra and the optical response, and some key consequences of this are described and demonstrated

The work undertaken is concerned with looking at how terahertz frequency radiation (here defined as 300 GHz -10 THz) propagates through media which have a random structure ("non-homogeneous materials"). Materials of this type are important in a wide range of applications, but are of particular interest in security and surveillance. Propagation of terahertz radiation through non-homogeneous materials is not well understood: both interference and scattering effects become important in this spectral range, where the wavelength and size and separation of the scattering centres are often commensurable. A simple model, which uses the phase change of a wave to describe its transmission through media having relatively small changes in refractive index is developed and compared with both exact theories and experimentally obtained measurements. Overall, a satisfactory agreement between the experimental data for transmission through arrays of cylinders, textiles and powders is seen. It is well known that pulses of terahertz radiation from optoelectronic sources have a complex shape. Post detection signal processing routines can be used to clean up the experimentally determined signals. The development of such algorithms is described, before they are applied to experimental results to determine: the minimum size of gaps between slabs to mimic voids in media; and the response of various compounds to a sharply terminated input pulse. The investigation of scattering from random structures requires the construction of a spectrometer having the capability to measure THz pulses scattered at different angles. Such a system ideally requires fibre-fed detection schemes to be used. The construction of a scattering spectrometer is described and its performance outlined. Pulses of terahertz which have been scattered by a sample of interest can be reconstructed, using methods from conventional tomography, to produce images of the phantom under test. Such measurements are outlined here. To our knowledge, this is the first time that tomography has been undertaken using a fixed sample and rotating detector arrangement.

Firstly, we give a general introduction to gravitational waves, the instruments used to detect them, potentially interesting sources, and the basics of gravitational wave data analysis with respect to the compact binary search. Following this, we look at a new class of approximants for inspiral waveforms. In these complete approximants, instead of truncating the binding energy and flux functions at the same post-Newtonian order, we instead keep terms such that the approximant corresponds in spirit to the dynamics of the system, with no missing terms in the acceleration. We compare the overlaps with an exact signal (in the adiabatic approximation) for a test mass orbiting a Schwarzchild black hole, for standard and complete approximants in the adiabatic approximation, and beyond the adiabatic approximation using Lagrangian models. A limited extension to the comparable mass case is also given. We then investigate two approaches to performing inspiral searches in a time-critical manner. Both involve splitting the search parameter space across several compute nodes. The first attempts to split the parameter space in an efficient manner by using information from previous runs. The second is balanced dynamically, with slave nodes requesting work off a master node. We then develop a new method for coincidence analysis. In this method, each trigger has associated with it an ellipsoidal region of the parameter space defined by the covariance matrix. Triggers from different detectors are deemed coincident if their ellipsoids are found to overlap. Compared to an algorithm which uses uncorrelated windows separately for each parameter, the method significantly reduces the background rate for comparable detection efficiency. We then give a summary of the current status of the ongoing search for high mass compact binary coalescences in the first calendar year of LIGOs fifth science run.