Our understanding of the physics of neutrino oscillations has evolved rapidly over the past decade or so, with results from the SNO, Super-K, MINOS and CHOOZ experiments, among others, producing results favouring a three-neutrino mixing model, and significantly constraining the parameter space for this mixing. There are still several important questions to be answered however: we do not know whether Θ13 is non-zero, or whether (sin2 2Θ23) is maximal; also, we do not know the sign of the large mass splitting ΔM2, or whether CP-violation occurs in the lepton sector. The latter is possibly the most exciting of all - leptonic CP- violation is a requirement for leptogenesis, and could therefore indicate a solution to the matter-antimatter asymmetry problem in cosmology. The T2K long-baseline neutrino experiment is one of a new generation of neutrino projects, which will make more precise measurements of Θ13 and Θ23 than has been achieved by previous experiments. It uses the Super-K water Čerenkov detector at Kamioka as a far detector, and also has a suite of new near detectors. These are largely scintillator-based, but use a novel photosensor, the silicon photomultiplier (SiPM), for light readout. T2K has been leading the effort to understand and model these new sensors, and the present work will describe the current state-of-the-art in device characterisation, and also the effort to ensure the quality of the devices installed in the calorimeter of the ND280 near detector. An important part of a long-baseline analysis is the extrapolation of the neutrino flux measured at the near detector to predict that at the far detector. Methods to do this have been developed by previous experiments; however T2K uses an innovative configuration whereby the main detectors are displaced from the neutrino beam centre, removing much of the high-energy tail in the neutrino flux to reduce background from non-quasielastic events. This thesis evaluates the effectiveness of two extrapolation techniques, used by previous experiments, for the T2K configuration.

The objective was to develop solid-state nuclear magnetic resonance (NMR) homonuclear correlation experiments for half-integer quadrupolar nuclei so as to study atomic proximities and connectivities in disordered materials. Nearby nuclear spins are coupled through space via their magnetic dipole moments. Dipolar broadening is removed by magic angle spinning (MAS) for isolated spin pairs. However, the noncommutation of the electric quadrupolar interaction with the dipolar interaction means that the latter will not be removed by MAS. This interplay between the dipolar and quadrupolar interactions, combined with the effects of multiple noncommutating homonuclear dipolar couplings, was investigated by observing spin-echo dephasing curves as well as magnetisation transfer in 2D spin diffusion experiments. Polycrystalline lithium diborate samples were synthesised to act as model compounds. The preparation of samples with differing 11B isotopic abundances enabled a comparison of samples with either predominantly isolated spin-pairs or multiple coupled nuclei. Spin diffusion experiments probed 11B–11B correlation at three magnetic field strengths, 80% and 25% 11B isotopic abundances, MAS rates from 4427 Hz to 7602 Hz and under DOR. Enhanced magnetisation transfer was observed for the higher 11B isotopic abundance and at slower spinning speeds. The latter dependence was reproduced by four-spin computer simulations. Secondorder quadrupolar broadened spin diffusion cross-peaks under MAS had a mixed positive and negative appearance for the 80% 11B sample. A similar effect was previously observed for four dipolar-coupled I = 1/2 nuclei. Spin-echo dephasing curves were recorded for 5%, 25% and 100% 11B isotopic abundances and MAS rates of 5 kHz to 20 kHz. Depletion of 11B isotopic abundance prolonged the coherence dephasing time because of a reduction of noncommuting homonuclear dipolar couplings. Faster dephasing was observed for the smaller CQ = 0.51MHz site; four-spin computer simulations showed this is consistent with the reintroduction of the dipolar coupling being most efficient when the MAS rate and first-order quadrupolar interaction are of the same magnitude. Speeding-up the MAS rate prolonged the dephasing time for the CQ = 2.56MHz site but not for the CQ = 0.51MHz site because of an interplay between the quadrupolar and multiple dipolar interactions. Through-bond Jcouplings between 11B nuclei were not detected, setting an upper bound of 2JBB <3 Hz in polycrystalline lithium diborate.

This thesis looks at various problems relating to the value distribution of certain discrete potentials. Chapter 1 - Background material is introduced, the motivation behind this work is explained, and existing results in the area are presented. Chapter 2 - By using a method based on a result of Cartan, the existence of zeros is shown for potentials in both the complex plane and real space. Chapter 3 - Using an argument of Hayman, we expand on an established result concerning these potentials in the complex plane. We also look at the consequences of a spacing of the poles. Chapter 4 - We extend the potentials in the complex plane to a generalised form, and establish some value distribution results. Chapter 5 - We examine the derivative of the basic potentials, and explore the assumption that it takes the value zero only finitely often. Chapter 6 - We look at a new potential in real space which has advantages over the previously examined ones. These advantages are explained. Appendix - The results of computer simulations relating to these problems are presented here, along with the programs used.

With the advantages of low cost, low power consumption, high reliability and potential for large scale integration, CMOS monolithically integrated active pixel chips have significant application in optical sensing systems. The optical front end presented in this thesis will have application in Optical Scanning Acoustic Microscope System (O-SAM), which involves a totally non-contact method of acquiring images of the interaction between surface acoustic waves (SAWs) and a solid material to be characterized. In this work, an ultra fast optical front-end using improved regulated cascade scheme is developed based on AMS 0.35mm CMOS technology. The receiver consists of an integrated photodiode, a transimpedance amplifier, a mixer, an IF amplifier and an output buffer. By treating the n-well in standard CMOS technology as a screening terminal to block the slow photo-generated bulk carriers and interdigitizing shallow p+ junctions as the active region, the integrated photodiode operates up to 4.9 GHz with no process modification. Its responsivity was measured to be 0.016 A/W. With multi-inductive-series peaking technique, the improved ReGulated-Cascade (RGC) transimpedance amplifier achieves an experimentally measured -3dB bandwidth of more than 6 GHz and a transimpedance gain of 51 dBW, which is the fastest reported TIA in CMOS 0.35mm technology. The 5 GHz Gilbert cell mixer produces a conversion gain of 11 dB, which greatly minimized the noise contribution from the IF stage. The noise figure and input IIP3 of the mixer were measured to be 15.7 dB and 1.5 dBm, respectively. The IF amplifier and output buffer pick up and further amplify the signal for post processing. The optical front end demonstrates a typical equivalent input noise current of 35 pA=pHz at 5 GHz, and a total transimpedance gain of 83 dB ohm whileconsuming a total current of 40 mA from 3.3 V power supply. The -3 dB bandwidth for the optical front end was measured to be 4.9 GHz. All the prototype chips, including the optical front end, and the individual circuits including the photodiode, TIA, mixer were probe-tested and all the measurements were taken with Anritsu VNA 37397D and Anritsu spectrum analyser MS2721A.

This thesis outlines problems in the estimation of concentration value of an absorber present in a medium that is scattering and shortcomings of using the currently available techniques for the characterisation of such a scattering medium. The work describes experiment and analytic techniques used to overcome these problems. This thesis explored experimentally the practicality of using polarisation subtraction technique to minimise the effects of scattering components on the measured data. This work also considered the case when this technique has not been used owing to its limited application, and to that end, the improved linear equation and nonlinear fitting models, and gradient processing method were developed on the basis of the assumed behaviour of how a medium’s scattering coefficient changes with wavelength to provide information about the fractional concentration value of an absorber. The performance of these techniques evaluated via simulation showed that linear equation model has the fastest processing speed, nonlinear fitting method is robust to system noise and is able to provide an overall more accurate estimate of value with mean of errors of less than ±1%. The gradient processing method has intermediate performances with accuracy of its estimated value improved by about 30% with an increase in the spectral resolution from 1 nm to 0.5 nm. This work concludes that gradient processing method would be employed if accuracy of estimated value, noise robustness and computing time are of concern. However, nonlinear fitting method would be chosen in case high accuracy of the estimated value is required. Both of these methods can be suitably used as complementary techniques to clinical assessment of skin grafts and burnt skin. The simultaneous solution of linear equation model works well if all the measurement parameters are known.

This thesis discusses the development of a novel scanning capacitance microscope (SCM) that enables the investigation of the local capacitance and conductivity of surfaces and near-surface nanostructures at cryogenic temperatures and high magnetic fields. Simultaneous atomic force microscopy (AFM) and SCM measurements can be made at a temperature of 1.5K and a magnetic field of 12T. The AFM/SCM sensor is based on a quartz-tuning fork with an etched metal tip. SCM measurements are made using an RF tuned filter design which allows changes in capacitance to be measured with sub-attofarad resolution and a bandwidth of 200Hz. Test measurements were made over an evaporated gold film. The capacitance distance curve was recovered from the measured quantities using a deconvolution scheme normally used for force-distance curves. Measurements have been made of a two-dimensional electron gas in the quantum Hall effect (QHE) regime. Highly conductive stripes form near the edge of the sample at integer Landau level filling factors in agreement with theoretical predictions. These measurements are the first direct imaging of the compressible stripes at the physical edge of a Hall bar device. Measurements were also made by point spectroscopy in a region that was locally depleted. Around this region a ring-shaped stripe of considerably larger width than at the sample edge is observed. The increased width was explained in terms of a shallower potential gradient compared to the physical edge of the sample. Preliminary measurements have demonstrated that the microscope is capable of imaging edge states whilst passing current through the device.

A prototype ASIC (EFT1) for silicon strip detector instrumentation has been designed and tested. The ASIC design contains the electronics necessary for preamplification, shaping, hit detection, and data readout control. The specific­ ation of the ASIC makes it suitable for charged particle spectroscopy applications with the implementation of multiple channels on a single chip reducing the cost compared to expensive discrete instrumentation. The ASIC contains features which have not been implemented before, or are at least unusual, on integrated instrumentation such as the ability to select two gain ranges, the use of a flat­top shaper to increase integral linearity and a current­ driven discriminator output with adjustable voltage to reduce crosstalk effects on sensitive inputs. The testing performed on the ASIC revealed errors that can be removed in further design of the chip which will be implemented using radiation­hard silicon technology.

An investigation is undertaken into methods of fast modulation and detection of submillimetre radiation. Detection at room temperature was achieved with travelling wave antennae coupled to a crystal rectifier. Metal-oxide-metal and metal-oxide-semiconductor rectifying junctions were studied. Generation of submillimetre radiation was performed by means of a hydrogen cyanide laser, operating primarily at a wavelength of 337 mum. The investigation was motivated by a need for an increase in output power from the laser which requires a fast switch operative at submillimetre wavelengths. Evaluation of a Q-switching technique, utilizing the near coincidences between absorption features in various vapours and the 337 mum emission line of the HCN laser was made. Further investigations were carried out on the transient properties of the plasma that forms the active medium of a pulsed excited HCN laser. Shift of the resonance condition by means of an ancillary discharge is undertaken as a Q-switching technique. Magneto-optical modulation as an alternative switching technique was also studied. To this end, the temperature-dependence of the magneto optical constants of seven different rare-earth iron garnets were studied at a wavelength of 337 mum. The properties investigated include the Faraday rotation, absorption coefficient and the room temperature refractive index. The theory of the magneto-optical effects at microwave and optical frequencies is reviewed and extended into the sub-millimetre region. Effects of magnetic anisotropy are discussed.

Research on Bose Einstein condensates has over the past few years developed into an interesting field of physics. Current research aims for the creation of working quantum simulators which may be able to help explain and understand condensed matter physics phenomena which as yet cannot be explained. The research leading up to the experiment outlined in this thesis is intended to contribute to the understanding of these phenomena particularly that of 2D quantum systems. In the course of this thesis trapping and manipulation schemes for dipole traps and optical lattices will be introduced. Numerical simulations have been conducted to assess the dependency of parameters leading to a stable, optimised dipole trap. The design of an aspherical dipole trap was used, set up and characterised. Numerical simulations of maximally localized Wannier functions were carried out to obtain and understand the interactions in optical lattices and to postulate further parameters for the experiment. A fast and stable computer control was devised using the latest field-programmable-gate-array (FPGA) technology. The robustness and versatility of this technology was proved by adapting the software to suit different hardware and using the control in four different experiments. The electronic systems for the hardware used have been developed to yield a timing of 25ns for the digital channels and 1μs for the analogue channels.

General relativity describes gravity as the curvature of space-time. The theory predicts the existence of gravitational waves (GWs), which can be described as ripples in space-time propagating at the speed of light. So far no direct detection of GWs has been achieved. The sensitivities of the currently leading laser interferometric GW detectors are limited by various noise sources, i.e. seismic, thermal, shot noises etc. Several conceptual studies are underway investigating new techniques that aim to improve sensitivities enough to fulfil the requirements of the next generation of detectors. One of these new techniques under investigation is displacement and frequency noise free interferometry (DFI). This thesis reports on the experimental demonstration of a new method of partial DFI that is effective in the GW detection frequency band. The isolation of a mimicked GW signal from displacement noise of one mirror is demonstrated for a detuned Fabry-Perot cavity. A significant reduction in the displacement noise of the cavity input mirror was achieved by properly combining the reflected and transmitted signals from the cavity. This result represents the first experimental demonstration of this recently proposed DFI scheme, and lays the foundations for future work aimed at implementing DFI schemes in up-coming laser interferometric GW detectors.