Since the beginning of the industrial revolution (1750 to 1800) the Earth’s atmospheric composition has undergone significant change as a result of human activities, in particular the burning of fossil fuels. As a consequence the atmospheric concentrations of a number of gases known to be influential to the Earth’s climate have increased far beyond natural levels. Atmospheric gases such as carbon dioxide which naturally exist in the Earth system have increased in correlation with anthropogenic emissions. The effect of this perturbation on the Earth system has been predicted through computer simulations to have undesirable consequences on the Earth’s future climate. The present measurement systems for atmospheric carbon dioxide have limited spatial coverage and temporal resolution which restricts their ability to accurately attribute observations of atmospheric composition to particular terrestrial sources and sinks. This inability to accurately locate and quantify the key carbon dioxide sources and sinks in the terrestrial and marine biospheres is hindering the understanding of the processes that are driving the Earth’s natural uptake of approximately half of the anthropogenic carbon dioxide emissions. With such uncertainty it is currently unknown precisely how the Earth’s climate will respond to global warming in the future. Through computer simulation it has been demonstrated that improving the spatial distribution of global measurements of atmospheric carbon dioxide is likely to advance the present understanding of the Earth’s terrestrial sources and sinks. Regions that require particular improvement in measurement coverage are the southern oceans owing to a lack of landmass on which to site instruments, and much of the tropics because of difficulties in locating instruments in some of the worlds more politically unstable regions. Satellite remote sensing instruments which measure atmospheric carbon dioxide from low Earth orbit provide some coverage of these sparsely sampled locations, however cloud cover often prevents measurements being made (particularly in the tropics), and limited latitudinal coverage caused by current instruments using passive remote sensing techniques prevents measurements at very high and low latitudes (including much of the southern ocean during local winter). An alternative remote sensing technique has been proposed in the scientific literature for measuring atmospheric carbon dioxide concentrations using laser emissions from a satellite platform known as total column differential absorption LiDAR (TC-DIAL). The TC-DIAL technique has been identified as having the theoretical potential to meet the coverage and precision requirements to greatly aid in identifying and quantifying terrestrial carbon dioxide sources and sinks. The TC-DIAL technique has the potential to achieve these goals largely owing to its unique capabilities of being able to make measurements during both the day and night and at all latitudes with a footprint which may be small enough to see between patchy cloud cover in the tropics. This thesis builds on previous studies of the TC-DIAL measurement technique from a satellite platform to assess its current and future capabilities to meet the observation requirements defined by the atmospheric carbon and modeling scientific communities. Particular investigations are carried out to assess the optimum system configuration in the context of global carbon modeling using up-to-date spectroscopy and instrument parameters for the latest technology. Optimum systems for both direct and heterodyne detection TC-DIAL instruments are defined, and it is found that direct detection provides the lowest retrieval errors under clear sky conditions. For a system based on current technology TC-DIAL retrievals are expected to have errors of approximately 0.68 ppm for direct detection and 1.01 ppm for heterodyne detection over a 50 km surface track. Using global cloud statistics two suitable pulse repetition frequencies (PRF) for a heterodyne detection system have been identified as 5 and 15 kHz. These PRF’s provide the minimum probability of an effect known as cross signal contamination occurring when measurements are made in the presence of cloud. In this thesis it is shown that the retrieval error incurred by cross signal contamination is > 16 ppm for a heterodyne detection TC-DIAL system measuring through cloud with optical depth > 2. The most important retrieval error component in TC-DIAL retrievals has been found to be the uncertainties introduced by the use of numerical weather prediction data for the ancillary atmospheric profiles. The limited spatial resolution of current NWP models (> 20 km) implies the uncertainties associated with the ancillary data are required to be treated as systematic, and as a consequence their errors dominate over other TC-DIAL retrieval errors following multiple pulse integration.

This thesis presents experimental and simulation results on electron acceleration from the interaction of ultra-intense, ultra-short lasers with underdense plasmas, based on two schemes of the Laser Wakefield Acceleration (LWFA) mechanism. Using the 100 TW laser, in LUll, France, with pulse durations of 500 fsec and intensities' greater than 5.1018 W/cm2 , electron energies of up to 200 MeV,)Here observed. The spectra of the electron beams exhibit a maxwellian distribution, which together-with the recording of the Raman satellites of the laser spectrum suggest that we operate in the Self Modulated-LWFA, making these beams the highest energy observed to date, in that scheme. Total charge estimates suggest that a 1% energy transfer to the electron beam is possible. Occasional non-maxwellian features in the electron spectra, backed up by simulations, suggest that mechanisms other than SM-LWFA are also present in the interaction. Most importantly, self-guiding channels of - cm scales are observed adding a new perspective in achieving a commercially viable LWF accelerator. In the classical short pulse regime of LWFA, the ASTRA (0.6 J, < 50 fsec) laser is used to compare electron acceleration, with and without an external waveguide. Maximum electron energy results in the self-guided regime are only 2x lower compared to the externally guided case. The stability and reproducibility of the beam however, is improved when the external waveguide is used. Electron beams with 200 MeV maximum energy and narrow energy spread are consistently observed. The appearance of these beams is strongly linked with ionisation effects, either from high ion states of waveguide wall material, or recombined gas. A particle tracking code shows that electrons released from ionisation processes within the laser pulse, and hence within the plasma wake, are trapped by the wake and accelerated, pro.ducing a bunch with low energy spread. These lay the basis for future experiments, envisaging improved stability, wall-plug energy transfer efficiency and high brilliance electron beams.

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This thesis studies the response of atoms and molecules to intense few-cycle laser pulses. It is the extremely high frequency dipole radiation generated from such a response that is of interest, both for its exploitation towards generating isolated attosecond pulses and because of the information such radiation contains concerning the laser pulse and electronic wavefunction responsible for its generation. Using a variety of models the process of high order harmonic generation in single atoms is studied in detail to reveal its underlying structure. The high harmonic spectrum is formed from bursts of radiation released every half-cycle of the laser field. The sensitivity of this half-cycle radiation to the precise waveform of the laser field is investigated. In particular the implications of these sensitivities to the stability of attosecond pulse production is studied. The work on single atom high harmonic generation is utilised towards investigations into the high harmonic generation from a volume of atoms. Propagation of the fields through such a volume greatly affects the final spectrum due to phase-matching. A new phenomenon is presented due to this phase-matching which leads tdthe manifestation of half-cycle cut-offs in the propagated spectra. A powerful new technique for measuring few-cycle pulse properties, utilising these half-cycle cut-offs, is developed and demonstrated. It is found capable of measuring the absolute carrier-envelope phase of the driving laser field to within 50 mrad, the highest accuracy of such a measurement achieved to date. The use of spatio-spectral filtering for isolating a half-cycle cut-off is proposed as a method for generating wavelength tunable attosecond pulses. Finally, work is carried out towards the development of a strong field approximation model capable of simulating high harmonic generation from molecules. Such a model is found to be suitable for such calculations and an interesting interference regime is commented on.

Lasers with stability of the order of 10.15 or more form the basis of frequency metrology and several other experiments including gravitational wave detection, high-precision spectroscopy and tests of relativity. This thesis describes the frequency stabilization of 1064nm, Nd:YAG lasers to ultra-stable, high finesse Fabry-Perot cavities using the PoundDrever- Halliocking scheme. These lasers will be used as flywheel oscillators for optical atomic clocks. The first part of this thesis describes the design and development of a stable laser using a cryogenic, all-sapphire, high finesse Fabry-Perot cavity. Two similar systems have been developed and the beat frequency between the two systems has been measured. This beat frequency measurement provides a measure of relative stability of the laser. In addition experiments have also been performed with ULE (ultra-low expansivity) glass cavities. The thermal expansivity of ULE has a zero near room temperature and a turning point was found. A beat frequency measurement was made for a pair of lasers locked to ULE cavities.The frequency stabilization techniques applied to the lasers described in this thesis will be used for future frequency standards based on optical transitions.

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The subject of this thesis is a study of the two-component nonlinear Schrodinger equation (NSE) in (1+1)-dimension. Two aitemative cases are possible, referred to as the focusing and defocusing cases in applications to studies in nonlinear optics. The main focus of the work in this thesis is on the defocusing case, but results known for the focusing case are also discussed and compared, where relevant. This thesis is comprised of two themes. The first is the effective integration of the NSE, using techniques of algebrogeometric theory. Here, the Baker-Akheizer formalism is developed and applied to the Manakov system. This formalism is used to derive the finite-gap solution, expressed in terms of Riemann theta-functions. The second is the derivation of soliton solutions from these finite-gap solutions, by considering an important limit; namely, the closing ofthe gap in the Riemanu surface associated with. the spectral curve yields explicit representations for soliton solutions. The scalar NSE is first considered by way of introducing and discussing relevant techniques. Then, it is shown how these methods can be extended to the vector case. Next, two particular cases are considered. Firstly, it is shown that the genus 1 case yields a dark-dark soliton solution in the limiting case. An aspect of the vector problem not found with the scalar case is the existence of dark-bright solitons. A single dark-bright soliton can be obtained by considering genus 2, not genus 1, in the soliton limit. A discussion of these derivations is an important feature of the thesis. We discuss next a solution obtained elsewhere introducing a separable ansatz for both components shown to be a genus 2 solution. We discuss the fact that the appropriate curve is hyperelliptic, and indicate how it is related to our trigonal curve by a birational map.