449 research outputs found

    The Design and Optimisation of Quasioptical Telescopes

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    The main focus of this thesis is the analysis and optimisation of systems that operate in the terahertz and submillimetre wavebands. Analysis is carried out on the MBI and ALMA interferometers, and on the HIFI instrument on the Herschel Space Observatory (HSO). MBI is a novel instrument designed to test the technique of bolometric nterferometry. ALMA is a 50 element hetrodyne interferometer, currently being constructed in Chile. It is demonstrated that in both MBI and ALMA, the coupling of the signal to the detector horns may be improved by imposing a phase on the field from the sky; a number of possible configurations are considered. HIFI is a high resolution spectrometer, one of three instruments on the HSO. Simulations of the lens antennas used to detect the radiation in the higher frequency channels in HIFI were carried out. A number of methods used to determine the phase centre of the beam from lens antennas are described, and use is made of the same optimisation techniques as for the MBI and ALMA work. As the beams propagating in these systems can be analysed accurately using the paraxial approximation, Gaussian Beam Mode Analysis can be used to simulate the field, and is the main analytical tool used here. Methods of beam shaping are investigated to gain an insight into how coupling may be increased in these systems, and also to design Diffractive Optical Elements (DOEs) for use at terahertz and submillimetre wavelengths in general. The standard methods of the Gerchberg-Saxton Algorithm, and unidirectional optimisation using Differential Evolution and Simulated Annealing are applied to design DOEs. A novel approach using Gaussian Beam Mode Analysis is described. Here, the Gaussian Beam mode coefficients describing a field are optimised to achieve a desired amplitude distribution at a specified plane or planes. This approach was found to achieve highly optimal results, and has a number of benefits over the other methods

    Computational Inverse Problems for Partial Differential Equations

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    The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges

    Ab-initio multimode linewidth theory for arbitrary inhomogeneous laser cavities

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    We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g. a bad-cavity correction to the Henry α\alpha factor and a multimode Schawlow--Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell--Bloch equations, we handle quantum and thermal noise by introducing random currents whose correlations are given by the fluctuation--dissipation theorem. We derive coupled-mode equations for the lasing-mode amplitudes and obtain a formula for the linewidths in terms of simple integrals over the steady-state lasing modes.Comment: 24 pages, 7 figure

    Traveltime based true amplitude migration

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    X-shaped space-time coherence in optical parametric generation

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    We study the spatiotemporal coherence properties of superfluorescence radiation generated in optical parametric amplification of quantum noise. We show that the angular dispersion properties of the spatiotemporal spectra, measured in different phase-matching conditions, lead to a clear X-shaped structure of the mutual correlation function of the radiation. Within a statistical picture, we interpret the generated superfluorescence as a stochastic \u201cgas\u201d of quasistationary modes characterized by a skewed correlation in the spatiotemporal domain, with characteristics similar to linear and nonlinear X waves not describable within a separable approach in space and time
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