3. Electronic Theses and Dissertations (ETDs) - All submissions

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    Long distance data transfer using spatial modes of light
    (2018) Gailele, Lucas Mushimanekgapi
    Free space optical communication has been the subject of interest recently and has been identified as an alternative to fibre communication. Communication using the spatial modes of light is the focus of this dissertation. While propagating in free space, spatial modes are able to carry orbital angular momentum (OAM). OAM carrying spatial modes are orthogonal throughout their propagation and they span the discrete infinite dimensional Hilbert space allowing for (in theory) infinite information transfer to be carried throughout propagation. We are particularly interested in Laguerre-Gaussian (LG) modes and the azimuthal (Vortex) modes to send information. We discuss the principle of generating and detecting spatial modes by tailoring the dynamic phase of the spatial mode of light using a spatial light modulator (SLM). We will also characterized the communication link by giving a detailed overview of optical turbulence and how we measure the optical turbulence parameter. We will also give a link budget calculation describing the performance of the communication system.
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    Forward and inverse spectral theory of Sturm-Liouville operators with transmission conditions
    (2017) Bartels, Casey Ann
    ForwardandinversespectralproblemsconcerningSturm-Liouvilleoperatorswithoutdiscontinuitieshavebeenstudiedextensively. Bycomparison,therehasbeenlimitedworktacklingthecase where the eigenfunctions have discontinuities at interior points, a case which appears naturally in physical applications. We refer to such discontinuity conditions as transmission conditions. We consider Sturm-Liouville problems with transmission conditions rationally dependent on the spectral parameter. We show that our problem admits geometrically double eigenvalues, necessitating a new analysis. We develop the forward theory associated with this problem and also consider a related inverse problem. In particular, we prove a uniqueness result analogous to that of H. Hochstadt on the determination of the potential from two sequences of eigenvalues. In addition, we consider the problem of extending Sturm’s oscillation theorem, regarding the number of zeroes of eigenfunctions, from the classical setting to discontinuous problems with general constant coefficient transmission conditions
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