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    METASURFACES AND WAVEGUIDES IN OPTICS

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    Genre
    Thesis/Dissertation
    Date
    2019
    Author
    Pallucchini, Luca
    Advisor
    Gutiérrez, Cristian E., 1950-
    Committee member
    Berhanu, Shiferaw
    Rider, Brian (Brian C.)
    Futer, David
    Riseborough, Peter
    Department
    Mathematics
    Subject
    Mathematics
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/3380
    
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    DOI
    http://dx.doi.org/10.34944/dspace/3362
    Abstract
    This thesis analyzes metasurfaces and waveguides in geometric optics. In the first and second chapters, we give a mathematical approach to study metasurfaces. A metasurface is a surface together with a function called phase discontinuity. The phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We give analytical conditions between the curvature of the surface and the set of refracted directions to guarantee the existence of phase discontinuities. The approach contains both the near and far field cases. A starting point is the formulation of a vector Snell’s law in the presence of abrupt discontinuities on the interfaces. Also, we derive the equations that the phase discontinuity function must satisfy in order for the metasurface to refract or reflect energy with a prescribed energy pattern, they are Monge-Amp\'ere partial differential equations, and we prove the existence of solutions. In the third chapter, we model energy losses in waveguides. In particular, we give quantitative estimates of the energy internally reflected in case of a straight guide and a circularly curved guide. We give a detailed ray tracing and internally reflected energy analysis for each striking point on the boundary of the guide.
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