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Adaptivity in bandstructure calculations of photonic crystals [Elektronische Ressource] / Axel Krämer

83 pages
¨Karlsruher Institut furTechnologieFachbereich MathematikAdaptivity in BandstructureCalculations of Photonic CrystalsAxel Kr¨amerVon der Fakult¨at fu¨r Mathematikdes Karlsruher Institut fu¨r Technologiezur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Willy D¨orfler2. Gutachter: PD Dr. Nicolas NeußVollzug der Promotion: 26. Januar 2011AcknowledgementsI am very grateful to Deutsche Forschungsgemeinschaft for the PhD scholarship.I enjoyed my work in the GRK 1294 and the working environment was excellent.I would especially like to thank Prof. Dr. Willy D¨orfler for supervising and sup-porting my thesis, many helpful discussions, and thought-provoking impulses. I amgrateful for his contributions to my work and for keeping me up to date with recentdevelopments inmyfieldofresearch. IwouldalsoliketothankPDDr.NicolasNeußfor his advice and for always being available to discuss problems.Last but not least, I would like to thank my colleagues from the GRK and theKIT for the nice working atmosphere and for helpful discussions.iiiContentsAcknowledgements iiiPreface viiChapter I. Introduction 11. Problem statement 11.1. Maxwell’s equations 11.2. Polarized modes 21.3. Periodic media and the band structure of a photonic crystal 3Chapter II. Adaptive bandstructure calculations 71. Approximating the bandstructure 72.
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