The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result of this analysis is a uniformly convergent power series representation of Bloch-wave eigenvalues in terms of the coupling constant k in the high-contrast limit k -> infinity. An explicit radius of convergence for this power series is obtained, and can be written explicitly in terms of the Bloch-wave vector, the Dirichlet eigenvalues of the inclusion geometry, and a lower bound on another spectrum known as the " generalized electrostatic resonances " . This lower bound is derived from geometric properties of the inclusion geometry for the photonic crystal.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-07072016-223744 |
| Date | 15 July 2016 |
| Creators | Viator Jr, Robert Paul |
| Contributors | Davidson, Mark, Shipman, Stephen, Lipton, Robert, Litherland, Richard, Hoffman, Jerome, Dey, Joyoni |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-07072016-223744/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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