Identifier

etd-07072016-223744

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

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.

Date

2016

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Lipton, Robert

DOI

10.31390/gradschool_dissertations.2462

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