Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

First part of this dissertation studies the problem of designing metamaterial crystals with double negative effective properties for applications in optics by investigating the conditions necessary for generating novel dispersion properties in a metamaterial crystal with subwavelength microstructure. This provides novel optical properties created through local resonances tied to the geometry of the media in subwavelength regime.

In the second part, this dissertation studies the representation formula used to describe band structures in photonic crystals with plasmonic inclusions. By using layer potential techniques, a magnetic dipole operator describing the tangential component of the electrical field generated by magnetic distribution is studied. Its compactness is proved and used to obtain the spectral representation formula for the magnetic field.

Date

6-19-2019

Committee Chair

Lipton, Robert

Available for download on Wednesday, June 17, 2020

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