Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the particles comprising the metasurface. Arising from this asymptotic formula is the polarization tensor which describes how the metasurface interacts with light based on the component particles’ dielectric permittivity and geometry. We then use the polarization tensor to derive key optical constants for the metasurface such as the reflection and transmission coefficients for normal incidence.

Date

7-16-2024

Committee Chair

Robert Lipton

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