Date of Award

Spring 2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

John A. Adam

Committee Member

Gordon Melrose

Committee Member

Daniel Gunlycke

Committee Member

Tony Slaba

Committee Member

Linda Vahala

Abstract

With applications in the areas of chemistry, physics, microbiology, meteorology, radar, astronomy, and many other fields, electromagnetic scattering is an important area of research. Many everyday phenomena that we experience are a result of the scattering of electromagnetic and acoustic waves. In this dissertation, the scattering of plane electromagnetic waves from radially inhomogeneous spheres and cylinders using both ray- and wave-theoretic principles is considered. Chapters 2 and 3 examine the use of the ray approach. The deviation undergone by an incident ray from its original direction is related to the angle through which the radius vector turns from the point at which the ray enters the sphere to its point of exit. This angle can be expressed in terms of a complicated improper integral. The resulting deviation for several different refractive index profiles (some being singular) is examined to investigate properties of the refractive index profiles that allow for direct transmission bows to exist. In Chapter 4, the complementary approach of wave-theoretic analysis leads to the construction of exact electromagnetic solutions for the asymptotic backscattered field produced by an incident plane wave. This has direct relevance to radar applications in particular. The radial eigenfunctions can be evaluated exactly (and also asymptotically) for the transverse electric and transverse magnetic modes. This allows a determination of the high-frequency backscattered field by means of a modified Watson transformation.

DOI

10.25777/ny68-hh36

ISBN

9781303882081

Included in

Mathematics Commons

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