The Mathematical Institute, University of Oxford, Eprints Archive

High frequency asymptotics of antenna/structure interactions

Coats, J. (2002) High frequency asymptotics of antenna/structure interactions. PhD thesis, University of Oxford.



This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors.

We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point.

In chapter 5 we review and extend the asymptotic results concerning illumination of a convex perfect conductor by an incident plane wave and outline the procedure for decoupling the electromagnetic surface field into two scalar modes. In chapter 6 we place a source on a perfect conductor and obtain a complete asymptotic solution for the fields. Special attention is paid to the asymptotic structure that smoothly matches between the leading order lit and shadow regions. We also investigate the degenerate case where one of the curvatures of the perfect conductor is zero. The case where the source is just off the surface is also investigated. In chapter 8 we use the Euler-Maclaurin summation formula to cheaply calculate the fields due to complicated arrays of point dipoles.

The final chapter combines many earlier results to consider more general sources on the surface of a perfect conductor. In particular we must introduce new asymptotic regions for open sources. This then enables us to consider the focussing of the surface field due to a finite source. The nature of the surface and geometrical optics fields depends on the size of the source in comparison to the curvatures of the surface on which they lie. We discuss this in detail and conclude with the practical example of a spiral antenna.

Item Type:Thesis (PhD)
Subjects:O - Z > Partial differential equations
A - C > Approximations and expansions
O - Z > Optics, electromagnetic theory
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:44
Deposited By: Eprints Administrator
Deposited On:11 Mar 2004
Last Modified:29 May 2015 18:15

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