Electrical and Computer Engineering ETDs

Publication Date

6-3-1964

Abstract

The central problem of this work will be the development of several approximation methods and the application thereof to the solution of second order linear differential equations which arise in connection with the propagation of electromagnetic radiation in inhomogeneous media. Chapter I is an introduction to the problem. Maxwell’s equations are written down and it is assumed that both σ, the conductivity, and ɛ, the permittivity, are scalar functions or position. Often the above function characterizing some or the properties of matter vary in physical situations. For example, in waveguides, there may be inserted layers of dielectric material along the length of the guide, in which case ɛ varies discontinuously with position. Again, the permittivity and conductivity of the atmosphere may vary as a function of height above the earth’s surface. We shall be primarily interested in wave propagation in plane, cylindrical, and in spherical coordinate systems. After writing down Maxwell’s equations, we shall develop the second order differential equations mentioned above in the coordinate systems of interest. It will be seen that such task will be simplified if assumption regarding the way in which ɛ and σ vary are used. In Chapter II, we shall develop the approximation methods mentioned earlier. These consist of iterative methods, iteration-­variation methods, and so-called "invariant imbedding" method, and finally one integral formulation method. In Chapter III, we shall apply the approximation methods developed in Chapter II to a discussion of several problems of some practical interest. Whenever possible, we shall compare the results we obtain with previous approximate, or with exact numerical, results.

Document Type

Thesis

Language

English

Degree Name

Electrical Engineering

Level of Degree

Masters

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

William Jackson Byatt

Second Committee Member

Donald Childress Thorn

Third Committee Member

Joseph S. Lambert

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