A theoretical and computational investigation of electromagnetic fields in complementary and self-complementary structures

This dissertation focuses on electromagnetic fields in complementary and self-complementary structures. As is well known, the Maxwell equations that govern the electric and magnetic vector fields exhibit a symmetry between these two fields. For any given field solution satisfying perfect electric conductor or perfect magnetic conductor conditions on surfaces of the defining structure, a second, dual or complementary solution, involving an interchange of electric and magnetic quantities, follows. In general, this second field solution satisfies different, dual or complementary conditions on the surfaces of the complementary structure. This complementary structure is obtained by replacing surfaces with perfect electric conductor boundary conditions in original defining structure, with surfaces with perfect "magnetic conductor" conditions, and conversely. When the original and complementary structures are described in terms of equivalent microwave networks, their impedance/admittance parameters are complementary.; This dissertation departs from previous work in that it rigorously treats the electromagnetic field within the waveguide-leads into a self-complementary structure. It is found that the modal field in the waveguide-lead must be a pure traveling TEM wave. This is a necessary feature of such self-complementary field solutions, and the dissertation provides a number of illustrative structures that support self-complementary field solutions. The characteristic impedances of these structures are obtained from their self-complementary property and independently through conformal mapping.; A new self-complementary waveguide structure is devised that illustrates circumstances when a self-complementary field solution fails to exist. A computer model was developed to analyze a related family of waveguide structures which differ only in an aspect ratio parameter and, independently, the corresponding complementary waveguide structure; for an aspect ratio of unity, the structure is self-complementary. Results are presented for a wide range of frequencies and aspect ratios. At low frequencies, when only one (TEM) mode propagates, a traveling wave self-complementary field solution in the input TEM mode waveguide-lead may be excluded on the basis of conservation of energy. In this frequency range, field solutions obtained for aspect ratios less than one and for aspect ratios greater than one exhibit a discontinuous behavior as the aspect ratio approaches one. Thus, no self-complementary field solution exists for the self-complementary waveguide structure, and the input impedances for aspect ratios greater and less than one do not, in any sense, approach the value predicted for a self-complementary solution. At high frequencies, when nearly pure traveling wave type solutions are obtained for the input TEM mode, the input impedances for aspect ratios greater and less than one do approach the value predicted for a self-complementary solution. (Abstract shortened by UMI.)...