Self-Complementary EM Fields in Self-Complementary Structures

I. Gheorghisor and W.K. Kahn (USA)


Modeling, waveguide, simulation, self-complementary fields and structures


This paper analyzes electromagnetic fields in complementary and self-complementary structures. As is well known, Maxwell’s equations exhibit a symmetry between the electric and magnetic fields. Self complementary field solutions (when these exist) on self complementary structures have particular properties of constant impedance (resistance) associated with pure traveling wave fields. The contribution of this paper is that it rigorously treats the electromagnetic field in a waveguide self-complementary structure, and it shows a self-complementary field solution as a pure traveling TEM wave. A new waveguide structure is devised that illustrates circumstances when a self-complementary field solution fails to exist in a self-complementary structure. A computer model was developed to analyze a family of waveguide structures that differ only in an aspect ratio parameter, an aspect ratio of 1.0 corresponding to the self complementary case. At low frequencies (one mode propagating), field solutions for the input TEM mode exhibit discontinuous behaviour as the aspect ratio approaches 1.0 from above and below. No self complementary field solution exists for the precisely self complementary waveguide structure, and the input impedances for aspect ratios greater and less than 1.0 do not, in any sense, approach the value predicted for a self complementary solution.

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