Eigenvalues in Uniform Waveguides Using Transmission Line Equivalences

In recent years the rapid development in millimeter wave frequencies, fiber optics and integrated optics has made the use of arbitrary shaped dielectric waveguides more common. This arbitrariness in the geometry of waveguides makes obtaining of analytical solutions even more difficult. It is shown that with the aid of transmission line equivalences, it is possible to make an approximation to calculate the propagation constants of some uniform waveguides. The first step of the method consists in covering the waveguide with a perfectly conducting shield. Even though this screening transforms the radiation type of modes of the open waveguide into discrete spectra, the surface type modes are not affected very much. The novel approach presented is to use as eigenfunctions in series expansions of fields, solutions of a structure which has the same external conducting surface as the screened structure, but which has a transverse geometry which is preferred more, the more it resembles the optical waveguide at hand, and which at the same time admits an analytical solution as opposed to the method of using as eigenfunctions, the solutions of a homogeneously filled structure for this aim.