Advancement of Algebraic Function Approximation in Eigenvalue Problems of Lossless Metallic Waveguides to Infinite Dimensions, Part III: Examples Verifying the Theory

Abstract

Verifications of the theory for extension of the algebraic function approximation in closed, lossless guiding system eigenvalue problems to infinite dimensions, are given. Numerical verifications are made on a closed circular guide loaded with a coaxial dielectric rod. The defective nature of an eigenvalue at the onset of a complex wave mode is demonstrated both in the algebraic function approximation and in infinite dimensions. At a cutoff frequency, for the exact infinite system, analyticity of the eigenvalue, but singularity of the propagation constant, are checked numerically. It is observed that in exact analysis too, by itself a complex wave mode does not take part in energy transportation, but a pair of complex conjugate modes behaves as an evanescent wave.