Advancement of Algebraic Function Approximation in Eigenvalue Problems of Lossless Metallic Waveguides to Infinite Dimensions, Part I: Properties of the Operator in Infinite Dimensions

Abstract

In an attempt to advance finite dimensional algebraic function approximation technique in eigenvalue problems of lossless metallic guides filled with anisotropic and/or inhomogeneous media, to exact analysis in infinite dimensions, properties of the linear operator in infinite dimensions corresponding to Maxwell's equations, are investigated. Some function theoretic aspects of this operator formalism for guidance phenomenon are discussed. It is found that this operator can be considered bounded and holomorphic. If not, because of poles the medium constituent matrices ε and μ may have, its inverse, which will be bounded and holomorphic, can be used to assess propagation constant behavior in the neighborhood of the singularity.