Application of Algebraic Function Theory to Backward Wave Problems

Abstract

The problem of studying backward wave mode characteristics of metallic waveguides filled with inhomogeneous and/or anisotropic media, is equivalent to understanding properties of the propagation constant of the guiding structure. In this paper we focus on metallic waveguides filled with inhomogeneous and/or anisotropic media that do not couple transverse to longitudinal field components and note that the propagation constant of such structures is the solution of an algebraic equation. This feature permits application of the well developed theory of algebraic functions to understanding of the backward wave mode behavior of the propagation constant. We show that the problem of assessment of backward wave modes for such guides fits exactly in this theory, and using this fact, numerous results are derived which may be used in the design of backward wave systems.