Mode nomenclature in imperfect waveguides

The problem of mode nomenclature in a general, lossy, inhomogeneous waveguide is discussed. It is shown that the limit approached by a given mode in a general guide, as the guide is conceptually reduced to a homogeneous, simple, perfect guide by continuous variation of parameters, depends on the path by which the reduction is carried out. This is because of the existence of branch points of the complex propagation constant, considered as a function of the guide parameters. Mode nomenclature in a general guide can be made unique in various ways, by dividing the complex propagation-constant plane into regions separated by branch cuts across which the designation of a given mode changes discontinuously. The theoretical analysis depends on the properties of implicit functions of a complex variable. Numerical illustrations are drawn from the work of Waldron and Bowe and of Morgan and Young on modes in lossy-wall helix waveguide.