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Abstract-The problem of studying modal characteristics of metallic waveguides filled with lossless inhomogeneous and/or anisotropic media, is one of studying properties of the propagation constant of the guiding structure. It is shown that modal behavior in the neighborhood of critical frequencies such as cutoff frequencies and frequencies marking the onset of complex wave mode intervals, can be modeled through approximation of the propagation constant by a root of an algebraic equation. The particular form of the algebraic function approximating the propagation constant is discussed in the neighborhood of a singularity. A numerical example is included to stress the viability of the technique.

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