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An analysis of leaky‐wave dispersion phenomena in the vicinity of cutoff using complex frequency plane singularities
Author(s) -
Hanson George W.,
Yakovlev Alexander B.
Publication year - 1998
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/98rs01440
Subject(s) - cutoff frequency , wavenumber , cutoff , dispersion (optics) , gravitational singularity , dispersion relation , complex plane , boundary value problem , boundary (topology) , mathematical analysis , frequency domain , physics , plane (geometry) , plane wave , function (biology) , modal dispersion , optics , mathematics , geometry , quantum mechanics , fiber optic sensor , evolutionary biology , optical fiber , dispersion shifted fiber , biology
In this paper we analyze characteristics of the dispersion function for leaky‐wave modes in the vicinity of cutoff for several representative waveguiding structures. Our principal purpose is to demonstrate that in the vicinity of leaky‐wave cutoff in open‐boundary waveguides (in the spectral‐gap region), dispersion behavior is controlled by the presence of branch points in the complex frequency plane. A similar situation occurs for the ordinary modes of homogeneously filled, perfefctly conducting cylindrical waveguides. These closed waveguides admit to simple analysis, leading to an explicit dispersion function which indicates frequency domain branch points. For open‐boundary waveguides, the presence of frequency domain branch points is obscured by the necessity of numerically solving an implicit dispersion equation. A set of sufficient conditions is provided here which defines these branch points in a unified manner for both open and closed waveguides. Identification of these points allows for rapid determination of important and interesting regions in both the frequency and wavenumber planes and leads to increased understanding of dispersion behavior, especially in the case of dielectric loss. Examples are shown for several waveguiding geometries to demonstrate the general nature of the presented formulation.