Abstract
The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found.
Highlights
Analysis of wave propagation in open metal-dielectric waveguides constitutes an important class of vector electromagnetic problems
We have reduced the boundary eigenvalue problem for the Maxwell equations describing normal waves in a broad class of non-homogeneously filled waveguides to an eigenvalue problem for an operator-function
We have proved fundamental properties of the spectrum of normal waves including the discreteness and a statement describing localization of eigenvalues of the operator-function on the complex plane
Summary
Analysis of wave propagation in open metal-dielectric waveguides constitutes an important class of vector electromagnetic problems. The spectral parameter appears only usually in the equations and does not enter into transmission conditions, and so we have an eigenvalue problem for the usually self-adjoint operator. For open (unshielded) structures, a complete theory of wave propagation is not constructed In this case the problem becomes much more complicated (due to the non-compactness of the corresponding operators). The first results on the investigation of such problems were recently obtained in [20, 23, 24, 25] for a circular waveguide These difficulties can be overcome by introducing a fictitious outer region (the exterior of the circle) and representing the solution in this region in terms of the Green’s function. This approach was used to study the shielded waveguide structures as well [21, 22]
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