Mathematical theory of normal waves in an open metal-dielectric regular waveguide of arbitrary cross section

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 formulat...

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Published inMathematical modelling and analysis Vol. 25; no. 3; pp. 391 - 408
Main Authors Smolkin, Eugene, Smirnov, Yury
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 13.05.2020
Subjects
Analysis
Boundary conditions
Cross-sections
discrete spectrum
Eigenvalues
Electromagnetic fields
Electromagnetism
Mathematical analysis
Maxwell's equations
non-linear eigenvalue problem
operator-function
Permeability
Propagation
Sobolev space
Sobolev spaces
Wave propagation
Waveguides
discrete spectrum
Maxwell's equations
non-linear eigenvalue problem
Sobolev spaces
operator-function
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.10682