Eigenwaves in a lossy metal-dielectric waveguide. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Smirnov, Yury; Smolkin, Eugene
• Is Part Of: Applicable analysis. Volume 99:Issue 1(2020)
• Page Start: 1
• Page End: 12
• Publication Date: 2020-01-02
• Subjects: Lossy metal-dielectric waveguide -- nonlinear eigenvalue problem -- Maxwell's equations -- operator-function -- spectrum -- double completeness of system of eigenvectors and associated vectors with a finite defect; 34B07 -- 47A10 -- 78A50 -- 35P10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1478084
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The problem of normal waves in a closed (shielded) 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 an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operator-function on the complex plane is found. We also consider properties of system of eigenvectors and associated vectors of the operator-function. Double completeness of system of eigenvectors and associated vectors with a finite defect is established.