Eigenwaves in a lossy metal-dielectric waveguide

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.

KEYWORDS:

• 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

AMS SUBJECT CLASSIFICATIONS:

• 34B07
• 47A10
• 78A50
• 35P10

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yury Smirnov  http://orcid.org/0000-0001-9040-628X

Eugene Smolkin  http://orcid.org/0000-0003-0168-0282

Additional information

Funding

This work was supported by the Ministry of Education and Science of the Russian Federation [grant number 1.894.2017/4.6].