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

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.

Keywords

• non-linear eigenvalue problem
• Maxwell's equations
• operator-function
• Sobolev spaces
• discrete spectrum