Existence of an Infinite Spectrum of Damped Leaky TE Waves in an Open Inhomogeneous Cylindrical Metal–Dielectric Waveguide

Abstract

We consider the problem about leaky waves in an inhomogeneous waveguide structure. This problem is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. A variational problem statement is used to determine the solution. The variational problem is reduced to studying an operator function. The properties of this operator function necessary for analyzing its spectral characteristics are investigated. Theorems about the discreteness of the spectrum and the distribution of the characteristic numbers of the operator function on the complex plane are proved. The existence of infinitely many damped leaky waves in a cylindrical waveguide is established.