Discreteness of the Leaky Wave Spectrum of an OpenInhomogeneous Metal–Dielectric Circular-Section Waveguide

We consider the leaky wave problem for an open inhomogeneous metal–dielectric circular-section waveguide. The problem is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. The inhomogeneity of the dielectric filling and the fact that the spectral parameter occurs in the matching conditions necessitate defining the solution of the problem in a special way. To define the solution, we use a variational statement of the problem. The variational problem is reduced to studying an operator function. The properties of the operator function needed for the analysis of its spectral characteristics are studied. Theorems on the discreteness of the spectrum and on the distribution of eigenvalues of the operator function on the complex plane are proved.