Analysis of the spectrum of azimuthally symmetric waves of an open inhomogeneous anisotropic waveguide with longitudinal magnetization

An eigenvalue problem for the normal waves of an inhomogeneous regular waveguide is considered. The problem reduces to the boundary value problem for the tangential components of the electromagnetic field in the Sobolev spaces. The inhomogeneity of the dielectric filler and the presence of the spectral parameter in the field-matching conditions necessitate giving a special definition of the solution to the problem. To define the solution, the variational formulation of the problem is used. The variational problem reduces to the study of an operator function nonlinearly depending on the spectral parameter. The properties of the operator function, necessary for the analysis of its spectral properties, are investigated. Theorems on the discreteness of the spectrum and on the distribution of the characteristic numbers of the operator function on the complex plane are proved. Real propagation constants are calculated. Numerical results are obtained using the Galerkin method. The numerical method proposed is implemented in a computer code. Calculations for a number of specific waveguiding structures are performed.