On spectrum's discrete nature in the problem of azimuthal symmetrical waves of an open nonhomogeneous anisotropic waveguide with longitudinal magnetization

Background. The aim of the work is to research a spectrum of the problem of propogating electromagnetic waves of an anisotrpopic magnetic nonhomogeneous waveguiding structure. Materials and methods. To find a solution we use variational problem formulation. The variational problem is reduced to studying of an operator-function that falls into nonlinear dependency from the spectral parameter. The article investigates properties of the operator-function necessary to analyze its spectral features. Results. We have proved theorems on the spectrum's discerete nature and on distribution of operator-function's eigenvalues on a complex plance. Conclusions. The suggested analytical method allows to prove the spectrum's discrete nature in the problem of azimuthal symmetrical waves of an open nonhomogeneous anisotropic waveguide with longitudinal magnetization. Besides, the given method may be used in research of spectral properties of more complicated waveguiding structures.