Surface TE-polarized waves in an inhomogeneous dielectric layer

The problem of normal waves in an inhomogeneous dielectric layer is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. Nonhomogeneous filling and entering of spectral parameter in transmission conditions lead to the necessity of special definition of solution to the problem. We formulate the definition of solution using variational relation. The variational problem is reduced to the study of an operator function. We investigate properties of the operators of the operator function needed for the analysis of its spectral properties. We prove theorem of discrete spectrum and theorem of localization of eigenvalues of the operator function on complex plane.