Added Solutions of Boundary Value Problems for Double-Layer Guiding Structures

Existence of the added waves in double-layered cylindrical guiding structures is considered in the article.The added waves ensure completeness of solutions of boundary value problems for layered guiding structures.It is shown that eigenvalues, corresponding added waves (or adjoint waves), can be detected at points of the Jordan’s multiplicity of the wavenumbers. At these points characteristics of two normal waves joint and complex waves originate. The added waves define frequency boundaries of a complex resonance which originates as a result of a exciting of couple of complex waves.