Recent advances in the spectral theory of open structures: Existence and distribution of the spectra of running waves for a class of open waveguides

We give a general description of mathematical background and a resume of the results about existence and distribution of the spectra of running waves in open waveguides, including metal-dielectric waveguides with arbitrary cylindrical in-homogeneities, layered concentric dielectric waveguides of circular cross section and Goubau lines with layered dielectric covers. The newly obtained results are reported concerning singularities (resonant states) of the transmission coefficient in the problems of the wave scattering by parallel-plate dielectric slabs in a waveguide and free space. The findings are based on recent advances in the spectral theory of open structures.