Conclusion

Abstract

The book deals with the problems of the electromagnetic wave propagation in a wide class of waveguide structures: from planar waveguides to waveguides of arbitrary cross section (including the shielded ones). The settings for the Maxwell are reduced to boundary eigenvalue problems for the longitudinal components of the electromagnetic field in Sobolev spaces using a universal approach applicable to all the considered waveguide families. To determine and analyze the solution, variational formulations are used and the problems are reduced to the study of the spectra of OVF; many of them are polynomial operator pencils. The discreteness of the eigenwave spectra is proved and the distribution of characteristic numbers on the complex plane is described.