Electromagnetic wave propagation in non-homogeneous waveguides

We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic field, excited in the waveguide in the presence of charges and currents. The field can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at infinity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreover, we propose and justify a method for approximating the scattering matrix for all k in the continuous spectrum, including thresholds; the presence of waveguide eigenvalues does not influence the method statement. The results of the thesis extend the area of electromagnetic waveguide theory and have numerous applications. Particularly, the asymptotic and numerical methods, developed in the thesis, can be used for design and analysis of complex waveguides with resonators, SHF splitters, etc. To prove the results, we extend the over-determined Maxwell system to an elliptic problem and study the latter in detail. The information on the Maxwell system comes from that, obtained for the elliptic problem.