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A waveguide coincides with a three-dimensional domain G having finitely manycylindrical outlets to infinity; the boundary of G is smooth. In G, we considerthe stationary Maxwell system with real spectral parameter k and identitymatrices of dielectric and magnetic permittivity. The boundary of G is supposedto be perfectly conductive. In the presence of charges and currents weinvestigate the solvability of the corresponding boundary value problemsupplemented with "intrinsic" radiation conditions at infinity. For all k inthe continuous spectrum of the problem (including the thresholds andeigenvalues), we describe a basis in the space of continuous spectrumeigenfunctions, define the scattering matrix, and prove it is unitary. To thisend, we extend the Maxwell system to an elliptic one and study the latter indetail. The information on the Maxwell boundary value problem comes from thatobtained for the elliptic problem.

The Maxwell system in waveguides with several ends