On Computation of Waveguide Scattering Matrices for the Maxwell System

The Maxwell system is considered in a waveguide with perfectly conducting boundary having several cylindrical outlets to infinity. A minimizer of a quadratic functional serves as an approximation to a row of the scattering matrix. To construct such a functional, we solve an auxiliary boundary value problem in the bounded domain obtained by cutting off, at a distance $R$, the waveguide outlets to infinity. As $R$ tends to infinity, the minimizer $a(R, k)$ tends at exponential rate to the corresponding row of the scattering matrix.