Radiation and scattering in electromagnetic waveguides near thresholds

Abstract

A waveguide occupies a three-dimensional domain G G with several cylindrical outlets to infinity and is described by the stationary Maxwell system with perfectly conductive boundary conditions. It is assumed that the medium filling the waveguide is homogeneous and isotropic at infinity in a limiting sense. The paper is devoted to description of the behavior of the scattering matrix, radiation conditions, and solutions as the spectral parameter tends to a threshold. In particular, it is shown that the scattering matrix has finite one-sided limits at every threshold and the limits are expressed in terms of the “scattering matrix stable near the threshold”.