Electromagnetic waveguides with several cylindrical ends and non-homogeneous anisotropic filling

摘要

A waveguide occupies a three-dimensional domain G having finitely many cylindrical ends. In the domain G, the stationary Maxwell system with perfectly conductive boundary conditions is considered. Permittivity ε and permeability μ are positive definite matrix-valued smooth functions in G. In every cylindrical end, the matrices ε and μ converge at infinity to positive definite matrix-valued smooth functions depending only on a point in the cylinder cross-section. A well-posed statement of the boundary value problem with intrinsic radiation conditions is established; a unitary scattering matrix is defined.