Existence result for Maxwell’s equations in half-waveguides

Maxwell’s equations are considered in a half-waveguide [Formula: see text] where [Formula: see text] is a bounded Lipschitz domain in [Formula: see text]. The electric permittivity [Formula: see text] and the magnetic permeability [Formula: see text] are assumed to be strictly positive and periodic outside a compact set. A standard radiation condition accompanies the equations. We give a result on existence and uniqueness in the form of a Fredholm alternative: When there is no bound state, i.e. no non-trivial solution of the homogeneous problem, then there is a unique solution for every right-hand side.