  The paper is concerned with well-posedness of TE and TM polarizations of
time-harmonic electromagnetic scattering by perfectly conducting periodic
surfaces and periodically arrayed obstacles with local perturbations. The
classical Rayleigh Expansion radiation condition does not always lead to
well-posedness of the Helmholtz equation even in unperturbed periodic
structures. We propose two equivalent radiation conditions to characterize the
radiating behavior of time-harmonic wave fields incited by a source term in an
open waveguide under impenetrable boundary conditions. With these open
waveguide radiation conditions, uniqueness and existence of time-harmonic
scattering by incoming point source waves, plane waves and surface waves from
locally perturbed periodic structures are established under either the
Dirichlet or Neumann boundary condition. A DtN operator without using the
Green's function is constructed for proving well-posedness of perturbed
scattering problems.
