The time-harmonic electromagnetic wave scattering by a biperiodic elastic body

This paper concentrates on an interaction scattering problem between the time-harmonic electromagnetic waves and an unbounded periodic elastic medium. The uniqueness results of the interaction problem are established for small frequencies or all frequencies except a discrete set in both the absorbing and nonabsorbing medium, and then the existence of solutions is derived by the classical Fredholm alternative. The perfectly matched layer (PML) method is proposed to truncate the unbounded scattering domain to a bounded computational domain. We prove the well-posedness of the solution for the truncated PML problem, where a homogeneous boundary condition is imposed on the outer boundary of the PML. The exponential convergence of the PML method is established in terms of the thickness and parameters of the PML. The proof is based on the PML extension and the exponential decay properties of the modified fundamental solution.