Scattering by periodic surfaces

Reflection behavior is examined for an interface having periodic height variation. Upon employing the Bloch theorem, in conjunction with the extended boundary condition, exact matrix equations are obtained for surface fields, as well as transmitted and reflected wave amplitudes. Tunneling considerations then lead to new energy constraints for problems of this type, in which propagating waves are coupled with evanescent modes. In the limit of surface corrugations shallow compared with impinging wavelength, analytic results are obtained confirming both the energy constraints and early computations by Rayleigh. Numerical results demonstrate the efficiency of the method. Subject Classification: 20.30.