Scattering of a TM plane wave from a periodic surface with finite extent: Perturbation solution

This paper studies the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent by the small perturbation method. We obtain the first and second order perturbed solutions explicitly, in terms of which the differential scattering cross section and the total scattering cross section per unit surface are calculated and are illustrated in figures. By comparison with results by a numerical method, it is concluded that the perturbed solution is reasonable even for a critical angle of incidence if the surface is small in roughness and gentle in slope and if the corrugation width is less than certain value. A brief discussion is given on multiple scattering effects.