Scattering of a TM Wave from a Periodic Surface with Finite Extent: Undersampling Approximation

This paper deals with the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent. For comparison, however, we briefly discuss the diffraction by the sinusoidal surface with infinite extent, where we use the concept of the total diffraction cross section per unit surface introduced previously. To solve a case where the sinusoidal corrugation width is much wider than wave length, we propose an undersampling approximation as a new numerical technique. For a small rough case, the total scattering cross section is calculated against the angle of incidence for several different corrugation widths. Then we find remarkable results, which are roughly summarized as follows. When the angle of incidence is apparently different from critical angles and diffraction beams are all scattered into non-grazing directions, the total scattering cross section increases proportional to the corrugation width and hence the total scattering cross section per unit surface (the ratio of the total scattering cross section to the corrugation width) becomes almost constant, which is nearly equal to the total diffraction cross section per unit surface in case of the sinusoidal surface with infinite extent. When the angle of incidence is critical and one of the diffraction beams is scattered into a grazing direction, the total scattering cross section per unit surface strongly depends on the corrugation width and approximately approaches to the total diffraction cross section per unit surface as the corrugation width gets wide. key words: numerical analysis, undersampling, Wood’s anomaly, total scattering cross section, multiple scattering