Electromagnetic diffraction from metallic deep cross-gratings

In order to have a benchmark solution for the electromagnetic scattering from a rough metallic surface, the particular case of a metallic plate hollowed with identical and regularly spaced cavities of sufficiently simple shape was studied. Hemispheroidal cavities allow us to carry out a rigorous theoretical statement (modal method) which particularly may be applied to very deep irregularities (strong ellipticity). Our numerical results are compared with previous ones obtained with a cross-grating of hemispherical cavities and mainly with an experimentation we have specially performed in the microwave range.