Wave diffraction by many element multilayer cylindrical gratings with dielectric layers

A rigorous theory of multielement multilayer cylindrical gratings placed inside or outside the dielectric layer is suggested. The diffraction characteristics of the combined gratings with various filings calculated in the far and near zones are presented and discussed. Resonance phenomena of complete reflection and transmission for combined gratings as well as the effects of the enlightenment and darkening of the grating in the presence of dielectric layer are revealed and investigated.