Reflection of plane waves from the array of complex-shape scatterers substrated by a dielectric shield

This work is devoted to the problem of the plane electromagnetic wave reflection from regular two-dimensional array of scatterers of complex shape situated near the surface of a dielectric shield (a metal-backed dielectric layer). Because of the three-dimensional geometry of scatterers this problem cannot be explicitly solved using boundary conditions for the scatterer surface together with the boundary conditions for the shield. We have to study the individual scatterer response separately in terms of the particle polarizabilities using the antenna model. Then the study of the electromagnetic interaction between the scatterers and dielectric leads to the problem of the local field which turns out be more complicated than that problem for the grids in free space. The calculations of the reflectance are made for an important sample of the structure: a grid of C-shaped particles on and over the surface of the shield. The results are validated by coincidence with the data obtained earlier for a special case.