Low-frequency scattering by passive periodic structures for oblique incidence: low-pass case

We derive the low-frequency behavior of the scattering coefficients from a low-pass structure which is periodic in a plane, and finite in the normal direction. The analysis is for oblique incidence of arbitrary polarization on a structure which can be anisotropic in both electric and magnetic material properties, and may contain metal inclusions. The metal inclusions can be modeled both as perfect electric conductors (PEC) and with a finite conductivity. It is found that the low-frequency reflection and transmission coefficients are proportional to the sum and difference of the electric and magnetic polarizabilities per unit area of the periodic structure. If the metal inclusions are modeled as PEC instead of as a finite conductivity, the first-order low-frequency reflection is larger, whereas the first-order transmission is smaller.