Diffraction of a plane wave by a multiserial lattice located in a dielectric layer

A modified zero field method is applied to solve the 2D problem of scattering by a multiserial lattice. The lattice consists of perfectly conducting elements and is situated in a homogeneous dielectric layer. The system of integral equations is derived and formulas for calculating the reflection and transmission coefficients are obtained for various geometries of the lattice elements. To increase the efficiency of the algorithm work, both polar and elliptic coordinates are applied to choose the auxiliary contour on which the zero field condition is stipulated.