Diffraction of electromagnetic waves on one-dimensional diffraction gratings formed by slots in an absolutely absorbing screen

Two-sided approximate boundary conditions are obtained for an absolutely absorbing (“black”) layer lying on a multilayer dielectric. Paired summation equations (PSEs) are obtained for the tangent components of the electric and magnetic field strengths at the slots. These equations are solved by the Galerkin method with basis functions in the form of Chebyshev and Legendre polynomials. The resulting system of linear algebraic equations has fast internal convergence. To control the accuracy of the obtained solution, a dual problem is solved – a lattice of “black stripes”. In this case, the unknowns in the PSU are the current density on the strips. The properties of lattices are analyzed.