Plane wave scattering by a cascaded diffraction grating (H-case)

The problem of a plane wave scattering on a multielement diffraction grating is considered in the paper. The diffracted field is sought for as a double-layer potential. The technique of integration contour deformation is utilized for Green function´s calculation. An accounting for a singularity of an integrand on a specially chosen part of the integration contour is adopted to derive a numerical solution. To reduce the computation time for Sommerfeld-type integral calculations essentially a Lagrange-type interpolation polynomial of several variables is constructed. By an integration contour deformation and accounting for residues from poles the estimation of the Green´s function at infinity is provided. A two-layered grating of two curvilinear screens on the period was considered