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Numerical investigation of resonance diffraction characteristics of cascaded gratings (TM-case)

The problem of a plane wave scattering on a multielement diffraction grating is considered. The diffracted field is sought for as a single-layer potential. The technique of integration path deformation is utilized for Green function's calculation. An accounting of a singularity of the integrand on a specially chosen part of the integration path 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 used. By an integration path deformation and accounting for residues from poles the estimation of the Green's function at infinity is provided. A two-layered cascaded grating with two curvilinear screens on the period was considered.