Solving the problem of electromagnetic wave diffraction at a finite plane grating with small elements

•Two approaches for the solution of the problem of diffraction on a plane finite grating are developed.•Comparison of the patterns obtained by both methods is made.•Verification of the optical theorem for different grating element shape is made.•Comparison of the results obtained for finite and infinite gratings is carried out.

Two approaches for solving the three-dimensional problem of wave diffraction at a finite grating consisting of bodies of revolution are proposed. An approximate solution is obtained for a grating with small elements. This solution is applied to consider gratings with a large number of elements. The coincidence of the results obtained by the two methods is shown. The reflection and transmission coefficients are compared for finite and infinite gratings.