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The diffraction of a scalar plane wave from a doubly-periodic surface onwhich either the Dirichlet or Neumann boundary condition is imposed is studiedby means of a rigorous numerical solution of the Rayleigh equation for theamplitudes of the diffracted Bragg beams. From the results of thesecalculations the diffraction efficiencies of several of the lowest orderdiffracted beams are calculated as functions of the polar and azimuthal anglesof incidence. The angular dependencies of the diffraction efficiencies displayfeatures that can be identified as Rayleigh anomalies for both types ofsurfaces. In the case of a Neumann surface additional features are present thatcan be attributed to the existence of surface waves on such surfaces. Some ofthe results obtained through the use of the Rayleigh equation are validated bycomparing them with results of a rigorous Green's function numericalcalculation.

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces