Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces
Alexei A. Maradudin
Department of Physics and Astronomy, University of California, Irvine CA 92697, U.S.A.
Centro de Enseñanza Técnica y Superior, Universidad Ensenada Camino a Microondas Trinidad s/n Km. 1, Moderna Oeste, 22860 Ensenada, B.C., México
Department of Theoretical Physics, Wroclaw University of Science and Technology, Wroclaw, Poland
Surface du Verre et Interfaces, UMR 125 CNRS/Saint-Gobain, F-93303 Aubervilliers, France
Department of Physics, NTNU — Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Department of Petroleum Engineering, University of Stavanger, NO-4036 Stavanger, Norway
Received January 30, 2018
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green’s function numerical calculation.
PACS: 43.20.+g General linear acoustics; PACS: 47.35.Rs Sound waves.
Key words: Dirichlet and Neumann surfaces, Rayleigh anomalies, scattering theory.