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

TL;DR

This paper investigates the diffraction patterns of scalar plane waves from doubly-periodic surfaces with Dirichlet or Neumann boundary conditions, revealing Rayleigh anomalies and surface wave effects through numerical analysis.

Contribution

It introduces a rigorous numerical approach to analyze diffraction efficiencies and identifies new features related to surface waves on Neumann surfaces.

Findings

Rayleigh anomalies observed in diffraction efficiencies

Additional surface wave features on Neumann surfaces

Validation of Rayleigh equation results with Green's function calculations

Abstract

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.