Scattering of waves from periodic surfaces

The scattering of waves from periodic surfaces is studied. We give a general review of this problem and compare three analytical methods for a conducting sinusoidal surface in detail for both TE and TM polarized waves. The three methods are: 1) the method developed by Masel, Merrill, and Miller (MMM); 2) the Modified Physical Optics (MPO) method; and 3) Waterman's Plane Harmonics (WPH) approach. We find the MMM method to be the most efficient one in terms of the rate and range of convergence. For dielectric media with periodic rough surfaces, an improved method is developed for calculating the reflected and transmitted powers. The results are used to compare with experimental data obtained at optical frequencies. It is shown that good agreement is achieved when the complex permittivity of the metal for the grating at the corresponding frequency is used.