Theoretical studies of the enhanced backscattering of light from one-dimensional randomly rough metal surfaces by the use of a nonlocal impedance boundary condition

Nonlocal impedance boundary conditions for p- and s-polarized electromagnetic fields at the curved interface between vacuum and a metal, defined by the equation x3 = ζ(x1), when the plane of incidence is the x1x3-plane, are derived. The conditions for the validity of a local impedance boundary condition are established. The results are used in computer simulation studies of the scattering of infrared and visible light from a large rms height, large rms slope, one-dimensional, randomly rough, metal surface. It is shown, by comparison with the results of formally exact simulations, that the use of a local impedance boundary condition, even for light in the visible region of the optical spectrum, yields accurate results with a significant saving of computational time.