Electromagnetic Scattering from Large Amplitude, Small Period Surface Roughness

Gary S Brown
ElectroMagnetic Interactions Laboratory
Bradley Department of Electrical & Computer Engineering
Virginia Polytechnic Institute & State University
Blacksburg, VA 24061

    Our understanding of scattering from rough surfaces rests primarily upon asymptotic analytical models and numerical results. The analytical results have been found to be much more accurate than was originally predicted. The numerical results have shown this to be true and have also extended our domain of understanding to situations where the asymptotic analytical results breakdown. Boundary perturbation theory is accurate when the surface features are small compared to the probing electromagnetic (em) wavelength. The Kirchhoff approximation is accurate when the roughness height and period are large compared to the electromagnetic wavelength. An appropriate combination of these two theories covers surfaces which are a mixture of small and large structure. The intermediate range where the surface height and the period are comparable to the em wavelength can be dealt with using numerical techniques.
    The one range of surface roughness that has not been addressed to date is that for which the roughness height is large while the surface period is small compared to the em wavelength. If the surface roughness period becomes sufficiently small compared to a wavelength, one might expect that the surface will become specular in it scattering characteristics. That is, from a scattering point of view, the surface effectively becomes flat. The purpose of our research is to investigate this limiting behavior in order to understand the scattering from such surfaces. Our goal is particularly focused on finding what happens to the currents on and the scattered fields from randomly rough surfaces comprising surface periods that are smaller than the incident em wavelength.
    Our approach focuses on the Magnetic Field Integral Equation (MFIE) for the surface current induced on a one-dimensionally rough, perfectly conducting surface. Unfortunately, in its primitive form, the MFIE is not particularly amenable to numerical solution for scattering by an extended surface. We therefore use a preconditioning technique that we developed in 1996 for summing an infinite number of multiple scatterings on the surface prior to an iterative solution. We demonstrate the robustness of the method by applying it to a surface containing a sinusoidal roughness. We show the rather unique behavior of the surface currents for both TE and TM polarizations once the period of the surface becomes less that one-half the incident electromagnetic wavelength. In addition, we demonstrate the specular nature of the field scattered by such a surface. It is interesting to note that this is an excellent example of wave diffraction producing exactly the same scattered field as a perfectly flat reflecting surface once the point of observation is just a few tenths of the em wavelength above the crests of the rough surface. Computations also show that the power scattered into the specular direction is equal to the incident power, to within a few hundredths of a dB.
    Results will be presented for a surface where the technique fails to converge indicating that our preconditioning must be applied a second time to presum some of the back and forth multiple scatterings on the surface before starting the iterative solution.