Scattering of the electromagnetic waves from a rough surface

Abstract The electromagnetic field scattered by a rough surface of a semi-infinite body is computed up to the second order of a perturbation scheme with the surface roughness as a perturbation parameter. The calculations are based on the equation of motion of the polarization within the Lorentz–Drude (plasma) model of polarizable, non-magnetic, homogeneous matter. The surface roughness contributes both to the main (specularly) reflected and refracted fields and diffuse scattering, or gives rise to secondary (second-order) diffraction peaks for a regular grating. The calculations are performed both for the s- and p-waves. Two-dimensional modes, resonant at certain frequencies, are identified, confined to and propagating only on the surface, as a consequence of the surface roughness. Keywords: surface roughnessscattered electromagnetic fieldLorentz–Drude modelpolarization motion Acknowledgements The author is indebted to his colleagues in the Department of Seismology, Institute of Earth's Physics, Magurele-Bucharest, for many enlightening discussions, and to the members of the Laboratory of Theoretical Physics at Magurele-Bucharest for many useful discussions and a throughout checking of this work. This work was partially supported by the Romanian Government Research grant PN-RU-3/0072/22/2011.