Proceedings Article | 26 September 2000

Proc. SPIE. 4100, Scattering and Surface Roughness III

KEYWORDS: Scattering, Metals, Dielectrics, Interfaces, Light scattering, Reflectivity, Surface roughness, Magnetism, Electromagnetism, Electromagnetic scattering

The physical system we consider in this work consists of vacuum in the region x_{3} $GTR (zetz) (x_{1}), and a dielectric medium characterized by a complex dielectric constant (epsilon) in the region x_{3} < (zetz) (x_{1}). The surface profile function (zetz) (x_{1}) is assumed to be a single-valued function of x_{1}, that is differentiable as many times as is necessary, and to constitute a zero-mean stationary, Gaussian random process. It has been recently been shown that a local relation can be written between L(x_{1}(omega) ) equalsV [deltaH_{2}$GTR(x_{1},x_{3}(omega) )/(delta) x_{3}]_{x3}equals0) and H(x_{1}(omega) ) equalsV [H_{2}$GTR(x_{1},x_{3}(omega) )]_{x3equals0}, where H_{2}$GTR(x_{1},x_{3}(omega) ) is the single nonzero component of the total magnetic field in the vacuum region, in the case of a p-polarized electromagnetic field whose plane of incidents is the x_{1}x_{3}-plane. This relation has the form L(x_{1}(omega) ) equals I(x_{1}(omega) )H(I(x_{1}(omega) ), where the surface impedance I(I(x_{1}(omega) ) depends on the surface profile function (zetz) (x_{1}) and on the dielectric constant (epsilon) of the dielectric medium. A completely analogous relation exists when L(x_{1}(omega) ) equalsV [(delta) E_{2}$GTR(x_{1},x_{3}(omega) )/(delta) x_{3}]_{x3equals0}) and H(x_{1}(omega) ) EQV [E_{2}(x_{1},x_{3}(omega) )]_{x3equals0}, where E_{2}$GTR(x_{1},x_{3}(omega) ) is the single nonzero component of the electric field in the vacuum region, in the case of an s-polarized electromagnetic field whose plane of incidence is the x_{1}x_{3}-plane. Our goal in this work is to obtain the relation between the values of L(x_{1}(omega) ) and H(x_{1}(omega) ) averaged over the ensemble of realizations of the surface profile function (zetz) (x_{1}). This we do by the use of projection operators and Green's second integral identity in the plane.