PROCEEDINGS ARTICLE | September 26, 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<SUB>3</SUB> $GTR (zetz) (x<SUB>1</SUB>), and a dielectric medium characterized by a complex dielectric constant (epsilon) in the region x<SUB>3</SUB> < (zetz) (x<SUB>1</SUB>). The surface profile function (zetz) (x<SUB>1</SUB>) is assumed to be a single-valued function of x<SUB>1</SUB>, that is differentiable as many times as is necessary, and to constitute a zero-mean stationary, Gaussian random process. It has been recently been shown that a local relation can be written between L(x<SUB>1</SUB>(omega) ) equalsV [deltaH<SUB>2</SUB>$GTR(x<SUB>1</SUB>,x<SUB>3</SUB>(omega) )/(delta) x<SUB>3</SUB>]<SUB>x3</SUB>equals0) and H(x<SUB>1</SUB>(omega) ) equalsV [H<SUB>2</SUB>$GTR(x<SUB>1</SUB>,x<SUB>3</SUB>(omega) )]<SUB>x3equals0</SUB>, where H<SUB>2</SUB>$GTR(x<SUB>1</SUB>,x<SUB>3</SUB>(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<SUB>1</SUB>x<SUB>3</SUB>-plane. This relation has the form L(x<SUB>1</SUB>(omega) ) equals I(x<SUB>1</SUB>(omega) )H(I(x<SUB>1</SUB>(omega) ), where the surface impedance I(I(x<SUB>1</SUB>(omega) ) depends on the surface profile function (zetz) (x<SUB>1</SUB>) and on the dielectric constant (epsilon) of the dielectric medium. A completely analogous relation exists when L(x<SUB>1</SUB>(omega) ) equalsV [(delta) E<SUB>2</SUB>$GTR(x<SUB>1</SUB>,x<SUB>3</SUB>(omega) )/(delta) x<SUB>3</SUB>]<SUB>x3equals0</SUB>) and H(x<SUB>1</SUB>(omega) ) EQV [E<SUB>2</SUB>(x<SUB>1</SUB>,x<SUB>3</SUB>(omega) )]<SUB>x3equals0</SUB>, where E<SUB>2</SUB>$GTR(x<SUB>1</SUB>,x<SUB>3</SUB>(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<SUB>1</SUB>x<SUB>3</SUB>-plane. Our goal in this work is to obtain the relation between the values of L(x<SUB>1</SUB>(omega) ) and H(x<SUB>1</SUB>(omega) ) averaged over the ensemble of realizations of the surface profile function (zetz) (x<SUB>1</SUB>). This we do by the use of projection operators and Green's second integral identity in the plane.