26 September 2000 Effective impedance boundary condition for the coherent scattering of light from a one-dimensional randomly rough surface
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Abstract
The physical system we consider in this work consists of vacuum in the region x3 $GTR (zetz) (x1), and a dielectric medium characterized by a complex dielectric constant (epsilon) in the region x3 < (zetz) (x1). The surface profile function (zetz) (x1) is assumed to be a single-valued function of x1, that is differentiable as many times as is necessary, and to constitute a zero-mean stationary, Gaussian random process. It has been recently been shown that a local relation can be written between L(x1(omega) ) equalsV [deltaH2$GTR(x1,x3(omega) )/(delta) x3]x3equals0) and H(x1(omega) ) equalsV [H2$GTR(x1,x3(omega) )]x3equals0, where H2$GTR(x1,x3(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 x1x3-plane. This relation has the form L(x1(omega) ) equals I(x1(omega) )H(I(x1(omega) ), where the surface impedance I(I(x1(omega) ) depends on the surface profile function (zetz) (x1) and on the dielectric constant (epsilon) of the dielectric medium. A completely analogous relation exists when L(x1(omega) ) equalsV [(delta) E2$GTR(x1,x3(omega) )/(delta) x3]x3equals0) and H(x1(omega) ) EQV [E2(x1,x3(omega) )]x3equals0, where E2$GTR(x1,x3(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 x1x3-plane. Our goal in this work is to obtain the relation between the values of L(x1(omega) ) and H(x1(omega) ) averaged over the ensemble of realizations of the surface profile function (zetz) (x1). This we do by the use of projection operators and Green's second integral identity in the plane.
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Tamara A. Leskova, Alexei A. Maradudin, "Effective impedance boundary condition for the coherent scattering of light from a one-dimensional randomly rough surface", Proc. SPIE 4100, Scattering and Surface Roughness III, (26 September 2000); doi: 10.1117/12.401665; https://doi.org/10.1117/12.401665
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