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Effective impedance boundary condition for the coherent scattering of light from a one-dimensional randomly rough surface
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Paper 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.

Paper Details

Date Published: 26 September 2000
PDF: 11 pages
Proc. SPIE 4100, Scattering and Surface Roughness III, (26 September 2000); doi: 10.1117/12.401665
Show Author Affiliations
Tamara A. Leskova, Institute of Spectroscopy (United States)
Alexei A. Maradudin, Univ. of California/Irvine (United States)

Published in SPIE Proceedings Vol. 4100:
Scattering and Surface Roughness III
Zu-Han Gu; Alexei A. Maradudin, Editor(s)

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