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Integral equation method (!EM) [Fung, 1994; Chen and Fung, 1995; Fung and Pan, 1987; Chen et al 2000], Wiener method [Ito, 1985; Ogura and Takahashi, 1995], small slope approximation (SSA) [Broschat, 1993; Voronovich, 1994a,b; Thorsos and Broschat, 1995] For the case of absorption and emissivity calculations, it was showl) that the results of SSA and SPM are identical for the half-space case [Irisov, 1994, 1997] Two-scale model is used to superimpose large scale roughness and small scale roughness [Plant, 1986; Yueh, 1997; Voronovich, 1996; Durden and Vesecky, 1985, 1990] Other notable methods include the Feynman diagrammatic method [DeSanto, 1974; DeSanto and Shisha, 1974; DeSanto and Wombell, 1991], full wave methods [Collin, 1994; Bahar and Fitzwater, 1989] as well as the mean field theory [Sentenac and Greffet, 1998; Greffet and Nieto-Vesperinas, 1998] In this chapter, we use the small perturbation method for electromagnetic wave scattering by two-dimensional random rough surfaces.



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In the next chapter, the Kirchhoff approach, the phase perturbation method, and the two-scale model are discussed..

exp(ikixx + ikiyY - ikizz)

(1.1.1)

incident upon a rough surface of perfect electric conductor. In (1.1.1), kix = ksinfhcos<pi' kiy = ksinOisin<pi, and k iz = k cos Oi. We also have kip = k sin Oi' The rough surface is characterized by a random height function

z = f(x, y), where f(x, y) is a random function with zero mean (J(x, y)) = 0 (Fig. 1.1.1). Let fmin and fmax be the minimum and maximum values, respectively, of the surface profile f(x, y). From Huygens' principle, the extinction theorem, and setting the tangential electric field equal to zero, we have (1.1.2a) for z > f(r1-) EiCf)+ ~ dS' ikTJG(r, r') . [n x H(r')] = { E r) (1.1.2b) for z < f(r1-)





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where r 1- denotes vector xx + yfJ in x-y plane. We can define surface field unknowns. For z' = magnetic field is defined as

multitude of structures that have now attained the age of 50. Introduced into the United States in the 1930s, from Germany, by Max C. Hanisch, Sr. (1882 1950), glued laminated timber is present in thousands of buildings.

f (x' , y'),

dS'TJn x H(r') = dr'.La(r'.L)

FIGURE 6.6 The color of a particular study makes it easy to read. You can adjust the color and opacity of any study to your preference.

(1.1.3)

We make use of the integral representation of dyadic Green's function as given in equation (2.1.20) of Volume 1. For z < fmin, we use the lower half of (1.1.2) to get

Ei(r) =

(f(X, y)ax(x, y)) = h2Cxx (0, 0) (f(x,y)~y(x,y)) = h 2Cyy (0,0) (f(x, Y)fxy(x, y)) = h 2CXY (0, 0)

(2.1.195a) (2.1.195b) (2.1.196)

(E s {1'))

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Jz (I - ksks)Eo exp --2=

A A (

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