Scattering of Light at Rough Surfaces

In this section we shall consider how the results obtained above for reflection from a plane surface are modified in the case of rough surfaces. We shall assume that the amplitude of surface roughness, (ry), can be treated as small and thus the solutions of Maxwell s equations can be expanded as a Taylor series in it (Maradudin and Mills 1975). We suppose for simplicity that above the surface z = (ry) is vacuum, while below it is the isotropic medium with a complex frequency-dependent dielectric function e = e co). The total dielectric function can then be written as 

Each term in this expansion obeys the equations which are obtained by substituting (3.125) and (3.129) into Eq. (3.128) and collecting the terms of the same order. It is easy to see that the zeroth-order equation  

18) This impHes that the corresponding root-mean-square height of the surface, rr, is much less than the wavelength of tight. 

19) This equation follows from Maxwell s equations see (Bom and Wolf 1975) for details. 

20) We exclude here the plane 2 = 0 and take into account that V-E= [l/eo(2)]V-D = 0. 

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