Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1999-11-02
Physics
Condensed Matter
Disordered Systems and Neural Networks
RevTeX, 10 pages, 4 figures
Scientific paper
We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light from a randomly rough one-dimensional surface, defined by the equation $x_3 = \zx$, where the surface profile function $\zx$ constitutes a zero-mean, stationary, Gaussian random process, through the effects of $S(q|k)$ on the angular intensity correlation function C(q,k|q',k'). The existence of both the C^{(1)} and C^{(10)} correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface. We show that the deviation of the statistics of the scattering matrix from circular Gaussian statistics and the C^{(10)} correlation function are determined by exactly the same statistical moment. As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case, the C^{(10)} correlation function should vanish. This result is confirmed by numerical simulation calculations.
Leskova Tamara A.
Maradudin Alexei A.
Simonsen Ingve
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