Transverse correlation length for randomly rough surfaces: two-dimensional roughness

Simeon Simeonov; Arthur R. McGurn; Alexei A. Maradudin

doi:10.1117/12.279237

26 September 1997 Transverse correlation length for randomly rough surfaces: two-dimensional roughness

Simeon Simeonov, Arthur R. McGurn, Alexei A. Maradudin

Proceedings Volume 3141, Scattering and Surface Roughness; (1997) https://doi.org/10.1117/12.279237
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

A numerical algorithm is used to generate two-dimensional surfaces defined by x₃ equals (zetz) (x), with x equals (x₁, X₂), where (zetz) (x) is a single-valued function of x that constitutes a zero- mean, stationary, isotropic, Gaussian random process defined by the properties <(zetz) (x)> equals 0, <(zetz) (x)(zetz) (x¹)> equals (sigma) ²W(x - x¹), and (sigma) ² equals <(zetz) ²(x)>. The angle brackets here denote an average over the ensemble of realizations of the surface profile function (zetz) (x). The results are used to compute the probability density P₁(x)[P₂(x)] that the nearest maximum (minimum) to a given maximum (minimum) is at a distance x from the latter; and the probability density P₃(x) that the nearest minimum to a given maximum is at a distance x. Results are presented for random surfaces defined by surface height autocorrelation functions W(x) equals exp(-x²/a²), a²/(x² + a²), and 2[(k₂² - k₁²)x²]^-1[k₂xJ₁(k₂x) - k₁xJ₁(k₁x)], where J₁(z) is a Bessel function. Results are also presented for a novel type of one-dimensional random surface used in recent experimental studies of enhanced backscattering.

Citation Download Citation

Simeon Simeonov, Arthur R. McGurn, and Alexei A. Maradudin "Transverse correlation length for randomly rough surfaces: two-dimensional roughness", Proc. SPIE 3141, Scattering and Surface Roughness, (26 September 1997); https://doi.org/10.1117/12.279237

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