Application of reduced Rayleigh equations to electromagnetic wave scattering by two-dimensional randomly rough surfaces

Abstract

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the surface height. Calculations can be greatly simplified with the use of reduced Rayleigh equations, because one of the unknown fields can be eliminated. We derive a new set of four reduced equations for the scattering amplitudes, which are applied to the cases of a rough conducting surface, and to a slab where one of the boundary is a rough surface. As in the one-dimensional case, numerical simulations show the appearance of enhanced backscattering for these structures.

Numerical studies of the transmission of light through a two-dimensional randomly rough interface

“…The function I(γ|q ) was evaluated by expanding the integrand in Eq. (17) in powers of ζ(x ) and calculating the Fourier transform of ζ n (x ) by the fast Fourier transform [2]. For these expansions we used the first N = 18 terms.…”

“…Soubret et al [17] also obtained a reduced Rayleigh equation for the transmission amplitudes in the case where light incident from one dielectric medium is transmitted into a second dielectric medium through a two-dimensional randomly rough interface. However, only perturbative solutions of this equation were obtained by them, and only for vacuum as the medium of incidence.…”

Application of Facet Scattering Model in Sar Imaging of Sea Surface Waves With Kelvin Wake

“…The small perturbation method (SPM) was firstly introduced for the scattering from rough surfaces, which is a perturbative expansion of the scattering amplitude with respect to a small height parameter [18,19]. The main limitation of the SPM is its restricted domain of validity, as it is valid for small root-mean-square (RMS) height/wavelength ratios.…”

Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers

“…One way to overcome these difficulties is to use integral equations called the reduced Rayleigh equations, they were first obtained by Celli et al 8 , and later have been generalized in Ref. 9 to take into account upward fields in the slab medium. When combining these equations we obtain an integral equation where only the scattering matrix of the whole structure has to be determined, next we have developed a systematic method to calculate the perturbative development.…”