Backscattering enhancement from anisotropic rough surfaces with the first- and second- order shadowed Kirchhoff approximation in high-frequency limit Christophe BOURLIER*, Gérard BERGINC** * IRCCyN UMR n° 6597 CNRS, Ecole Polytechnique de l'Université de Nantes, Bat IRESTE, Division SETRA, Rue Christian Pauc, La Chantrerie, BP 50609, 44306 NANTES Cedex 3, France. Tel : (33) 2 40 68 32 25, Fax : (33) 2 40 68 32 33, email : christophe.bourlier@polytech.univ-nantes.fr ** THALES Optronique, Rue Guynemer, BP 55, 78283 Guyancourt Cedex, France One of the most interesting phenomena associated with rough-surface scattering is the backscattering enhancement effect [1]. This phenomenon is associated with the appearance of a well-defined peak in the backscattering direction of the intensity of the incoherently scattered component of the electromagnetic field. Enhanced backscattering has been observed experimentally [2]-[4] and numerically [5]-[7] from numerical Monte-Carlo Method. One such type involves surfaces with relatively large slopes for which predictions of the standard Kirchhoff approximation and of the small perturbation method of one-order are inaccurate because of the small slope limitations of these approximate theories. Although other approximate theories such as higher-order Kirchhoff approximation [8], integral equation [9] and full- wave [10] theories have been developed to explain the backscattering enhancement phenomenon. They remain restricted in their domains of validity and the random surface is assumed to be Gaussian as the numerical method. In addition, these analytical theories include the shadowing effects from the shadowing function with single reflection. Recently, Bourlier et al. have given a rigorous formulation of the shadowing effect with double reflection [11]. For a stationary one-dimensional surface (1-D), Bourlier et al. [12] have re-formulated the second-order Kirchhoff approximation combined to the geometric optics approximation by including the shadowing function with double reflection. This approach can be applied for surface slope rms greater than 0.5 and for surface height rms larger than the half-wavelength. The purpose of this paper is to extend the previous model to a 2-D anisotropic surface and compared it with measurements or/and numerical methods in order to study its validity domain. The incoherent scattering coefficient is then proportional to two surface slope probabilities for which the slopes would speculary reflected the beams in the double scattering process. In addition, the probabilities are related between them by a propagating function accounting for the shadow, and the analysis does not require that the surface is described as a Gaussian process. [1] A. Ishimaru 1991 Backscattering enhancement: from radar cross sections to electron and light localizations to roughsurface scattering IEEE Ant. Prop. Mag. 33 7–11. [2] K. A. O’Donnell and E. R. Mendez 1987 Experimental study of scattering from characterized random surfaces J. Opt. Soc. Am. A 4(7) 1194-1205. [3] M. E. Knotts and K. A. O’Donnell 1994 Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness J. Opt. Soc. Am. A 11(2) 697-710. [4] A. A. Maradudin, J. Q. Lu, P. Tran, R. F. Wallis, V. Celli, Z. H. Gu, A. R. McGurn, E. R. Mendez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty and A. J. Sant 1992 Enhanced backscattering from one- and two-dimensional random surfaces Rev. Mex. Fis. 38 343–397. [5] J. T. Jonhson L. Tsang R. T. Shin K. Pak C. H. Chan A. Ishimaru and Y. Kuga 1996 Backscattering enhancement of electromagnetics waves from two-dimensional perfectly conducting random rough surfaces: A comparison of Monte Carlo simulations with experimental data IEEE Trans. Ant. Prop. 11 748-756. [6] L. Tsang J. A. Kong K.-H. Ding and C. On Ao 2001 Scattering of Electromagnetic Waves. Numerical solutions (New York, John Wiley & Sons). [7] D. Torrungrueng and J. T. Johnson 2001 Numerical studies of backscattering enhancement of electromagnetic waves from two-dimensional JOSA A 18(10) 2518-2526. [8] A. Ishimaru C. Le Y. Kuga L. A. Sengers and T. K. Chan 1996 Polarimetric scattering theory for high slope rough surfaces PIER (Progress In Electromagnetic Research, EMW, Chief Editor J.A Kong) 14 1-36. [9] C. Y. Hsieh 2000 Prediction of IEM model for backscattering enhancement Electromagnetics 20(3) 205-231. [10] E. Bahar and M. El-Shenawee 1994 Vertically and horizontally polarized diffuse double-scatter cross sections of one-dimensional random rough surfaces that exhibit enhanced-backscatter-full-wave solutions JOSA A 11(8) 2271- 2285. [11] C. Bourlier G. Berginc and J. Saillard 2002 Monostatic and bistatic statistical shadowing functions from a one- dimensional stationary randomly rough surface: II. Multiple scattering Waves in Random Media 12(1) 175-200. [12] C. Bourlier and G. Berginc 2003 Electromagnetic scattering from 1-D rough surface with the first- and second- order Kirchhoff approximation in high-frequency limit. Part I. Theoretical study for any process Submitted to Waves in Random Media, february 2003.