Vol. 34

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Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System

By Richard Dusséaux and Rodrigo De Oliveira
Progress In Electromagnetics Research, Vol. 34, 63-88, 2001


We present a method giving the field scattered by a plane surface with a cylindrical local perturbation illuminated by a plane wave. The theory is based on Maxwell's equations in covariant form written in a nonorthogonal coordinate system fitted to the surface profile. The covariant components of electric and magnetic vectors are solutions of a differential eigenvalue system. A Method of Moments (PPMoM) with Pulses for basis and weighting functions is applied for solving this system in the spectral domain. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. Their amplitudes are found by solving the boundary conditions. Above a given deformation, the Rayleigh integral is valid and becomes identified with one of covariant components of the scattered field. Applying the PPMo Method to this equality, we obtain the asymptotic field and the scattering pattern. The method is numerically investigated in the far-field zone, by means of convergence tests on the spectral amplitudes and on the power balance criterion. The theory is verified by comparison with results obtained by a rigorous method.


Richard Dusséaux and Rodrigo De Oliveira, "Scattering of a Plane Wave by a 1-Dimensional Rough Surface Study in a Nonorthogonal Coordinate System," Progress In Electromagnetics Research, Vol. 34, 63-88, 2001.


    1. Chandezon, J., D. Maystre, and G. Raoult, "A new theoritical method for diffraction gratings and its numerical application," J. Optics (Paris), Vol. 11, 235-241, 1980.

    2. Elson, J. M. and R. H. Ritchie, "Photon interaction at a rough metal surface," Phys. Rev., Vol. B4, 4129-4138, 1971.

    3. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, New York, 1941.

    4. Neviere, M. and E. Popov, "New theoretical method for electromagnetic wave diffraction by a metallic or dielectric cylinder, bare or coated with a thin dielectric layer," Journal Elect. Waves Appl., Vol. 12, 1265-1296, 1998.

    5. Harrington, R. F., FieldComputation by Moment Methods, Mc Millan, London, 1968.

    6. Van Den Berg, P. M. and J. T. Fokkema, "The Rayleigh hypothesis in the theory of diffraction by a perturbation in a plane surface," Radio Sci., Vol. 15, 723-732, 1980.

    7. Millar, R. F., "The Rayleigh hypothesis and a related least-square solution to scattering problems for periodic surfaces and other scatterers," Radio Sci., Vol. 8, 785-796, 1973.

    8. Afifi, S., "Propagation et diffraction d’une onde electromagnetique dans des structures aperiodiques,", Ph.D. Dissertation, Universite Blaise Pascal, Clermont-Ferrand, France, 1986.

    9. Benali, A., J. Chandezon, and J. Fontaine, "A new theory for scattering of electromagnetic waves from conducting or dielectric rough surfaces," IEEE Trans. Antennas Propagat., Vol. 40, No. 2, 141-148, 1992.

    10. Guizal, B., G. Granet, and J. Chandezon, "Diffraction d’une onde electromagnetique par une surface aperiodique," OHD’97 symposium, 264-266, Clermont-Ferrand, France, 1997.

    11. Baudier, C. and R. Dusseaux, "Scattering of an E-polarized plane wave by one-dimensional rough surfaces: Numerical applicability domain of a Rayleigh method in the far-field zone," Journal of Elect. Waves and Appli.,, to be published.

    12. De Santo, J. A., "Exact spectral formalism for rough-surface," J. Opt. Soc. Am. A, Vol. 2, 2202-2207, 1989.

    13. Maystre, D., "Electromagnetic scattering from perfectly conducting rough surfaces in the resonance region," IEEE Trans. Antennas Propagat., Vol. 31, No. 6, 885-895, 1983.

    14. Faure-Geors, H. and D. Maystre, "Improvement of the Kirchhoff approximation for scattering from rough surface," J. Opt Soc. Am. A, Vol. 6, 532-542, 1989.

    15. Axline, R. M. and A. K. Fung, "Numerical computation of scattering from a perfectly conducting random surface," IEEE Trans. Antennas Propagat., Vol. 26, No. 3, 482-488, 1978.

    16. Li, L., "Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited," J. Opt Soc. Am. A, Vol. 11, 2816-2828, 1994.

    17. Dusseaux, R., C. Faure, J. Chandezon, and F. Molinet, "New perturbation theory of diffraction gratings and its application to the study of ghosts," J. Opt. Soc. Am. A, Vol. 12, 1271-1282, 1995.

    18. Dusseaux, R., P. Chambelin, and C. Faure, "Analysis of rectangular waveguide H-plane junctions in nonorthogonal coordinate system," Progress In Electromagnetic Research, Vol. 28, 205-229, 2000.

    19. Popov, E. and L. Mashev, "Conical diffraction mounting. Generalization of a rigourous differential method," J. Optics (Paris), Vol. 17, No. 4, 175-180, 1986.

    20. Zribi, M., V. Ciarletti, and O. Taconet, "Validation of a rough surface model based on fractional brownian geometry with SIRC and ERSAME radar data over Orgeval," Remote Sens. Environ., Vol. 72, 65-72, 2000.