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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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SCATTERING OF AN E||-POLARIZED PLANE WAVE BY ONE-DIMENSIONAL ROUGH SURFACES: NUMERICAL APPLICABILITY DOMAIN OF A RAYLEIGH METHOD IN THE FAR-FIELD ZONE

By C. Baudier and R. Dusséaux

Full Article PDF (1,138 KB)

Abstract:
The field scattered by a perfectly conducting plane surface with a perturbation illuminated by an E//-polarized plane wave is determined by means of a Rayleigh method. This cylindrical surface is described by a local function. The scattered field is supposed to be represented everywhere in space by a superposition of a continuous spectrum of outgoing plane waves. A "triangle/Dirac" method of moments applied to the Dirichlet boundary condition in the spectral domain allows the wave amplitudes to be obtained. For a half cosine arch,the proposed Rayleigh method is numerically investigated in the far-field zone,b y means of convergence tests on the spectral amplitudes and on the power balance criterion. We show that the Rayleigh integral can be used for perturbations,the amplitudes of which are close to half the wavelength.

Citation:
C. Baudier and R. Dusséaux, "Scattering of an E||-Polarized Plane Wave by One-Dimensional Rough Surfaces: Numerical Applicability Domain of a Rayleigh Method in the Far-Field Zone," Progress In Electromagnetics Research, Vol. 34, 1-27, 2001.
doi:10.2528/PIER01010501
http://www.jpier.org/PIER/pier.php?paper=0101051

References:
1. 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.
doi:10.1029/RS015i004p00723

2. Millar, R. F., "The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers," Radio Sci., Vol. 8, 785-796, 1973.
doi:10.1029/RS008i008p00785

3. Harrington, R. F., Field Computation by Moment Methods, Mc Millan, London, 1968.

4. Jones, D. S., Methods in Electromagnetic Wave Propagation, Clarendon Press, Oxford, 1979.

5. Petit, R. and M. Cadilhac, "Sur la diffraction d’une onde plane par un reseau infiniment conducteur," C. R. Acad. Sci. B, 468-471, 1966.

6. Millar, R. F., "On the Rayleigh assumption in scattering by a periodic surface," Proc. Camb. Phil. Soc., Vol. 65, 773-791, 1969.
doi:10.1017/S0305004100003613

7. Millar, R. F., "On the Rayleigh assumption in scattering by a periodic surface - II," Proc. Camb. Phil. Soc., Vol. 69, 217-225, 1971.
doi:10.1017/S0305004100046570

8. Van den Berg, P. M. and J. T. Fokkema, "The Rayleigh hypothesis in the theory of reflection by a grating," J. Opt. Soc. Am., Vol. 69, 27-31, 1979.
doi:10.1364/JOSA.69.000027

9. Keller, J. B., "Singularities and Rayleigh’s hypothesis for diffraction gratings," J. Opt. Soc. Am. A, Vol. 17, 456-457, 2000.
doi:10.1364/JOSAA.17.000456

10. Van den Berg, P. M., "Reflection by a grating: Rayleigh methods," J. Opt. Soc. Am. A, Vol. 71, 1224-1229, 1981.
doi:10.1364/JOSA.71.001224

11. Hugonin, J. P., R. Petit, and M. Cadilhac, "Plane-wave expansions used to describe the field diffracted by a grating," J. Opt. Soc. Am., Vol. 71, 593-598, 1981.
doi:10.1364/JOSA.71.000593

12. Wirgin, A., "Reflection from a corrugated surface," J. Acoust. Soc. Am., Vol. 68, 1980.
doi:10.1121/1.384728

13. Bagieu, M. and D. Maystre, "Waterman and Rayleigh methods for diffraction grating problems: extension of the convergence domain," J. Opt. Soc. Am. A, Vol. 15, 1566-1576, 1998.
doi:10.1364/JOSAA.15.001566

14. Bagieu, M. and D. Maystre, "Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings," J. Opt. Soc. Am. A, Vol. 16, 284-292, 1999.
doi:10.1364/JOSAA.16.000284

15. Kleev, A. I. and A. B. Manenkov, "The convergence of pointmatching techniques," IEEE Trans. Antennas Propagat., Vol. 37, 50-54, 1989.
doi:10.1109/8.192163

16. Christiansen, S. and R. E. Kleinman, "On a misconception involving point collocation and the Rayleigh hypothesis," IEEE Trans. Antennas Propagat., Vol. 44, No. 10, 1309-1316, 1996.
doi:10.1109/8.537324

17. Manenkov, A. B., "Comments on ‘On a misconception involving point collocation and the Rayleigh hypothesis’," IEEE Trans. Antennas Propagat., Vol. 46, 1765, 1998.
doi:10.1109/8.736647

18. Maystre, D., "Electromagnetic scattering from perfectly conducting rough surfaces in the resonance region," IEEE Trans. Antennas Propagat., Vol. 31, No. 6, 885-895, 1983.
doi:10.1109/TAP.1983.1143159

19. Maystre, D. and J. P. Rossi, "Implemen tation of a rigourous vector theory of speckle for two-dimensional microrough surfaces," J. Opt. Soc. Am., Vol. 3, 1276-1282, 1986.
doi:10.1364/JOSAA.3.001276

20. 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.
doi:10.1109/TAP.1978.1141871

21. DeSanto, J. A., "Exact spectral formalism for rough-surface scattering," J. Opt. Soc. Am. A, Vol. 2, 2202-2207, 1985.
doi:10.1364/JOSAA.2.002202

22. Petit, R., Ondes Electromagnetiques en Radioelectricite et en Optique, Masson (ed.), Paris, 1993.

23. Shannon, C. E., "Mathematical theory of communication," Bell System Tech. J., Vol. 27, 379-423, 1948.
doi:10.1002/j.1538-7305.1948.tb01338.x

24. Afifi, S., "Propagation et diffraction d’une onde electromagnetique dans des structures aperiodiques,", These d’Universite, Univ ersite Blaise Pascal de Clermont-Ferrand, France, 1986.

25. 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.
doi:10.1109/8.127397

26. Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, New York and London, 1941.

27. Kong, J. A., Electromagnetic Wave Theory, John Wiley and Sons, 1990.


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