Vol. 34
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
0000-00-00
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
, Vol. 34, 1-27, 2001
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 Richard 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," , Vol. 34, 1-27, 2001.
doi:10.2528/PIER01010501
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.