Vol. 57
Latest Volume
All Volumes
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]
2005-09-27
Electromagnetic Scattering by a Set of Objects: an Integral Method Based on Scattering Operator
By
Progress In Electromagnetics Research, Vol. 57, 55-84, 2006
Abstract
The paper presents the Scattering Operator Method, which is devoted to the problem of scattering from a set of N cylindrical ob jects. By contrast with the Scattering Matrix Method, which has been used by many groups in the last twenty years, it applies to any kind of cylinder shape, regardless of the relative location of the cylinders. The theory is based on a mathematical result: it is possible to define in the vicinity of the surface of each cylinder two complementary parts of the field: the total incident field and the field scattered by this cylinder. These two parts are the Calderon projectors of the values of the total fields on the surface of the cylinder. The validity of the method is checked on two examples. It is shown that the theory avoids some problems encountered in integral method like evaluations of singular or hypersingular integrals, or instabilities due to internal resonance of ob jects.
Citation
Daniel Maystre , "Electromagnetic Scattering by a Set of Objects: an Integral Method Based on Scattering Operator," Progress In Electromagnetics Research, Vol. 57, 55-84, 2006.
doi:10.2528/PIER05040901
http://www.jpier.org/PIER/pier.php?paper=0504091
References

1. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals, University Press, Princeton, 1995.

2. Reinex, A. and B. Jecko, "A new photonic band gap equivalent model using Finite Difference Time Domain method," Annales des Télécommunications, Vol. 51, 656-662, 1996.

3. Chew, W. C., L. Gürel, Y. M. Wang, G. Otto, R. L. Wagner, and Q. H. Liu, "A generalized recursive algorithm for wave-scattering solutions in two dimensions," IEEE Trans. on Microwave Theory and Techniques, Vol. 40, 716-723, 1992.
doi:10.1109/22.127521

4. Defos du Rau, M., "Diffusion electromagnétique dépendante dans les milieux hétérogènes denses. Présentation d'un modele mixte en vue de l'étude des matériaux hétérogènes," Ph.D. Thesis, 1997.

5. Elsherbeni, A. Z. and A. Kishk, "Modeling of cylindrical ob jects by circular dielectric or conducting cylinders," IEEE Trans. on Antennas and Propagation, Vol. 40, 96-99, 1992.
doi:10.1109/8.123363

6. Felbacq, D., G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A, Vol. 11, 2526-2538, 1994.

7. Nicorovici, N. A., R. C. McPhedran, and L. C. Botten, "Photonic band gaps for arrays of perfectly conducting cylinders," Phys. Rev. E, Vol. 52, 1135-1145, 1995.
doi:10.1103/PhysRevE.52.1135

8. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwaves Theory Tech., Vol. 47, 2075-2084, 1999.
doi:10.1109/22.798002

9. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, 4773-4776, 1996.
doi:10.1103/PhysRevLett.76.4773

10. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
doi:10.1126/science.1058847

11. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp., Vol. 10, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

12. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 86, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

13. Garcia, N. and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett., Vol. 88, 1-4, 2002.

14. Maystre, D. and S. Enoch, "Perfect lenses made with left handed materials: Alice's mirror," J. Opt. Soc. Am. A, Vol. 21, 122-131, 2004.
doi:10.1364/JOSAA.21.000122

15. Chew, W. C., J. M. Jin, E. Michielsen, and J. Song (eds.), Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

16. Taflove, A., Computational Electrodynamics: The finite Difference Time Domain Method, Artech House, Boston, 1995.

17. Hafner, C., The Generalized Multipole Technique for Computational Electromagnetics, Artech House, Boston, 1990.

18. Silvester, P. P. and G. Pelosi, Finite Elements for Wave Electromagnetics, IEEE Press, New York, 1994.

19. Maystre, D. and P. Vincent, "Diffraction d'une onde électromagnétique plane par un objet cylindrique non infini- ment conducteur de section arbitraire," Opt. Commun., Vol. 5, 327-330, 1972.
doi:10.1016/0030-4018(72)90025-9

20. Abramovitz, M. and I. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1970.

21. Courant, R. and D. Hilbert, Methods of Mathematical Physics, Vol. 2, Vol. 2, Interscience, New-York, 1962.

22. Kong, J. A., Electromagnetic Wave Theory, EMW Publishing, Cambridge, 2000.

23. Roger, A., "Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix," Electromagnetics, Vol. 2, 69-83, 1982.

24. Maystre, D. and M. Cadilhac, "Singularities of the continuation of the fields and validity of Rayleigh's hypothesis," Journal of Mathematical Physics, Vol. 26, 2201-2204, 1985.
doi:10.1063/1.526847

25. Schwartz, L., Mathematics for the Physical Sciences, Addison-Wesley, Reading, Mass., 1966.

26. Cessenat, M., "The use of the calderon pro jectors and the capacity operators in scattering," Scattering in Volumes and Surfaces, 255-268, 1990.