Vol. 59
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]
2006-01-06
C-Method: Several Aspects of Spectral Theory of Gratings
By
, Vol. 59, 113-149, 2006
Abstract
The goal of the present paper is two folded. The first, the methodological one, is the complementation of well established in diffraction theory of gratings C method with certain elements of spectral theory and the development of interactive numerical algorithm that made feed back conjunction between diffraction and spectral problems. As a natural result the second goal appeared: the appearing of such tool for numerical experiments resulted in profound qualitative and quantitative study of rather peculiar phenomena in resonant scattering from periodic surface. Special attention has been paid to the investigation of electromagnetic waves diffraction from periodic boundaries of material with single and double negative parameters.
Citation
Anatoly Poyedinchuk Yury Tuchkin Nataliya Yashina Jean Chandezon Gerard Granet , "C-Method: Several Aspects of Spectral Theory of Gratings," , Vol. 59, 113-149, 2006.
doi:10.2528/PIER05050901
http://www.jpier.org/PIER/pier.php?paper=0505091
References

1. Petit, R. (ed.), Electromagnetic Theory of Gratings, Springer- Verlag, Heidelberg, 1980.

2. Galishnikova, T. N. and A. S. Il'insky, Numerical Methods in Diffraction Problems, Moscow, Publishing House of Moscow State University, 1987.

3. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, 1983.

4. Shestopalov, V. P., Yu. A. Tuchkin, A. Ye. Poyedinchuk, and Yu. K. Sirenko, "Novel methods of solving of direct and inverse problems of diffraction theory," Analytical Regularization of Boundary Value Problems in Electromagnetics, 1997.

5. Shestopalov, V. P., Method of Rieman-Hilbert Problem in Theory of Electromagnetic Wave Diffraction and Propagation, Vol. 59, Publishing House of Kharkov University, Kharkov, 1971.

6. Shestopalov, V. P., L. N. Litvinenko, S. A. Masalov, and V. G. Sologub, Wave Diffraction by Gratings, Publ. of Kharkov National University, Kharkov, 1973.

7. Shestopalov, V. P. and Yu. K. Sirenko, Dynamic Theory of Gratings, Kiyev, Naukova Dumka, 1989.

8. Bass, F. G. and I. M. Fuks, Wave Scattering by Statistical ly Rough Surface, Moscow, Nauka, 1972.

9. Popov, E. and M. Neviere, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A, Vol. 17, 1773-1784, 2000.

10. Chandezon, J., D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Optics, Vol. 11, 235-241, 1980.
doi:10.1088/0150-536X/11/4/005

11. Chandezon, J., M. T. Depuis, G. Cornet, and D. Maystre, "Multicoated gratings: a differential formalism applicable in the entire optical region," Journal of Optical Society of Am., Vol. 72, 839-846, 1982.

12. Plumey, J-P., G. Granet, and J. Chandezon, "Differential covariant formalism for solving Maxwell's equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces," IEEE Trans. On Antennas and Propag., Vol. 43, 835-842, 1995.
doi:10.1109/8.402203

13. Granet, G., J-P. Plumey, and J. Chandezon, "Some topics in extending the C method to multilayer-coated gratings of different profiles," Pure Appl. Opt., Vol. 5, 141-155, 1996.
doi:10.1088/0963-9659/5/2/002

14. Plumey, J-P., B. Guizal, and J. Chandezon, "Coordinate transformation method as applied to asymmetric gratings with vertical facets," Journal of Optical Society of Am. A, Vol. 14, No. 3, 610-617, 1997.

15. Li, L., J. Chandezon, G. Granet, and J-P. Plumey, "A rigorous and efficient grating analysis method made easy for optical engineers," Appl. Opt., Vol. 38, 304-313, 1999.

16. Chandezon, J., A. Ye. Poyedinchuk, Yu. A. Tuchkin, and N. P. Yashina, "Mathematical modeling of electromagnetic wave scattering by wavy periodic boundary between two media," Progress In Electromagnetics Research, Vol. 38, 130-143, 2002.

17. Sveshnikov, A. G., Incomplete Galerkin Method, 1076-1079, Doklady Akademy Nauk SSSR, 236, 1977.

18. Vasilenko, Yu. N., A. S. Il'insky, and Yu. Ya. Kharlanov, "Model of lens antenna of waveguides with irregular cross section," Radiotekhnika I Electronica, Vol. 42, 295-301, 1997.

19. Yasuura, K. and Y. Okuno, "Numerical analysis of diffraction 148 Poyedinchuk et al. from a grating by the mode matching method with a smoothing procedure," Journal of Optical Society of Am. A, Vol. 72, 1012-1025, 1982.

20. Popovidi-Zaridze, R. S. and Z. S. Tsverikmozashvili, "Numerical investigation of diffraction problems by means of modified method of non-orthogonal series," Jurnal Vychislitel'noy Matematiki i Matematicheskoy Fiziki, Vol. 17, 384-393, 1977.

21. Babich, V. I. and V. S. Buldyrev, Asymptotical Methods in Diffraction Theory, Nauka, Moscow, 1972.

22. Borovikov, V. A. and B. Ye. Kinber, Geometrical Theory of Diffraction, Sviaz, Moscow, 1978.

23. Vainshtein, L. A., Electromagnetic Waves, Sovetskoye Radio Publishing House, Moscow, 1957.

24. Bliokh, K. Yu. and Yu. P. Bliokh, "What are left-handed media and what is interesting about them," Uspehi Fizicheskih Nauk, Vol. 174, No. 4, 2004.

25. Mittra, R. and S. W. Lee, Analytical Technique in the Theory of Guided Waves, The Macmillan Company, 1971.

26. Andersen, J. B. and V. V. Solodukhov, "Field behavior near a dielectric wedge," IEEE Transaction on Antennas and Propag., Vol. 26, 598-602, 1978.
doi:10.1109/TAP.1978.1141899

27. Yanushauskas, A. I., Multiple Trigonometric Series, Nauka Publishing House, Novosibirsk, 1986.

28. Hormander, L., The Analysis of Linear Partial Differential Operators, Vol 1: Distribution theory and Fourier analysis, Springer, 1983.

29. Tuchkin, Yu. A., "Analytical regularization of one class of integral equation in diffraction theory," Doklady Akademii Nauk Ukrainy, Vol. 10, 345-350, 1998.

30. Poyedinchuk, A. Ye., V. P. Shestopalov, and N. P. Yashina, "Spectral theory of coaxial waveguide resonators," USSR. Computer Mathematics and Mathematical Physics, Vol. 26.552-562, 552-562, 1986.

31. Pochanina, I. E. and N. P. Yashina, "Electromagnetic properties of open waveguide resonators," Electromagnetics, Vol. 13, 325-341, 1993.

32. Poyedinchuk, Ye., Yu. A. Tuchkin, and V. P. Shestopalov, "Regularization of spectral problems of wave scattering on unclosed screens," Doklady Acad. Nauk SSSR, Vol. 295, 1358-1362, 1987.

33. Veselago, V. G., "Electrodynamics of materials with both negative ε and μ," Uspekhi Fizicheskih Nauk., Vol. 2, 517-526, 1967.

34. Felbacq, D. and A. Moreau, "Direct evidence of negative refraction at media with negative ε and μ," J. Opt. A: Pure Appl. Opt., Vol. 5, 9, 2003.
doi:10.1088/1464-4258/5/3/102

35. Maystre, D. and S. Enoch, "Perfect lenses made with left-handed materials: Alice's mirror?," J. Opt. Soc. Am. A, Vol. 21, 122-1312004, 1312.

36. Traub, J. F., Iterative Methods for the Solution of Equations, Prentice-Hall, 1964.

37. Wilkinson, J. H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.

38. Wilkinson, J. H. and C. Reinch, Handbook for Automatic Computation, Springer-Verlag, New York, 1971.

39. Melezhik, P. N., A. Ye. Poyedinchuk, Yu. A. Tuchkin, and V. P. Shestopalov, "About analytical origins of eigen mode coupling," Soviet Doklady, Vol. 300, 456-463, 1988.

40. Bespyatih, Yu. I., I. Ye. Dikshtaine, and D. I. Ermakov, "Surface polaritons on the boundary between composite media with a dispersion of permittivity and permeability," Padiotechnika & Electronica, Vol. 48, 449-458, 2003.

41. Chandezon, J., G. Granet, A. Poyedinchuk, and N. Yashina, "Rigorous model for the materials with negative permittivity and permeability electromagnetic study," PIERS 2004, Vol. '' S 2004.

42. Yashina, N., A. Poyedinchuck, S. Panin, G. Granet, and M. Ney, "FS periodic coatings made of metamaterials: numerical synthesis and optimization," APMC 2004, 15-18, 2004.