Diffraction at a curved grating: TM and TE cases, homogenization

Journal of Mathematical Analysis and Applications

Volumn 202, Issue 3, 1996, Pages 995-1026

  Abboud, Toufic ^a   Ammari, Habib ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030587353     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0357     Document Type: Article

References (21)

1. 1. T. Abboud and H. Ammari, Diffraction at a biperiodic curved structure: Homogenization, C. R. Acad. Sci. Paris Sér. I 320 (1995), 301-306.
2. 2. T. Abboud and H. Ammari, Diffraction at a curved grating: Approximation by an infinite plane grating, C. R. Acad. Sci. Paris Sér. I 320 (1995), 113-118.
3. 3. Y. Achdou, Effect of a thin metallized coating on the reflection of an electromagnetic wave, C. R. Acad. Sci. Paris Sér. I 314 (1992), 217-222.
4. 4. Y. Achdou, O. Pironneau, and A. Zebic, "Effective Boundary Conditions for Thin Coating," Publication du Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 1994.
5. 5. H. D. Alber, A quasi-periodic boundary value problem for the Laplacien and continuation of its resolvent, Proc. Roy. Soc. Edinburgh Sect. A 82 (1979).
6. 6. T. S. Angel, R. E. Kleinman, and F. Hettlich, The resistive and conductive problem for the exterior Helmholtz equation, SIAM J. Appl. Math. 6 (1990), 1607-1622.
7. 7. M. Artola and M. Cessenat, Scattering of an electromagnetic wave by a stendered composite slob join side by side with a thick perfect conductor. I. Inclusions with high conductivity, C. R. Acad. Sci. Paris Sér. I 313 (1991), 231-236.
8. 8. A. Bendali and K. Lemrabet, "The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation," SIAM J. Appl. Math. (1996), in press.
9. 9. A. Bensoussan, J. L. Lions, and G. Papanicolaou, "Asymptotic Analysis for Periodic Structures," Amsterdam, North-Holland, 1978.
10. 10. X. Chen and A. Friedman, Maxwell's equations in a periodic structure, Trans. Amer. Math. Soc. 323 (1991), 465-507.
11. 11. D. Cioranescu and J. Saint Jean Paulin, Homogenization in open sets with holes, J. Math. Anal. Appl. 71 (1979), 590-607.
12. 12. M. Codegone, On the acoustic impedance condition for ondulated boundary, Ann. Inst. H. Pioncaré Phys. Théor. 36 (1992), 1-18.
13. 13. R. R. DeLyster and E. F. Kuester, Homogenization analysis of electromagnetic strip gratings, J. Elect. Waves Appl. 11 (1991), 1217-1236.
14. 14. B. Engquist and J. C. Nédélec, Effective boundary conditions for acoustic and electro-magnetic scattering in thin layers, to appear.
15. 15. R. F. Harrington and J. R. Mautz, An impedance sheet approximation for thin dielectric shells, IEEE Trans. Antennas and Propagation (1975), 531-534.
16. 16. S. N. Karp and F. C. Karal, Generalized impedance boundary conditions for surface wave structures, in "Electromagnetic Wave Theory, Part I" (J. Brown, Ed.), Pergamon, New York, 1965.
17. 17. J. C. Nédélec, "Quelques propriétés des dérivées logarithmiques des fonctions de Hankel," Ecole Polytechnique, Tech. Rep. No. 259, Centre de Mathématiques Appliquées, 1992.
18. 18. J. C. Nédélec and F. Starling, Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell's equations, SIAM J. Math. Anal. 22 (1991), 1679-1701.
19. 19. T. B. A. Senior and J. L. Volakis, Derivation and application of a class of generalized boundary conditions, IEEE Trans. Antennas and Propagation 37 (1989).
20. 20. C. H. Wilcox, "Scattering Theory for Diffraction Gratings," Appl. Math. Sci., Vol. 46, Springer-Verlag, New York/Berlin, 1984.
21. 21. "Electromagnetic Theory of Gratings" (R. Petit, Ed.), Topics in Current Physics, Vol. 22, Springer-Verlag, Heidelberg, 1980.