Free access
Issue
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
Page(s) 1167 - 1184
DOI http://dx.doi.org/10.1051/m2an/2012063
Published online 17 June 2013
  1. T. Abboud, Electromagnetic waves in periodic media, in Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, Newark, DE. SIAM, Philadelphia (1993) 1–9.
  2. H. Alber, A quasi-periodic boundary value problem for the laplacian and the continuation of its resolvent. Proc. Royal Soc. Edinburgh 82 (1979) 251–272. [CrossRef]
  3. T. Arens, Scattering by biperiodic layered media: The integral equation approach.Habilitation Thesis, Universität Karlsruhe (2010).
  4. G. Bao, Variational approximation of Maxwell’s equations in biperiodic structures. SIAM J. Appl. Math. 57 (1997) 364–381. [CrossRef]
  5. G. Bao, L. Cowsar and W. Masters, Mathematical modeling in optical science. SIAM Frontiers Appl. Math. SIAM, Philadelphia (2001).
  6. G. Bao and D.C. Dobson, On the scattering by a biperiodic structure. Proc. Amer. Math. Soc. 128 (2000) 2715–2723. [CrossRef] [MathSciNet]
  7. A.-S. Bonnet-Bendhia and F. Starling, Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem. Math. Methods Appl. Sci. 17 (1994) 305–338. [CrossRef]
  8. S.N. Chandler-Wilde and P. Monk, Existence, uniqueness, and variational methods for scattering by unbounded rough surfaces. SIAM. J. Math. Anal. 37 (2005) 598–618. [CrossRef] [MathSciNet]
  9. M. Costabel, M. Dauge and S. Nicaise, Corner Singularities and Analytic Regularity for Linear Elliptic Systems. Part I: Smooth domains. http://hal.archives-ouvertes.fr/hal-00453934/.
  10. D. Dobson and A. Friedman, The time-harmonic Maxwell’s equations in a doubly periodic structure. J. Math. Anal. Appl. 166 (1992) 507–528. [CrossRef]
  11. D.C. Dobson, A variational method for electromagnetic diffraction in biperiodic structures. Math. Model. Numer. Anal. 28 (1994) 419–439.
  12. H. Haddar and A. Lechleiter, Electromagnetic wave scattering from rough penetrable layers. SIAM J. Math. Anal. 43 (2011) 2418–2433. [CrossRef] [MathSciNet]
  13. W. McLean, Strongly Elliptic Systems and Boundary Integral Operators. Cambridge University Press, Cambridge, UK (2000).
  14. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford Science Publications, Oxford (2003).
  15. F. Rellich, Darstellung der Eigenwerte von Δu + λu = 0 durch ein Randintegral. Math. Zeitschrift 46 (1940) 635–636. Doi: 10.1007/BF01181459. [CrossRef]
  16. G. Schmidt, On the diffraction by biperiodic anisotropic structures. Appl. Anal. 82 (2003) 75–92. [CrossRef]
  17. C. Wilcox, Scattering Theory for Diffraction Gratings. Appl. Math. Sci. Springer-Verlag 46 (1984).

Recommended for you