Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 2
118
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

, &
Pages 317-333 | Received 16 Mar 2010, Accepted 23 Jun 2010, Published online: 23 Nov 2010

References

  • Petit , R (ed.) . 1980 . Electromagnetic Theory of Gratings , Berlin : Springer .
  • Kirsch , A . 1995 . “ An inverse problem for periodic structures ” . In Inverse Scattering and Potential Problems in Mathematical Physics , Edited by: Kleinman , RE , Kress , R and Martensen , E . 75 – 93 . Frankfurt : Peter Lang .
  • Nachman , A . 1988 . Reconstructions from boundary measurements . Ann. Math. , 128 : 531 – 576 .
  • Uhlmann , G . 2009 . Electrical impedance tomography and Calderón problem . Inverse Probl. , 25 123011
  • Strycharz , B . 1998 . An acoustic scattering problem for periodic, inhomogeneous media . Math. Methods Appl. Sci. , 21 : 969 – 983 .
  • Strycharz , B . 1999 . Uniqueness in the inverse transmission scattering problem for periodic midia . Math. Methods Appl. Sci. , 22 : 753 – 772 .
  • Ammari , H . 1995 . Uniqueness theorems for an inverse problems in a doubly periodic structure . Inverse Probl. , 11 : 823 – 833 .
  • Bao , G and Zhou , Z . 1998 . An inverse problem for scattering by a doubly periodic structure . Trans. Amer. Math. Soc. , 350 : 4089 – 4103 .
  • Bao , G , Zhang , H and Zou , J . 2010 . Unique determination of periodic polyhedral structures by scattered electromagnetic fields . Trans. Amer. Math. Soc. , (in press)
  • Sylvester , J and Uhlmann , G . 1990 . “ The Dirichlet to Neumann map and applications ” . In Inverse Problems in Partial Differential Equations , Edited by: Colton , D , Ewing , R and Rundell , W . 101 – 139 . Philadelphia : SIAM .
  • Isakov , V . 2007 . On uniqueness in the inverse conductivity problem with local data . Inverse Probl. Imaging , 1 : 95 – 105 .
  • Abboud , T . 1993 . Formulation variationnelle des équations de Maxwell dans un réseau bipéiodique de R 3 . C.R. Acad. Sci. Paris , 317 : 245 – 248 .
  • Bao , G . 1997 . Variational approximation of Maxwell's equations in biperiodic structures . SIAM J. Appl. Math. , 57 : 364 – 381 .
  • Dobson , D . 1994 . A variational method for electromagnetic diffraction in biperiodic structures . Math. Model. Numer. Anal. , 28 : 419 – 439 .
  • Dobson , D and Friedman , A . 1992 . The time-harmonic Maxwell equations in a doubly periodic structure . J. Math. Anal. Appl. , 166 : 507 – 528 .
  • Elschner , J and Schmidt , G . 1998 . Diffraction in periodic structures and optimal design of binary gratings: I. Direct problems and gradient formulas . Math. Methods Appl. Sci. , 21 : 1297 – 1342 .
  • A. Kirsch, Diffraction by periodic structures, in Proceedings of Lapland Conference on Inverse Problems, L. Päivärinta and E. Somersalo, eds., Springer, Berlin, 1993, pp. 87–102.
  • Nédélec , JC and Starling , F . 1991 . Integral equation method in a quasi-periodic diffraction problem for the time-harmonic Maxwell equations . SIAM J. Math. Anal. , 22 : 1679 – 1701 .
  • Schmidt , G . 2003 . On the diffraction by biperiodic anisotropic structures . Appl. Anal. , 82 : 75 – 92 .
  • Bonnet-Bendhia , AS and Starling , F . 1994 . Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem . Math. Methods Appl. Sci. , 17 : 305 – 338 .
  • Chandler-Wilder , SN and Zhang , B . 1998 . Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate . Proc. R. Soc. Lond. , A454 : 519 – 542 .
  • Zhang , B and Chandler-Wilde , SN . 1998 . Acoustic scattering by an inhomogeneous layer on a rigid plate . SIAM J. Appl. Math. , 58 : 1931 – 1950 .
  • Bao , G , Li , P and Wu , H . 2010 . An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures . Math. Comput. , 79 : 1 – 34 .
  • Buffa , A , Costabel , M and Sheen , D . 2002 . On traces for H(curl, Ω) in Lipschitz domains . J. Math. Anal. Appl. , 276 : 847 – 867 .
  • Cessenat , M . 1996 . Mathematical Methods in Electromagnetism , Singapore : World Scientific .
  • Okaji , T . 2002 . Strong unique continuation property for the time harmonic Maxwell equations . J. Math. Soc. Japan , 54 : 89 – 122 .
  • Ammari , H and Bao , G . 2008 . Coupling finite element and boundary element method for the scattering by periodic chiral structures . J. Comput. Math. , 26 : 261 – 283 .
  • Hu , G , Qu , F and Zhang , B . 2010 . Direct and inverse problems for electromagnetic scattering by a doubly periodic structure with a partially coated dielectric . Math. Methods Appl. Sci. , 33 : 147 – 156 .
  • Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory, , 2nd , Berlin : Springer .
  • M. Wartha, Untersuchung der eigenwerte beim Sturm-Liuouvilleschen Eigenwertproblem mit quasiperiodischen randbedingungen, Diplomarbeit, Unversity Erlangen-Nürnberg, 1995.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.