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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 8
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Articles

On the inverse scattering from anisotropic periodic layers and transmission eigenvalues

ORCID Icon, , &
Pages 3065-3081 | Received 24 Mar 2020, Accepted 24 Sep 2020, Published online: 20 Oct 2020

References

  • Arens T, Grinberg N. A complete factorization method for scattering by periodic structures. Computing. 2005;75:111–132.
  • Arens T, Kirsch A. The factorization method in inverse scattering from periodic structures. Inverse Probl. 2003;19:1195–1211.
  • Bao G, Cui T, Li P. Inverse diffraction grating of Maxwell's equations in biperiodic structures. Optics Express. 2014;22:4799–4816.
  • Elschner J, Hu G. An optimization method in inverse elastic scattering for one-dimensional grating profiles. Commun Comput Phys. 2012;12:1434–1460.
  • Haddar H, Nguyen T-P. Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers. Comput Math Appl. 2017;74:2831–2855.
  • Jiang X, Li P. Inverse electromagnetic diffraction by biperiodic dielectric gratings. Inverse Probl. 2017;33:085004.
  • Lechleiter A, Nguyen D-L. Factorization method for electromagnetic inverse scattering from biperiodic structures. SIAM J Imaging Sci. 2013;6:1111–1139.
  • Nguyen D-L. Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves. Appl Anal. 2014;93:1458–1476.
  • Sandfort K. The factorization method for inverse scattering from periodic inhomogeneous media [PhD thesis]. Karlsruher Institut für Technologie; 2010.
  • Yang J, Zhang B, Zhang R. A sampling method for the inverse transmission problem for periodic media. Inverse Probl. 2012;28:035004.
  • Nguyen T-P. Differential imaging of local perturbations in anisotropic periodic media. Inverse Probl. 2020:36: 034004.
  • Cakoni F, Colton D, Haddar H. On the determination of Dirichlet or transmission eigenvalues from far field data. C R Acad Sci Paris. 2010;348:379–383.
  • Kirsch A, Lechleiter A. The inside–outside duality for scattering problems by inhomogeneous media. Inverse Probl. 2013;29:104011.
  • Harris I, Cakoni F, Sun J. Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids. Inverse Probl. 2014;30:035016.
  • Kleefeld A, Pieronek L. Computing interior transmission eigenvalues for homogeneous and anisotropic media. Inverse Probl. 2018;34:105007.
  • Cakoni F, Haddar H, Harris I. Homogenization of the transmission eigenvalue problem for periodic media and application to the inverse problem. Inverse Probl Imag. 2015;9:1025–1049.
  • Cakoni F, Colton D, Haddar H. Inverse scattering theory and transmission eigenvalues. SIAM; 2016.
  • Bonnet-Bendhia A-S, Starling F. Guided waves by electromagnetic gratings and non-uniqueness examples for the diffraction problem. Math Method Appl Sci. 1994;17:305–338.
  • Lechleiter A, Nguyen D-L. A trigonometric Galerkin method for volume integral equations arising in TM grating scattering. Adv Comput Math. 2014;40:1–25.
  • Kirsch A, Grinberg N. The factorization method for inverse problems. New York, NY: Oxford University Press; 2008. (Oxford Lecture Series in Mathematics and its Applications; 36).
  • Cakoni F, Kirsch A. On the interior transmission eigenvalue problem. Int J Comput Sci Math. 2010;3:142–167.

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