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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 22603–22608

Revolution analysis of three-dimensional arbitrary cloaks

Guillaume Dupont, Sébastien Guenneau, Stefan Enoch, Guillaume Demesy, André Nicolet, Frédéric Zolla, and André Diatta  »View Author Affiliations

Optics Express, Vol. 17, Issue 25, pp. 22603-22608 (2009)

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We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics [1] to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(160.1190) Materials : Anisotropic optical materials
(260.2110) Physical optics : Electromagnetic optics
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

Original Manuscript: October 12, 2009
Revised Manuscript: November 12, 2009
Manuscript Accepted: November 14, 2009
Published: November 24, 2009

Guillaume Dupont, Sébastien Guenneau, Stefan Enoch, Guillaume Demesy, André Nicolet, Frédéric Zolla, and André Diatta, "Revolution analysis of three-dimensional arbitrary cloaks," Opt. Express 17, 22603-22608 (2009)

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  1. J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006). [CrossRef] [PubMed]
  2. U. Leonhardt, "Optical conformal mapping," Science 312,1777 (2006). [CrossRef] [PubMed]
  3. A. Alu and N. Engheta, "Achieving Transparency with Plasmonic and Metamaterial Coatings," Phys. Rev. E 95,016623 (2005). [CrossRef]
  4. G. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462,3027 (2006). [CrossRef]
  5. F. Zolla, S. Guenneau, A. Nicolet, and J.B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069 (2007). [CrossRef] [PubMed]
  6. A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).
  7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006). [CrossRef] [PubMed]
  8. P. Zhang, Y. Jin, and S. He, "Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak," Appl. Phys. Lett. 93, 243502 (2008). [CrossRef]
  9. U. Leonhardt and T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110 (2009). [CrossRef]
  10. W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007). [CrossRef]
  11. M. Farhat, S. Guenneau, A. B. Movchan, and S. Enoch, "Achieving invisibility over a finite range of frequencies," Opt. Express 16, 5656-5661 (2008). [CrossRef] [PubMed]
  12. C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009). [CrossRef]
  13. Y. You, G. W. Kattawar, and P. Yang, "Invisibility cloaks for toroids," Opt. Express 17, 6591 (2009). [CrossRef] [PubMed]
  14. A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994). [CrossRef]
  15. R. V. Kohn, H. Shen,M. S. Vogelius, andM. I.Weinstein, "Cloaking via change of variables in electric impedance tomography," Inverse Probl. 24, 015016 (2008). [CrossRef]
  16. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008). [CrossRef]
  17. A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584-1586 (2008). [CrossRef] [PubMed]

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