Abstract

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics 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

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
    [CrossRef]
  2. U. Leonhardt, "Optical conformal mapping," Science 312,1777 (2006).
    [CrossRef]
  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]
  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]
  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]
  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]
  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]

2009 (3)

U. Leonhardt and T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Y. You, G. W. Kattawar, and P. Yang, "Invisibility cloaks for toroids," Opt. Express 17, 6591 (2009).
[CrossRef]

2008 (5)

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]

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]

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]

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]

A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584-1586 (2008).
[CrossRef]

2007 (2)

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

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]

2006 (4)

J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

U. Leonhardt, "Optical conformal mapping," Science 312,1777 (2006).
[CrossRef]

G. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462,3027 (2006).
[CrossRef]

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]

2005 (1)

A. Alu and N. Engheta, "Achieving Transparency with Plasmonic and Metamaterial Coatings," Phys. Rev. E 95,016623 (2005).
[CrossRef]

2003 (1)

A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).

1994 (1)

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, "Achieving Transparency with Plasmonic and Metamaterial Coatings," Phys. Rev. E 95,016623 (2005).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Cheng, Q.

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]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Chin, J. Y.

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]

Cui, T. J.

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]

Cummer, S. A.

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]

Engheta, N.

A. Alu and N. Engheta, "Achieving Transparency with Plasmonic and Metamaterial Coatings," Phys. Rev. E 95,016623 (2005).
[CrossRef]

Enoch, S.

Farhat, M.

Feng, Y.

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Genon, A.

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Greenleaf, A.

A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).

Guenneau, S.

He, S.

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]

Hu, L.

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Jiang, W. X.

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]

Jin, Y.

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]

Justice, B. J.

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]

Kattawar, G. W.

Kildiev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Kohn, R. V.

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]

Lassas, M.

A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).

Legros, W.

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Leonhardt, U.

U. Leonhardt and T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

U. Leonhardt, "Optical conformal mapping," Science 312,1777 (2006).
[CrossRef]

Li, Z.

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]

Liu, R.

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]

Meys, B.

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Milton, G.

G. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462,3027 (2006).
[CrossRef]

Mock, J. J.

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]

Movchan, A. B.

Nicolet, A.

Nicorovici, N. A.

G. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462,3027 (2006).
[CrossRef]

Pendry, J. B.

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]

Pendry, J.B.

Qiu, C.W.

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Remacle, J.F.

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Schurig, D.

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]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Shen, H.

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]

Shurig, D.

J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

Smith, D. R.

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]

Smith, D.R.

J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

Starr, A. F.

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]

Tyc, T.

U. Leonhardt and T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

Uhlmann, G.

A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).

Vogelius, M. S.

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]

Xu, X.

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

Yang, P.

You, Y.

Zhang, P.

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]

Zolla, F.

Appl. Phys. Lett. (1)

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]

Inverse Probl. (1)

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]

J. Appl. Phys. (1)

A. Nicolet, J.F. Remacle, B. Meys, A. Genon and W. Legros, "Transformation methods in computational electromagnetics," J. Appl. Phys. 756036 (1994).
[CrossRef]

Math. Res. Lett. (1)

A. Greenleaf, M. Lassas and G. Uhlmann, "On nonuniqueness for Calderons inverse problem," Math. Res. Lett. 10, 685-693 (2003).

Nat. Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildiev, and V. M. Shalaev, "Optical Cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (3)

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]

C.W. Qiu, L. Hu, X. Xu, and Y. Feng, "Spherical cloaking with homogeneous isotropic multilayered structures," Phys. Rev. E 79, 047602 (2009).
[CrossRef]

A. Alu and N. Engheta, "Achieving Transparency with Plasmonic and Metamaterial Coatings," Phys. Rev. E 95,016623 (2005).
[CrossRef]

Proc. R. Soc. London A (1)

G. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462,3027 (2006).
[CrossRef]

Science (4)

J.B. Pendry, D. Shurig and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef]

U. Leonhardt, "Optical conformal mapping," Science 312,1777 (2006).
[CrossRef]

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]

U. Leonhardt and T. Tyc, "Broadband invisibility by non-euclidean cloaking," Science 323, 110 (2009).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics