Abstract

The material properties of toroidal invisibility cloaks are derived based on the coordinate transformation method. The permittivity and permeability tensors for toroidal cloaks are substantially different from those for spherical cloaks, but quite similar to those for 2D cylindrical cloaks because a singularity is involved at the inner boundary in both the cases. The cloaking effect is confirmed by the electric field distribution in the vicinity of toroidal cloaks simulated from the generalized discrete-dipole approximation (DDA) method. This study extends the concept of electromagnetic cloaking of arbitrarily-shaped objects to a complex geometry.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Opt. 43, 773-793 (1996).
    [CrossRef]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
    [CrossRef]
  4. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
    [CrossRef] [PubMed]
  5. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  6. U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
    [CrossRef]
  7. D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
    [CrossRef] [PubMed]
  8. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  9. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  10. B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
    [CrossRef]
  11. H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
    [CrossRef]
  12. D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  13. W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
    [CrossRef]
  14. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
    [CrossRef]
  15. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, "Invisibility cloaks for irregular particles using coordinate transformations," Opt. Express 16, 6134-6145 (2008).
    [CrossRef] [PubMed]
  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]
  18. C. Li and F. Li, "Two-dimensional electromagnetic cloaks with arbitrary geometries," Opt. Express 16, 13414-13420 (2008).
    [CrossRef] [PubMed]
  19. C. Li, K. Yao, and F. Li, "Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries," Opt. Express 16, 19366-19374 (2008).
    [CrossRef]
  20. W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
    [CrossRef]
  21. H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (2008).
    [CrossRef] [PubMed]
  22. J. Hu, X. Zhou and G. Hu, "Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation," Opt. Express 17, 1308-1320 (2009).
    [CrossRef] [PubMed]
  23. 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, 977-980 (2006).
    [CrossRef] [PubMed]
  24. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Two-dimensional metamaterial structure exhibiting reduced visibility at 500 nm," Opt. Lett. 33, 1342-1344 (2008).
    [CrossRef] [PubMed]
  25. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
    [CrossRef]
  26. P. Collins and J. McGuirk, "A novel methodology for deriving improved material parameter sets for simplified cylindrical cloaks," J. Opt. A 11, 015104 (2009).
    [CrossRef]
  27. S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, "A route to quasi-perfect invisibility cylindrical cloaks without extreme values in the parameters," http://arxiv.org/abs/0812.1995 (2008).
  28. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  29. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  30. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  31. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, "Zero-backscatter cloak for aspherical particles using a generalized DDA formalism," Opt. Express 16, 2068-2079 (2008).
    [CrossRef] [PubMed]

2009 (2)

J. Hu, X. Zhou and G. Hu, "Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation," Opt. Express 17, 1308-1320 (2009).
[CrossRef] [PubMed]

P. Collins and J. McGuirk, "A novel methodology for deriving improved material parameter sets for simplified cylindrical cloaks," J. Opt. A 11, 015104 (2009).
[CrossRef]

2008 (13)

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Two-dimensional metamaterial structure exhibiting reduced visibility at 500 nm," Opt. Lett. 33, 1342-1344 (2008).
[CrossRef] [PubMed]

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, "Zero-backscatter cloak for aspherical particles using a generalized DDA formalism," Opt. Express 16, 2068-2079 (2008).
[CrossRef] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, "Invisibility cloaks for irregular particles using coordinate transformations," Opt. Express 16, 6134-6145 (2008).
[CrossRef] [PubMed]

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] [PubMed]

C. Li and F. Li, "Two-dimensional electromagnetic cloaks with arbitrary geometries," Opt. Express 16, 13414-13420 (2008).
[CrossRef] [PubMed]

C. Li, K. Yao, and F. Li, "Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries," Opt. Express 16, 19366-19374 (2008).
[CrossRef]

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (2008).
[CrossRef] [PubMed]

2007 (4)

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

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

2006 (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, 977-980 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

1996 (1)

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

1994 (1)

1988 (1)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1973 (1)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Cai, W.

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

Chen, H.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Cheng, Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (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]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shavlaev, "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]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Collins, P.

P. Collins and J. McGuirk, "A novel methodology for deriving improved material parameter sets for simplified cylindrical cloaks," J. Opt. A 11, 015104 (2009).
[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]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977-980 (2006).
[CrossRef] [PubMed]

Davis, C. C.

Draine, B. T.

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Flatau, P. J.

Guenneau, S.

Hu, G.

Hu, J.

Hung, Y. J.

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]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (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, 977-980 (2006).
[CrossRef] [PubMed]

Kattawar, G. W.

Kildishev, A. V.

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

Kong, J. A.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
[CrossRef]

Li, C.

Li, F.

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]

Lin, X. Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (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]

Luo, Y.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Ma, H.

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (2008).
[CrossRef] [PubMed]

McGuirk, J.

P. Collins and J. McGuirk, "A novel methodology for deriving improved material parameter sets for simplified cylindrical cloaks," J. Opt. A 11, 015104 (2009).
[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, 977-980 (2006).
[CrossRef] [PubMed]

Nicolet, A.

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
[CrossRef]

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Qiu, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (2008).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Ran, L.

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

Shavlaev, V. M.

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

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (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, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

Smolyaninov, I. I.

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, 977-980 (2006).
[CrossRef] [PubMed]

Wang, J.

Ward, A. J.

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

Werner, D. H.

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Wu, B.-I.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Approximation approach of designing practical cloaks with arbitrary shapes," Opt. Express 16, 15449-15454 (2008).
[CrossRef] [PubMed]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

Yan, W.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

Yang, P.

Yao, K.

You, Y.

Yu, G. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Zhai, P.-W.

Zhang, B.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Zhang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Zhou, X.

Zolla, F.

Appl. Phys. Lett. (1)

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Astrophys. J. (2)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, "Refraction and geometry in Maxwell’s equations," J. Mod. Opt. 43, 773-793 (1996).
[CrossRef]

J. Opt. A (1)

P. Collins and J. McGuirk, "A novel methodology for deriving improved material parameter sets for simplified cylindrical cloaks," J. Opt. A 11, 015104 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. D: Appl. Phys. (1)

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Nat. Photon. (1)

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

New J. Phys. (2)

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys. 8, 247 (2006).
[CrossRef]

U. Leonhardt, "Notes on conformal invisibility devices," New J. Phys. 8, 118 (2006).
[CrossRef]

New. J. Phys. (1)

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New. J. Phys. 10, 043040 (2008).
[CrossRef]

Opt. Express (8)

Opt. Lett. (2)

Photon. Nanostruct.: Fundam. Applic. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Zhang, B, Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Phys. Rev. B (1)

B. Zhang, H. Chen, B.-I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
[CrossRef]

Phys. Rev. E (2)

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]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interaction with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Science (3)

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

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, 977-980 (2006).
[CrossRef] [PubMed]

Other (1)

S. Xi, H. Chen, B. Zhang, B.-I. Wu, and J. A. Kong, "A route to quasi-perfect invisibility cylindrical cloaks without extreme values in the parameters," http://arxiv.org/abs/0812.1995 (2008).

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.


Figures (5)

Fig. 1.
Fig. 1.

(a) A toroid with b = R/2; (b) The toroidal coordinates spanned by unit vectors er , eu and ev ; (c) A toroidal cloak with b = R/2 and a = b/2.

Fig. 2.
Fig. 2.

3-D view of the propagation of light rays (blue lines) and associated wave fronts (red lines) in a toroidal cloak.

Fig. 3.
Fig. 3.

Diagonal components of the permittivity and permeability tensors for a toroidal cloak with b = R/2 and a = b/2. The angle u varies from 0° to 90°.

Fig. 4.
Fig. 4.

Same as Fig. 3, except that b = R/10.

Fig. 5.
Fig. 5.

The DDA simulation of the electric field distributions in the vicinity of toroidal cloaks subject to incident plane waves. (a) a=3/4b, b=R/2 and R=0.45λ ; (b) a=3/4b, b = 3/4R, and R = 1.196λ. The scales are in units of λ.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

x = ( R + r sin u ) cos v ,
y = ( R + r sin u ) sin v ,
z = r cos u ,
r ' = a + b a b r , u ' = u , v ' = v ,
ε i ' j ' = μ i ' j ' = det ( Λ i ' i ) 1 Λ i ' i Λ j ' j ,
ε ' = μ ' = det ( Λ ) 1 ΛΛ T .
( x , y , z ) ( r , u , v ) ( r ' , u ' , v ' ) ( x ' , y ' , z ' ) .
Λ 1 = ( r , u , v ) ( x , y , v ) , Λ 2 = ( r ' , u ' , v ' ) ( r , u , v ) , Λ 3 = ( x ' , y ' , z ' ) ( r ' , u ' , v ' ) .
Λ = ( x ' , y ' , z ' ) x , y , z = Λ 3 Λ 2 Λ 1 .
ε ' = μ ' = det ( Λ 1 1 ) det ( Λ 3 ) det ( Λ 2 ) Λ 3 Λ 2 Q 1 1 Λ 2 T Λ 3 T ,
T ruv = ( D Λ 3 1 ) T xyz ( D Λ 3 1 ) T ,
ε ' ruv = μ ' ruv = det ( Λ 1 1 ) det ( Λ 3 ) det ( Λ 2 ) D Λ 2 Q 1 1 Λ 2 T Q 3 D 1 ,
Q 1 = diag [ 1 , r 2 , ( R + r sin u ) 2 ] ,
Λ 2 = diag [ b a b , 1,1 ] ,
Q 3 = diag [ 1 , r ' 2 , ( R + r ' sin u ) 2 ] ,
D = diag [ 1 , r ' , ( R + r ' sin u ) 2 ] .
ε r r = μ r r = r a r ( b a ) R + b ( r a ) sin u ( b a ) ( R + r sin u ) ,
ε u u = μ u u = r r a ( b a ) R + b ( r a ) sin u ( b a ) ( R + r sin u ) ,
ε v v = μ v v = b 2 b a r a r R + r sin u ( b a ) R + b ( r a ) sin u ,
ε r = μ r = r R 1 r ,
ε ϕ = μ ϕ = r r R 1 ,
ε z = μ z = ( R 2 R 2 R 1 ) 2 r R 1 r ,

Metrics