Abstract

We propose a generalized transformation for a nonmagnetic invisibility cloak with minimized scattering. In comparison with the previous transformation, it has been demonstrated that the unphysical singularity at the inner boundary and the limitation of the thickness of the cloak shell can be removed by choosing the appropriate transformation function. Furthermore, our generalized transformation is used to design two different nonmagnetic cloaks without considering the unphysical singularity and the limitation of the thickness. Based on the effective medium theory, an alternating layered system composed of two isotropic materials is employed to realize these cloaks. Moreover, through calculating the scattering cross section of the cloak, it is found that such a nonmagnetic cloak can only work in a narrow frequency range.

© 2011 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Lenohardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef]
  3. 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]
  4. S. A. Cummer, B. I. Popa, D. R. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
    [CrossRef]
  6. I. I. Smolyaninov, Y. J. Huang, and C. C. Davis, “Two-dimensional metamaterial structure exhibiting reduced visibility at 500 nm,” Opt. Lett. 33, 1342–1344 (2008).
    [CrossRef] [PubMed]
  7. R. Weder, “A rigorous analysis of high-order electromagnetic cloaks,” J. Phys. A 41, 065207 (2008).
    [CrossRef]
  8. M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
    [CrossRef]
  9. Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
    [CrossRef]
  10. 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]
  11. Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
    [CrossRef] [PubMed]
  12. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered system using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
    [CrossRef]
  13. M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B 77, 233104 (2008).
    [CrossRef]
  14. M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
    [CrossRef] [PubMed]
  15. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
    [CrossRef] [PubMed]
  16. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
    [CrossRef] [PubMed]
  17. H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
    [CrossRef]
  18. D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptical electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505(2008).
    [CrossRef]
  19. H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
    [CrossRef]
  20. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
    [CrossRef]
  21. W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
    [CrossRef]
  22. X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
    [CrossRef]
  23. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
    [CrossRef]
  24. W. Li, J. Guan, Z. Sun, W. Wang, and Q. Zhang, “A near-perfect invisibility cloak constructed with homogeneous materials,” Opt. Express 17, 23410–23416 (2009).
    [CrossRef]
  25. J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
    [CrossRef] [PubMed]

2010

J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
[CrossRef]

2009

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

W. Li, J. Guan, Z. Sun, W. Wang, and Q. Zhang, “A near-perfect invisibility cloak constructed with homogeneous materials,” Opt. Express 17, 23410–23416 (2009).
[CrossRef]

2008

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

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
[CrossRef]

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

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

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered system using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B 77, 233104 (2008).
[CrossRef]

R. Weder, “A rigorous analysis of high-order electromagnetic cloaks,” J. Phys. A 41, 065207 (2008).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

2007

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[CrossRef] [PubMed]

Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
[CrossRef] [PubMed]

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef] [PubMed]

2006

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]

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

U. Lenohardt, “Optical conformal mapping,” Science 312, 1777–1780 (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]

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

2005

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Belov, P. A.

M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B 77, 233104 (2008).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Chan, C. T.

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered system using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

Chen, H.

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered system using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. R. 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.

Economou, E. N.

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Feng, Y. J.

Feng, Y. T.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Guan, J.

Guenneau, S.

Huang, Y.

Huang, Y. J.

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Jiang, T.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Y. Huang, Y. J. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
[CrossRef] [PubMed]

Jiang, X.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[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]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Ksfesake, M.

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Kwon, D. H.

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

Lai, Y.

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

Lee, C. W.

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

Lenohardt, U.

U. Lenohardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

Li, W.

Liang, Z.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Lu, C. H.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Luo, Y.

J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Ma, H.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

Milton, G. W.

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[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]

Mortensen, N. A.

J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
[CrossRef]

Ng, J.

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

Nicolet, A.

Pendry, J. B.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and mirage effect,” Opt. Lett. 32, 1069–1071 (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]

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]

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

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Popa, B. I.

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

Qiu, M.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef] [PubMed]

Ruan, Z.

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef] [PubMed]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

Schurig, D.

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]

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]

Schurig, D. R.

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

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B 77, 233104 (2008).
[CrossRef]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[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]

S. A. Cummer, B. I. Popa, D. R. 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]

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]

Smolyaninov, I. I.

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

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]

Sun, Z.

Wang, W.

Weder, R.

R. Weder, “A rigorous analysis of high-order electromagnetic cloaks,” J. Phys. A 41, 065207 (2008).
[CrossRef]

Werner, D. H.

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

Wu, B. I.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Xi, S.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Xu, X. F.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Xu, Z. Z.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Yan, M.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

M. Yan, Z. Ruan, and M. Qiu, “Scattering characteristics of simplified cylindrical invisibility cloaks,” Opt. Express 15, 17772–17782 (2007).
[CrossRef] [PubMed]

Yan, W.

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
[CrossRef]

Yao, P.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

Zhang, J.

J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Zhang, Q.

Zhao, L.

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Zhou, J.

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Zolla, F.

Appl. Phys. Lett.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

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

W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

W. Yan, M. Yan, and M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93, 021909 (2008).
[CrossRef]

J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96, 113511(2010).
[CrossRef]

J. Phys. A

R. Weder, “A rigorous analysis of high-order electromagnetic cloaks,” J. Phys. A 41, 065207 (2008).
[CrossRef]

J. Phys. D

X. F. Xu, Y. T. Feng, L. Zhao, T. Jiang, C. H. Lu, and Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D 41, 215504 (2008).
[CrossRef]

Nat. Photon.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photon. 1, 224–227 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104 (2007).
[CrossRef]

H. Chen, J. Ng, C. W. Lee, Y. Lai, and C. T. Chan, “General transformation for the reduced invisibility cloak,” Phys. Rev. B 80, 085112 (2009).
[CrossRef]

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered system using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B 77, 233104 (2008).
[CrossRef]

Phys. Rev. E

S. A. Cummer, B. I. Popa, D. R. 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.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[CrossRef]

J. Zhou, T. Koschny, M. Ksfesake, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Science

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

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

U. Lenohardt, “Optical conformal mapping,” Science 312, 1777–1780 (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]

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Figures (10)

Fig. 1
Fig. 1

(a) Coordination transformation function between the virtual space and the physical space. (b) Reduced material parameters as a function of normalized radius ( r / a ).

Fig. 2
Fig. 2

Spatial distribution of the magnetic field and the power-flow lines for various kinds of cloak: (a) ideal cloak, (b) linear cloak, and (c) and (d), division cloaks with b = 3 a and b = 1.5 a , respectively.

Fig. 3
Fig. 3

Magnetic field distribution of the division cloak with different material loss: (a) loss 0.005, (b) loss 0.01, and (c) loss 0.02

Fig. 4
Fig. 4

Magnetic field distribution of divisional cloaks with 10 and 20 layers. Each layer is composed of two isotropic materials, A and B. (a) Layered A–B for 10 layers. (b) Layered B–A for 10 layers. (c) Layered A–B for 20 layers. (d) Layered B–A for 20 layers.

Fig. 5
Fig. 5

Spatial field distribution for the divisional cloak with (a) small and (b) large perturbation at the outer surface.

Fig. 6
Fig. 6

Spatial distribution of magnetic field and the power-flow lines for logarithmic cloaks: (a)  b = 3 a and (b)  b = 2 a .

Fig. 7
Fig. 7

Magnetic field distribution of the logarithmic cloak with different material loss: (a) loss 0.005, (b) loss 0.01, and (c) loss 0.02.

Fig. 8
Fig. 8

Magnetic field distribution of logarithmic cloak with 10 and 20 layers. Each layer is composed of two isotropic materials, A and B. (a) Layered A–B for 10 layers. (b) Layered B–A for 10 layers. (c) Layered A–B for 20 layers. (d) Layered B–A for 20 layers.

Fig. 9
Fig. 9

Spatial field distribution for the logarithmic cloak with varying roughness at the outer surface: (a) small perturbation and (b) large perturbation.

Fig. 10
Fig. 10

Normalized total scattering cross section (normalized to the perfect magnetic conductor cylinder) as a function of frequency. The black, red, and blue curves represent the divisional, logarithmic, and linear cloaks.

Equations (14)

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

r = f ( r ) , θ = θ , z = z .
ε r = μ r = f ( r ) / ( r f ( r ) ) , ε θ = μ θ = 1 / ε r , ε z = μ z = f ( r ) f ( r ) / r .
ε r = ( f ( r ) / r ) 2 , ε θ = ( f ( r ) ) 2 , μ z = 1.
Z | r = b = μ z / ε θ = 1 / f ( b ) .
f ( b ) = 1 , f ( a ) = 0 , f ( b ) = b .
f ( r ) = g ( r ) m a m ( r a ) m , g ( b ) m a m ( b a ) m = b , g ( b ) m a m m ( b a ) m 1 + g ( b ) m a m ( b a ) m = 1 ,
f ( r ) = m a m ( r a ) m , m a m ( b a ) m = b , m a m m ( b a ) m 1 = 1.
r = f ( r ) = b 2 ( r a ) ( b a ) 2 + a ( r a ) .
ε r = b 4 ( r a ) 2 [ ( b a ) 2 + a ( r a ) ] 2 r 2 , ε θ = b 4 ( b a ) 4 [ ( b a ) 2 + a ( r a ) ] 4 , μ z = 1.
ε ¯ = [ ε r 0 0 ε θ ] = [ 2 ε A ε B ε A + ε B 0 0 ε A + ε B 2 ] .
ε A = ε θ + ε θ 2 ε r ε θ , ε B = ε θ ε θ 2 ε r ε θ .
r = f ( r ) = b ln ( 1 + p ( r a ) ) ln ( 1 + p ( b a ) ) ,
[ 1 + p ( b a ) ] ln [ 1 + p ( b a ) ] = p b .
ε r = b 2 ln 2 [ 1 + p ( r a ) ] r 2 ln 2 [ 1 + p ( b a ) ] , ε θ = p 2 b 2 [ 1 + p ( r a ) ] 2 ln 2 [ 1 + p ( b a ) ] , μ z = 1.

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