Abstract

We employ the analytical solutions for the spatial transformation of the electromagnetic fields to obtain and analyze explicit expressions for the structure of the electromagnetic fields in invisibility cloaks. Similar approach can be also used for analyzing beam splitters and field concentrators. We study the efficiency of nonideal electromagnetic cloaks and discuss the effect of scattering losses on the cloak invisibility.

© 2008 Optical Society of America

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References

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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. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  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. M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
    [Crossref]
  5. Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
    [Crossref] [PubMed]
  6. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Improvement of cylindrical cloaking with the SHS lining,” Opt. Express 15, 12717–12734 (2007).
    [Crossref] [PubMed]
  7. H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [Crossref] [PubMed]
  8. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [Crossref]
  9. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
    [Crossref] [PubMed]
  10. 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]
  11. 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]
  12. 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(R) (2007).
    [Crossref]
  13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
    [Crossref]
  14. L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Radiophys. Quantum Electron. 4, 964–967 (1961).
  15. A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
    [Crossref]
  16. E. J. Post, Formal Structure of Electromagnetics (Wiley, New York, 1962).
  17. The components Eabc differ from zero only for the indices a≠ b≠c; the index permutation changes the sign of the totally antisymmetric symbol, and E123=1.
  18. 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]

2008 (2)

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. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
[Crossref]

2007 (7)

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(R) (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]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

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, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

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

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Improvement of cylindrical cloaking with the SHS lining,” Opt. Express 15, 12717–12734 (2007).
[Crossref] [PubMed]

2006 (5)

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

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

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (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]

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

1961 (1)

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Radiophys. Quantum Electron. 4, 964–967 (1961).

Cai, 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]

Chan, C.T.

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(R) (2007).
[Crossref]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (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(R) (2007).
[Crossref]

H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

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]

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]

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. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[Crossref]

Dolin, L. S.

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Radiophys. Quantum Electron. 4, 964–967 (1961).

Greenleaf, A.

Guenneau, S.

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(R) (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, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
[Crossref]

Kong, J. A.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
[Crossref]

H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Kurylev, Y.

Lassas, M.

Leonhardt, U.

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
[Crossref] [PubMed]

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(R) (2007).
[Crossref]

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (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(R) (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.

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]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

Nicolet, A.

Pendry, J.

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

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]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the 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]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

Popa, B. I.

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

Post, E. J.

E. J. Post, Formal Structure of Electromagnetics (Wiley, New York, 1962).

Qiu, M.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[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.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
[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.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

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]

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]

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

Shalaev, V. M.

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]

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. 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. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (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]

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]

Uhlmann, G.

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]

Wu, B.I.

H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Yan, M.

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

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(R) (2007).
[Crossref]

Zhang, B.

H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Zhang, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
[Crossref]

Zolla, F.

Appl. Phys. Lett. (1)

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]

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]

Opt. Express (2)

Opt. Lett. (1)

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. B (2)

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(R) (2007).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations”, Phys. Rev. B 77, 125127 (2008).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

H. Chen, B.I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (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]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99, 113903 (2007).
[Crossref] [PubMed]

Radiophys. Quantum Electron. (1)

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Radiophys. Quantum Electron. 4, 964–967 (1961).

Science (3)

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

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (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 (2)

E. J. Post, Formal Structure of Electromagnetics (Wiley, New York, 1962).

The components Eabc differ from zero only for the indices a≠ b≠c; the index permutation changes the sign of the totally antisymmetric symbol, and E123=1.

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Figures (3)

Fig. 1.
Fig. 1.

Structure of the magnetic field Hx for (a) arbitrary-shaped cloak and (b) multiple cloaks produced by the space transformation Eq. (6) for a=0.3, b=0.6, and β=2. The cloak is illuminated by a plane wave, H0 x =exp(yy) for κy =5.4. Center of the cloak is shown by red line, in (a), and dots, in (b).

Fig. 2.
Fig. 2.

(a,b) Scattering patterns for non-ideal cloak for TE and TM waves. Red lines (1) indicate scattering from bare metallic cylinder, while blue line (2) corresponds to the scattering from the cloaked cylinder with truncation level r0 =0.05b and α=0. Black curves (3) correspond to the scattering on the dielectric cloak with (a) α=0.1 and (b) α=0.02.

Fig. 3.
Fig. 3.

Field distribution for TE waves for (a) ideal cloak; (b) for impedance mismatched cloak with α=0.03, (c) for lossy cloak with α=i×0.03

Equations (9)

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

g ij ( x ) = y i y j x a x b δ ab ,
ε eff ln = 1 g y l x a y n x b ε 0 ab ,
μ eff ln = 1 g y l x a y n x b μ 0 ab ,
E ˜ n = x b y n E b , E b = y n x b E ˜ n .
H ˜ k = x c y k H c , H c = y k x c H ˜ k .
r = b a ( b R b a ) β
r eff δ a ( d R d r r = a ) 1 ,
δ ε ˜ ab = α g x a y i x b y i
j eff i ω 4 π α ε ̂ 1 E v ,

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