Abstract

We introduce a novel concept of an inside-out (or inverse) cloak for electromagnetic waves based on the coordinate transformation of Maxwell’s equations. This concept can be employed for creating absorbing non-reflecting media as matching layers in numerical simulations. In contrast to the commonly used perfectly matched layers, such absorbing boundaries are characterized by physically meaningful parameters, and the concept can be used in various numerical simulation schemes.

© 2008 Optical Society of America

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  1. J. B. Pendry, D. Shurig, 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. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794
    [CrossRef] [PubMed]
  4. 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]
  5. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
    [CrossRef] [PubMed]
  6. H. S. Chen, B. I. Wu, B. L. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak," Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  7. Z. C. 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]
  8. B. L. Zhang, H. S. Chen, B. I. Wu, Y. Luo, L. X. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (2007).
    [CrossRef]
  9. W. Cai, U. K. Chettiar, A. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
    [CrossRef]
  10. Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11133
    [CrossRef] [PubMed]
  11. A. Greenleaf, Y. Kurylev, M. Lassas and G. Uhlmann, "Improvement of cylindrical cloaking with the SHS lining," Opt. Express 15, 12717-12734 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-12717
    [CrossRef] [PubMed]
  12. M. Yan, Z. Ruan, and M. Qiu, "Cylindrical invisibility cloak with simplified material parameters is inherently visible," Phys. Rev. Lett. 99, 233901 (2007).
    [CrossRef]
  13. D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14772
    [CrossRef] [PubMed]
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    [CrossRef]
  18. A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
    [CrossRef]
  19. Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
    [CrossRef]
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2007 (9)

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

Z. C. 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]

B. L. Zhang, H. S. Chen, B. I. Wu, Y. Luo, L. X. 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. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (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, 1069-1071 (2007).
[CrossRef] [PubMed]

Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11133
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-12717
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14772
[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]

2006 (5)

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794
[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. Shurig, 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]

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]

2005 (1)

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

1995 (1)

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

1978 (1)

S. Efimov, "Compression of electromagnetic waves by anisotropic media (nonreflecting crystal model)," Radiophys. Quantum Electron. 21, 916-920 (1978).
[CrossRef]

Cai, W.

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

Chen, H. S.

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

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

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[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, 977-980 (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]

Efimov, S.

S. Efimov, "Compression of electromagnetic waves by anisotropic media (nonreflecting crystal model)," Radiophys. Quantum Electron. 21, 916-920 (1978).
[CrossRef]

Feng, Y.

Greenleaf, A.

Guenneau, S.

Huang, Y.

Jiang, T.

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.

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

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Kivshar, Y. S.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Kong, J. A.

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

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

Kurylev, Y.

Lassas, M.

Lee, J. F.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Leonhardt, U.

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

Luo, Y.

B. L. Zhang, H. S. Chen, B. I. Wu, Y. Luo, L. X. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101 (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. C. 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.

Noskov, R. E.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14772
[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]

J. B. Pendry, D. Shurig, 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. 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]

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794
[CrossRef] [PubMed]

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]

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. C. 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]

Ran, L. X.

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

Ruan, Z. C.

Z. C. 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]

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14772
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794
[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]

Shadrivov, I. V.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Shalaev, V. M.

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

Shurig, D.

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

Smith, D. R.

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772-14782 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14772
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794
[CrossRef] [PubMed]

J. B. Pendry, D. Shurig, 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. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E. 74, 036621 (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, 977-980 (2006).
[CrossRef] [PubMed]

Uhlmann, G.

Wu, B. I.

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

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

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. C. 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]

Zhang, B. L.

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

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

Zharov, A. A.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Zharova, N. A.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Zolla, F.

Appl. Phys. Lett. (1)

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

IEEE Trans. Antennas Propag. (1)

Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
[CrossRef]

New Journal of Physics (1)

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, and Y. S. Kivshar, "Birefringent left-handed metamaterials and perfect lenses for vectorial fields," New Journal of Physics 7, 220 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

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

Phys. Rev. E. (1)

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. (3)

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

Z. C. 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]

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

Radiophys. Quantum Electron. (1)

S. Efimov, "Compression of electromagnetic waves by anisotropic media (nonreflecting crystal model)," Radiophys. Quantum Electron. 21, 916-920 (1978).
[CrossRef]

Science (3)

J. B. Pendry, D. Shurig, 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 (3)

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," arXiv: 0706.2452v1 (2007).

E. J. Post, "Formal structure of electromagnetics: general covariance and electromagnetics," (North-Holland Pub., Amsterdam, 1962).

A. Taflove and S. C. Hagness, "Computational Electrodynamics: The Finite-Difference Time-Domain Method," (Artech House, Norwood, MA, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Top: One-dimensional coordinate transformation. All space for |z|>a is squeezed into the layer a<|z|<b. Bottom left: material parameters, curves 1 and 2 show ε zz =µ zz|| and ε, respectively. Bottom right: results of the one-dimensional FDTD simulations of the propagation of the electromagnetic wave incident from the source located at z=0 on the right matching layer (shaded). Shown is the magnetic field amplitude vs. the normalized coordinate z=/2πc.

Fig. 2.
Fig. 2.

Sharp (left) and smooth (right) transition between the matching layers for the xx component of the inverse tensor of the effective dielectric permittivity.

Fig. 3.
Fig. 3.

Magnetic field distribution for the problem of the Gaussian beam incident on the edge of simulation domain.

Fig. 4.
Fig. 4.

Same as in Fig. 3 for the beam incident on the corner of simulation domain.

Equations (3)

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ε i j = J i k J k j det ( J l m ) ,       J i k = x i X j ,
ρ = a 2 + r ( b 2 a ) ( b r ) ,
ρ = a 2 + r ( 1.05 b 2 a ) ( 1.05 b r )

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