Abstract

Omni-directional electromagnetic field concentrators have been recently reported by Marco Rahm et al. [Photon. Nanostruct.: Fundam. Applic. 6, 87 (2008)] based on form-invariant coordinate transformations related to its Jacobi transformation matrix. Using transverse-electric wave illumination, we reduced the complex material parameters of the concentrator for future practical implementation. Concentrators with different set of permittivity and permeability tensors are proposed. The electromagnetic concentrating performance and the scattering properties at the inner and outer boundary of these concentrators are theoretically and numerically analyzed. Finally we obtain a set of material tensors for a concentrator that simultaneously has perfect matched interior and exterior interfaces.

© 2008 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. 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]
  3. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  4. H. Y. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  5. M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035112 (2008).
    [CrossRef]
  6. W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, "Design of oblate cylindrical perfect lens using coordinate transformation," Opt. Express 16, 8094-8105 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-11-8094.
    [CrossRef] [PubMed]
  7. L. Lin, W Wang, C. Du, and X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-6815.
    [CrossRef]
  8. 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. Appl. 6, 87 (2008).
    [CrossRef]
  9. L Lin, W. Wang, C. Wang, C. Du, and X. Luo, "A cone-shaped concentrator with varying performances of concentrating," Opt. Express 16, 6809-6814 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-6809.
    [CrossRef]
  10. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
    [CrossRef] [PubMed]
  11. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  12. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  13. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  14. 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]
  15. 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]
  16. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
    [CrossRef]
  17. H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. G. Ma, and C. T. Chan, "Extending the bandwidth of electromagnetic cloaks," Phys. Rev. B 76, 241104(R) (2007).
    [CrossRef]
  18. 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]
  19. 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]

2008

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035112 (2008).
[CrossRef]

W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, "Design of oblate cylindrical perfect lens using coordinate transformation," Opt. Express 16, 8094-8105 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-11-8094.
[CrossRef] [PubMed]

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. Appl. 6, 87 (2008).
[CrossRef]

2007

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]

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]

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

H. Y. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

2006

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]

L Lin, W. Wang, C. Wang, C. Du, and X. Luo, "A cone-shaped concentrator with varying performances of concentrating," Opt. Express 16, 6809-6814 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-6809.
[CrossRef]

L. Lin, W Wang, C. Du, and X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-6815.
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9794.
[CrossRef] [PubMed]

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

2003

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Brock, J. B.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Cai, W.

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

Chan, C. T.

H. Y. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Chen, H. Y.

H. Y. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Chettiar, U. K.

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

Chuang, I. L.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Cui, J.

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. Appl. 6, 87 (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]

Du, C.

Guenneau, S.

Houck, A. A.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

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. Photonics 1, 224 (2007).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Leonhardt, U.

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

Lin, L

Lin, L.

Luo, X.

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]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Nicolet, A.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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. Appl. 6, 87 (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]

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), 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]

Psaltis, D.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035112 (2008).
[CrossRef]

Qiu, M.

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. Appl. 6, 87 (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. Appl. 6, 87 (2008).
[CrossRef]

Ruan, Z.

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]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[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. Appl. 6, 87 (2008).
[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), 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]

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]

Shalaev, V. M.

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

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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. Appl. 6, 87 (2008).
[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), 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]

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]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[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]

Tsang, M.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035112 (2008).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wang, C.

Wang, W

Wang, W.

Yan, M.

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]

Yang, X.

Zolla, F.

Appl. Phys. Lett.

H. Y. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Photon. Nanostruct. Fundam. Appl.

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. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. B

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035112 (2008).
[CrossRef]

Phys. Rev. E

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.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell???s Law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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

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

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of 2D concentrator, including three rigions separated by three circles with radius being R1, R2 and R3 respectively from the inner circle to the outer one.

Fig. 2.
Fig. 2.

Electric field distributions in the vicinity of the concentrators with reduced parameters. Three graphs from left to right denote the concentrator of the first kind (a), the second kind (b) and the third kind (c). All the concentrators have the same size with R1=0.02m and R2=0.04m and R3=0.06m.

Fig. 3.
Fig. 3.

Time-averaged total energy density around the concentrators for the first case (a), the second (b) and the third (c)

Equations (10)

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r′ = { R 1 r R 2 0 r R 1 ( R 3 R 1 ) r ( R 3 R 2 ) ( R 2 R 1 ) R 3 ( R 3 R 2 ) R 1 < r R 3
ε ̂ ij = Q 1 Q 2 Q 3 ( Q i Q j ) 1 δ ij
μ ̂ ij = Q 1 Q 2 Q 3 ( Q i Q j ) 1 δ ij
Q 1 = R 2 R 1 , Q 2 = R 2 R 1 , Q 3 = 1
Q 1 = ( R 3 R 2 ) ( R 3 R 1 ) , Q 2 = R 3 R 2 R 3 R 1 [ 1 + 1 r ( R 2 R 1 R 3 R 2 ) R 3 ] , Q 3 = 1
ε ̂ ij = μ ̂ ij = { [ 1 0 0 0 1 0 0 0 ( R 2 R 1 ) 2 ] 0 r R 1 [ ( r + M ) r 0 0 0 r ( r + M ) 0 0 0 N ( r + M ) r ] R 1 < r R 3
1 r r ( r μ ϕ E z r ) + 1 μ r r 2 ( 2 E z ϕ 2 ) + ε z k 0 2 E z = 0
μ r = [ ( r + M ) r ] 2 , ε z = N , μ ϕ = 1
μ r = N [ ( r + M ) r ] 2 , ε z = N , μ ϕ = N
ε ̂ ij = μ ̂ ij = [ 1 0 0 0 1 0 0 0 ( R 2 R 1 ) 2 ] ε z = μ r = μ ϕ = R 2 R 1

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