Abstract

Invisible cloak derived from the coordinate transformation requires its constitutive material to be anisotropic. In this work, we present a cloak of graded-index isotropic material based on the geometrical optics theory. The cloak is realized by concentric multilayered structure with designed refractive index to achieve the low-scattering and smooth power-flow. Full-wave simulations on such a design of a cylindrical cloak are performed to demonstrate the cloaking ability to incident wave of any polarization. Using normal nature material with isotropy and low absorption, the cloak shows light on a practical path to stealth technology, especially that in the optical range.

© 2008 Optical Society of America

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References

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  1. A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623-036632 (2005).
  2. A. Alù and N. Engheta, "Cloaking and transparency for collections of particles with metamaterial and plasmonic covers," Opt. Express 15, 7578-7590 (2007).
    [CrossRef] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
    [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, 036621-036625 (2006).
  5. W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
    [CrossRef]
  6. D. -H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502-113504 (2008).
    [CrossRef]
  7. D. -H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505-013505 (2008).
    [CrossRef]
  8. Y. You, G. W. Kattawar, P. W. Zhai, and Ping Yang, "Invisibility cloaks for irregular particles using coordinate transformations," Opt. Express 16, 6134-6145 (2008).
    [CrossRef] [PubMed]
  9. 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]
  10. D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
    [CrossRef]
  11. Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials,"Opt. Express 15, 11133-11141 (2007).
    [CrossRef] [PubMed]
  12. 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]
  13. W. Cai U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
    [CrossRef]
  14. S. P. Morgan, "General solution of the luneberg lens problem," J. Appl. Phys. 29, 1358-1368 (1958).
    [CrossRef]
  15. N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
    [CrossRef]
  16. A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
    [CrossRef]
  17. M. V. K. Chari and P. P. Silverster, Finite Elements in Electrical and Magnetic Field Problems (John Wiley & Sons, 1980).

2008 (4)

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

D. -H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502-113504 (2008).
[CrossRef]

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

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

2007 (3)

2006 (4)

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

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. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-036625 (2006).

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]

2005 (1)

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623-036632 (2005).

2002 (1)

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

2000 (1)

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

1998 (1)

A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
[CrossRef]

1958 (1)

S. P. Morgan, "General solution of the luneberg lens problem," J. Appl. Phys. 29, 1358-1368 (1958).
[CrossRef]

Alu, A.

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623-036632 (2005).

Alù, A.

Cheng, Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Cui, T. J.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[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, 036621-036625 (2006).

Engheta, N.

A. Alù and N. Engheta, "Cloaking and transparency for collections of particles with metamaterial and plasmonic covers," Opt. Express 15, 7578-7590 (2007).
[CrossRef] [PubMed]

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623-036632 (2005).

Feng, Y.

Garcia, N.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

Huang, Y.

Jessie, Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Jiang, T.

Jiang, W. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith. "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kattawar, G. W.

Kroll, N.

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

Kwon, D. -H.

D. -H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502-113504 (2008).
[CrossRef]

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

Lakhtakia, A.

A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
[CrossRef]

Lin, X. Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Maksimenko, S. A.

A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
[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]

Morgan, S. P.

S. P. Morgan, "General solution of the luneberg lens problem," J. Appl. Phys. 29, 1358-1368 (1958).
[CrossRef]

Pendry, J. B.

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]

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. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-036625 (2006).

Ponizovskaya, E. V.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

Popa, B-I

S. A. Cummer, B-I Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-036625 (2006).

Schultz, S.

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

Schurig, D.

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. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621-036625 (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]

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]

Slepyan, G. Y.

A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
[CrossRef]

Smith, D. R.

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]

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, 036621-036625 (2006).

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

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[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]

Vier, D. C.

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

Werner, D. H.

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

D. -H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502-113504 (2008).
[CrossRef]

Xiao, J. Q.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

You, Y.

Yu, G. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Zhai, P. W.

Appl. Phys. Lett. (4)

D. -H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502-113504 (2008).
[CrossRef]

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

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, " Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246-2248 (2000).
[CrossRef]

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

Carbon (1)

A. Lakhtakia, G. Y. Slepyan, S. A. Maksimenko,  et al, "Effective medium theory of the microwave and infrared properties of composites with carbon nanotube inclusions," Carbon 36, 1833-1839 (1998).
[CrossRef]

J. Appl. Phys. (1)

S. P. Morgan, "General solution of the luneberg lens problem," J. Appl. Phys. 29, 1358-1368 (1958).
[CrossRef]

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

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," J. Phys. D: Appl. Phys. 41, 085504-085507 (2008).
[CrossRef]

Nature Photon. (1)

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

Opt. Express (4)

Phys. Rev. E (2)

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, 036621-036625 (2006).

A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623-036632 (2005).

Science (2)

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]

Other (1)

M. V. K. Chari and P. P. Silverster, Finite Elements in Electrical and Magnetic Field Problems (John Wiley & Sons, 1980).

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Figures (5)

Fig. 1.
Fig. 1.

Refraction of rays in different areas and the two consisted lenses.

Fig. 2.
Fig. 2.

(a) The refractive index distribution of the cloaking shell along the radius and multilayered approximation (N=40) to this continuous distribution; (b) the model of the 2D cylindrical multilayered cloaking structure with an inner diameter a=λ, outer diameter b=2λ, each color contains four layers.

Fig. 3.
Fig. 3.

The computational domain for the 2D cylindrical cloaking structure: the boundary condition around the domain is radiation; the top and bottom faces are PMC.

Fig. 4.
Fig. 4.

Distribution of magnetic-field around the cloaked object (a) with a multilayered cloak, (b) without the cloak and distribution of Poynting vectors around the cloaked object (c) with a multilayered cloak and (d) without the cloak. The black circles outline the cloak.

Fig. 5.
Fig. 5.

The calculated magnetic-field distribution in the vicinity of the conducting cylinder (a) with a multilayered cloak, (b) without cloak for elliptically polarized incident wave; and the electronic-field distribution (c) with a cloak of concentric layered structure, (d) without the cloak for a line source. The black circles outline the cloak.

Equations (1)

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n = ( 1 + r 1 2 r 2 ) r 1 2 ,

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