Abstract

By using the coordinate transformation theory, we propose a media that is used to control the propagation of electromagnetic (EM) waves with the front shape and size being kept and thus to guide the wave energy along one certain direction, whatever the wave shape may be. We obtain the general formula of designing such media and present the typical example in the cylindrical EM wave case. Such media have many potential applications such as super waveguides, high direction antennas, wave-shape adapters, and other types of EM devices. The approaches presented in this paper are also applicable to acoustic waves.

© 2009 Optical Society of America

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  1. J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  2. D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (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, Science 314, 977 (2006).
    [CrossRef] [PubMed]
  4. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
    [CrossRef] [PubMed]
  5. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
    [CrossRef]
  6. L. Lin, W. Wang, C. Du, and X. Luo, Opt. Express 16, 6809 (2008).
    [CrossRef] [PubMed]
  7. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
    [CrossRef]
  8. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
    [CrossRef]
  9. H. Chen and C. T. Chan, Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  10. H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
    [CrossRef] [PubMed]
  11. L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, Opt. Express 16, 6815 (2008).
    [CrossRef] [PubMed]
  12. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
    [CrossRef]
  13. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
    [CrossRef]
  14. D. H. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  15. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, Opt. Express 16, 6134 (2008).
    [CrossRef] [PubMed]
  16. W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
    [CrossRef]
  17. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
    [CrossRef]

2008 (13)

H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, Opt. Express 16, 6815 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

D. H. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, Opt. Express 16, 6134 (2008).
[CrossRef] [PubMed]

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

L. Lin, W. Wang, C. Du, and X. Luo, Opt. Express 16, 6809 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

2007 (1)

H. Chen and C. T. Chan, Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

2006 (3)

J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Chan, C. T.

H. Chen and C. T. Chan, Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Chen, B.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

H. Chen and C. T. Chan, Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

Cheng, Q.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Chin, J. Y.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Cui, J.

Cui, T. J.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Du, C.

Jiang, W. X.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (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, Science 314, 977 (2006).
[CrossRef] [PubMed]

Kattawar, G. W.

Kong, J. A.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Kwon, D. H.

D. H. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Li, Z.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Lin, L.

Liu, R.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Ma, H.

H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Ma, H. F.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[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, Science 314, 977 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef] [PubMed]

Qiu, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, 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, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

Smith, D. R.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, Opt. Express 14, 9794 (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, Science 314, 977 (2006).
[CrossRef] [PubMed]

Wang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

Wang, W.

Werner, D. H.

D. H. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

Yan, W.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

Yang, P.

Yang, X. M.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

You, Y.

Zhai, P.-W.

Zhang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

D. H. Kwon and D. H. Werner, Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

H. Chen and C. T. Chan, Appl. Phys. Lett. 90, 241105 (2007).
[CrossRef]

New J. Phys. (1)

W. Yan, M. Yan, Z. Ruan, and M. Qiu, New J. Phys. 10, 043040 (2008).
[CrossRef]

Opt. Express (4)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, Photonics Nanostruct. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Phys. Rev. B (1)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Phys. Rev. E (1)

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Science (2)

J. B. Pendry, D. Schurig and D. R. Smith, Science 312, 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, Science 314, 977 (2006).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Phase-front S is transmitted in region Σ and will be moved to S after a time interval. So arbitrary point O on S will reach the position P in the free space and will reach the position P in region Σ, respectively.

Fig. 2
Fig. 2

Cylindrical equal phase surface is transmitted in region Σ. Here, O, P, and P have the same meanings as those in Fig. 1; A is the position where the wave fronts cross the boundary of the region Σ.

Fig. 3
Fig. 3

The distributions of electric fields and the time-average power flows (dashed lines) are simulated for the cases a cylindrical EM wave propagates (a) in the WSKM and (b) in the free space. The calculation domains are all assumed to be the free space except region III of (a), which is filled with WSKM metamaterials.

Equations (12)

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

f ( x , y , z ) = 0 .
x x p k x = y y p k y = z z p k z ,
f i ( x o , y o , z o ) = k i , i = x , y , z ,
OP = OP .
x p = x o + ( x p x o ) 2 + ( y p y o ) 2 + ( z p z o ) 2 ,
y p = y o , z p = z o .
α ( x p , y p , z p ) = Q α ( x p , y p , z p ) Q T det Q ,
Q λ η = λ p η p , λ , η = x , y , z .
x p = r + R ( x p r 1 ) , y p = R y p r .
ε = μ = [ ( r 2 + R 2 y p 2 r 2 ) R x p R y p r 2 0 R y p r 2 R x p r 2 0 0 0 r 2 R x p ] ,
x p = R + x p R 2 y p 2 R 2 W 2 x a R R 2 y p 2 ,
y p = y p R 2 y p 2 x p .

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