Abstract

Transformation optics is extended to the design of two-dimensional (2D) cloaks with non-conformal inner and outer boundaries. General and explicit expressions of the transformed medium parameters are derived, which are of the utmost importance in a cloak design procedure. A 2D cloak with irregular and non-conformal boundaries is designed as an example. Full-wave simulations combined with Huygens’ Principle are applied to verify the invisibility of the cloak to external incident waves. All the theoretical and numerical results verify the effectiveness of the proposed method. The generalization in this Paper highly improves the flexibilities for cloak design.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  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]
  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).
    [CrossRef] [PubMed]
  4. U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys 8, 247 (2006).
    [CrossRef]
  5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon. 1, 224-227 (2007).
    [CrossRef]
  6. 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]
  7. 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]
  8. H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y. Jiang, H. Ma, and C. T. Chan, "Extending the bandwidth of electromagnetic cloaks," Phys. Rev. B 76, 241104 (2007).
    [CrossRef]
  9. 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]
  10. Y. Huang, Y. J. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007).
    [CrossRef] [PubMed]
  11. M. Yan, Z. C. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
    [CrossRef] [PubMed]
  12. G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express 16, 1413-1422 (2008).
    [CrossRef] [PubMed]
  13. Y. Zhao, C. Argyropoulos, and Y. Hao, "Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures," Opt. Express 16, 6717-6730 (2008).
    [CrossRef] [PubMed]
  14. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
  15. 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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
    [CrossRef]
  16. H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  17. H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
    [CrossRef]
  18. D. H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  19. C. Li and F. Li, "Two-dimensional electromagnetic cloaks with arbitrary geometries," Opt. Express 16, 13414-13420 (2008).
    [CrossRef] [PubMed]
  20. W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
    [CrossRef]
  21. Y. You, G. W. Kattawar, P-W Zhai, and P. Yang, "Invisibility cloaks for irregular particles using coordinate transformations," Opt. Express 16, 6134-6145 (2008).
    [CrossRef] [PubMed]
  22. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
    [CrossRef]
  23. D. H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  24. X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, "Numerical design of arbitrarily shaped electromagnetic cloaks," International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565-1568 (2008)
    [CrossRef]

2008 (9)

G. Isic, R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express 16, 1413-1422 (2008).
[CrossRef] [PubMed]

Y. Zhao, C. Argyropoulos, and Y. Hao, "Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures," Opt. Express 16, 6717-6730 (2008).
[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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

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

C. Li and F. Li, "Two-dimensional electromagnetic cloaks with arbitrary geometries," Opt. Express 16, 13414-13420 (2008).
[CrossRef] [PubMed]

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

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

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (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, 013505 (2008).
[CrossRef]

2007 (10)

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

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).

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

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]

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

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]

Y. Huang, Y. J. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133-11141 (2007).
[CrossRef] [PubMed]

M. Yan, Z. C. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

2006 (4)

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]

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]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys 8, 247 (2006).
[CrossRef]

Argyropoulos, C.

Cai, W.

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

Chan, C. T.

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

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

Chen, B. W.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

Chen, H.

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

Chen, H. Y.

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

Cheng, Q.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Chettiar, U. K.

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

Chin, J. Y.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Cui, T. J.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," 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, "Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transfromations 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]

Feng, Y. J.

Gajic, R.

Greenleaf, A.

Guenneau, S.

Hao, Y.

Hingerl, K.

Huang, Y.

Isic, G.

Jiang, T.

Jiang, W. X.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Jiang, X. Y.

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

Kattawar, G. W.

Kildishev, A. V.

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

Kong, J. A.

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.

Kwon, D. H.

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

Lassas, M.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys 8, 247 (2006).
[CrossRef]

Li, C.

Li, F.

Li, Z.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Liang, Z. X.

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

Liu, R. P.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Ma, H.

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

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (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]

Nicolet, A.

Novakovic, B.

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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).

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]

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]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys 8, 247 (2006).
[CrossRef]

Popovic, Z. V.

Qiu, M.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

M. Yan, Z. C. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (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]

Ruan, Z. C.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

M. Yan, Z. C. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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. Photon. 1, 224-227 (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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

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]

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.

Wang, J. F.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

Werner, D. H.

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

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]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

Yan, M.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[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]

M. Yan, Z. C. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Express 15, 17772-17782 (2007).
[CrossRef] [PubMed]

Yan, W.

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

Yang, P.

Yao, P. J.

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

You, Y.

Zhai, P-W

Zhang, B. L.

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]

Zhang, J. Q.

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

Zhao, Y.

Zolla, F.

Appl. Phys. Lett. (3)

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

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

Nat. Photon. (1)

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

New J. Phys (1)

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New J. Phys 8, 247 (2006).
[CrossRef]

New J. Phys. (1)

W. Yan, M. Yan, Z. C. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

Opt. Express (8)

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 Transfromations of Maxwell’s Equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2007).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. E (1)

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

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]

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]

Science (2)

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 (1)

X. Hou, Q. Xu, P. Niu, and F. L. Teixeira, "Numerical design of arbitrarily shaped electromagnetic cloaks," International Conference on Microwave and Millimeter Wave Technology, 2008, ICMMT 2008 3, 1565-1568 (2008)
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Generalized coordinate transformation. (a) The original space. (b) The transformed space. The region with r≤R2(θ) (shaded) in (a) is transformed to the region with R1(θ’)≤r’≤R2(θ’) (shaded) in (b).

Fig. 2.
Fig. 2.

Electric field distribution in the vicinity of the cloak obtained based on analytical field transformation. The green lines show the flow of EM power.

Fig. 3.
Fig. 3.

Full-wave simulation results for electric field distribution in the vicinity of the PEC cylinder without cloak.

Fig. 4.
Fig. 4.

Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with non-conformal boundaries (excited by a TM plane wave).

Fig. 5.
Fig. 5.

Full-wave simulation results for electric field distribution in the vicinity of the cloaked PEC cylinder with irregular shape (excited by a TM cylindrical wave).

Fig. 6.
Fig. 6.

The scatter width of the cloaked and uncloaked PEC cylinder for different incident directions. The dotted lines are for PEC cylinder without cloak. The solid lines are for PEC cylinder with cloak. The blue, red, black, and green lines are for the incident direction (angle)+x(θ i=0°), -x(θ i=180°), +y(θ i=90°), -y(θ i=270°), respectively.

Tables (1)

Tables Icon

Table 1. Some parameters to describe and compare the scatter properties

Equations (21)

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

x = r cos θ , y = r sin θ .
r ' = R 1 ( θ ) + R 2 ( θ ) R 1 ( θ ) R 2 ( θ ) r , θ ' = θ , z ' = z .
x ' = r ' cos θ ' , y ' = r ' sin θ '
x ' = x x 2 + y 2 R 1 ( tan 1 y x ) + x R 2 ( tan 1 y x ) R 1 ( tan 1 y x ) R 2 ( tan 1 y x ) ,
y ' = y x 2 + y 2 R 1 ( tan 1 y x ) + y R 2 ( tan 1 y x ) R 1 ( tan 1 y x ) R 2 ( tan 1 y x ) ,
z ' = z .
ε i ' j ' = det ( Λ i i ' ) 1 Λ i i ' Λ j j ' ε ij , μ i ' j ' = det ( Λ i i ' ) 1 Λ i i ' Λ j j ' μ ij ,
ε x ' x ' = { [ r ' R 1 ( θ ' ) ] 2 + U 2 } cos 2 θ ' 2 U r ' sin θ ' cos θ ' + r ' 2 sin 2 θ ' r ' [ r ' R 1 ( θ ' ) ] ,
ε x ' y ' = ε y ' x ' = { U 2 R 1 ( θ ' ) [ 2 r ' R 1 ( θ ' ) ] } sin θ ' cos θ ' + U r ' ( cos 2 θ ' sin 2 θ ' ) r ' [ r ' R 1 ( θ ' ) ] ,
ε y ' y ' = { [ r ' R 1 ( θ ' ) ] 2 + U 2 } sin 2 θ ' + 2 U r ' sin θ ' cos θ ' + r ' 2 cos 2 θ ' r ' [ r ' R 1 ( θ ' ) ] ,
ε z ' z ' = r ' R 1 ( θ ' ) r ' [ R 2 ( θ ' ) R 2 ( θ ' ) R 1 ( θ ' ) ] 2 .
U = [ r ' R 1 ( θ ' ) ] R 1 ( θ ' ) d R 2 ( θ ' ) d θ ' [ r ' R 2 ( θ ' ) ] d R 1 ( θ ' ) d θ ' R 2 ( θ ' ) R 2 ( θ ' ) [ R 2 ( θ ' ) R 1 ( θ ' ) ] .
ε x ' x ' = [ r ' τ R 2 ( θ ' ) ] 2 cos 2 θ ' + τ 2 [ d R 2 ( θ ' ) d θ ' ] 2 cos 2 θ ' 2 τ r ' d R 2 ( θ ' ) d θ ' sin θ ' cos θ ' + r ' 2 sin 2 θ ' r ' [ r ' τ R 2 ( θ ' ) ]
ε x ' y ' = ε y ' x ' ' = τ R 2 ( θ ' ) [ 2 r ' τ R 2 ( θ ' ) ] sin θ ' cos θ ' + τ 2 sin θ ' cos θ ' [ d R 2 ( θ ' ) d θ ' ] 2 + τ r ' d R 2 ( θ ' ) d θ ' ( cos 2 θ ' sin 2 θ ' ) r ' [ r ' τ R 2 ( θ ' ) ]
ε y ' y ' = [ r ' τ R 2 ( θ ' ) ] 2 sin 2 θ ' + τ 2 [ d R 2 ( θ ' ) d θ ' ] 2 sin 2 θ ' + 2 τ r ' d R 2 ( θ ' ) d θ ' sin θ ' cos θ ' + r ' 2 cos 2 θ ' r ' [ r ' τ R 2 ( θ ' ) ]
ε z ' z ' = ( 1 1 τ ) 2 r ' τ R 2 ( θ ' ) r '
n = 0 A n cos ( n θ ' ) + n = 1 B n sin ( n θ ' )
R 1 ( θ ' ) = [ 12 + 2 cos ( θ ' ) + sin ( 2 θ ' ) 2 sin ( 3 θ ' ) ] / 30 ,
R 2 ( θ ' ) = [ 10 + sin ( θ ' ) sin ( 2 θ ' ) + 2 cos ( 5 θ ' ) ] / 12 ,
E i ' = q i q i ' E i
σ = k 0 r ̂ 0 × C [ ( n ̂ × E c ) η 0 r ̂ 0 × ( n ̂ × H c ) ] exp ( i k r ' · r ̂ 0 ) d l 2 4 E i 2

Metrics