Abstract

Transformation optics opens an exciting gateway to design electromagnetic "invisibility" cloaks with anisotropic and inhomogeneous medium. In this paper, we establish a generalized transformation procedure to highly improve the flexibilities for the design of two-dimensional (2D) cloaks. The general expressions for the complex medium parameters are developed, which can be readily applied to design 2D cloaks with arbitrary geometries. An example of 2D cloak with irregular cross section is designed and studied by full-wave simulations. The Huygens' Principle is applied to quantitatively evaluate its unusual electromagnetic behaviors. All the theoretical and numerical results verify the effectiveness of the proposed approach. The generalization in this Paper makes a great step forward for the flexible design of electromagnetic cloaks with arbitrary shapes.

© 2008 Optical Society of America

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  1. J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
    [CrossRef]
  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 (2006).
    [CrossRef]
  3. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006).
    [CrossRef]
  4. U. Leonhardt, 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. Photonics 1, 224 (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]
  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]
  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. F. Zolla, S. Guenneau, A. Nicolet, J. B. Pendry, "Cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069 (2007).
    [CrossRef]
  10. 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 (2008).
    [CrossRef]
  11. H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  12. 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]
  13. D. H. Kwon, D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]

2008 (2)

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

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 (2008).
[CrossRef]

2007 (7)

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, J. B. Pendry, "Cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069 (2007).
[CrossRef]

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

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]

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]

2006 (4)

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (2006).
[CrossRef]

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

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

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, 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]

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]

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]

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 (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 (2006).
[CrossRef]

Guenneau, S.

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 (2006).
[CrossRef]

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]

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]

Kwon, D. H.

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

Leonhardt, U.

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

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 (2006).
[CrossRef]

Nicolet, A.

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 (2008).
[CrossRef]

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

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (2006).
[CrossRef]

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

Philbin, T. G.

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

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 (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 (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]

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 (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 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (2006).
[CrossRef]

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]

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 (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 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (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 (2006).
[CrossRef]

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, D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," 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]

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.

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]

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]

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]

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]

Zolla, F.

Appl. Phys. Lett. (2)

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

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

Nat. Photonics (1)

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

New J. Phys (1)

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

Opt. Express (1)

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 (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. 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]

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]

Science (2)

J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (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 (2006).
[CrossRef]

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