Abstract

An effective method for designing wave shape transformers (WSTs) is investigated by adopting the coordinate transformation theory. Following this method, the devices employed to transform electromagnetic (EM) wave fronts from one style with arbitrary shape and size to another style, can be designed. To verify this method, three examples in 2D spaces are also presented. Compared with the methods proposed in other literatures, this method offers the general procedure in designing WSTs, and thus is of great importance for the potential and practical applications possessed by such kinds of devices.

© 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).
    [CrossRef] [PubMed]
  3. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," Phys. Rev. Lett. 100, 063903 (2008).
    [CrossRef] [PubMed]
  4. 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. Applic. 6, 87-95 (2008).
    [CrossRef]
  5. 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]
  6. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
    [CrossRef]
  7. D.-Hoon Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  8. 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]
  9. W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
    [CrossRef]
  10. W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped Objects," Phys. Rev. E 77, 066607 (2008).
    [CrossRef]
  11. L , Lin, W. Wang, C. Du, and X. Luo, "A cone-shaped concentrator with varying performances of concentrating," Opt. Express 16, 6809-6814 (2008).
    [CrossRef] [PubMed]
  12. W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
    [CrossRef]
  13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
    [CrossRef]
  14. H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
    [CrossRef]
  15. H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
    [CrossRef] [PubMed]
  16. L. Lin, W. Wang, J. Cui, C. Du, X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2008).
    [CrossRef] [PubMed]
  17. W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
    [CrossRef]
  18. 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 (2000).
    [CrossRef] [PubMed]
  19. F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
    [CrossRef]
  20. B.-I. Popa and S. A. Cummer, "Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials," Phys. Rev. Lett. 100, 207401 (2008).
    [CrossRef] [PubMed]

2008 (15)

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

D.-Hoon Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (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. Yan, M. Yan, Z. Ruan, and M. Qiu, "Coordinate transformations make perfect invisibility cloaks with arbitrary shape," New J. Phys. 10, 043040 (2008).
[CrossRef]

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

L , Lin, W. Wang, C. Du, and X. Luo, "A cone-shaped concentrator with varying performances of concentrating," Opt. Express 16, 6809-6814 (2008).
[CrossRef] [PubMed]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," 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, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

L. Lin, W. Wang, J. Cui, C. Du, X. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation theory," Opt. Express 16, 6815-6821 (2008).
[CrossRef] [PubMed]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

B.-I. Popa and S. A. Cummer, "Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials," Phys. Rev. Lett. 100, 207401 (2008).
[CrossRef] [PubMed]

2007 (1)

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

2006 (3)

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).
[CrossRef] [PubMed]

2000 (1)

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 (2000).
[CrossRef] [PubMed]

Chan, C. T.

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

Chaubet, M.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Chen, B.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

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

Cheng, Q.

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

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Chin, J. Y.

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

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

Cui, J.

Cui, T.

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

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," 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, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

B.-I. Popa and S. A. Cummer, "Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials," Phys. Rev. Lett. 100, 207401 (2008).
[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]

Du, C.

Houzet, G.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Jiang, W.

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

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (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.

Kong, J. A.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Lheurette, E.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Li, Z.

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

Lin, L

Lin, L.

Lippens, D.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Liu, R.

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

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Ma, H.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

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]

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 (2000).
[CrossRef] [PubMed]

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 (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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," 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, "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).
[CrossRef] [PubMed]

Popa, B.-I.

B.-I. Popa and S. A. Cummer, "Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials," Phys. Rev. Lett. 100, 207401 (2008).
[CrossRef] [PubMed]

Qiu, M.

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

Qu, S.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
[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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," 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, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Ruan, Z.

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

Schultz, S.

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 (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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," 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, "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]

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. Applic. 6, 87-95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," 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, "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).
[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 (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]

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 (2000).
[CrossRef] [PubMed]

Wang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

Wang, W.

Xu, Z.

H. Ma, S. Qu, Z. Xu, and J. Wang, "Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams," Appl. Opt. 47, 4193 (2008).
[CrossRef] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Yan, M.

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

Yan, W.

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

Yang, P.

Yang, X.

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

You, Y.

Zhai, P.-W.

Zhang, F.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Zhang, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Zhao, X.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Zhou, X.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

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

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces," Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

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

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

J. Appl. Phys. (1)

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, "Negative-zero-positive metamaterial with omega-type metal inclusions," J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (4)

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 transformations of Maxwell's equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A 77, 013825 (2008).
[CrossRef]

Phys. Rev. B (1)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations," Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

B.-I. Popa and S. A. Cummer, "Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials," Phys. Rev. Lett. 100, 207401 (2008).
[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 (2000).
[CrossRef] [PubMed]

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]

Cited By

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Figures (5)

Fig. 1.
Fig. 1.

The wave front is transformed from surface S1 to surface S2. As a result, starting from an arbitrary point A on S1, the wave vector line will be AC when the wave propagates in the free space, and will be AB when the wave propagates in the WST, respectively.

Fig. 2.
Fig. 2.

The sketch of the geometrical relationship employed in designing a WST, where, the WST transforms the wave front (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane.

Fig. 3.
Fig. 3.

The sketch of the geometrical relationship employed in designing a photon funnel, where the incident wave is supposed to be right traveling and is compressed in the y-axis direction.

Fig. 4.
Fig. 4.

(Color online) The electric-field distributions when waves propagate in WSTs, where, the wave shape is transformed (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane. The dashed lines (green) sketch the time-average power flows. The parameter L in the two parts is 20 wavelengths.

Fig. 5.
Fig. 5.

(Color online) The electric-field distributions when waves propagate in photon funnels. Here two cases are considered: (a), using a photon funnel, a plane wave is compressed; and (b), using the complex of a WST and a photon funnel, a cylindrical wave is transformed to a plane wave and then is compressed to be a thin beam. The dashed lines (green) sketch the timeaverage power flows. The parameter L corresponding to regions ∑ and ∑2 is 7 wavelengths, and to region ∑1 is 20 wavelengths, respectively.

Equations (45)

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

S 1 : f ( x , y , z ) = 0 ,
S 2 : g ( x , y , z ) = 0 .
l p L = l p L .
x x p k x = y y p k y = z z p k z ,
f i ( x a , y a , z a ) = k i , i = x , y , z ,
L = x b x a , l p = x p x a .
x p = L L l p + x a , y p = y a , z p = z a .
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 .
Q x η = x p η p = 1 L [ l p ( x b η p x a η p ) + L l p η p ] x a η p ,
Q λ η = λ p η p = λ a η p , λ = y , z ; η = x , y , z .
S i : x = R i cos θ i + x i , y = R i sin θ i , i = 1 , 2 .
x a = R 1 cos θ 1 + x 1 , y a = R 1 sin θ 1 ,
x b = R 2 cos θ 2 + x 2 , y b = y a ,
l b = ( x p x a ) 1 + tan 2 θ 1 ,
θ 1 = arctan ( y p x p x 1 ) , θ 2 = π arctan ( R 1 R 2 sin θ 1 ) .
θ 1 x p = y p ( x p x 1 ) 2 + y p 2 , θ 1 y p = x p x 1 ( x p x 1 ) 2 + y p 2 ,
θ 2 η p = R 1 cos θ 1 R 2 2 R 1 2 sin 2 θ 1 × θ 1 η p ,
x a η p = R 1 sin θ 1 θ 1 η p , y a η p = R 1 cos θ 1 θ 1 η p ,
x b η p = R 2 sin θ 2 θ 2 η p ,
l p η p = ( x p x a ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s + x a η p ) 1 + tan 2 θ 1 · s = { 1 , η = x 0 , η = y
Q x η = 1 L { ( x p R 1 cos θ 1 x 1 ) ( R 2 sin θ 2 cos θ 1 R 2 2 R 1 2 sin 2 θ 1 + sin θ 1 ) R 1 1 + tan 2 θ 1 θ 1 η p
+ ( R 2 cos θ 2 R 1 cos θ 1 + x 2 x 1 ) [ ( x p R 1 cos θ 1 x 1 ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s R 1 sin θ 1 θ 1 η p ) 1 + tan 2 θ 1 ] } + R 1 sin θ 1 θ 1 η p , s = { 1 , η = x 0 , η = y
Q y η = R 1 cos θ 1 θ 1 η p , η = x , y .
θ 1 = arcsin y p R 1 , θ 2 = π arcsin y p R 2 ,
x p = L x p R 1 cos θ 1 x 1 R 2 cos θ 2 R 1 cos θ 1 + x 2 x 1 1 1 + tan 2 θ 1 + R 1 cos θ 1 + x 1 ,
y p = ( x p x 1 ) tan θ 1 .
S 1 : x = R 1 cos θ 1 + x 1 , y = R 1 sin θ 1 ,
S 2 : y = k ( x x 2 ) ,
x b = R 1 sin θ 1 + k x 2 k , y b = y a .
x b η p = R 1 cos θ 1 k θ 1 η p , η = x , y .
Q x η = 1 L { ( x p R 1 cos θ 1 x 1 ) ( cos θ 1 k + sin θ 1 ) R 1 1 + tan 2 θ 1 θ 1 η p
+ ( R 1 sin θ 1 + k x 2 k R 1 cos θ 1 x 1 ) [ ( x p R 1 cos θ 1 x 1 ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s R 1 sin θ 1 θ 1 η p ) 1 + tan 2 θ 1 ] } + R 1 sin θ 1 θ 1 η p , s = { 1 , η = x 0 , η = y
Q y η = R 1 cos θ 1 θ 1 η p , η = x , y .
θ 1 x p = y p ( x p x 1 ) 2 + y p 2 , θ 1 y p = x p x 1 ( x p x 1 ) 2 + y p 2 ,
θ 1 = arcsin y p ' R 1 ,
x p = L x p ' R 1 cos θ 1 x 1 R 1 sin θ 1 + k x 2 k R 1 cos θ 1 x 1 1 1 + tan 2 θ 1 + R 1 cos θ 1 + x 1 ,
y p = ( x p x 1 ) tan θ 1 .
y = k ( x x 1 ) + y 1 ,
y p ' y b = y p y c = y p y 1 ,
y p ' = y p y 1 y b , x p ' = x p .
Q xx = 1 , Q xy = 0 , Q yx = k y p y 1 , Q yy = y b y 1 .

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