Abstract

We propose and design a kind of annular focusing lens based on transformation optics. Based on the method of eigen-mode expansions, closed-form expressions are derived to analyze the proposed annular lens rigorously. We show that the annular lens has excellent focusing property. Even when a barrier (such as a conducting cylinder) exists in the center of the lens, the analytical results demonstrate that the waves are still guided to propagate smoothly and focused on a spot.

© 2014 Optical Society of America

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  1. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
    [CrossRef]
  2. W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12, 26–33 (2009).
    [CrossRef]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef]
  4. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef]
  5. S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  6. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef]
  7. 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]
  8. 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. Nanostr. Fundam. Appl. 6, 87–95 (2008).
  9. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]
  10. W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).
  11. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef]
  12. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
    [CrossRef]
  13. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
  14. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
    [CrossRef]
  15. W. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
    [CrossRef]
  16. W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
    [CrossRef]
  17. A. Einstein, “Lens-like action of a star by the deviation of light in the gravitational field,” Science 84, 506–507 (1936).
    [CrossRef]
  18. G. Bekeft and G. W. Farnell, “A homogeneous dielectric sphere as a microwave lens,” Can. J. Phys. 34, 792–803 (1956).
  19. T. A. Rhys, “The design of radially symmetric lenses,” IEEE Trans. Antennas Propag. 18, 497–506 (1970).
    [CrossRef]
  20. B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).
  21. H. Mosallaei and Y. Rahmat-Samii, “Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization,” IEEE Trans. Antennas Propag. 49, 60–69 (2001).
    [CrossRef]
  22. R. K. Luneburg, Mathematical Theory of Optics (Cambridge University, 1964).
  23. A. S. Gutman, “Modified Luneburg lens,” J. Appl. Phys. 25, 855–859 (1954).
    [CrossRef]

2013 (1)

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

2012 (1)

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

2010 (3)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).

W. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
[CrossRef]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

2009 (3)

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12, 26–33 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

2008 (3)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (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 transformations of Maxwell’s equations,” Photon. Nanostr. Fundam. Appl. 6, 87–95 (2008).

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

2007 (2)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (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]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

2002 (1)

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

2001 (1)

H. Mosallaei and Y. Rahmat-Samii, “Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization,” IEEE Trans. Antennas Propag. 49, 60–69 (2001).
[CrossRef]

1970 (1)

T. A. Rhys, “The design of radially symmetric lenses,” IEEE Trans. Antennas Propag. 18, 497–506 (1970).
[CrossRef]

1956 (1)

G. Bekeft and G. W. Farnell, “A homogeneous dielectric sphere as a microwave lens,” Can. J. Phys. 34, 792–803 (1956).

1954 (1)

A. S. Gutman, “Modified Luneburg lens,” J. Appl. Phys. 25, 855–859 (1954).
[CrossRef]

1936 (1)

A. Einstein, “Lens-like action of a star by the deviation of light in the gravitational field,” Science 84, 506–507 (1936).
[CrossRef]

Bekeft, G.

G. Bekeft and G. W. Farnell, “A homogeneous dielectric sphere as a microwave lens,” Can. J. Phys. 34, 792–803 (1956).

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef]

Chen, H. Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, T.

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

Cheng, Q.

W. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12, 26–33 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

Cui, T. J.

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12, 26–33 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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, 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. Nanostr. Fundam. Appl. 6, 87–95 (2008).

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Ebling, J. P.

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

Einstein, A.

A. Einstein, “Lens-like action of a star by the deviation of light in the gravitational field,” Science 84, 506–507 (1936).
[CrossRef]

Eleftheriades, G. V.

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

Farnell, G. W.

G. Bekeft and G. W. Farnell, “A homogeneous dielectric sphere as a microwave lens,” Can. J. Phys. 34, 792–803 (1956).

Gutman, A. S.

A. S. Gutman, “Modified Luneburg lens,” J. Appl. Phys. 25, 855–859 (1954).
[CrossRef]

Han, D. Z.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

Jiang, W. X.

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

W. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
[CrossRef]

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12, 26–33 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

Kong, J. A.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef]

Lai, Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (Cambridge University, 1964).

Luo, C. Y.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

Ma, H. F.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).

W. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
[CrossRef]

Mei, Z. L.

W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef]

Mosallaei, H.

H. Mosallaei and Y. Rahmat-Samii, “Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization,” IEEE Trans. Antennas Propag. 49, 60–69 (2001).
[CrossRef]

Neff, C. W.

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]

Ng, J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (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 transformations of Maxwell’s equations,” Photon. Nanostr. Fundam. Appl. 6, 87–95 (2008).

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Qiu, C. W.

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

Qiu, 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]

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. Nanostr. Fundam. Appl. 6, 87–95 (2008).

Rahmat-Samii, Y.

H. Mosallaei and Y. Rahmat-Samii, “Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization,” IEEE Trans. Antennas Propag. 49, 60–69 (2001).
[CrossRef]

Rebeiz, G. M.

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

Rhys, T. A.

T. A. Rhys, “The design of radially symmetric lenses,” IEEE Trans. Antennas Propag. 18, 497–506 (1970).
[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. Nanostr. Fundam. Appl. 6, 87–95 (2008).

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]

Schoenlinner, B.

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

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. Nanostr. Fundam. Appl. 6, 87–95 (2008).

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[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 transformations of Maxwell’s equations,” Photon. Nanostr. Fundam. Appl. 6, 87–95 (2008).

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

Wu, B.-I.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef]

Wu, X.

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

Xiao, J. J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[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]

Yang, X. M.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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]

Zhang, B.

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef]

Zhang, S.

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

Zhang, Z. Q.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Adv. Funct. Mater. (1)

W. X. Jiang, C. W. Qiu, T. Chen, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23, 4028–4034 (2013).
[CrossRef]

Appl. Phys. Lett. (2)

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. 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. X. Jiang, H. F. Ma, and Q. Cheng, “Illusion media: generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).
[CrossRef]

Can. J. Phys. (1)

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IEEE Trans. Microwave Theor. Tech. (1)

B. Schoenlinner, X. Wu, J. P. Ebling, G. V. Eleftheriades, and G. M. Rebeiz, “Wide-scan spherical-lens antennas for automotive radars,” IEEE Trans. Microwave Theor. Tech. 50, 2166–2175 (2002).

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Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).

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Photon. Nanostr. Fundam. Appl. (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. Nanostr. Fundam. Appl. 6, 87–95 (2008).

Phys. Rev. E (1)

S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
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W. X. Jiang, C. Y. Luo, H. F. Ma, Z. L. Mei, and T. J. Cui, “Enhancement of current density by dc electric concentrator,” Sci. Rep. 2, 956 (2012).

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Figures (5)

Fig. 1.
Fig. 1.

Illustration of annular focusing lens. (a) When a plane wave is incident on a dielectric cylinder, the light rays focus on one point after passing through the dielectric cylinder. (b) When a plane wave is incident on a PEC cylinder, the light rays are reflected without penetrating into the cylinder. (c) When a plane wave is incident on a PEC cylinder enclosed by an annular lens, the light rays focus on one point after propagating around the PEC cylinder. (d) Virtual space for the transformation, (e) physical space for the transformation, and (f) configuration of scattering of plane wave by a metallic cylinder coated with an annular focusing lens.

Fig. 2.
Fig. 2.

Analytical electric-field distributions Ez of the annular lens with the focusing spot at the boundary of the lens. The material parameters of the virtual dielectric cylinder are ε1=ε2=4, μ1=μ2=1. (a) Annular focusing lens. (b) Virtual dielectric cylinder. (c) Electric-field amplitude distributions |Ez| of the annular focusing lens. (d) Numerical electric-field distributions of the annular focusing lens. The material parameters are the same as the annular lens in (a). (e) Analytical electric-field intensity distributions along the line y=0; the red solid line represents the fields of the annular focusing lens, and the blue cross curves represent the fields of the homogeneous dielectric cylindrical lens.

Fig. 3.
Fig. 3.

Analytical electric-field distributions Ez of the annular lens with the focusing spot outside the lens. The material parameters of the virtual dielectric cylinder are ε1=ε2=2, μ1=μ2=1. (a) Annular focusing lens. (b) Virtual dielectric cylinder. (c) Electric-field amplitude distributions |Ez| of the annular focusing lens. (d) Analytical electric-field intensity distributions along the line y=0; the red solid line represents the fields of the annular focusing lens, and the blue cross curves represent the fields of the homogeneous dielectric cylindrical lens.

Fig. 4.
Fig. 4.

Analytical electric-field distributions Ez of the annular focusing lens with the focusing spot inside the lens. The material parameters of the virtual dielectric cylinder are ε1=ε2=9, μ1=μ2=1. (a) Annular focusing lens. (b) Virtual dielectric cylinder. (c) Electric-field amplitude distributions |Ez| of the annular focusing lens. (d) Analytical electric-field intensity distributions along the line y=0; the red solid line represents the fields of the annular focusing lens, and the blue cross curves represent the fields of the homogeneous dielectric cylindrical lens.

Fig. 5.
Fig. 5.

Analytical electric-field distributions Ez of the double-layer annular focusing lens. The material parameters of the virtual dielectric cylinder are ε1=3.315, ε2=2.224. (a) Double-layer annular focusing lens. (b) Virtual double-layer simplified Luneburg cylindrical lens. (c) Electric-field amplitude distributions |Ez| of the double-layer annular focusing lens. (d) Analytical electric-field intensity distributions along the line y=0; the red solid line represents the fields of the double-layer annular focusing lens, and the blue cross curves represent the fields of the double-layer simplified Luneburg cylindrical lens.

Equations (26)

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fR=n2(n1),
r={k1r+a0rak2(ra)+barc,φ=φ,z=z,
ε¯=Λ·ΛT|Λ|ε0,μ¯=Λ·ΛT|Λ|μ0,
εz=k32rarε1,μr=rarμ1,μφ=rraμ1;
εz=k42k4(rb)+ak4rε2,μr=k4(rb)+ak4rμ2,μφ=k4rk4(rb)+aμ2,
rεzr(rμφEzr)+1μrεz2Ezφ2+k02r2Ez=0,
(ra)22Ezr2+(ra)Ezr+2Ezφ2+k02k32(ra)2n12Ez=0;
r122Ezr2+r1Ezr+2Ezφ2+k02k42r12n22Ez=0,
(ra)22Ψ(r)r2+(ra)Ψ(r)r+(k02k32(ra)2n12n2)Ψ(r)=0,
2Φ(φ)φ2+n2Φ(φ)=0;
r122Ψ(r)r2+r1Ψ(r)r+(k02k42r12n22n2)Ψ(r)=0,
2Φ(φ)φ2+n2Φ(φ)=0.
Ez=Fn(k0k3n1(ra))ejnφ;
Ez=Fn(k0k4n2r1)ejnφ,
E1zi=n=0jnεnJn(k0r)cos(nφ),
E1z=n=0jnεn(Jn(k0r)+BnHn(2)(k0r))cos(nφ),rc,
E2z=n=0(CnJn(k0k4n2r1)+DnHn(2)(k0k4n2r1))cos(nφ),b<rc,
E3z=n=0(EnJn(k0k3n1(ra))+FnHn(2)(k0k3n1(ra)))cos(nφ),a<rb,
jnεnJn(k0c)+BnHn(2)(k0c)=CnJn(k0n2c)+DnHn(2)(k0n2c),
CnJn(k0n2a)+DnHn(2)(k0n2a)=EnJn(k0n1a)+FnHn(2)(k0n1a),
EnJn(k0k3n1δ)+FnHn(2)(k0k3n1δ)=0.
jnεnJn(k0c)+BnHn(2)(k0c)CnJn(k0n2c)+DnHn(2)(k0n2c)=k4n2μφ2,
CnJn(k0n2a)+DnHn(2)(k0n2a)EnJn(k0n1a)+FnHn(2)(k0n1a)=k3μφ2k4μφ3n1n2.
Cn=Gntn/(Mntn+Lnwn),Dn=wnCn/tn,Bn=CnJn(k0cn2)+DnHn(2)(k0cn2)Jn(k0c)Hn(2)(k0c),En=CnJn(k0n2a)Hn(2)(k0k3n1δ)+DnHn(2)(k0n2a)Hn(2)(k0k3n1δ)un,Fn=CnJn(k0n2a)Jn(k0k3n1δ)+DnHn(2)(k0n2a)Jn(k0k3n1δ)un,
Gn=jnεnJn(k0c)Hn(2)(k0c)jnεnJn(k0c)Hn(2)(k0c),wn=ε1μ1vnJn(k0n2a)ε2μ2unJn(k0n2a),Mn=Jn(k0cn2)Hn(2)(k0c)ε2μ2Jn(k0cn2)Hn(2)(k0c),Ln=Hn(2)(k0cn2)Hn(2)(k0c)ε2μ2Hn(2)(k0cn2)Hn(2)(k0c),tn=ε2μ2unHn(2)(k0n2a)ε1μ1vnHn(2)(k0n2a),un=Hn(2)(k0n1a)Jn(k0k3δn1)Hn(2)(k0k3δn1)Jn(k0n1a),
vn=Hn(2)(k0n1a)Jn(k0k3n1δ)Hn(2)(k0k3n1δ)Jn(k0n1a).

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