Abstract

Loss severely degrades the cloaking effect of the device designed by traditional transformation. In this letter, we propose gain-assisted transformation optics to overcome the loss problem by introducing gain media into a spherical cloak. The gain media, which can amplify the electromagnetic fields, is controlled precisely to compensate the inherent loss in experimental realization of cloaks. We discuss the significance of controlling embedded gain materials in the context of the inverse design mechanism, which allows us to wisely select realizable materials with constant gain and loss along the radius. For practical realizations, isotropic spherical gain-assisted cloak is designed. Full-wave simulations validate the proposed design concept, which can be utilized to alleviate the inevitable loss problem in transformational optical devices.

© 2011 OSA

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    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  4. Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
    [CrossRef] [PubMed]
  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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  6. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  7. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
    [CrossRef] [PubMed]
  15. A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
    [CrossRef]
  16. C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
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2011 (3)

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

A. Boltasseva and H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011).
[CrossRef] [PubMed]

2010 (3)

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
[CrossRef] [PubMed]

2009 (6)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

B. Zhang, H. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
[CrossRef] [PubMed]

2008 (1)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

2007 (1)

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Atwater, H. A.

A. Boltasseva and H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011).
[CrossRef] [PubMed]

Barbastathis, G.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Boltasseva, A.

A. Boltasseva and H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011).
[CrossRef] [PubMed]

Chan, C. T.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Chen, H.

B. Zhang, H. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Chen, H. Y.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Chen, X.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Chettiar, U. K.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cummer, S. A.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Drachev, V. P.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Feng, Y. J.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
[CrossRef] [PubMed]

Govyadinov, A. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

Hamm, J. M.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

Hashemi, H.

H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
[CrossRef] [PubMed]

Hess, O.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

Hu, L.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
[CrossRef] [PubMed]

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Jiang, K.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Joannopoulos, J. D.

H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
[CrossRef] [PubMed]

Johnson, S. G.

H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
[CrossRef] [PubMed]

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Lai, Y.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Liu, X.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

Luo, Y.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

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(5912), 366–369 (2009).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ni, X. J.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Noginov, M. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

Novitsky, A.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Pendry, J. B.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Podolskiy, V. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

Pusch, A.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

Qiu, C. W.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
[CrossRef] [PubMed]

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Schurig, D.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (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(5912), 366–369 (2009).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Tsakmakidis, K. L.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Wu, B. I.

B. Zhang, H. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Wuestner, S.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

Xiao, S. M.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Xu, X. F.

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
[CrossRef] [PubMed]

Yuan, H. K.

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
[CrossRef] [PubMed]

B. Zhang, H. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
[CrossRef]

Zhang, B. L.

H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
[CrossRef] [PubMed]

Zhang, J.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Zhang, S.

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, Z. Q.

Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[CrossRef] [PubMed]

Zouhdi, S.

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refractive index and gain-assisted dispersion management,” Appl. Phys. Lett. 91(19), 191103 (2007).
[CrossRef]

N. J. Phys. (1)

A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization,” N. J. Phys. 11(11), 113001 (2009).
[CrossRef]

Nat Commun (1)

X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun 2, 176 (2011).
[CrossRef] [PubMed]

Nat. Lett. (1)

S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterial,” Nat. Lett. 466(7307), 735–738 (2010).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

C. W. Qiu, L. Hu, X. F. Xu, and Y. J. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4 Pt 2), 047602 (2009).
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Phys. Rev. Lett. (5)

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
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H. Hashemi, B. L. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104(25), 253903 (2010).
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B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106(3), 033901 (2011).
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Prog. Electromagn. Res. (1)

B. Zhang, H. Chen, and B. I. Wu, “Practical limitations of an invisibility cloak,” Prog. Electromagn. Res. 97, 407–416 (2009).
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Science (5)

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
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Other (1)

C. A. Balanis, Advanced Engineering Electromagnetics, (John Wiley & Sons, 1989).

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Figures (4)

Fig. 1
Fig. 1

Permittivity along the radial direction with different C. (a) Real part of radial parameter. (b) Imaginary part of radial parameter. (c) Real part of transverse parameter. (d) Imaginary part of transverse parameter. The permeability curve will be exactly the same since μ r = ε r and μ t = ε t , resulting in impedance match.

Fig. 2
Fig. 2

Snapshots of the total electric field for the spherical gain-assisted cloak with C = 0.5 . (a) x-z plane, (b) y-z plane.

Fig. 3
Fig. 3

(a) Differential cross section (exactly the same definition in Ref [15]) for the gain-assisted cloak with different compensation when C = 0.5. (b) The normalized total scattering cross sections σ/σL (normalized by σL of the loss cloak with non-compensation) as a function of the gain introduced. The scattering cross section is defined exactly the same as that in Ref [17].

Fig. 4
Fig. 4

(a) Constitutive parameters of media-A and media-B along radial direction for isotropic cloak with C = 0.5. (b) Differential cross section for isotropic cloaks designed by the old set and new set parameter profiles with different layer number (N = 20 and N = 40).

Equations (13)

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ε / ε 0 = μ / μ 0 = J · J T / det ( J ) ,
ε / ε 0 = μ / μ 0 = diag [ ξ r ( r ) , ξ t ( r ) , ξ t ( r ) ] ,
b = a b ξ t ( r 1 ) d r 1 .
b = a b Re [ ξ t ( r 1 ) ] d r 1 ,
0 = a b Im [ ξ t ( r 1 ) ] d r 1 .
Re [ ξ t ] = b g ( r ) / a b g ( r 1 ) d r 1 .
Im [ ξ t ] = d F ( r ) d r = F ( r ) .
ξ t ( r ) = b g ( r ) / a b g ( r 1 ) d r 1 + i F ( r ) .
ξ r ( r ) = ( b a r g ( r 1 ) d r 1 r a b g ( r 1 ) d r 1 + i F ( r ) F ( a ) r ) 2 / ( b g ( r ) a b g ( r 1 ) d r 1 + i F ( r ) ) .
r = b a r g ( r 1 ) d r 1 / a b g ( r 1 ) d r 1 + i [ F ( r ) F ( a ) ] .
r = b ( r a ) / ( b a ) + i C [ | r ( a + b ) / 2 | ( b a ) / 2 ] .
ξ t ( r ) = b b a + i C u ( r a + b 2 ) ,
ξ r ( r ) = ( b ( r a ) ( b a ) + i C | r a + b 2 | i C b a 2 ) 2 / r 2 ξ t ( r ) ,

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