Abstract

Localization of an electromagnetic field can be achieved by transformation optics using metamaterials. A coordinate transformation structure different from traditional resonator is proposed. Wherein, arbitrary frequency of the whole band of electromagnetic wave can be localized without energy loss, i.e., the modes in this structure are continuous. Theoretical analysis and numerical simulation show that the material parameter variations at the outer boundary of the structure have little influence on the localization property. When realizable physical structure is considered, multi-layer approximation should be applied. The calculated results show that the estimated localization time is about 100 ns for an 8-layer inhomogeneous approximation, and it could reach several seconds for a 30-layer homogeneous approximation. The present work may present a new application of transformation optics.

© 2010 OSA

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  1. A. Ward and J. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
    [CrossRef]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  4. U. Leonhardt, “Notes on conformal invisibility devices,” N. J. Phys. 8(7), 118 (2006).
    [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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  6. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 036621 (2006).
    [CrossRef] [PubMed]
  7. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
    [CrossRef]
  8. J. Lee, J. Blair, V. Tamma, Q. Wu, S. Rhee, C. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
    [CrossRef] [PubMed]
  9. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  10. 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]
  11. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
    [CrossRef]
  12. 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]
  13. L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
    [CrossRef]
  14. B. Zhang and B. I. Wu, “Electromagnetic detection of a perfect invisibility cloak,” Phys. Rev. Lett. 103(24), 243901 (2009).
    [CrossRef]
  15. L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
    [CrossRef]
  16. W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
    [CrossRef]
  17. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
    [CrossRef] [PubMed]
  18. A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
    [CrossRef] [PubMed]
  19. J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express 17(6), 4758–4772 (2009).
    [CrossRef] [PubMed]

2009 (7)

J. Lee, J. Blair, V. Tamma, Q. Wu, S. Rhee, C. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
[CrossRef] [PubMed]

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]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

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]

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

B. Zhang and B. I. Wu, “Electromagnetic detection of a perfect invisibility cloak,” Phys. Rev. Lett. 103(24), 243901 (2009).
[CrossRef]

J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express 17(6), 4758–4772 (2009).
[CrossRef] [PubMed]

2008 (3)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
[CrossRef] [PubMed]

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
[CrossRef]

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 (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

2006 (6)

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

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

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

U. Leonhardt, “Notes on conformal invisibility devices,” N. J. Phys. 8(7), 118 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

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

1996 (1)

A. Ward and J. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

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]

Blair, J.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
[CrossRef] [PubMed]

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Cardenas, J.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Chettiar, U.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[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]

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

Gabrielli, L.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Hendi, A.

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

Henn, J.

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[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]

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.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Lee, J.

Leonhardt, U.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, “Notes on conformal invisibility devices,” N. J. Phys. 8(7), 118 (2006).
[CrossRef]

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]

Lipson, M.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Milton, G.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

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]

Park, W.

Pendry, J.

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

A. Ward and J. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Pendry, J. B.

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]

Poitras, C.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Popa, B. I.

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

Qiu, M.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
[CrossRef]

Rhee, S.

Schurig, D.

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

Shalaev, V.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 036621 (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]

Summers, C.

Tamma, V.

Tyc, T.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

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]

Ward, A.

A. Ward and J. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Wu, B. I.

B. Zhang and B. I. Wu, “Electromagnetic detection of a perfect invisibility cloak,” Phys. Rev. Lett. 103(24), 243901 (2009).
[CrossRef]

Wu, Q.

Xu, J.

Yan, M.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
[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 and B. I. Wu, “Electromagnetic detection of a perfect invisibility cloak,” Phys. Rev. Lett. 103(24), 243901 (2009).
[CrossRef]

Zhang, L.

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
[CrossRef]

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]

J. Xu and X. Zhang, “Cloaking radiation of moving electron beam and relativistic energy loss spectra,” Opt. Express 17(6), 4758–4772 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

J. Mod. Opt. (1)

A. Ward and J. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

L. Zhang, M. Yan, and M. Qiu, “The effect of transformation order on the invisibility performance of a practical cylindrical cloak,” J. Opt. A, Pure Appl. Opt. 10(9), 095001 (2008).
[CrossRef]

N. J. Phys. (1)

U. Leonhardt, “Notes on conformal invisibility devices,” N. J. Phys. 8(7), 118 (2006).
[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]

Nat. Photonics (2)

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

Opt. Express (3)

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

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

Phys. Rev. Lett. (3)

B. Zhang and B. I. Wu, “Electromagnetic detection of a perfect invisibility cloak,” Phys. Rev. Lett. 103(24), 243901 (2009).
[CrossRef]

A. Hendi, J. Henn, and U. Leonhardt, “Ambiguities in the scattering tomography for central potentials,” Phys. Rev. Lett. 97(7), 073902 (2006).
[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]

Science (5)

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]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[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(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]

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

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Figures (9)

Fig. 1
Fig. 1

Coordinate transformation of cloak and the electromagnetic localization structure (ELS). (a)→(b): coordinate transformation of cloak. (c)→(d): coordination transformation of ELS. R1< R2< R3< R4, R4→ + ∞.

Fig. 2
Fig. 2

Distribution of permittivity and permeability in the coordinate transformation region of the proposed structure (R2<r’<R3, R2 = 0.1 m, R3 = 0.4 m in Fig. 1(d)).

Fig. 3
Fig. 3

Calculated region and simulation parameters. (a) Parameters for eigenfrequency simulation; (b) Parameters for harmonic propagation simulation.

Fig. 4
Fig. 4

Field distributions of the calculated modes ( p = 1 ). (a) at 1.899744 GHz. (b) the enlargement of the red box in (a). (c) the meshed grids of simulation region in (b). The colored vertical bar represents field amplitude (arb. units).

Fig. 5
Fig. 5

Influence of transformation order n on internal power localization. Red lines denote the inner and outer boundaries of the proposed structure. (a) p = −1; (b) p = −0.55. The colored vertical bar represents field amplitude (arb. units).

Fig. 6
Fig. 6

Electric field distribution (Ez) in the proposed structure calculated using different transformation orders.

Fig. 7
Fig. 7

Influence of shifted length of the outer boundary of the proposed structure on its localization function. Iouter is the energy at the new outer boundary (r’ = R3-L). Iinner is the energy at the field source (r’ = 0.02 m).

Fig. 8
Fig. 8

(a) Localization of electromagnetic field in the proposed structure using an 8-layer approximation. The colored vertical bar represents field amplitude (arb. units). (b) Localized field distribution (Ez) of the proposed structure under an 8-layer approximation.

Fig. 9
Fig. 9

Localization time of the proposed structure. In the left upper insert, R2 = 0.1 m, R3 = 0.4 m, the radius of the outer boundary is 0.402 m.

Equations (4)

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r = R 2 R 3 R 2 p r p + R 3 ,                         θ = θ ,                         z = z
ε r = μ r = p r R 3 r
ε θ = μ θ = 1 ε r
ε z = μ z = R 2 2 ( R 2 R 3 ) 2 / p ( r R 3 ) ( 2 / p 1 ) p r

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