Abstract

By using optimized transformation function, we research on a minimized scattering nonmagnetic concentrator, which can realize impedance matching at the inner and the outer boundaries. It has been demonstrated that the optimized transformation function method can improve the concentrating performance remarkably. The cylindrical anisotropic shell can be mimicked by radial symmetrical sectors which alternate in composition between two profiles of isotropic dielectrics, and the permittivity in each sector can be properly determined by the effective medium theory. The nonmagnetic concentrator has been validated by full-wave finite element simulations. We can believe that this work will improve the flexibilities for the EM concentrator design.

© 2013 OSA

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  1. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
    [CrossRef] [PubMed]
  4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  5. D. Schurig, J. B. Pendry, D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
    [CrossRef] [PubMed]
  6. C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
    [CrossRef] [PubMed]
  7. Y. Huang, Y. Feng, T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
    [CrossRef] [PubMed]
  8. M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
    [CrossRef] [PubMed]
  9. C. W. Qiu, L. Hu, X. Xu, Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(4), 047602 (2009).
    [CrossRef] [PubMed]
  10. C. W. Qiu, L. Hu, S. Zouhdi, “Isotropic non-ideal cloaks providing improved invisibility by adaptive segmentation and optimal refractive index profile from ordering isotropic materials,” Opt. Express 18(14), 14950–14959 (2010).
    [CrossRef] [PubMed]
  11. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
    [CrossRef]
  12. W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
    [CrossRef]
  13. X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
    [CrossRef]
  14. J. Zhang, Y. Luo, N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
    [CrossRef]
  15. L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
    [CrossRef]
  16. L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
    [CrossRef]
  17. L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
    [CrossRef]
  18. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
    [CrossRef]
  19. J. J. Yang, M. Huang, C. F. Yang, Z. Xiao, J. H. Peng, “Metamaterial electromagnetic concentrators with arbitrary geometries,” Opt. Express 17(22), 19656–19661 (2009).
    [CrossRef] [PubMed]
  20. W. Wang, L. Lin, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, X. G. Luo, “Electromagnetic concentrators with reduced material parameters based on coordinate transformation,” Opt. Express 16(15), 11431–11437 (2008).
    [CrossRef] [PubMed]
  21. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
    [CrossRef]
  22. K. Zhang, Q. Wu, J. H. Fu, L. W. Li, “Cylindrical electromagnetic concentrator with only axial constitutive parameter spatially variant,” J. Opt. Soc. Am. B 28(6), 1573–1577 (2011).
    [CrossRef]
  23. S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
    [CrossRef]
  24. B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
    [CrossRef]
  25. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, “Designs for optical cloaking with high-order transformations,” Opt. Express 16(8), 5444–5452 (2008).
    [CrossRef] [PubMed]

2011 (4)

L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

K. Zhang, Q. Wu, J. H. Fu, L. W. Li, “Cylindrical electromagnetic concentrator with only axial constitutive parameter spatially variant,” J. Opt. Soc. Am. B 28(6), 1573–1577 (2011).
[CrossRef]

2010 (2)

2009 (5)

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[CrossRef] [PubMed]

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

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

J. J. Yang, M. Huang, C. F. Yang, Z. Xiao, J. H. Peng, “Metamaterial electromagnetic concentrators with arbitrary geometries,” Opt. Express 17(22), 19656–19661 (2009).
[CrossRef] [PubMed]

2008 (6)

W. Wang, L. Lin, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, X. G. Luo, “Electromagnetic concentrators with reduced material parameters based on coordinate transformation,” Opt. Express 16(15), 11431–11437 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

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

W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[CrossRef]

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

2007 (2)

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

Y. Huang, Y. Feng, T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[CrossRef] [PubMed]

2006 (5)

J. B. Pendry, D. Schurig, 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]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Cai, W.

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

Chen, H. S.

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

Chen, X. S.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

Cheng, Q.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Chettiar, U. K.

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

Chin, J. Y.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Cui, J. H.

Cui, T. J.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Du, C. L.

Enoch, S.

M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[CrossRef] [PubMed]

Farhat, M.

M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[CrossRef] [PubMed]

Feng, Y.

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

Y. Huang, Y. Feng, T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[CrossRef] [PubMed]

Feng, Y. J.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Fu, J. H.

Guenneau, S.

M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[CrossRef] [PubMed]

Hu, L.

Huang, L. J.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

Huang, M.

Huang, Y.

Jiang, T.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Y. Huang, Y. Feng, T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15(18), 11133–11141 (2007).
[CrossRef] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

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

Kong, J. A.

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

Leonhardt, U.

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

Li, L. W.

Li, Z. F.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

Lin, L.

Liu, R. P.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Lu, C. H.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Lu, W.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

Luo, X. G.

Luo, Y.

J. Zhang, Y. Luo, N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[CrossRef]

Ma, H.

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Ma, J. X.

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Mortensen, N. A.

L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
[CrossRef]

J. Zhang, Y. Luo, N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Novitsky, A.

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, 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, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Peng, J. H.

Peng, L.

L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
[CrossRef]

Qiu, C. W.

C. W. Qiu, L. Hu, S. Zouhdi, “Isotropic non-ideal cloaks providing improved invisibility by adaptive segmentation and optimal refractive index profile from ordering isotropic materials,” Opt. Express 18(14), 14950–14959 (2010).
[CrossRef] [PubMed]

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

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Qiu, M.

W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[CrossRef]

Qu, S.

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Ran, L.

L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
[CrossRef]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

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

D. Schurig, J. B. Pendry, D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

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

Smith, D. R.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Tsai, D. P.

B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, C. T.

Wang, J.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

Wang, W.

Wood, B.

B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Wu, B. I.

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

Wu, Q.

Xi, S.

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

Xiao, Z.

Xu, X.

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

Xu, X. F.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Xu, Z. Z.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Yan, M.

W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[CrossRef]

Yan, W.

W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[CrossRef]

Yang, C. F.

Yang, J. J.

Yang, X. M.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

Zhang, B.

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

Zhang, J.

J. Zhang, Y. Luo, N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[CrossRef]

Zhang, K.

Zhao, L.

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Zhou, D. M.

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Generalized transformation for nonmagnetic invisibility cloak with minimized scattering,” J. Opt. Soc. Am. B 28(4), 922–928 (2011).
[CrossRef]

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

Zouhdi, S.

Appl. Phys. Lett. (3)

W. Yan, M. Yan, M. Qiu, “Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering,” Appl. Phys. Lett. 93(2), 021909 (2008).
[CrossRef]

J. Zhang, Y. Luo, N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010).
[CrossRef]

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. P. Liu, D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92(26), 264101 (2008).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. D Appl. Phys. (2)

L. Peng, L. Ran, N. A. Mortensen, “The scattering of a cylindrical invisibility cloak: reduced parameters optimization,” J. Phys. D Appl. Phys. 44(13), 135101 (2011).
[CrossRef]

X. F. Xu, Y. J. Feng, L. Zhao, T. Jiang, C. H. Lu, Z. Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008).
[CrossRef]

Nat. Photonics (1)

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

Opt. Commun. (1)

L. J. Huang, D. M. Zhou, J. Wang, Z. F. Li, X. S. Chen, W. Lu, “Scattering characteristics of nonmagnetic invisibility cloak with minimized scattering,” Opt. Commun. 284(24), 5523–5530 (2011).
[CrossRef]

Opt. Express (6)

Photon. Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invarant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. B (2)

S. Xi, H. S. Chen, B. Zhang, B. I. Wu, J. A. Kong, “Route to low-scattering cylindrical cloaks with finite permittivity and permeability,” Phys. Rev. B 79(15), 155122 (2009).
[CrossRef]

B. Wood, J. B. Pendry, D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

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

C. W. Qiu, A. Novitsky, H. Ma, S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(1), 016604 (2009).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. Farhat, S. Guenneau, S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Science (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, 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

Sketch of the cylindrical nonmagnetic concentrator.

Fig. 2
Fig. 2

Comparison of different coordinate transformation functions in core and circular region.

Fig. 3
Fig. 3

The material parameter values for the concentrator constructed through the polynomial function. (a) The material parameter value in core region. (b) The material parameter value in circular region.

Fig. 4
Fig. 4

(a) Magnetic field distribution of the concentrator with linear transformation function, (b) Normalized power flow of the concentrator with linear transformation function, (c) Magnetic field distribution of the concentrator with polynomial transformation function, (d) Normalized power flow of the concentrator with polynomial transformation function.

Fig. 5
Fig. 5

Normalized power flow of the concentrator with linear transformation and polynomial transformation on the centre line of core region ( x=0,y[0.2,0.2] ).

Fig. 6
Fig. 6

The normalized far field scattering patterns of the nonmagnetic concentrator with different transformation functions. The black dashed curve indicates the case of linear transformation, and the red real curve indicates the case of polynomial transformation.

Fig. 7
Fig. 7

The region permittivity patterns without magnetic response for (a) profile-A of core region, (b) profile-B of core region, (c) profile-A of circular region, (d) profile-B of circular region.

Fig. 8
Fig. 8

Transverse magnetic field distributions of ( 2M=80 ) layered nonmagnetic concentrator with (a) linear transformation, and (b) polynomial transformation.

Fig. 9
Fig. 9

Transverse magnetic field distributions of ( 2M=160 ) layered nonmagnetic concentrator with (a) linear transformation function, and (b) polynomial transformation function.

Equations (12)

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

r =f(r), θ =θ, z =z
ε r = μ r = f(r) r f (r) , ε θ = μ θ = 1 ε r , ε z = μ z = f (r)f(r) r
ε r = ( f(r) r ) 2 , ε θ = ( f (r)) 2 , μ z =1
f cor (r)= R 2 R 1 r
f cir (r)= R 3 R 2 R 3 R 1 ( r+ R 2 R 1 R 3 R 2 R 3 )
ε ( cor )r = ε ( cor )θ = ( R 2 R 1 ) 2 , μ (cor)z =1 ε ( cir )r = ε ( cir )θ = ( R 3 R 2 R 3 R 1 ) 2 , μ (cir)z =1
f cor (0)=0, f cor ( R 1 )= R 2 , f cir ( R 1 )= R 2 f cir ( R 3 )= R 3 , f cir ( R 3 )=1, f cor ( R 1 )= f cir ( R 1 )
f cor (r)=( R 1 R 2 R 1 2 ) r 2 + 2 R 2 R 1 R 1 r
f cir (r)=A r 3 +B r 2 +Cr+D
ε (cor)r = ( R 1 R 2 R 1 2 r+ 2 R 2 R 1 R 1 ) 2 , ε (cor)θ = (2 R 1 R 2 R 1 2 r+ 2 R 2 R 1 R 1 ) 2 , μ (cor)z =1
ε (cir)r = (A r 2 +Br+C+D/r) 2 , ε (cir)θ = (3A r 2 +2Br+C) 2 , μ (cir)z =1
ε r = ε A + ε B 2 , 1 ε θ = 1 2 ε A + 1 2 ε B

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