Abstract

Mimicking the ideal cloak, which is anisotropic and inhomogeneous, can be achieved by alternating homogeneous isotropic materials, whose permittivity and permeability of each isotropic coating can be determined from effective medium theory. An improved two-fold method is proposed by optimally discretizing the cloak and re-ordering the combination of the effective parameters of each layer to form a smooth step-index profile. The roles of impedance matching and index matching are investigated for cloaking effects. Smoothing the index profile leads to better invisibility than that obtained by smoothing the impedance profile, since the forward scattering can be further diminished. Nonlinear-transformation-based spherical ideal cloaks are studied, and improved design method is explored together with different segmentation schemes. Significant improvement in invisibility is always observed for the optimal segmentation in virtual space with the proposed two-fold design method no matter how nonlinear the coordinate transformation is.

© 2010 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  2. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794-9804 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt,“Optical conformal mapping,” Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  4. G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
    [CrossRef]
  5. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  6. A. Alu and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15, 3318 – 3332 (2007).
    [CrossRef] [PubMed]
  7. L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
    [CrossRef]
  8. X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (2009).
    [CrossRef]
  9. D. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  10. W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
    [CrossRef]
  11. C. W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloak,” Phys. Rev. E 80, 016604 (2009).
    [CrossRef]
  12. Y. You, G. W. Kattawar, P. W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134 - 6145 (2008).
    [CrossRef] [PubMed]
  13. H. Ma, S. Qu, Z. Xu, and J. Wang, “Approximation approach of designing practical cloaks with arbitrary shapes,” Opt. Express 16, 15449 - 15454 (2008).
    [CrossRef] [PubMed]
  14. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977 (2006).
    [CrossRef] [PubMed]
  15. 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] [PubMed]
  16. A. Novitsky, C. W. Qiu, and S. Zouhdi, “Transformation-based spherical cloaks designed by an implicit transformation-independent method: Theory and optimization,” New J. Phys. 11, 113001 (2009).
    [CrossRef]
  17. 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] [PubMed]
  18. C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
    [CrossRef]
  19. B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
    [CrossRef] [PubMed]
  20. W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, “Non-magnetic cloak without reflection,” arXiv:0707.3641v1.
  21. R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
    [CrossRef]
  22. C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (2009).
    [CrossRef]
  23. M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
    [CrossRef]
  24. P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
    [CrossRef]
  25. J. C. E. Sten, “DC fields and analytical image solutions for a radially anisotropic spherical conductor,” IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995).
    [CrossRef]
  26. B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
    [CrossRef]

2009 (6)

X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (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] [PubMed]

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

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

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

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

2008 (8)

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

Y. You, G. W. Kattawar, P. W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134 - 6145 (2008).
[CrossRef] [PubMed]

H. Ma, S. Qu, Z. Xu, and J. Wang, “Approximation approach of designing practical cloaks with arbitrary shapes,” Opt. Express 16, 15449 - 15454 (2008).
[CrossRef] [PubMed]

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

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

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

2007 (4)

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] [PubMed]

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
[CrossRef]

A. Alu and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15, 3318 – 3332 (2007).
[CrossRef] [PubMed]

2006 (5)

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

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

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

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

G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

2005 (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

1995 (1)

J. C. E. Sten, “DC fields and analytical image solutions for a radially anisotropic spherical conductor,” IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995).
[CrossRef]

Alitalo, P.

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

Alu, A.

Briane, M.

G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Cai, X.

X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (2009).
[CrossRef]

Caloz, C.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
[CrossRef]

Chen, H.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Cheng, Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (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] [PubMed]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

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, 366–369 (2009).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Cummer, S. A.

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (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, 977 (2006).
[CrossRef] [PubMed]

Deng, Q.

X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (2009).
[CrossRef]

Engheta, N.

Feng, Y.

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

Fung, T. H.

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

Gao, L.

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

Hu, G.

X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (2009).
[CrossRef]

Hu, L.

C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E 79, 047602 (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] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Justice, B. J.

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

Jylha, L.

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

Kattawar, G. W.

Kong, J. A.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Kwon, D.

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

Leonhardt, U.

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

Li, L. W.

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Lin, X. Q.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (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] [PubMed]

Luukkonen, O.

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

Ma, H.

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

H. Ma, S. Qu, Z. Xu, and J. Wang, “Approximation approach of designing practical cloaks with arbitrary shapes,” Opt. Express 16, 15449 - 15454 (2008).
[CrossRef] [PubMed]

Milton, G.W.

G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[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, 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, 977 (2006).
[CrossRef] [PubMed]

Novitsky, A.

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

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

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780 (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, 977 (2006).
[CrossRef] [PubMed]

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

Popa, B. I.

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

Qiu, C. W.

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

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

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

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Qiu, C.-W.

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

Qu, S.

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

H. Ma, S. Qu, Z. Xu, and J. Wang, “Approximation approach of designing practical cloaks with arbitrary shapes,” Opt. Express 16, 15449 - 15454 (2008).
[CrossRef] [PubMed]

Russer, P.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
[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, 977 (2006).
[CrossRef] [PubMed]

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

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

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] [PubMed]

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

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

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

Starr, A. F.

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

Sten, J. C. E.

J. C. E. Sten, “DC fields and analytical image solutions for a radially anisotropic spherical conductor,” IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995).
[CrossRef]

Tretyakov, S. A.

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

Venermo, J.

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

Wang, J.

Weder, R.

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

Werner, D. H.

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

Willis, J. R.

G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Wu, B. I.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Xu, X.

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

Xu, Z.

Yang, P.

Yeo, T. S.

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

You, Y.

Yu, G. X.

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

Yu, K. W.

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

Zedler, M.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
[CrossRef]

Zhai, P. W.

Zhang, B.

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

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] [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,” New J. Phys. 11, 113001 (2009).
[CrossRef]

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE Trans. Antennas Propagat. (1)

P. Alitalo, O. Luukkonen, L. Jylha, J. Venermo, S. A. Tretyakov, “Transmission-line networks cloaking objects from electromagnetic fields,” IEEE Trans. Antennas Propagat. 56, 416-424 (2008).
[CrossRef]

IEEE Trans. Diel. Elec. Insul. (1)

J. C. E. Sten, “DC fields and analytical image solutions for a radially anisotropic spherical conductor,” IEEE Trans. Diel. Elec. Insul. 2, 360-367 (1995).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmissionline matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55, 2930-2941 (2007).
[CrossRef]

J. Appl. Phys. (1)

X. Cai, Q. Deng, and G. Hu, “Experimental study on electromagnetic wave transparency for coated metallic cylinders,” J. Appl. Phys. 105, 103112 (2009).
[CrossRef]

J. Phys. A: Math. Theor. (1)

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A: Math. Theor. 41, 065207 (2008).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

W. X. Jiang, T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, “Arbitrarily ellipticalCcylindrical invisible cloaking,” J. Phys. D: Appl. Phys. 41, 085504 (2008).
[CrossRef]

New J. Phys. (2)

G.W. Milton,M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

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

Opt. Express (4)

Phys. Rev. A (1)

B. I. Popa and S. A. Cummer, “Cloaking with optimized homogeneous anisotropic layers,” Phys. Rev. A 79, 023806 (2009).
[CrossRef]

Phys. Rev. E (5)

C. W. Qiu, L. W. Li, T. S. Yeo, and S. Zouhdi, “Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies,” Phys. Rev. E 75, 026609 (2007).
[CrossRef]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

L. Gao, T. H. Fung, K. W. Yu, and C.-W. Qiu, “Electromagnetic transparency by coated spheres with radial anisotropy,” Phys. Rev. E 78, 046609 (2008).
[CrossRef]

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

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

Phys. Rev. Lett. (2)

B. Zhang, H. Chen, B. I. Wu, and J. A. Kong, “Extraordinary surface voltage effect in the invisibility cloak with an active device inside,” Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Science (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780 (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, 977 (2006).
[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, 366–369 (2009).
[CrossRef] [PubMed]

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

Other (1)

W. Cai, U. K. Chettiar, A. K. Kildishev, G. W. Milton, and V. M. Shalaev, “Non-magnetic cloak without reflection,” arXiv:0707.3641v1.

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Figures (8)

Fig. 1.
Fig. 1.

The geometry of a NTB spherical cloak, which is to be discretized into totally M anisotropic layers (the upper-left illustration shows the geometry of n-th anisotropic layer whose width is rn r n−1). The thickness of each anisotropic layer may not be the same to maintain good invisibility. Each anisotropic layer will be divided into 2 isotropic layers of equal thickness, characterized by medium A and medium B as the lower-left illustration shows. Therefore the whole non-ideal cloak becomes an AB…AB isotropic multilayered structure with the total layer number of 2M. In this paper, M = 40 and R 2 = 2R 1 = 2λ are chosen.

Fig. 2.
Fig. 2.

The shadowed region denotes the n-th discretized anisotropic layer as in the upper-left illustration in Fig. 1. Before converting an discretized anisotropic layer into 2 isotropic sub-layers, we consider three positions generally (i.e., left → r = r n−1; middle → r = (r n−1+rn )/2; right → r = rn ). In each case, this anisotropic layer’s parameters, determined from Eq. (2), are uniform and constant within.

Fig. 3.
Fig. 3.

The scattering cross section of the NTB spherical cloak versus the transformation nonlinearity, approximated by an isotropic non-ideal cloak. Three choices of positions (L, M, R in Fig. 2) under two sets of isotropic materials (a) new set and (b) old set are investigated and compared.

Fig. 4.
Fig. 4.

Bistatic RCS for (a) x=0.1; (b) x=4; and (c) x=20. The RCS is normalized by λ 2 0, where λ 0 denotes the wavelength in free space. The curves characterized by old and new correspond to the isotropic non-ideal cloaks designed by Eq. (4) and Eq. (5), respectively.

Fig. 5.
Fig. 5.

Total and forward scattering cross sections for isotropic non-ideal cloaks designed by the old set (blue and green lines) and new set (red and black lines) versus the nonlinearity x in the coordinate transformation.

Fig. 6.
Fig. 6.

The real part of Ex on the x–z plane of the improved cloaks designed by new set for (a)x=0.1; (b) x=20. The inset in (b) only shows the total electric field outside the cloak (i.e., r > R 2) excluding the region in white (0 < r < R 2). The working frequency is chosen to be 2GHz.

Fig. 7.
Fig. 7.

The bistatic RCSs of the isotropic cloaks designed by new and old sets for (a)x=0.1; (b) x=20. In each set, “virtual” and “physical” cases of discretizations are compared.

Fig. 8.
Fig. 8.

The impedance (a) and index (b) profiles of x = 20 isotropic cloaks for two cases: 1) the traditional old set when the ideal x = 20 cloak is equally divided in “physical” space; 2) the current two-fold method

Equations (10)

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

r = f ( r ) = r x R 1 x R 2 x R 1 x R 2 ,
ε r = μ r = R 2 ( r x R 1 x ) 2 x ( R 2 x R 1 x ) r x + 1
ε t = μ t = x R 2 r x 1 R 2 x R 1 x .
r n = f 1 ( r n ) = [ R 2 x R 1 x R 1 x n M + 1 ] 1 x · R 1 , n = 1 , 2 , . . . , M ,
ε A = μ A = ε t + ε t 2 ε t ε r
ε B = μ B = ε t ε t 2 ε t ε r .
ε A = μ B = ε t + ε t 2 ε t ε r
ε B = μ A = ε t ε t 2 ε t ε r ,
ζ t = ( ζ A + ζ B ) 2
ζ r = 2 ζ A ζ B ( ζ A + ζ B ) , ζ = ε o r μ .

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