Abstract

The transmission line modeling method is used to get the time domain response of a dispersive cylindrical cloak to an electromagnetic (EM) plane wave that is slightly nonmonochromatic. Our objective is to numerically study two important phenomena derived from the dispersive nature of the invisibility shell: frequency shifts and time delays. On one hand, the frequency domain representation of the cloak’s response shows that the frequency center is shifted once the EM wave has crossed the cloak; the shift intensity representation spans the entire rainbow spectrum depending on the observation angle. On the other hand, such a full-wave simulation constitutes tangible evidence of the existence of time delays when the EM wave passes through the device. We show that this phenomenon depends on the employed coordinate transformation.

© 2009 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  2. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  3. 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]
  4. P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
    [CrossRef]
  5. B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (2008).
    [CrossRef] [PubMed]
  6. P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118, 1203-1208 (1971).
    [CrossRef]
  7. P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microwave Theory Tech. 35, 370-377 (1987).
    [CrossRef]
  8. C. Blanchard, J. Portí, B.-I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, “Time domain simulation of electromagnetic cloaking structures with TLM method,” Opt. Express 16, 6461-6470 (2008).
    [CrossRef] [PubMed]
  9. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
    [CrossRef]
  10. P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
    [CrossRef]
  11. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  12. H. Chen and C. T. Chan, “Time delays and energy transport velocities in three dimensional ideal cloaking devices,” J. Appl. Phys. 104, 033113 (2008).
    [CrossRef]
  13. C. Blanchard, J. Portí, J. A. Morente, A. Salinas, and B.-I. Wu, “Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method,” Opt. Express 16, 9344-9350 (2008).
    [CrossRef] [PubMed]
  14. Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717-6730 (2008).
    [CrossRef] [PubMed]
  15. R. Allen and M. J. Clark, “Application of the symmetrized transmission-line matrix method to the cold modeling of magnetrons,” Int. J. Numer. Model. 1, 61-70 (1988).
    [CrossRef]
  16. J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
    [CrossRef]
  17. C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).
  18. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
    [CrossRef]
  19. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).
  20. A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022 (2008).
    [CrossRef]
  21. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  22. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  23. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91, 111105 (2007).
    [CrossRef]

2008 (7)

P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
[CrossRef]

B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (2008).
[CrossRef] [PubMed]

C. Blanchard, J. Portí, B.-I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, “Time domain simulation of electromagnetic cloaking structures with TLM method,” Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, “Time delays and energy transport velocities in three dimensional ideal cloaking devices,” J. Appl. Phys. 104, 033113 (2008).
[CrossRef]

C. Blanchard, J. Portí, J. A. Morente, A. Salinas, and B.-I. Wu, “Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method,” Opt. Express 16, 9344-9350 (2008).
[CrossRef] [PubMed]

Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717-6730 (2008).
[CrossRef] [PubMed]

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022 (2008).
[CrossRef]

2007 (2)

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

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

2006 (3)

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

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

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

2005 (1)

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

2003 (1)

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

2002 (1)

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

2001 (1)

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
[CrossRef]

1988 (1)

R. Allen and M. J. Clark, “Application of the symmetrized transmission-line matrix method to the cold modeling of magnetrons,” Int. J. Numer. Model. 1, 61-70 (1988).
[CrossRef]

1987 (1)

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microwave Theory Tech. 35, 370-377 (1987).
[CrossRef]

1971 (1)

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118, 1203-1208 (1971).
[CrossRef]

Allen, R.

R. Allen and M. J. Clark, “Application of the symmetrized transmission-line matrix method to the cold modeling of magnetrons,” Int. J. Numer. Model. 1, 61-70 (1988).
[CrossRef]

Argyropoulos, C.

Besser, B. P.

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

Beurle, R. L.

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118, 1203-1208 (1971).
[CrossRef]

Blanchard, C.

Cai, W.

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

Chan, C. T.

H. Chen and C. T. Chan, “Time delays and energy transport velocities in three dimensional ideal cloaking devices,” J. Appl. Phys. 104, 033113 (2008).
[CrossRef]

Chen, H.

H. Chen and C. T. Chan, “Time delays and energy transport velocities in three dimensional ideal cloaking devices,” J. Appl. Phys. 104, 033113 (2008).
[CrossRef]

B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (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]

C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).

Chettiar, U. K.

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

Clark, M. J.

R. Allen and M. J. Clark, “Application of the symmetrized transmission-line matrix method to the cold modeling of magnetrons,” Int. J. Numer. Model. 1, 61-70 (1988).
[CrossRef]

Cummer, S. A.

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

Du, H.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Eleftheriades, G. V.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

Hao, Y.

Heyman, E.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Hoefer, W. J. R.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
[CrossRef]

Iyer, A. K.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

Jiang, X.

P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
[CrossRef]

Johns, P. B.

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microwave Theory Tech. 35, 370-377 (1987).
[CrossRef]

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Electr. Eng. 118, 1203-1208 (1971).
[CrossRef]

Kildishev, A. V.

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

Kong, J. A.

C. Blanchard, J. Portí, B.-I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, “Time domain simulation of electromagnetic cloaking structures with TLM method,” Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (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]

Kremer, P. C.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Leonhardt, U.

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

Liang, Z.

P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
[CrossRef]

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Maci, S.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022 (2008).
[CrossRef]

Milton, G. W.

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

Molina-Cuberos, G. J.

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

Morente, J. A.

C. Blanchard, J. Portí, J. A. Morente, A. Salinas, and B.-I. Wu, “Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method,” Opt. Express 16, 9344-9350 (2008).
[CrossRef] [PubMed]

C. Blanchard, J. Portí, B.-I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, “Time domain simulation of electromagnetic cloaking structures with TLM method,” Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).

Pendry, J. B.

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

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
[CrossRef]

Pitaevskii, L. P.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984).

Popa, B. -I.

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

Portí, J.

Portí, J. A.

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Salinas, A.

Schurig, D.

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

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

Schwingenschuh, K.

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

Shalaev, V. M.

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

Smith, D. R.

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

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

So, P. P. M.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
[CrossRef]

Wu, B. -I.

C. Blanchard, J. Portí, J. A. Morente, A. Salinas, and B.-I. Wu, “Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method,” Opt. Express 16, 9344-9350 (2008).
[CrossRef] [PubMed]

C. Blanchard, J. Portí, B.-I. Wu, J. A. Morente, A. Salinas, and J. A. Kong, “Time domain simulation of electromagnetic cloaking structures with TLM method,” Opt. Express 16, 6461-6470 (2008).
[CrossRef] [PubMed]

B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (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]

C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).

Yaghjian, A. D.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022 (2008).
[CrossRef]

Yao, P.

P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Phys. Lett. 76, 4773-4776 (1996).
[CrossRef]

Zhang, B.

B. Zhang, B.-I. Wu, H. Chen, and J. A. Kong, “Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave,” Phys. Rev. Lett. 101, 063902 (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]

C. Blanchard, B. Zhang, B.-I. Wu, J. A. Portí, H. Chen, J. A. Morente, and A. Salinas, “Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept,” J. Opt. Soc. Am. B 26 (to be published).

Zhao, Y.

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

P. Yao, Z. Liang, and X. Jiang, “Limitation of the electromagnetic cloak with dispersive material,” Appl. Phys. Lett. 92, 031111 (2008).
[CrossRef]

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

Icarus (1)

J. A. Morente, G. J. Molina-Cuberos, J. A. Portí, K. Schwingenschuh, and B. P. Besser, “A study of the propagation of electromagnetic waves in Titan's atmosphere with the TLM numerical method,” Icarus 162, 374-384 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (4)

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microwave Theory Tech. 35, 370-377 (1987).
[CrossRef]

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
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Figures (12)

Fig. 1
Fig. 1

(a) Magnetic field ( × 10 3 ) mapping in the vicinity of a cloaked PEC cylinder at 2 GHz. Four regions are apparent: 1, cylinder; 2, cloaking shell; 3, free space with total field; 4, scattered-field region where incident field is subtracted. (b) Far-field pattern comparison between the cloaked and the bare cylinders.

Fig. 2
Fig. 2

Frequency domain representation of the incoming wave (function h) for ω = 2 π × 2   GHz and g = 5 × 10 7 s 1 .

Fig. 3
Fig. 3

SW of a PEC cylinder with/without the cloaking shell around. The scattering is reduced in a narrowband around the 2 GHz working frequency.

Fig. 4
Fig. 4

Two different curves of dispersion for the constitutive parameter ε r at r = 0.105   m . Curves 1 and 2 correspond to A r ( r ) = 0.10 / r and 0.21 / r , respectively.

Fig. 5
Fig. 5

Frequency domain representation of the transmitted wave in the forward direction. The frequency centers of the pulses are blueshifted. The red dashed curve corresponds to A r ( r ) = 0.10 / r (i.e., curve 1 in Fig. 4), while the blue dotted curve corresponds to A r ( r ) = 0.21 / r (i.e., curve 2 in Fig. 4). The frequency shift depends on the relation of dispersion.

Fig. 6
Fig. 6

Dispersion of the r component of the permittivity at three different points inside the cloak. At r = R 1 , ε r takes, of course, the zero value at the working frequency (2 GHz). But when r increases, the frequency that renders ε r = 0 increases.

Fig. 7
Fig. 7

Incident, scattered, and total fields for a cloak whose working frequency is 2 GHz. It is illuminated by an EM plane wave with frequencies of (a) 1.99 GHz (red light) and (b) 2.01 GHz (blue light). For the red light, a destructive interference is observed, while the interference is constructive for the blue light.

Fig. 8
Fig. 8

Distribution of the shifted frequency center in terms of the observation angle for a quasi-monochromatic EM wave traveling from left to right.

Fig. 9
Fig. 9

Ratio between the total and incident fields, for f = 1.99 and 2.01   GHz , in terms of the direction of observation.

Fig. 10
Fig. 10

Velocity distribution in a dispersive cloak along three different directions. The optics constants μ z ( ω ) and ε r ( ω ) of the cloak follow a Drude model [18].

Fig. 11
Fig. 11

H-field plot in terms of the normalized time. The envelope of the signal does not reach x 0 at the same time depending on whether the cloaking structure is present or not.

Fig. 12
Fig. 12

Time delay (normalized by T 0 ) in terms of the distance y from the x axis.

Equations (17)

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r = f α ( r ) = [ ( r R 1 ) / ( R 2 R 1 ) ] 1 / α R 2 ,
ε r = μ r = r R 1 r ,
ε φ = μ φ = r r R 1 ,
ε z = μ z = ( R 2 R 2 R 1 ) 2 r R 1 r ,
μ z ( ω ) = A z ( r ) ω 0 2 ω 2 [ A z ( r ) μ z ( ω 0 ) ] ,
ε r ( ω ) = A r ( r ) ω 0 2 ω 2 [ A r ( r ) ε r ( ω 0 ) ] ,
A z ( r ) = 2 Δ t Δ z Z 0 r Δ r Δ φ μ 0 ,     A r ( r ) = Δ t Δ r Y 0 r Δ φ Δ z ε 0 ,
h ( t ) = sin [ ω t ] exp [ g 2 ( t t m ) 2 ] ,
H z inc ( r ) = H 0   exp [ i ω c r   cos   φ ] ,
E r inc ( r ) = E 0   exp [ i ω c r   cos   φ ] sin   φ ,
E φ inc ( r ) = E 0   exp [ i ω c r   cos   φ ] cos   φ .
H z = H z inc [ f ( r ) ] ,
E r = f ( r ) E r inc [ f ( r ) ] ,
E φ = f ( r ) r E φ inc [ f ( r ) ] ,
W ¯ = 1 4 [ ε 0 d ( ω ε i k ) d ω E i E k + μ 0 d ( ω μ i k ) d ω H i H k ] ,
S ¯ = 1 2 | Re [ E × H ] | .
u = c 2 R 2 ( r R 1 r ) 2 cos 2 φ + sin 2 φ ( R 2 R 1 ) [ ( R 2   sin   φ R 2 R 1 ) 2 d ( ω ε r ) d ω + ( r R 1 r R 2   cos   φ R 2 R 1 ) 2 d ( ω ε φ ) d ω + d ( ω μ z ) d ω ] ,

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