Abstract

We present a full-wave analysis method on the transmission of a Gaussian light pulse through a spherical invisibility cloak with causal dispersions. The spatial energy distribution of the Gaussian light pulse is distorted after the transmission. A volcano-shaped spatial time-delay distribution of the transmitted light pulse is demonstrated as a concrete example in our physical model. Both the time-delay and the energy transport depend on the polarization of light waves. This study helps to provide a complete picture of energy propagation through an invisibility cloak.

© 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. U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  3. 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]
  4. 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, 977-980 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
    [CrossRef]
  7. P. Yao, Z. Liang, and X. Jiang, "Limitations of the electromagnetic cloak with dispersive material," Appl. Phys. Lett. 92, 031111 (2008).
    [CrossRef]
  8. 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]
  9. 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]
  10. B. Zhang, H. Chen, B. I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101(R) (2007).
    [CrossRef]
  11. 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]
  12. Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
    [CrossRef] [PubMed]
  13. B. Zhang, H. Chen, B. I. Wu, 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]
  14. L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York and London, 1960).
  15. Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford and New York, 1964).

2008 (5)

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

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, H. Chen, B. I. Wu, 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]

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (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]

2007 (3)

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (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 (5)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (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]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (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]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (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, 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]

B. Zhang, H. Chen, B. I. Wu, 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]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (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]

Jiang, X.

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

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (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, 977-980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Kong, J. A.

B. Zhang, H. Chen, B. I. Wu, 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]

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]

Leonhardt, U.

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Liang, Z.

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

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Mock, J. 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, 977-980 (2006).
[CrossRef] [PubMed]

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (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]

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]

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, 977-980 (2006).
[CrossRef] [PubMed]

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]

Qiu, M.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Ruan, Z.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Schurig, D.

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]

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, 977-980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Smith, D. R.

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, 977-980 (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]

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]

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, 977-980 (2006).
[CrossRef] [PubMed]

Sun, X.

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008).
[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]

B. Zhang, H. Chen, B. I. Wu, 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]

Yan, M.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Yao, P.

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

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

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]

B. Zhang, H. Chen, B. I. Wu, 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]

Appl. Phys. Lett. (2)

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

Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

J. Appl. Phys. (1)

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]

Nature Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. E (1)

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]

Phys. Rev. Lett. (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]

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]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B. I. Wu, 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]

Science (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford and New York, 1964).

L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York and London, 1960).

B. Zhang, H. Chen, B. I. Wu, Y. Luo, L. Ran, and J. A. Kong, "Response of a cylindrical invisibility cloak to electromagnetic waves," Phys. Rev. B 76, 121101(R) (2007).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Propagation of a narrow-band Gaussian pulse through a frequency-dispersive spherical invisibility cloak with a target plane set up at z = 2.4μm. The pulse peak is at z = -120μm when t = 0. R 2 = 2R 1 = 1.8μm.

Fig. 2.
Fig. 2.

Ex field distribution when the Gaussian pulse is passing through the dispersive spherical cloak at (a) t = 400fs and (b) t = 460fs.

Fig. 3.
Fig. 3.

Instantaneous Poynting power Sz at (0.9,0,2.4), (0.45,0,2.4) and (0,0,2.4)μm in the target plane compared to the incident signal in absence of the cloak and the PEC core.

Fig. 4.
Fig. 4.

(a) Time delay distribution and (b) normalized accumulated energy distribution of the signal arriving at the target plane after passing through a dispersive spherical invisibility cloak. In (a), maximum delay is 35.1fs while the delay at the center is 27.9fs. In (b), the minimum is 0.7638 while it is 0.9075 at the center.

Equations (6)

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

ε r ( r , f ) = ε t ( 1 f p 2 f ( f + i γ 1 ) ) ,
μ r ( r , f ) = μ t ( 1 F 1 + i γ 2 / f f 0 2 / f 2 ) ,
E ¯ inc ( r ¯ , t ) = x ̂ { 0 E inc ( ω ) e ik ( z + d 1 ) iωt } ,
E ¯ inc ( r ¯ , t ) = x ̂ { n = 0 E n e in k 0 ( z + d 1 ) in ω 0 t } ,
E ¯ ( r ¯ , t ) = { n = N 1 N 2 [ x ̂ E n e in k 0 ( z + d 1 ) + E ¯ scat ( r ¯ ) ] e in ω 0 t } ,
S z ( t , x , y , d 2 ) = E ¯ ( t , x , y , d 2 ) × H ¯ ( t , x , y , d 2 ) · z ̂ ,

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