Abstract

Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we proposed an electromagnetic cloak structure that does not require metamaterials with subwavelength structured inclusions to realize the anisotropy or inhomogeneity of the material parameters. We constructed a concentric layered structure of alternating homogeneous isotropic materials that can be treated as an effective medium with the required radius-dependent anisotropy. With proper design of the permittivity or the thickness ratio of the alternating layers, we demonstrated the low-reflection and power-flow bending properties of the proposed cloaking structure through rigorous analysis of the scattered electromagnetic fields. The proposed cloaking structure could be possibly realized by normal materials, therefore may lead to a practical path to an experimental demonstration of electromagnetic cloaking, especially in the optical range.

© 2007 Optical Society of America

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References

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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. A. Alu and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  3. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  4. D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9840 (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. F. Zolla, S. Guenneau, A. Nicolet and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
    [CrossRef] [PubMed]
  7. 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]
  8. W. Cai U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics,  1, 224-227 (2007).
    [CrossRef]
  9. G.W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027-3059 (2006).
    [CrossRef]
  10. B. Wood, J. B. Pendry, and D. P. Tsai, "Directed subwavelength imaging using a layered metal-dielectric system." Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  11. A. A. Govyadinov and V. A. Podolskiy, "Metamaterial photonic funnels for subdiffraction light compression and propagation," Phys. Rev. B 73, 155108 (2006).
    [CrossRef]
  12. Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
    [CrossRef] [PubMed]
  13. A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations." Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  14. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects." Science 315, 1699-1701 (2007).
    [CrossRef]
  15. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range." Science 315, 1699-1701 (2007).
    [CrossRef] [PubMed]
  16. R. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961).
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    [CrossRef]
  18. C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).
  19. J. D. Jackson, Classical electrodynamics, (John Wiley, New York, 1999).
  20. J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, "Transmission of THz radiation through InSb gratings of subwavelength apertures," Opt. Express 13, 847-859 (2005).
    [CrossRef] [PubMed]
  21. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  22. N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
    [CrossRef]
  23. N. Garcia, E. V. Ponizowskaya, H. Zhu, J. Q. Xiao, and A. Pons, "Wide photonic band gaps at the visible in metallic nanowire arrays embedded in a dielectric matrix," Appl. Phys. Lett. 82, 3147-3149 (2003).
    [CrossRef]

2007

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

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects." Science 315, 1699-1701 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range." Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

F. Zolla, S. Guenneau, A. Nicolet and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

2006

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]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (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, 9794-9840 (2006).
[CrossRef] [PubMed]

G.W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027-3059 (2006).
[CrossRef]

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

A. A. Govyadinov and V. A. Podolskiy, "Metamaterial photonic funnels for subdiffraction light compression and propagation," Phys. Rev. B 73, 155108 (2006).
[CrossRef]

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations." Phys. Rev. B 74, 075103 (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. 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]

2005

2003

N. Garcia, E. V. Ponizowskaya, H. Zhu, J. Q. Xiao, and A. Pons, "Wide photonic band gaps at the visible in metallic nanowire arrays embedded in a dielectric matrix," Appl. Phys. Lett. 82, 3147-3149 (2003).
[CrossRef]

2002

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

1990

J. C. Monzon, "On the application of Sommerfeld representation in a two-dimensional rotationally invariant anisotropic medium." IEEE Trans.Antennas and Propag. 38, 1028-1034 (1990).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Antennas and Propag.

J. C. Monzon, "On the application of Sommerfeld representation in a two-dimensional rotationally invariant anisotropic medium." IEEE Trans.Antennas and Propag. 38, 1028-1034 (1990).
[CrossRef]

Appl. Phys. Lett.

N. Garcia, E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett. 80, 1120-1122 (2002).
[CrossRef]

N. Garcia, E. V. Ponizowskaya, H. Zhu, J. Q. Xiao, and A. Pons, "Wide photonic band gaps at the visible in metallic nanowire arrays embedded in a dielectric matrix," Appl. Phys. Lett. 82, 3147-3149 (2003).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Phys. Rev. B

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

A. A. Govyadinov and V. A. Podolskiy, "Metamaterial photonic funnels for subdiffraction light compression and propagation," Phys. Rev. B 73, 155108 (2006).
[CrossRef]

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations." Phys. Rev. B 74, 075103 (2006).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. E

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

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]

Proc. R. Soc. London A

G.W. Milton and N. A. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London A 462, 3027-3059 (2006).
[CrossRef]

Science

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (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, 977-980 (2006).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects." Science 315, 1699-1701 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range." Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

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

Other

C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (John Wiley, New York, 1983).

J. D. Jackson, Classical electrodynamics, (John Wiley, New York, 1999).

R. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961).

Supplementary Material (2)

» Media 1: MOV (3759 KB)     
» Media 2: MOV (3761 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

TM wave incident on an infinite conducting cylinder (in yellow) shelled with (a) concentric layers structure with alternating layers of dielectric A and B, (b) equivalent anisotropic cylindrical medium with radius-dependent, anisotropic material parameters. Both of the shells have inner and outer radius of a and b, respectively.

Fig. 2.
Fig. 2.

Comparison of the far-field scattering patterns for a bare conducting cylinder, the conducting cylinder shelled with a concentric layered structure of different number of layers, and that shelled with an anisotropic cylindrical medium. All values have been normalized to the scattering pattern of the bare conducting cylinder at θ=0.

Fig. 3.
Fig. 3.

The relative permittivity components required for an ideal reduced set of parameter (εr(r), εθ(r)), and that for the corresponding layered structure with alternating dielectric A and B (εA(m), εB(m)). The inset describes the anisotropic shell divided into stepwise homogeneous N-layer (with permittivity as εr(m), εθ(m)), and the mimic of each layer by alternating layers of dielectric A and B (totally 2N layers).

Fig. 4.
Fig. 4.

The calculated magnetic-field distribution around the conducting cylinder (a) with a cloak of concentric layered structure (movie, 3.67 MB) [Media 1], and (b) without cloak (movie, 3.67 MB) [Media 2], (c) the far-field scattering pattern. Power-flow lines (in black) in (a) show the smooth deviation of electromagnetic power around the cloaked object. The white circles outline the cloak.

Fig. 5.
Fig. 5.

The magnetic-field distribution around the conducting cylinder, (a) with a cloak of layered structure, and (b) without cloak, for a TM incident wave from a line source. The white circles outline the cloak.

Equations (13)

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

ε θ = ε A + η ε B 1 + η ,
1 ε r = 1 1 + η ( 1 ε A + η ε B ) .
η = d B d A .
H z i = H 0 n = n = j n J n ( k 0 r ) e jn θ ,
H z s = H 0 n = n = C n j n H n ( 2 ) ( k 0 r ) e jn θ ,
H z m t = H 0 n = n = j n ( A mn J n ( k m r ) + B mn H n ( 2 ) ( k m r ) ) e jn θ ,
E r = 1 r j ω μ k 2 H z θ , E θ = j ω μ k 2 H z r .
H z i = ω ε 0 I m 4 H 0 ( 2 ) ( k 0 r r 0 ) .
ξ ( θ ) = n = n = C n e jn θ 2 .
ε r = μ r = r a r , ε θ = μ θ = r r a ,
ε z = μ z = ( b b a ) 2 r a r .
μ z = 1 , ε θ = ( b b a ) 2 ,
ε r = ( b b a ) 2 ( r a r ) 2 .

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