Abstract

We show in principle how to cloak a region of space to make its contents classically invisible or transparent to waves. The method uses sensors and active sources near the surface of the region, and could operate over broad bandwidths. A general expression is given for calculating the necessary sources, and explicit, fully causal simulations are shown for scalar waves. Vulnerability to broad-band probing is discussed, and any active scheme should detectable by a quantum probe, regardless of bandwidth.

©2006 Optical Society of America

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References

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  1. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [Crossref]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  4. G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. Roy. Soc. A 462, 3027–3059 (2006).
    [Crossref]
  5. E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Modern Opt. 40, 785–792 (1993).
    [Crossref]
  6. N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
    [Crossref]
  7. A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
    [Crossref]
  8. J. E. Ffowcs Williams “Review Lecture: Anti-Sound,” Proc. Roy. Soc. London A 395, 63–88 (1984)
    [Crossref]
  9. P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic Press, London, 1992), pp. 290–293.
  10. E. Friot and C. Bordier, “Real-time active suppression of scattered acoustic radiation,” J. Sound Vib. 278, 563–580 (2004).
    [Crossref]
  11. E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).
  12. Yu. I. Bobrovnitskii, “A new solution to the problem of an acoustically transparent body,” Acoust. Phys. 50, 647–650 (2004).
    [Crossref]
  13. J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 56, 99–107 (1939).
    [Crossref]
  14. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  15. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  16. D. A. B. Miller, “Huygens’s wave propagation principle corrected,” Opt. Lett. 16, 1370–1372 (1991).
    [Crossref] [PubMed]
  17. C. H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984 (IEEE, New York, 1984), 175–179.
    [PubMed]
  18. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
    [Crossref]
  19. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802 (1982).
    [Crossref]
  20. D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
    [Crossref]

2006 (4)

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. Roy. Soc. A 462, 3027–3059 (2006).
[Crossref]

E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).

2005 (1)

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

2004 (2)

Yu. I. Bobrovnitskii, “A new solution to the problem of an acoustically transparent body,” Acoust. Phys. 50, 647–650 (2004).
[Crossref]

E. Friot and C. Bordier, “Real-time active suppression of scattered acoustic radiation,” J. Sound Vib. 278, 563–580 (2004).
[Crossref]

2003 (1)

A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

1994 (1)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
[Crossref]

1993 (1)

E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Modern Opt. 40, 785–792 (1993).
[Crossref]

1991 (1)

1984 (1)

J. E. Ffowcs Williams “Review Lecture: Anti-Sound,” Proc. Roy. Soc. London A 395, 63–88 (1984)
[Crossref]

1982 (2)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802 (1982).
[Crossref]

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[Crossref]

1939 (1)

J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 56, 99–107 (1939).
[Crossref]

Alu, A.

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

A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[Crossref]

Bennett, C. H.

C. H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984 (IEEE, New York, 1984), 175–179.
[PubMed]

Bobrovnitskii, Yu. I.

Yu. I. Bobrovnitskii, “A new solution to the problem of an acoustically transparent body,” Acoust. Phys. 50, 647–650 (2004).
[Crossref]

Bordier, C.

E. Friot and C. Bordier, “Real-time active suppression of scattered acoustic radiation,” J. Sound Vib. 278, 563–580 (2004).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Brassard, G.

C. H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984 (IEEE, New York, 1984), 175–179.
[PubMed]

Chu, L. J.

J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 56, 99–107 (1939).
[Crossref]

Dieks, D.

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[Crossref]

Elliott, S. J.

P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic Press, London, 1992), pp. 290–293.

Engheta, N.

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

A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[Crossref]

Friot, E.

E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).

E. Friot and C. Bordier, “Real-time active suppression of scattered acoustic radiation,” J. Sound Vib. 278, 563–580 (2004).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Guillermin, R.

E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).

Habashy, T.

E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Modern Opt. 40, 785–792 (1993).
[Crossref]

Leonhardt, U.

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

McPhedran, R. C.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
[Crossref]

Miller, D. A. B.

Milton, G. W.

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. Roy. Soc. A 462, 3027–3059 (2006).
[Crossref]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
[Crossref]

Nelson, P. A.

P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic Press, London, 1992), pp. 290–293.

Nicorovici, N. A.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
[Crossref]

Nicorovici, N.-A. P.

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. Roy. Soc. A 462, 3027–3059 (2006).
[Crossref]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Stratton, J. A.

J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 56, 99–107 (1939).
[Crossref]

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Williams, J. E. Ffowcs

J. E. Ffowcs Williams “Review Lecture: Anti-Sound,” Proc. Roy. Soc. London A 395, 63–88 (1984)
[Crossref]

Winninger, M.

E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).

Wolf, E.

E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Modern Opt. 40, 785–792 (1993).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Wootters, W. K.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802 (1982).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Zurek, W. H.

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802 (1982).
[Crossref]

Acoust. Phys. (1)

Yu. I. Bobrovnitskii, “A new solution to the problem of an acoustically transparent body,” Acoust. Phys. 50, 647–650 (2004).
[Crossref]

Acta Acust. (1)

E. Friot, R. Guillermin, and M. Winninger, “Active control of scattered acoustic radiation: a real-time implementation for a three-dimensional object,” Acta Acust. 92, 278–288 (2006).

IEEE Trans. Antennas Propag. (1)

A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antennas Propag. 51, 2558–2571 (2003).
[Crossref]

J. Modern Opt. (1)

E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Modern Opt. 40, 785–792 (1993).
[Crossref]

J. Sound Vib. (1)

E. Friot and C. Bordier, “Real-time active suppression of scattered acoustic radiation,” J. Sound Vib. 278, 563–580 (2004).
[Crossref]

Nature (1)

W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature 299, 802 (1982).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

D. Dieks, “Communication by EPR devices,” Phys. Lett. A 92, 271–272 (1982).
[Crossref]

Phys. Rev. (1)

J. A. Stratton and L. J. Chu, “Diffraction Theory of Electromagnetic Waves,” Phys. Rev. 56, 99–107 (1939).
[Crossref]

Phys. Rev. B (1)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 490, 8479–8482 (1994).
[Crossref]

Phys. Rev. E (1)

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

Proc. Roy. Soc. A (1)

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. Roy. Soc. A 462, 3027–3059 (2006).
[Crossref]

Proc. Roy. Soc. London A (1)

J. E. Ffowcs Williams “Review Lecture: Anti-Sound,” Proc. Roy. Soc. London A 395, 63–88 (1984)
[Crossref]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

Science (2)

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Other (4)

P. A. Nelson and S. J. Elliott, Active Control of Sound (Academic Press, London, 1992), pp. 290–293.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

C. H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 1984 (IEEE, New York, 1984), 175–179.
[PubMed]

Supplementary Material (3)

» Media 1: AVI (781 KB)     
» Media 2: AVI (824 KB)     
» Media 3: AVI (777 KB)     

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Figures (3)

Fig. 1.
Fig. 1. (a). Illustration of a pulse incident on a volume to be cloaked solely on the basis of local response near the surface. (b) Arrangement of sources and sensors for cloaking of scalar waves.

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Fig. 2.
Fig. 2. Simulation results, shown for an equatorial (x-y) plane of the spherical volume to be cloaked, at a time t=+25 in the still figures, for the propagation of a pulse from left to right through the volume. The vertical color bar shows the false color scale. (a) Coordinates, position of cloaked volume (dashed circle), and point P for Fig. 3 results. (b) Movie of original unperturbed pulse (876 KB), focused approximately at the center of the volume, and arriving there approximately at time t=0. (c) Movie of approximate “quasi-cloaking” (930 KB), using surface sources with values derived only from local measurements. Significant distortion of the transmitted pulse is seen. (d) Movie of approximate “true cloaking” (894 KB), with surface source values calculated from the measured wave at current and past times at all the measurement points near the sphere surface; the propagated pulse is then substantially unchanged.

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Fig. 3.
Fig. 3. Simulated wave amplitude as a function of time t at a point P on the x axis 29.5 units to the right of the center, as shown in Fig. 2. Solid line – unperturbed wave. Dashed line – approximate “true cloaking”. Dot-dashed line – approximate “quasi-cloaking”.

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Equations (3)

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p out = f in δ a s ; p in = − p out δ a s
ｐ = Ｃ ｆ
ｐ true = 𝖢 ( ｆ − 𝖦 𝖢 ｆ ) = 𝖢 ( 𝗅 − 𝖦 𝖢 ) ｆ

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