Abstract

It is shown how a recently proposed method of cloaking is effective over a broad range of frequencies. The method is based on three or more active devices. The devices, while not radiating significantly, create a “quiet zone” between the devices where the wave amplitude is small. Objects placed within this region are virtually invisible. The cloaking is demonstrated by simulations with a broadband incident pulse.

©2009 Optical Society of America

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References

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  1. F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” (2009). Accepted for publication in Phys. Rev. Lett., arXiv:0906.1544v1 [math-ph].
  2. D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12,457–12,466 (2006).
    [Crossref]
  3. R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A 41, 065,207 (2008).
    [Crossref]
  4. A. G. Ramm, “Invisible obstacles,” Ann. Polon. Math. 90, 145–148 (2007).
    [Crossref]
  5. L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Izv. Vyssh. Uchebn. Zaved. Radiofizika 4, 964–967 (1961).
  6. M. Kerker, “Invisible bodies,” J. Opt. Soc. Am. 65, 376–379 (1975).
    [Crossref]
  7. A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016,623 (2005).
    [Crossref]
  8. A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
    [Crossref] [PubMed]
  9. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref] [PubMed]
  10. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  11. H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183,518 (2007).
  12. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
    [Crossref]
  13. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
    [Crossref]
  14. A. N. Norris, “Acoustic cloaking theory,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 464, 2411–2434 (2008).
    [Crossref]
  15. 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]
  16. M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
    [Crossref]
  17. M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
    [Crossref]
  18. M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
    [Crossref]
  19. 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]
  20. 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]
  21. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [Crossref] [PubMed]
  22. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].
  23. G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 462, 3027–3059 (2006).
    [Crossref]
  24. N.-A. P. Nicorovici, G.W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
    [Crossref] [PubMed]
  25. G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
    [Crossref]
  26. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  27. N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
    [Crossref]
  28. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  29. O. P. Bruno and S. Lintner, “Superlens-cloaking of small dielectric bodies in the quasistatic regime,” J. Appl. Phys. 102, 124,502 (2007).
    [Crossref]
  30. Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
    [Crossref]
  31. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203,901 (2008).
    [Crossref]
  32. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
    [Crossref]
  33. J. E. Ffowcs Williams, “Review Lecture: Anti-Sound,” Proc. R. Soc. A 395, 63–88 (1984).
    [Crossref]
  34. A. W. Peterson and S. V. Tsynkov, “Active control of sound for composite regions,” SIAM J. Appl. Math. 67, 1582–1609 (2007).
    [Crossref]
  35. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
    [Crossref]
  36. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, vol. 93 of Applied Mathematical Sciences, 2nd ed. (Springer-Verlag, Berlin, 1998).

2009 (7)

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (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]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
[Crossref]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

2008 (6)

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A 41, 065,207 (2008).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203,901 (2008).
[Crossref]

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

A. N. Norris, “Acoustic cloaking theory,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 464, 2411–2434 (2008).
[Crossref]

2007 (6)

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183,518 (2007).

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

O. P. Bruno and S. Lintner, “Superlens-cloaking of small dielectric bodies in the quasistatic regime,” J. Appl. Phys. 102, 124,502 (2007).
[Crossref]

A. W. Peterson and S. V. Tsynkov, “Active control of sound for composite regions,” SIAM J. Appl. Math. 67, 1582–1609 (2007).
[Crossref]

A. G. Ramm, “Invisible obstacles,” Ann. Polon. Math. 90, 145–148 (2007).
[Crossref]

N.-A. P. Nicorovici, G.W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
[Crossref] [PubMed]

2006 (6)

D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12,457–12,466 (2006).
[Crossref]

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]

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]

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]

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

2005 (1)

A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016,623 (2005).
[Crossref]

2003 (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1994 (1)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

1984 (1)

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

1975 (1)

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

1961 (1)

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Izv. Vyssh. Uchebn. Zaved. Radiofizika 4, 964–967 (1961).

Alú, A.

A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016,623 (2005).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Botten, L. C.

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]

Brun, M.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
[Crossref]

Bruno, O. P.

O. P. Bruno and S. Lintner, “Superlens-cloaking of small dielectric bodies in the quasistatic regime,” J. Appl. Phys. 102, 124,502 (2007).
[Crossref]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].

Chan, C. T.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183,518 (2007).

Chen, H.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183,518 (2007).

Cherednichenko, K.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (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]

Colton, D.

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, vol. 93 of Applied Mathematical Sciences, 2nd ed. (Springer-Verlag, Berlin, 1998).

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]

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[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]

Dolin, L. S.

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Izv. Vyssh. Uchebn. Zaved. Radiofizika 4, 964–967 (1961).

Engheta, N.

A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016,623 (2005).
[Crossref]

Enoch, S.

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

Farhat, M.

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

Ffowcs Williams, J. E.

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

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
[Crossref] [PubMed]

Guenneau, S.

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
[Crossref]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

Guevara Vasquez, F.

F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” (2009). Accepted for publication in Phys. Rev. Lett., arXiv:0906.1544v1 [math-ph].

Jacob, Z.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[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]

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]

Kerker, M.

Kildishev, A. V.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

Kress, R.

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, vol. 93 of Applied Mathematical Sciences, 2nd ed. (Springer-Verlag, Berlin, 1998).

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

Lai, Y.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
[Crossref] [PubMed]

Leonhardt, U.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
[Crossref]

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

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203,901 (2008).
[Crossref]

Lintner, S.

O. P. Bruno and S. Lintner, “Superlens-cloaking of small dielectric bodies in the quasistatic regime,” J. Appl. Phys. 102, 124,502 (2007).
[Crossref]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].

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]

McPhedran, R. C.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[Crossref]

N.-A. P. Nicorovici, G.W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
[Crossref] [PubMed]

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

Miller, D. A. B.

D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12,457–12,466 (2006).
[Crossref]

Milton, G. W.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[Crossref]

G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 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 49, 8479–8482 (1994).
[Crossref]

F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” (2009). Accepted for publication in Phys. Rev. Lett., arXiv:0906.1544v1 [math-ph].

Milton, G.W.

N.-A. P. Nicorovici, G.W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
[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]

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, 977–980 (2006).
[Crossref] [PubMed]

Movchan, A. B.

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
[Crossref]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

Nicorovici, N. A.

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

Nicorovici, N.-A. P.

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[Crossref]

N.-A. P. Nicorovici, G.W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15, 6314–6323 (2007).
[Crossref] [PubMed]

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

Norris, A. N.

A. N. Norris, “Acoustic cloaking theory,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 464, 2411–2434 (2008).
[Crossref]

Onofrei, D.

F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” (2009). Accepted for publication in Phys. Rev. Lett., arXiv:0906.1544v1 [math-ph].

Pendry, J.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203,901 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Peterson, A. W.

A. W. Peterson and S. V. Tsynkov, “Active control of sound for composite regions,” SIAM J. Appl. Math. 67, 1582–1609 (2007).
[Crossref]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

Rahm, M.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

Ramm, A. G.

A. G. Ramm, “Invisible obstacles,” Ann. Polon. Math. 90, 145–148 (2007).
[Crossref]

Schurig, D.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

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]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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]

Smolyaninov, I. I.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

Smolyaninova, V. N.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

Starr, A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

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]

Tsynkov, S. V.

A. W. Peterson and S. V. Tsynkov, “Active control of sound for composite regions,” SIAM J. Appl. Math. 67, 1582–1609 (2007).
[Crossref]

Tyc, T.

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
[Crossref]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
[Crossref] [PubMed]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Weder, R.

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A 41, 065,207 (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]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

Zhang, Z.-Q.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

Ann. Polon. Math. (1)

A. G. Ramm, “Invisible obstacles,” Ann. Polon. Math. 90, 145–148 (2007).
[Crossref]

Appl. Phys. Lett. (2)

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91, 183,518 (2007).

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 061903 (2009).
[Crossref]

Commun. Math. Phys. (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Full-wave invisibility of active devices at all frequencies,” Commun. Math. Phys. 275, 749–789 (2007).
[Crossref]

Izv. Vyssh. Uchebn. Zaved. Radiofizika (1)

L. S. Dolin, “To the possibility of comparison of three-dimensional electromagnetic systems with nonuniform anisotropic filling,” Izv. Vyssh. Uchebn. Zaved. Radiofizika 4, 964–967 (1961).

J. Appl. Phys. (1)

O. P. Bruno and S. Lintner, “Superlens-cloaking of small dielectric bodies in the quasistatic regime,” J. Appl. Phys. 102, 124,502 (2007).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. A (1)

R. Weder, “A rigorous analysis of high-order electromagnetic invisibility cloaks,” J. Phys. A 41, 065,207 (2008).
[Crossref]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref] [PubMed]

New J. Phys. (2)

G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob, “Solutions in folded geometries, and associated cloaking due to anomalous resonance,” New J. Phys. 10, 115,021 (2008).
[Crossref]

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]

Opt. Express (2)

Phys. Rev. B (2)

N. A. Nicorovici, R. C. McPhedran, and G. W. Milton, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479–8482 (1994).
[Crossref]

M. Farhat, S. Guenneau, S. Enoch, and A. B. Movchan, “Cloaking bending waves propagating in thin elastic plates,” Phys. Rev. B 79, 033102 (2009).
[Crossref]

Phys. Rev. E (1)

A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016,623 (2005).
[Crossref]

Phys. Rev. Lett. (6)

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell,” Phys. Rev. Lett. 100, 024,301 (2008).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101, 134,501 (2008).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093,901 (2009).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203,901 (2008).
[Crossref]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102, 213,901 (2009).
[Crossref]

Physiol. Meas. (1)

A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas. 24, 413–419 (2003).
[Crossref] [PubMed]

Proc. R. Soc. A (1)

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

Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. (2)

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

A. N. Norris, “Acoustic cloaking theory,” Proc. R. Soc. Lon. Ser. A. Math. Phys. Sci. 464, 2411–2434 (2008).
[Crossref]

Science (5)

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]

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]

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 and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
[Crossref]

SIAM J. Appl. Math. (1)

A. W. Peterson and S. V. Tsynkov, “Active control of sound for composite regions,” SIAM J. Appl. Math. 67, 1582–1609 (2007).
[Crossref]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[Crossref]

Other (3)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Cloaking at Optical Frequencies,” (2009). ArXiv:0904.3508v1 [physics.optics].

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, vol. 93 of Applied Mathematical Sciences, 2nd ed. (Springer-Verlag, Berlin, 1998).

F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” (2009). Accepted for publication in Phys. Rev. Lett., arXiv:0906.1544v1 [math-ph].

Supplementary Material (2)

» Media 1: MOV (2316 KB)     
» Media 2: MOV (3770 KB)     

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Figures (5)

Fig. 1.
Fig. 1. Wave field at the central frequency ω 0 when the cloaking devices are (a) inactive and (b) active. Only the real part of the fields is displayed, with a linear color scale going from -1 (dark blue) to 1 (dark red). All fields have been rescaled by |ui (x,ω)| to remove the geometric spreading of the point source.

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Fig. 2.
Fig. 2. Reduction of the scattering in percent achieved by the cloaking devices over the bandwidth, measured in the L 2 norm on |x|=20λ 0. The ordinates scale is logarithmic.

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Fig. 3.
Fig. 3. Cloaking for a circular wave pulse. Top row: devices inactive (Movie 1). Bottom row: devices active (Movie 2). The visualization window in x is as in Fig. 1 and the scale is linear, relative to the maximum amplitude on the plane of the incident field at each time.

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Fig. 4.
Fig. 4. Cloak performance in terms of the cloaked region radius α, as measured by (a) ‖ui +ud ‖/‖ui ‖ with the L 2 norm on |x|=α and (b) ‖ud ‖/‖ui ‖ with the L 2 norm on |x|=γ. Dashed, solid and dash-dotted lines correspond toω/(2π)=1.2GHz, 2.4GHz and 3.6G

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Fig. 5.
Fig. 5. Estimate of the radius of circular cloaking devices relative to the radius of the cloaked region α. Dashed, solid and dash-dotted lines correspond to ω/(2π)=1.2GHz, 2.4GHz and 3.6GHz, respectively. The device radius is estimated as the largest of the distances from a device point x m to the level-set |ud |=100max|x|=α |ui (x,ω)|. If the devices were perfect circles, any device radius below the dotted line (at cos(π/6)δ/α=5√3/2) would indicate that the devices do not touch, i.e. they are three disjoint devices.

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Equations (1)

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

ud Xω=∑m=1D∑bm,nn=−NNHn(1) (k∣X−Xm∣) exp [inθm] ,

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