Abstract

Invisibility cloaks have been one of the major breakthroughs in the field of metamaterials, and several techniques are currently available to suppress the electromagnetic scattering from different objects. So far, however, theoretical and experimental results have consistently shown fundamental challenges in terms of the bandwidth and size of the object to be hidden. Understanding the bandwidth limitations of cloaking therefore becomes important to assess the applicability and potential of cloaking devices in practical scenarios. While it is generally accepted that cloaking is difficult to achieve, no work to date has quantified this issue for general invisibility devices. Here, by applying the Bode–Fano theory of broadband matching, we derive fundamental bounds on bandwidth and performance for general passive cloaking schemes applied to planar objects, determined by the properties of the object to be hidden, and then explore their implications in three-dimensional scenarios. Our results define a general framework to estimate the ultimate performance of passive cloaks and suggest that fundamentally new directions, involving nonlinearities and active metamaterials, become necessary to realize broadband cloaking, opening a new phase in the quest for invisibility.

© 2016 Optical Society of America

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References

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2015 (4)

R. Fleury, F. Monticone, and A. Alù, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
[Crossref]

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Phys. Rev. Appl. 4, 014005 (2015).
[Crossref]

A. N. Norris, “Acoustic integrated extinction,” Proc. R. Soc. A 471, 20150008 (2015).
[Crossref]

A. N. Norris, “Acoustic cloaking,” Acoust. Today 11(1), 38–46 (2015).

2014 (3)

F. Monticone and A. Alù, “Physical bounds on electromagnetic invisibility and the potential of superconducting cloaks,” Photon. Nanostruct. 12, 330–339 (2014).
[Crossref]

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

J. S. Choi and J. C. Howell, “Paraxial ray optics cloaking,” Opt. Express 22, 29465–29478 (2014).
[Crossref]

2013 (3)

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

2012 (3)

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

C. Craeye and A. Bhattacharya, “Rule of thumb for cloaking bandwidth based on a wave-packet argument,” IEEE Trans. Antennas Propag. 60, 3516–3520 (2012).
[Crossref]

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

2011 (5)

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

A. Plakhov and V. Roshchina, “Invisibility in billiards,” Nonlinearity 24, 847–854 (2011).
[Crossref]

P. Alitalo and S. A. Tretyakov, “Broadband electromagnetic cloaking realized with transmission-line and waveguiding structures,” Proc. IEEE 99, 1646–1659 (2011).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

2010 (1)

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[Crossref]

2009 (3)

A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[Crossref]

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

F. Guevara Vasquez, G. W. Milton, and D. Onofrei, “Broadband exterior cloaking,” Opt. Express 17, 14800–14805 (2009).
[Crossref]

2008 (3)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E 78, 045602 (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]

2007 (1)

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

2006 (4)

D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12457–12466 (2006).
[Crossref]

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

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

M. Gustafsson and S. Nordebo, “Bandwidth, Q factor, and resonance models of antennas,” Prog. Electromagn. Res. 62, 1–20 (2006).
[Crossref]

2005 (2)

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref]

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

1950 (1)

R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

Alitalo, P.

P. Alitalo and S. A. Tretyakov, “Broadband electromagnetic cloaking realized with transmission-line and waveguiding structures,” Proc. IEEE 99, 1646–1659 (2011).
[Crossref]

Alù, A.

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Phys. Rev. Appl. 4, 014005 (2015).
[Crossref]

R. Fleury, F. Monticone, and A. Alù, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
[Crossref]

F. Monticone and A. Alù, “Physical bounds on electromagnetic invisibility and the potential of superconducting cloaks,” Photon. Nanostruct. 12, 330–339 (2014).
[Crossref]

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[Crossref]

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E 78, 045602 (2008).
[Crossref]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref]

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

Argyropoulos, C.

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

Bhattacharya, A.

C. Craeye and A. Bhattacharya, “Rule of thumb for cloaking bandwidth based on a wave-packet argument,” IEEE Trans. Antennas Propag. 60, 3516–3520 (2012).
[Crossref]

Bode, H.

H. Bode, Network Analysis and Feedback Amplifier Design (David Van Nostrand, 1945).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bückmann, T.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

Chan, C. T.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Chen, H.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[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]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Chen, P.-Y.

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Choi, J. S.

Conway, J.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

Craeye, C.

C. Craeye and A. Bhattacharya, “Rule of thumb for cloaking bandwidth based on a wave-packet argument,” IEEE Trans. Antennas Propag. 60, 3516–3520 (2012).
[Crossref]

Engheta, N.

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E 78, 045602 (2008).
[Crossref]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref]

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

Enoch, S.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Fano, R. M.

R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

Farhat, M.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Fleury, R.

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Phys. Rev. Appl. 4, 014005 (2015).
[Crossref]

R. Fleury, F. Monticone, and A. Alù, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
[Crossref]

Guenneau, S.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Guevara Vasquez, F.

Gustafsson, M.

M. Gustafsson and S. Nordebo, “Bandwidth, Q factor, and resonance models of antennas,” Prog. Electromagn. Res. 62, 1–20 (2006).
[Crossref]

Hao, Y.

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

Hashemi, H.

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[Crossref]

Howell, J. C.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jiang, X.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Joannopoulos, J.

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[Crossref]

Joannopoulos, J. D.

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

Johnson, S.

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[Crossref]

Johnson, S. G.

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

Kadic, M.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

Kallos, E.

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

Kong, J. A.

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]

Lederer, F.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

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]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

Liang, Z.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Ma, H.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

McCauley, A. P.

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

McPhedran, R.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Miller, D. A. B.

Milton, G. W.

Monticone, F.

R. Fleury, F. Monticone, and A. Alù, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
[Crossref]

F. Monticone and A. Alù, “Physical bounds on electromagnetic invisibility and the potential of superconducting cloaks,” Photon. Nanostruct. 12, 330–339 (2014).
[Crossref]

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

Nordebo, S.

M. Gustafsson and S. Nordebo, “Bandwidth, Q factor, and resonance models of antennas,” Prog. Electromagn. Res. 62, 1–20 (2006).
[Crossref]

Norris, A. N.

A. N. Norris, “Acoustic integrated extinction,” Proc. R. Soc. A 471, 20150008 (2015).
[Crossref]

A. N. Norris, “Acoustic cloaking,” Acoust. Today 11(1), 38–46 (2015).

Onofrei, D.

Oskooi, A.

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

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

Plakhov, A.

A. Plakhov and V. Roshchina, “Invisibility in billiards,” Nonlinearity 24, 847–854 (2011).
[Crossref]

Pozar, D. M.

D. M. Pozar, Microwave Engineering, 3rd ed. (Wiley, 2011).

Qiu, C.-W.

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

Rockstuhl, C.

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

Roshchina, V.

A. Plakhov and V. Roshchina, “Invisibility in billiards,” Nonlinearity 24, 847–854 (2011).
[Crossref]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref]

Schittny, R.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

Schurig, D.

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

Shen, L.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Smith, D. R.

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

Sounas, D. L.

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Phys. Rev. Appl. 4, 014005 (2015).
[Crossref]

Staffaroni, M.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

Tang, J.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

Tretyakov, S. A.

P. Alitalo and S. A. Tretyakov, “Broadband electromagnetic cloaking realized with transmission-line and waveguiding structures,” Proc. IEEE 99, 1646–1659 (2011).
[Crossref]

Tyc, T.

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

Vedantam, S.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

Wang, H.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Wegener, M.

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

Wu, B.-I.

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]

Yablonovitch, E.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

Yao, P.

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Zhang, B.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[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]

Zhang, X.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Zheludev, N. I.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Zheng, B.

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Acoust. Today (1)

A. N. Norris, “Acoustic cloaking,” Acoust. Today 11(1), 38–46 (2015).

IEEE Trans. Antennas Propag. (1)

C. Craeye and A. Bhattacharya, “Rule of thumb for cloaking bandwidth based on a wave-packet argument,” IEEE Trans. Antennas Propag. 60, 3516–3520 (2012).
[Crossref]

J. Franklin Inst. (1)

R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” J. Franklin Inst. 249, 57–83 (1950).
[Crossref]

Nat. Commun. (1)

H. Chen, B. Zheng, L. Shen, H. Wang, X. Zhang, N. I. Zheludev, and B. Zhang, “Ray-optics cloaking devices for large objects in incoherent natural light,” Nat. Commun. 4, 2652 (2013).
[Crossref]

Nonlinearity (1)

A. Plakhov and V. Roshchina, “Invisibility in billiards,” Nonlinearity 24, 847–854 (2011).
[Crossref]

Opt. Express (3)

Photon. Nanostruct. (2)

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Photon. Nanostruct. 10, 166–176 (2012).
[Crossref]

F. Monticone and A. Alù, “Physical bounds on electromagnetic invisibility and the potential of superconducting cloaks,” Photon. Nanostruct. 12, 330–339 (2014).
[Crossref]

Phys. Rev. A (2)

H. Hashemi, C.-W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter-bandwidth product limitation of isolated-object cloaking,” Phys. Rev. A 86, 013804 (2012).
[Crossref]

H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Phys. Rev. A 84, 023815 (2011).
[Crossref]

Phys. Rev. Appl. (2)

R. Fleury, F. Monticone, and A. Alù, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
[Crossref]

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional cloaking based on metasurfaces with balanced loss and gain,” Phys. Rev. Appl. 4, 014005 (2015).
[Crossref]

Phys. Rev. B (4)

M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, R. McPhedran, C. Rockstuhl, and F. Lederer, “Understanding the functionality of an array of invisibility cloaks,” Phys. Rev. B 84, 235105 (2011).
[Crossref]

A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[Crossref]

E. Kallos, C. Argyropoulos, Y. Hao, and A. Alù, “Comparison of frequency responses of cloaking devices under nonmonochromatic illumination,” Phys. Rev. B 84, 045102 (2011).
[Crossref]

H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B 76, 241104(R) (2007).
[Crossref]

Phys. Rev. E (2)

A. Alù and N. Engheta, “Effects of size and frequency dispersion in plasmonic cloaking,” Phys. Rev. E 78, 045602 (2008).
[Crossref]

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

Phys. Rev. Lett. (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]

H. Hashemi, B. Zhang, J. Joannopoulos, and S. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Phys. Rev. Lett. 104, 253903 (2010).
[Crossref]

P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Phys. Rev. Lett. 111, 233001 (2013).
[Crossref]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[Crossref]

Phys. Rev. X (1)

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

Proc. IEEE (1)

P. Alitalo and S. A. Tretyakov, “Broadband electromagnetic cloaking realized with transmission-line and waveguiding structures,” Proc. IEEE 99, 1646–1659 (2011).
[Crossref]

Proc. R. Soc. A (1)

A. N. Norris, “Acoustic integrated extinction,” Proc. R. Soc. A 471, 20150008 (2015).
[Crossref]

Prog. Electromagn. Res. (1)

M. Gustafsson and S. Nordebo, “Bandwidth, Q factor, and resonance models of antennas,” Prog. Electromagn. Res. 62, 1–20 (2006).
[Crossref]

Science (4)

R. Schittny, M. Kadic, T. Bückmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
[Crossref]

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

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

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

Other (4)

N. Engheta and R. W. Ziolkowski, eds., Metamaterials: Physics and Engineering Explorations (Wiley-IEEE, 2006).

H. Bode, Network Analysis and Feedback Amplifier Design (David Van Nostrand, 1945).

D. M. Pozar, Microwave Engineering, 3rd ed. (Wiley, 2011).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Supplementary Material (1)

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» Supplement 1: PDF (1956 KB)      Supplemental Documentation

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Figures (4)

Fig. 1.
Fig. 1.

Issues with broadband cloaking. (a), (b) A broadband light beam is reflected/scattered by an obstacle (a dielectric slab or a sphere), leading to distorted transmission. (c) Scattering performance of typical cloaking devices (blue, plasmonic cloaking [4]; orange, transformation-optics cloaking [3]) applied to an impenetrable spherical object (black) (details in Supplement 1). (d) Under broadband illumination, e.g., containing all the wavelengths/colors of the visible spectrum, a narrow-band cloak has typically the effect of simply “redistributing” the scattering among the different wavelengths, e.g., making the object invisible for a certain color, while largely increasing the scattering for other colors. (e) The proposed cloaking bounds allow determining whether broadband cloaking—for example, encompassing the entire visible range [green dashed curve in (c)]—is possible.

Fig. 2.
Fig. 2.

Physical bounds on 1D cloaking. (a), (b) Dielectric slab normally illuminated by a plane wave and amplitude of its reflection coefficient Γ (black curve), as a function of frequency (normalized to the frequency of its first Fabry–Perot resonance f FP ). Relative permittivity of the slab is ε = 10 . (c) Equivalent lumped-element circuit that locally models the slab response in the neighborhood of a Fabry–Perot resonance [red curve in (b)]. A generic passive cloak in front of the slab is represented by a reactive matching network aimed at reducing the reflection around the frequency of interest f c . (d) Physical bound on the cloaking performance, in terms of fractional cloaking bandwidth B = Δ f / f c and in-band reflection coefficient | Γ b | , for a slab with ε = 10 and thickness d = λ c / 10 at the cloaking wavelength λ c . The thick red line indicates the performance of the optimal passive cloak. (e) Examples of planar mantle cloaks applied to the slab considered in (d), showing how they perform in relation to the physical bound at three different levels of reflection, as indicated by the red line segments [corresponding to the red circles in (d)]. The mantle cloaks are made of stacked metasurfaces, as shown in the inset, with optimized reactance and separation (details in Supplement 1).

Fig. 3.
Fig. 3.

Physical bounds on 3D cloaking. (a) Spherical scatterer illuminated by a plane wave. The scattering wavefront results from the superposition of multiple spherical harmonics. (b) Amplitude of the first three scattering coefficients, for an impenetrable sphere of radius a = λ c at the wavelength of interest. (c) Equivalent circuit for the nth scattering coefficient. The reflection coefficient Γ RLC , n of the circuit locally approximates the scattering coefficient c n , while the nonscattered energy dissipates on the unitary resistor. (d) Physical bound on the cloaking performance, in terms of fractional bandwidth B = Δ f / f c and in-band scattering reduction, for the sphere considered in (b). The thick red line indicates the performance of the optimal passive cloak. The performance of a typical transformation-optics cloak (orange curve) and a plasmonic cloak (blue) is also plotted (details in Supplement 1). (e) Normalized scattering cross section (SCS) of the uncloaked object (black curve) and of the two cloaking devices considered in (d), compared to the physical bound (dashed red line).

Fig. 4.
Fig. 4.

Optimal passive cloaks. (a) Normalized scattering cross section of a moderately large dielectric sphere (black curve; diameter d = λ c / 2 at the cloaking wavelength λ c , and relative permittivity ε = 5 ) and of the same object surrounded by a Chebyshev-like cloak composed of two concentric metasurfaces (blue curve, details in Supplement 1). An illustration of the cloak is shown in the inset (only one hemisphere of the outer layer is shown). The physical bound is indicated by the dashed red line. (b) Scaling of the maximum fractional bandwidth, determined by our derived bounds, across the electromagnetic spectrum, from the millimeter-wave range to visible frequencies, for an impenetrable sphere of radius a = 1    m . The cloak aims at restoring the incident field distribution (in amplitude and phase) all around the obstacle. Three levels of scattering reduction are considered.

Equations (4)

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B ln ( 1 | Γ b | ) c 0 d ( ε 1 ) f c ,
SCS λ c 2 2 π n = 1 N ( 2 n + 1 ) [ exp ( 1 / Δ f max [ C n , ± TM ] ) + exp ( 1 / Δ f max [ C n , ± TE ] ) ] ,
C n , ± = [ d Y n ( ω ) d ω ± Y n ( ω ) ω ] ω = ω c ,
SCS π a 2 2 exp ( 1 B 2 π k 0 a ) .

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