Abstract

Despite much interest and progress in optical spatial cloaking, a three-dimensional (3D), transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. Here we experimentally demonstrate such a cloak using ray optics, albeit with some edge effects. Our device requires no new materials, uses isotropic off-the-shelf optics, scales easily to cloak arbitrarily large objects, and is as broadband as the choice of optical material, all of which have been challenges for current cloaking schemes. In addition, we provide a concise formalism that quantifies and produces perfect optical cloaks in the small-angle (‘paraxial’) limit.

© 2014 Optical Society of America

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  1. G. Gbur, “Invisibility physics: Past, present, and future,” Prog. Optics 58, 65–114 (2013).
    [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. M. McCall, “Transformation optics and cloaking,” Contemp. Phys. 54, 273–286 (2013).
    [Crossref]
  5. B. Zhang, “Electrodynamics of transformation-based invisibility cloaking,” Light. Sci. Appl. 1, e32 (2012).
    [Crossref]
  6. 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]
  7. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
    [Crossref]
  8. J. S. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [Crossref] [PubMed]
  9. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
    [Crossref] [PubMed]
  10. J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
    [Crossref]
  11. D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
    [Crossref]
  12. M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
    [Crossref] [PubMed]
  13. J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498, 205–208 (2013).
    [Crossref] [PubMed]
  14. S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
    [Crossref] [PubMed]
  15. B. L. Zhang, Y. A. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106, 033901 (2011).
    [Crossref] [PubMed]
  16. X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
    [Crossref]
  17. 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. Comm. 4, 2652 (2013).
    [Crossref]
  18. T. R. Zhai, X. B. Ren, R. K. Zhao, J. Zhou, and D. H. Liu, “An effective broadband optical ’cloak’ without metamaterials,” Laser Phys. Lett. 10, 066002 (2013).
    [Crossref]
  19. J. C. Howell, J. B. Howell, and J. S. Choi, “Amplitude-only, passive, broadband, optical spatial cloaking of very large objects,” Appl. Opt. 53, 1958–1963 (2014).
    [Crossref] [PubMed]
  20. E. Wolf and T. Habashy, “Invisible bodies and uniqueness of the inverse scattering problem,” J. Mod. Opt. 40, 785–792 (1993).
    [Crossref]
  21. A. I. Nachman, “Reconstructions from boundary measurements,” Ann. Math. 128, 531–576 (1988).
    [Crossref]
  22. A. J. Devaney, “Nonuniqueness in inverse scattering problem,” J. Math. Phys. 19, 1526–1531 (1978).
    [Crossref]
  23. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2010), 7th ed.
  24. A. E. Siegman, Lasers (University Science Books, 1986).
  25. M. Bass, Handbook of Optics- Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), Vol. 1, 3rd ed.
  26. J. E. Greivenkamp, Field Guide to Geometrical Optics (SPIE, 2004).
    [Crossref]
  27. P. P. Clark and C. Londono, “1990 International Lens Design Conference lens design problems: the design of a NonLens,” in “1990 Intl Lens Design Conf,” (Proc. SPIE, 1991), 1354, pp. 555–569.
    [Crossref]
  28. D. Buralli, OPT 441- Geometrical Optics (The Institute of Optics, University of Rochester, 2010).
  29. A. Nussbaum, Optical System Design (Prentice Hall PTR, 1998).
  30. A. Nussbaum, “Teaching of advanced geometric optics,” Appl. Opt. 17, 2128–2129 (1978).
  31. J. Bentley, “Optics 444- Lens Design,” (2012). Course lecture notes.

2014 (2)

S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
[Crossref] [PubMed]

J. C. Howell, J. B. Howell, and J. S. Choi, “Amplitude-only, passive, broadband, optical spatial cloaking of very large objects,” Appl. Opt. 53, 1958–1963 (2014).
[Crossref] [PubMed]

2013 (7)

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498, 205–208 (2013).
[Crossref] [PubMed]

G. Gbur, “Invisibility physics: Past, present, and future,” Prog. Optics 58, 65–114 (2013).
[Crossref]

M. McCall, “Transformation optics and cloaking,” Contemp. Phys. 54, 273–286 (2013).
[Crossref]

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
[Crossref]

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (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. Comm. 4, 2652 (2013).
[Crossref]

T. R. Zhai, X. B. Ren, R. K. Zhao, J. Zhou, and D. H. Liu, “An effective broadband optical ’cloak’ without metamaterials,” Laser Phys. Lett. 10, 066002 (2013).
[Crossref]

2012 (3)

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref] [PubMed]

B. Zhang, “Electrodynamics of transformation-based invisibility cloaking,” Light. Sci. Appl. 1, e32 (2012).
[Crossref]

2011 (2)

B. L. Zhang, Y. A. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106, 033901 (2011).
[Crossref] [PubMed]

X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
[Crossref]

2010 (1)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

2008 (1)

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

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

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]

1993 (1)

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

1988 (1)

A. I. Nachman, “Reconstructions from boundary measurements,” Ann. Math. 128, 531–576 (1988).
[Crossref]

1978 (2)

A. J. Devaney, “Nonuniqueness in inverse scattering problem,” J. Math. Phys. 19, 1526–1531 (1978).
[Crossref]

A. Nussbaum, “Teaching of advanced geometric optics,” Appl. Opt. 17, 2128–2129 (1978).

Alu, A.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

Barbastathis, G.

B. L. Zhang, Y. A. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106, 033901 (2011).
[Crossref] [PubMed]

Bass, M.

M. Bass, Handbook of Optics- Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), Vol. 1, 3rd ed.

Bentley, J.

J. Bentley, “Optics 444- Lens Design,” (2012). Course lecture notes.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2010), 7th ed.

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Brule, S.

S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
[Crossref] [PubMed]

Buralli, D.

D. Buralli, OPT 441- Geometrical Optics (The Institute of Optics, University of Rochester, 2010).

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. Comm. 4, 2652 (2013).
[Crossref]

Chen, P. Y.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

Chen, X. Z.

X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
[Crossref]

Choi, J. S.

Clark, P. P.

P. P. Clark and C. Londono, “1990 International Lens Design Conference lens design problems: the design of a NonLens,” in “1990 Intl Lens Design Conf,” (Proc. SPIE, 1991), 1354, pp. 555–569.
[Crossref]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Devaney, A. J.

A. J. Devaney, “Nonuniqueness in inverse scattering problem,” J. Math. Phys. 19, 1526–1531 (1978).
[Crossref]

Enoch, S.

S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
[Crossref] [PubMed]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref] [PubMed]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref] [PubMed]

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref] [PubMed]

Gbur, G.

G. Gbur, “Invisibility physics: Past, present, and future,” Prog. Optics 58, 65–114 (2013).
[Crossref]

Greivenkamp, J. E.

J. E. Greivenkamp, Field Guide to Geometrical Optics (SPIE, 2004).
[Crossref]

Guenneau, S.

S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
[Crossref] [PubMed]

Habashy, T.

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

Howell, J. B.

Howell, J. C.

Javelaud, E. H.

S. Brule, E. H. Javelaud, S. Enoch, and S. Guenneau, “Experiments on seismic metamaterials: Molding surface waves,” Phys. Rev. Lett. 112, 133901 (2014).
[Crossref] [PubMed]

Jiang, K.

X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
[Crossref]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Kerkhoff, A.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

Landy, N.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
[Crossref]

Leaird, D. E.

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498, 205–208 (2013).
[Crossref] [PubMed]

Leonhardt, U.

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

Li, J. S.

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

Liu, D. H.

T. R. Zhai, X. B. Ren, R. K. Zhao, J. Zhou, and D. H. Liu, “An effective broadband optical ’cloak’ without metamaterials,” Laser Phys. Lett. 10, 066002 (2013).
[Crossref]

Liu, X. G.

B. L. Zhang, Y. A. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106, 033901 (2011).
[Crossref] [PubMed]

Londono, C.

P. P. Clark and C. Londono, “1990 International Lens Design Conference lens design problems: the design of a NonLens,” in “1990 Intl Lens Design Conf,” (Proc. SPIE, 1991), 1354, pp. 555–569.
[Crossref]

Lukens, J. M.

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498, 205–208 (2013).
[Crossref] [PubMed]

Luo, Y.

X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
[Crossref]

Luo, Y. A.

B. L. Zhang, Y. A. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. 106, 033901 (2011).
[Crossref] [PubMed]

McCall, M.

M. McCall, “Transformation optics and cloaking,” Contemp. Phys. 54, 273–286 (2013).
[Crossref]

Melin, K.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Moreno, G.

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

Nachman, A. I.

A. I. Nachman, “Reconstructions from boundary measurements,” Ann. Math. 128, 531–576 (1988).
[Crossref]

Nussbaum, A.

A. Nussbaum, “Teaching of advanced geometric optics,” Appl. Opt. 17, 2128–2129 (1978).

A. Nussbaum, Optical System Design (Prentice Hall PTR, 1998).

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref] [PubMed]

Pendry, J. B.

X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Comm. 2, 176 (2011).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

J. S. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[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, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Rainwater, D.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[Crossref]

Ren, X. B.

T. R. Zhai, X. B. Ren, R. K. Zhao, J. Zhou, and D. H. Liu, “An effective broadband optical ’cloak’ without metamaterials,” Laser Phys. Lett. 10, 066002 (2013).
[Crossref]

Schurig, D.

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]

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. Comm. 4, 2652 (2013).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Smith, D. R.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
[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]

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

Soric, J. C.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alu, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alu, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14, 013054 (2012).
[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]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

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. Comm. 4, 2652 (2013).
[Crossref]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Weiner, A. M.

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498, 205–208 (2013).
[Crossref] [PubMed]

Wolf, E.

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

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 2010), 7th ed.

Zhai, T. R.

T. R. Zhai, X. B. Ren, R. K. Zhao, J. Zhou, and D. H. Liu, “An effective broadband optical ’cloak’ without metamaterials,” Laser Phys. Lett. 10, 066002 (2013).
[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. Comm. 4, 2652 (2013).
[Crossref]

B. Zhang, “Electrodynamics of transformation-based invisibility cloaking,” Light. Sci. Appl. 1, e32 (2012).
[Crossref]

Zhang, B. L.

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Supplementary Material (4)

» Media 1: MOV (3488 KB)     
» Media 2: MOV (8087 KB)     
» Media 3: MOV (6153 KB)     
» Media 4: MOV (6824 KB)     

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Figures (6)

Fig. 1
Fig. 1

Example of a practical paraxial cloak. (a)–(c) A hand is cloaked for varying directions, while the background image is transmitted properly. See ( Media 1) and ( Media 2) for videos. (d) On-axis view of the ray optics cloaking device. (e) Setup using practical, easy to obtain optics, for demonstrating paraxial cloaking principles. (Photos by J. Adam Fenster, videos by Matthew Mann / University of Rochester)

Fig. 2
Fig. 2

Investigating ‘perfect’ paraxial cloaking with rays. (a) A ‘perfect’ ray optics cloaking box. Rays exit the box as if the box was filled with the surrounding medium. Non-zero volume inside hides an object. Angles do not change, but the positions shift proportionally to the ray angles and box length. The image seen by the observer should match the object exactly. (b)–(d) Diagrams for a two lens (b), three lens (c), or four lens (d) system. f’s are the focal lengths, t’s are the distances between the elements. (e) All possible four lens, symmetric, perfect paraxial cloaks for rays. Plot of t1/f2 (solid), t2/f2 (dashed), and L/f2 (dotted) as a function of a ≡ f1/f2. Assumed symmetric left and right halves (f1 = f4, f2 = f3, and t1 = t3). L is the total length of the system. The physical feasibility and presence of a non-empty cloaking region must be checked separately.

Fig. 3
Fig. 3

A symmetric three lens cloak. Two diverging lenses are combined into one diverging lens, and placed in the center of two converging lenses. (a) Simulation in CODE V. Entrance pupil is 75 mm, and field-of-view is −3.5° to 3.5°. Object is placed at infinity. Ray bundles propagate from left to right, through the lenses, then are traced back to the first lens. This allows comparison of the image (dashed) rays, as seen by an observer on the right, with the original (solid) rays. We see that the angles are similar, and the transverse shifts are not large. (b) 3D rendering of (a). The cloaking region is a 3D triangular-ring between the first and last lenses (shaded area). (c–g) Experimental demonstration of the three lens cloak. The lines seen through the lenses match those on the background wall. The inner portion of the ruler is cloaked. Images at various camera-viewing angles: (c) On-axis (0°), (d) 0.55°, (e) 0.83°, (f) 1.11°. (g) Side profile of experimental setup.

Fig. 4
Fig. 4

CODE V simulation of a symmetric, perfect paraxial cloak, with four lenses using rays. Four achromatic doublets are placed with separations determined from Eq. (1). Entrance pupil is 50 mm, with −1.5° to 1.5° field-of-view. Simulations are shown with no separate optimization. Object is placed at infinity. (a) Zoomed-in region of (b) with image rays (dashed; traced back to the first lens) added to compare with the original rays (solid). We see that the angles are nearly identical, and the transverse shifts are small. (b) Full simulation using off-the-shelf optics. (c) 3D rendering. The cloaking region (shaded) is a cylindrical region between the first and last lenses. (d) Scaling of (b) by a factor of 2. The cloaking size is doubled in each dimension by doubling the optical curvatures, lengths and entrance pupil. Only the length scales distinguish (d) from (b).

Fig. 5
Fig. 5

Experimental demonstration of a ‘perfect’ paraxial cloak with four lenses. Camera was focused on the wall. The grids on the wall can be seen clearly, and match the background for all colors and viewing angles. The middle of the ruler is cloaked inside the lens system for all angles shown. Images at various camera-viewing angles: (a) −0.65°, (b) on-axis (0°), (c) 0.47°, (d) 0.95°. (e) Side profile of experimental setup. See ( Media 3) and ( Media 4) for videos. (Videos by Matthew Mann / University of Rochester)

Fig. 6
Fig. 6

Light rays and the ‘ABCD’ matrix. Ray optics picture in the paraxial approximation. We assume a rotationally symmetric system (about the z-axis), with light traveling from left to right. The optical system (box in the center) can be described by an ‘ABCD’ matrix. This matrix maps the initial position (y) and paraxial angle (u) to those exiting the system (y′, u′). The “object space” is the space before the ABCD system, with index of refraction n. Likewise, the “image space” is the space after the system, with index of refraction n′. In this diagram, y > 0, u > 0, y′ < 0, and u′ < 0, for our sign convention [28].

Equations (19)

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[ A B C D ] perfect cloak = [ 1 L / n 0 1 ] .
[ A B C D ] thin lens = [ 1 0 1 / f 1 ] ,
[ 1 0 1 / f 2 1 ] . [ 1 t 0 1 ] [ 1 0 1 / f 1 1 ] = [ 1 t / f 1 t ( f 1 + f 2 t ) / ( f 1 f 2 ) 1 t / f 2 ] .
[ 1 0 1 / f 3 1 ] [ 1 t 2 0 1 ] [ 1 0 1 / f 2 1 ] [ 1 t 1 0 1 ] [ 1 0 1 / f 1 1 ] .
f 2 = ( f 1 t 1 ) ( f 3 t 2 ) f 1 + f 3 t 1 t 2 .
[ f 3 ( f 1 t 1 ) f 1 ( f 3 t 2 ) t 1 + t 2 + t 1 t 2 ( f 1 + f 3 t 1 t 2 ) ( f 1 t 1 ) ( f 3 t 2 ) 0 f 1 ( f 3 t 2 ) f 3 ( f 1 t 1 ) ] .
t 1 t 2 ( f 1 + f 3 t 1 t 2 ) ( f 1 t 1 ) ( f 3 t 2 ) = 0 .
f 2 = ( t 1 f 1 ) / 2 ,
2 t 1 2 / ( f 1 t 1 ) = 0 .
t 1 = f 1 + f 2 .
[ 1 f 1 ( 2 t 1 2 + f 1 ( 2 t 1 + t 2 ) ) / ( f 1 t 1 ) 2 0 1 ] .
t 2 = 2 f 2 ( f 1 + f 2 ) / ( f 1 f 2 ) .
L = 2 t 1 + t 2 = 2 f 1 ( f 1 + f 2 ) / ( f 1 f 2 ) .
f 1 = ( 1 ± 2 ) f 2 .
u tan θ θ ,
[ y n u ] = [ A B C D ] [ y n u ] ,
M t = [ 1 t / n t 0 1 ] .
[ y n u ] = [ 1 L / n 0 1 ] [ y n u ] = [ y + L u n u ] .
i = 1 N [ 1 ( z i z i 1 ) / n i 0 1 ] = [ 1 ( z N z N 1 ) / n N 0 1 ] [ 1 ( z 2 z 1 ) / n 2 0 1 ] [ 1 ( z 1 z 0 ) / n 1 0 1 ] .

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