Abstract

Toward the goal of achieving broadband and omnidirectional invisibility, we propose a method for practical invisibility cloaking. We call this “digital cloaking,” where space, angle, spectrum, and phase are discretized. Experimentally, we demonstrate a two-dimensional (2D) planar, ray optics, digital cloak by using lenticular lenses, similar to “integral imaging” for three-dimensional (3D) displays. Theoretically, this can be extended to a good approximation of an “ideal” 3D cloak. With continuing improvements in commercial digital technology, the resolution limitations of a digital cloak can be minimized.

© 2016 Optical Society of America

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References

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  1. G. Gbur, “Invisibility physics: past, present, and future,” Prog. Opt. 58, 65–114 (2013).
    [Crossref]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [Crossref]
  4. M. McCall, “Transformation optics and cloaking,” Contemp. Phys. 54, 273–286 (2013).
    [Crossref]
  5. R. Fleury, F. Monticone, and A. Alu, “Invisibility and cloaking: origins, present, and future perspectives,” Phys. Rev. Appl. 4, 037001 (2015).
    [Crossref]
  6. J. S. Choi and J. C. Howell, “Paraxial full-field cloaking,” Opt. Express 23, 15857–15862 (2015).
    [Crossref]
  7. J. S. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [Crossref]
  8. N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
    [Crossref]
  9. 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]
  10. J. S. Choi and J. C. Howell, “Paraxial ray optics cloaking,” Opt. Express 22, 29465–29478 (2014).
    [Crossref]
  11. R. Schittny, M. Kadic, T. Bueckmann, and M. Wegener, “Invisibility cloaking in a diffusive light scattering medium,” Science 345, 427–429 (2014).
    [Crossref]
  12. C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (2014).
    [Crossref]
  13. M. Bass, J. M. Enoch, and V. Lakshminarayanan, “Vision and vision optics,” in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), Vol. 3.
  14. F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
    [Crossref]
  15. G. Lippmann, “Epreuves reversibles. Photographies integrales,” C. R. Acad. Sci. 146, 446–451 (1908).
  16. J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photon. 5, 456–535 (2013).
    [Crossref]
  17. A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
    [Crossref]
  18. S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
    [Crossref]

2015 (2)

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

J. S. Choi and J. C. Howell, “Paraxial full-field cloaking,” Opt. Express 23, 15857–15862 (2015).
[Crossref]

2014 (5)

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]

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

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

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (2014).
[Crossref]

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

2013 (4)

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. Geng, “Three-dimensional display technologies,” Adv. Opt. Photon. 5, 456–535 (2013).
[Crossref]

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

2009 (2)

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

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]

2006 (2)

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

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

1908 (1)

G. Lippmann, “Epreuves reversibles. Photographies integrales,” C. R. Acad. Sci. 146, 446–451 (1908).

Alu, A.

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

Antoniou, G.

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

Bass, M.

M. Bass, J. M. Enoch, and V. Lakshminarayanan, “Vision and vision optics,” in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), Vol. 3.

Bueckmann, T.

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

Choi, J. S.

Courtial, J.

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

Della Giovampaola, C.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (2014).
[Crossref]

Engheta, N.

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (2014).
[Crossref]

Enoch, J. M.

M. Bass, J. M. Enoch, and V. Lakshminarayanan, “Vision and vision optics,” in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), Vol. 3.

Fleury, R.

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

Gbur, G.

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

Geng, J.

Hamilton, A. C.

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

Howell, J. B.

Howell, J. C.

Kadic, M.

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

Lakshminarayanan, V.

M. Bass, J. M. Enoch, and V. Lakshminarayanan, “Vision and vision optics,” in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), Vol. 3.

Landy, N.

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

Leonhardt, U.

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

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]

Lippmann, G.

G. Lippmann, “Epreuves reversibles. Photographies integrales,” C. R. Acad. Sci. 146, 446–451 (1908).

McCall, M.

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

Milton, G. W.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
[Crossref]

Monticone, F.

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

Onofrei, D.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
[Crossref]

Orife, E.

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

Oxburgh, S.

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

Pendry, J. B.

J. S. 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]

Schittny, R.

R. Schittny, M. Kadic, T. Bueckmann, 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]

Smith, D. R.

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

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

Vasquez, F. G.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
[Crossref]

Wegener, M.

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

White, C. D.

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

C. R. Acad. Sci. (1)

G. Lippmann, “Epreuves reversibles. Photographies integrales,” C. R. Acad. Sci. 146, 446–451 (1908).

Contemp. Phys. (1)

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

J. Opt. A (1)

A. C. Hamilton and J. Courtial, “Generalized refraction using lenslet arrays,” J. Opt. A 11, 065502 (2009).
[Crossref]

Nat. Mater. (2)

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

C. Della Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13, 1115–1121 (2014).
[Crossref]

Opt. Express (2)

Phys. Rev. Appl. (1)

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

Phys. Rev. Lett. (2)

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

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active exterior cloaking for the 2D Laplace and Helmholtz equations,” Phys. Rev. Lett. 103, 073901 (2009).
[Crossref]

Proc. SPIE (1)

S. Oxburgh, C. D. White, G. Antoniou, E. Orife, and J. Courtial, “Transformation optics with windows,” Proc. SPIE 9193, 91931E (2014).
[Crossref]

Prog. Opt. (1)

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

Science (3)

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

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

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

Other (1)

M. Bass, J. M. Enoch, and V. Lakshminarayanan, “Vision and vision optics,” in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), Vol. 3.

Supplementary Material (4)

NameDescription
» Supplement 1: PDF (1469 KB)      Supplemental document
» Visualization 1: MP4 (14695 KB)      Cloak observed from changing horizontal positions, compared to without cloak. Camera was 260 cm from display screen. Movie sped up by 200% from original. 13.4 deg total viewing range. Centers of cloak and camera aligned (0 deg , x = 0) at 13 s (of 20 s clip).
» Visualization 2: MP4 (11935 KB)      Example scan of background objects by input camera on a horizontal slider. A shorter scan distance than Visualization 1 sufficed for the setup we demonstrated.
» Visualization 3: MP4 (5880 KB)      The actual input scan used for generating our cloaked image, but sped up by 500%, reduced frame rate (30 fps (frames per second) versus 60 fps), with reduced bitrate (5 Mbps from 26 Mbps).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Integral imaging detection [zoomed-in portion of (b)]. A superpixel, placed at the focusing plane of a lenslet, collects rays with the same position as the lens. These rays are then spatially separated into pixels, such that one ray angle (or “view”) maps to one pixel. Display (output) is the reverse of the detection scheme shown here. (b) A digital integral cloak. Cross section of two parallel 2D surfaces, with a few sample rays. The input “surface” (lens array and plate) captures input light rays. The output surface displays rays as if they passed through ambient space only (dashed lines).

Fig. 2.
Fig. 2.

(a) and (b) 2D digital integral cloak setup. The input camera on a slider (input plane) scans horizontally to gather input rays. The lenslet array on the display screen (output plane) emits rays according to Eq. (1). The space between the input and output planes (separated by L ) is the cloaked region. (c)–(f) With the cloak. Screenshots by an “observer” camera that moved horizontally (from Visualization 1). Viewing angles from the screen center to observer camera: (c)  4.1 ° , (d) 0.0°, (e) 2.0°, (f) 6.7°. (c′)–(f′) Without the cloak. The cloaking screen in (c)–(f) horizontally matches (c′)–(f′), respectively, in size, alignment, and parallax motion.

Fig. 3.
Fig. 3.

(a)–(d) Digital integral cloak longitudinal ( z ) demonstration. The observer (camera) was at different distances in front of the display screen of the cloak: (a) 272 cm, (b) 235 cm, (c) 203 cm, and (d) 150 cm. The cloak displays more of the background objects, spatially, for closer observation.

Fig. 4.
Fig. 4.

(a) Ideal spherically symmetric cloak. Example rays (solid arrows) enter and exit the cloak (circle in 2D, sphere in 3D). Dashed arrows show how the rays appear to have traveled inside the cloak (where objects are invisible). Cloak is spherically symmetric, so it works for all ray angles (omnidirectional). (b) Discretized symmetric cloak. Solid arrows depict some rays of light that enter and exit. The surface of the cloak is discretized, so that each superpixel in space can both detect and emit multiple discrete ray positions and angles. A digital cloak uses digital detection and display technologies.

Equations (1)

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[ x f n tan θ f ] z = z f = [ 1 ( z f z i ) / n 0 1 ] [ x i n tan θ i ] z = z i .

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