Abstract

An ideal invisibility cloak makes any object within itself indistinguishable from its surrounding—for all colors, directions, and polarizations of light. Nearly ideal cloaks have recently been realized for turbid light-scattering media under continuous-wave illumination. Here, we ask whether these cloaks also work under pulsed illumination. Our time-resolved imaging experiments on simple core–shell cloaks show that they do not: they appear bright with respect to their surrounding at early times and dark at later times, leading to vanishing image contrast for time-averaged detection. Furthermore, we show that the same holds true for more complex cloaking architectures designed by spatial coordinate transformations. We discuss implications for diffuse optical tomography and possible applications in terms of high-end security features.

© 2015 Optical Society of America

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References

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[Crossref]

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

2013 (3)

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

S. Guenneau, T. M. Puvirajesinghe, J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

2012 (3)

S. Guenneau, C. Amra, D. Veynante, Opt. Express 20, 8207 (2012).
[Crossref]

Y. Liu, X. Zhang, Nanoscale 4, 5277 (2012).
[Crossref]

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

2010 (1)

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

2008 (1)

V. M. Shalaev, Science 322, 384 (2008).
[Crossref]

2006 (3)

J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006).
[Crossref]

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

A. P. Calderón, Comput. Appl. Math. 25, 133 (2006).

2005 (1)

A. Alù, N. Engheta, Phys. Rev. E 72, 016623 (2005).
[Crossref]

2003 (1)

A. Greenleaf, M. Lassas, G. Uhlmann, Math. Res. Lett. 10, 685 (2003).

2001 (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

1956 (1)

E. H. Kerner, Proc. Phys. Soc. London Sect. B 69, 802 (1956).

1855 (1)

A. Fick, Ann. Phys. 170, 59 (1855).
[Crossref]

Alù, A.

A. Alù, N. Engheta, Phys. Rev. E 72, 016623 (2005).
[Crossref]

Amra, C.

Aubry, A.

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

Bai, X.

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Bückmann, T.

R. Schittny, M. Kadic, T. Bückmann, M. Wegener, Science 345, 427 (2014).
[Crossref]

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

Calderón, A. P.

A. P. Calderón, Comput. Appl. Math. 25, 133 (2006).

Choe, R.

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Del Biance, S.

F. Martelli, S. Del Biance, A. Ismaelli, G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, 2010).

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Engheta, N.

A. Alù, N. Engheta, Phys. Rev. E 72, 016623 (2005).
[Crossref]

Fick, A.

A. Fick, Ann. Phys. 170, 59 (1855).
[Crossref]

Gao, D.

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Gao, F.

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Greenleaf, A.

A. Greenleaf, M. Lassas, G. Uhlmann, Math. Res. Lett. 10, 685 (2003).

Guenneau, S.

S. Guenneau, T. M. Puvirajesinghe, J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

S. Guenneau, C. Amra, D. Veynante, Opt. Express 20, 8207 (2012).
[Crossref]

Han, T.

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Ismaelli, A.

F. Martelli, S. Del Biance, A. Ismaelli, G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, 2010).

Kadic, M.

R. Schittny, M. Kadic, T. Bückmann, M. Wegener, Science 345, 427 (2014).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

Kerner, E. H.

E. H. Kerner, Proc. Phys. Soc. London Sect. B 69, 802 (1956).

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Lassas, M.

A. Greenleaf, M. Lassas, G. Uhlmann, Math. Res. Lett. 10, 685 (2003).

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

Liu, Y.

Y. Liu, X. Zhang, Nanoscale 4, 5277 (2012).
[Crossref]

Maier, S. A.

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

Martelli, F.

F. Martelli, S. Del Biance, A. Ismaelli, G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, 2010).

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Milton, G. W.

G. W. Milton, The Theory of Composites (Cambridge University, 2002).

Pendry, J. B.

J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Pendry, J. P.

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

Puvirajesinghe, T. M.

S. Guenneau, T. M. Puvirajesinghe, J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

Qiu, C. W.

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Schittny, R.

R. Schittny, M. Kadic, T. Bückmann, M. Wegener, Science 345, 427 (2014).
[Crossref]

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

Schurig, D.

J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Shalaev, V. M.

V. M. Shalaev, Science 322, 384 (2008).
[Crossref]

Shi, X.

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

Smith, D. R.

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Sun, H.

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

Thong, J. T. L.

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Uhlmann, G.

A. Greenleaf, M. Lassas, G. Uhlmann, Math. Res. Lett. 10, 685 (2003).

Veynante, D.

Wegener, M.

R. Schittny, M. Kadic, T. Bückmann, M. Wegener, Science 345, 427 (2014).
[Crossref]

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

Xu, H.

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

Yodh, A. G.

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Zaccanti, G.

F. Martelli, S. Del Biance, A. Ismaelli, G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, 2010).

Zhang, B.

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

Zhang, X.

Y. Liu, X. Zhang, Nanoscale 4, 5277 (2012).
[Crossref]

Ann. Phys. (1)

A. Fick, Ann. Phys. 170, 59 (1855).
[Crossref]

Comput. Appl. Math. (1)

A. P. Calderón, Comput. Appl. Math. 25, 133 (2006).

IEEE Signal Process. Mag. (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, IEEE Signal Process. Mag. 18(6), 57 (2001).
[Crossref]

J. R. Soc. Interface (1)

S. Guenneau, T. M. Puvirajesinghe, J. R. Soc. Interface 10, 20130106 (2013).
[Crossref]

Math. Res. Lett. (1)

A. Greenleaf, M. Lassas, G. Uhlmann, Math. Res. Lett. 10, 685 (2003).

Nanoscale (1)

Y. Liu, X. Zhang, Nanoscale 4, 5277 (2012).
[Crossref]

Opt. Express (1)

Phys. Rev. E (1)

A. Alù, N. Engheta, Phys. Rev. E 72, 016623 (2005).
[Crossref]

Phys. Rev. Lett. (3)

R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110, 195901 (2013).
[Crossref]

H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301 (2014).
[Crossref]

T. Han, X. Bai, D. Gao, J. T. L. Thong, C. W. Qiu, Phys. Rev. Lett. 112, 054302 (2014).
[Crossref]

Proc. Phys. Soc. London Sect. B (1)

E. H. Kerner, Proc. Phys. Soc. London Sect. B 69, 802 (1956).

Rep. Prog. Phys. (2)

T. Durduran, R. Choe, W. B. Baker, A. G. Yodh, Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

M. Kadic, T. Bückmann, R. Schittny, M. Wegener, Rep. Prog. Phys. 76, 126501 (2013).
[Crossref]

Science (5)

R. Schittny, M. Kadic, T. Bückmann, M. Wegener, Science 345, 427 (2014).
[Crossref]

J. P. Pendry, A. Aubry, D. R. Smith, S. A. Maier, Science 337, 549 (2012).
[Crossref]

J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 (2006).
[Crossref]

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

V. M. Shalaev, Science 322, 384 (2008).
[Crossref]

Other (3)

F. Martelli, S. Del Biance, A. Ismaelli, G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, 2010).

C. M. Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Springer, 2001).

G. W. Milton, The Theory of Composites (Cambridge University, 2002).

Supplementary Material (1)

» Supplement 1: PDF (432 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the experimental setup for time-resolved diffusive light transmission experiments. The tank (not filled here for illustration) with the cylindrical core–shell structure inside is illuminated by a pulsed divergent red laser. The diffusively transmitted light is collected point-wise by a horizontally moveable multimode fiber and is fed into a time-correlated single-photon counting unit.

Fig. 2.
Fig. 2.

Measured spatially and temporally resolved diffusive light transmission through the water–paint mixture in the tank (a) without any sample, (b) with the obstacle, and (c) with the cloak centered in the tank. Each panel shows a color-coded contour plot of the spatially and temporally resolved photon count rate per time bin ( = 4 ps ). The curve on top shows the photon count rate integrated over all time bins. The black data points on the left-hand side are a vertical cut through the center of the contour plot (see dashed white line), with the extracted decay times τ indicated in red. The gray data correspond to ballistic light transmission through the empty tank. Comparison of panels (a) and (c) reveals the failure of the core–shell cloaking in the transient regime, as the cloak’s maximum photon count is higher by about a factor of 2 and occurs earlier than for the reference.

Fig. 3.
Fig. 3.

Numerical solutions of the time-dependent diffusion equation corresponding to the experimental results shown in Fig. 2. Parameters of the numerical model as explained in Supplement 1 are tank thickness L = 60 mm ; diameters 2 R 1 = 32.1 mm and 2 R 2 = 39.8 mm of the core and shell, respectively; diffusivities D 0 = 7.58 × 10 8 cm 2 / s , D 1 = 0 cm 2 / s , and D 2 = 158.72 × 10 8 cm 2 / s of the surrounding, core, and shell, respectively; photon lifetimes τ 0 = 9.5 ns and τ 12 = 0.2 s in the surrounding and on the cylinder surface, respectively; and photon loss velocity K = 0.743 × 10 9 cm / s .

Fig. 4.
Fig. 4.

Calculated photon density distributions on the tank’s rear surface for (a) a lossless core–shell and (b) a transformation-optics (TO)-based cloak under homogeneous illumination of the front surface. Parameters are R 2 / R 1 = 1.25 (hence D 2 / D 0 = 4.56 for the core–shell cloak) and L / ( 2 R 2 ) = 1.5 . The solid curves are horizontal cuts of the normalized photon density. The first row shows static results where both cloaks work perfectly. The remaining rows show snapshots of the transient behavior after an illumination pulse at t = 0 , with the photon density of the reference case of a homogeneous medium added as dashed curves for comparison. The times given are normalized to the diffusive time constant τ diff = L 2 / ( π 2 D 0 ) . Both cloaks show a similar transient behavior: they appear too bright for early times and cast a shadow for later times, similar to the experiments shown in Fig. 2.

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