Abstract

We propose a one-way invisible cloak using transformation optics of parity-time (PT) symmetric optical materials. At the spontaneous PT-symmetry breaking point, light is scattered only for incidence along one direction since the phase-matching condition is unidirectionally satisfied, making the cloak one-way invisible. Moreover, optical scattering from the one-way cloak can be further engineered to realize more interesting effects, for example, creating a unidirectional optical illusion of the concealed object.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  18. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
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2013 (1)

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

2012 (2)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

2011 (6)

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

C. He, X. L. Zhang, L. Feng, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 99, 151112 (2011).
[CrossRef]

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, J. Opt. 13, 024003 (2011).
[CrossRef]

2010 (2)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

C. T. West, T. Kottos, and T. Prosen, Phys. Rev. Lett. 104, 054102 (2010).
[CrossRef]

2009 (4)

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nat. Mater. 8, 568 (2009).
[CrossRef]

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

2008 (4)

2007 (3)

A. Greenleaf, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

2006 (1)

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

2005 (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

2003 (1)

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Almeida, V.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nat. Mater. 8, 568 (2009).
[CrossRef]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Boardman, A.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, J. Opt. 13, 024003 (2011).
[CrossRef]

Cai, W. S.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chan, C. T.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, H. Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Chen, Y. F.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

C. He, X. L. Zhang, L. Feng, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 99, 151112 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Chettiar, U. K.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Favaro, A.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, J. Opt. 13, 024003 (2011).
[CrossRef]

Fegadolli, W. S.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

Feng, L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

C. He, X. L. Zhang, L. Feng, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 99, 151112 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Gabitov, I. R.

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Ge, L.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Gharghi, M.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

Gladden, C.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Greenleaf, A.

A. Greenleaf, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Han, D. Z.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

He, C.

C. He, X. L. Zhang, L. Feng, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 99, 151112 (2011).
[CrossRef]

Huang, J.

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Kildishev, A. V.

A. V. Kildishev and V. M. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, Nat. Photonics 1, 224 (2007).
[CrossRef]

Kinsler, P.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, J. Opt. 13, 024003 (2011).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Kottos, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

C. T. West, T. Kottos, and T. Prosen, Phys. Rev. Lett. 104, 054102 (2010).
[CrossRef]

Lai, Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Lassas, M.

A. Greenleaf, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef]

Leonhardt, U.

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nat. Mater. 8, 568 (2009).
[CrossRef]

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

Lin, Z.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Litchinitser, N. M.

Liu, Y. M.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef]

Lu, M. H.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

C. He, X. L. Zhang, L. Feng, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 99, 151112 (2011).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Maimistov, A. I.

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

McCall, M. W.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, J. Opt. 13, 024003 (2011).
[CrossRef]

Miri, M. A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Ng, J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, Nature 481, 62 (2012).
[CrossRef]

Oliveira, J. B. E.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

Onishchukov, G.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Pendry, J. B.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, Opt. Express 16, 11555 (2008).
[CrossRef]

J. Li and J. B. Pendry, Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef]

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

Peschel, U.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, Nature 438, 335 (2005).
[CrossRef]

Prosen, T.

C. T. West, T. Kottos, and T. Prosen, Phys. Rev. Lett. 104, 054102 (2010).
[CrossRef]

Rahm, M.

Ramezani, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Nature 488, 167 (2012).
[CrossRef]

Roberts, D. A.

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Sagdeev, R. Z.

Scherer, A.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Schurig, D.

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

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nat. Phys. 6, 192 (2010).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, Opt. Express 16, 11555 (2008).
[CrossRef]

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

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Stone, A. D.

Y. D. Chong, L. Ge, and A. D. Stone, Phys. Rev. Lett. 106, 093902 (2011).
[CrossRef]

Tyc, T.

U. Leonhardt and T. Tyc, Science 323, 110 (2009).
[CrossRef]

Uhlmann, G.

A. Greenleaf, M. Lassas, and G. Uhlmann, Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef]

Valentine, J.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nat. Mater. 8, 568 (2009).
[CrossRef]

West, C. T.

C. T. West, T. Kottos, and T. Prosen, Phys. Rev. Lett. 104, 054102 (2010).
[CrossRef]

Xiao, J. J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef]

Xu, Y. L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. B. E. Oliveira, V. Almeida, Y. F. Chen, and A. Scherer, Nat. Mater. 12, 108 (2013).
[CrossRef]

L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, Y. F. Chen, Y. Fainman, and A. Scherer, Science 333, 729 (2011).
[CrossRef]

Yin, X. B.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

Zentgraf, T.

M. Gharghi, C. Gladden, T. Zentgraf, Y. M. Liu, X. B. Yin, J. Valentine, and X. Zhang, Nano Lett. 11, 2825 (2011).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, Nat. Mater. 8, 568 (2009).
[CrossRef]

Zhang, X.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Coordinate transformation to expand the red point (r=0) in the virtual space (rb) to a hollow hole (ra) in the physical space (arb). (b) Corresponding complex permittivities of the PT symmetric potential in virtual and physical spaces, respectively.

Fig. 2.
Fig. 2.

Numerical mappings of the total electric field in (a), (b) the virtual space and (c), (d) the physical space. In (a) and (c) where light is incident from left, strong backscattered reflection can be clearly observed because of the satisfied phase matching. However, in (b) and (d) where light is incident from right, phase is mismatched and thus light propagates without exciting any scattered light.

Fig. 3.
Fig. 3.

Numerical mappings of the total electric field with a TE-polarized point source impinging on a PEC cylinder (rλ) (a), (b) without and (c), (d) with the PT cloak (λr2.5λ). The point source is located at (a), (c) (5λ, 0) and (b), (d) (5λ, 0), respectively. The radius of the source is 0.2λ.

Fig. 4.
Fig. 4.

(a) Purple, red, and blue curves represent the normalized scattering fields of the cloaked PEC cylinder, where the point source is located at (3λ, 0), (5λ, 0), and (7λ, 0), respectively. (b) Comparison of the normalized scattering fields from the cloaked PEC cylinder (red) and a concave PEC mirror (black), where the point source is located at (5λ, 0). (c) and (d) are the corresponding simulated field distributions for the cloaked PEC cylinder and the concave PEC mirror, respectively.

Equations (3)

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

Ez=Ein(x)exp(ik1x)+Esc(x)exp(ik2x).
[dEindxdEscdx]=[iω2ζ2k1c2exp(iβx)iω2ζ2k1c2exp[i2βx]iω2ζ2k2c2iω2ζ2k2c2exp(iβx)][EinEsc],
dEindx=0,dEscdx=iω2ζ2k2c2Ein.

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