Abstract

We introduce a Fourier analysis method to design temporal cloaks for hiding events in time domain. The cloaks are constructed with two linear time-invariant filters with different transfer functions, which can create a temporal gap and then closed it orderly, making any events occurring during the gap not detectable outside. We further reveal that even a no-gap temporal cloak can also hide events. All the analytical results are verified by fast Fourier transformation simulations.

© 2013 OSA

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References

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  1. U. Leonhardt, “Optical Conformal Mapping,” Science312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
    [CrossRef] [PubMed]
  4. 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,” Science314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  5. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
    [CrossRef] [PubMed]
  6. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
    [CrossRef]
  7. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
    [CrossRef] [PubMed]
  8. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. K. Wu and G. P. Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express18(19), 19894–19901 (2010).
    [CrossRef] [PubMed]
  17. Q. Cheng, K. Wu, and G. P. Wang, “All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies,” Opt. Express19(23), 23240–23248 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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  20. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).
  21. R. Bracewell, The Fourier Transform and Its Applications, (McGraw Hill, 2000).
  22. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
    [CrossRef]
  23. J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput.19(90), 297–301 (1965).
    [CrossRef]

2012 (1)

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

2011 (4)

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

K. Wu, Q. Cheng, and G. P. Wang, “Fourier optics theory for invisibility cloaks,” J. Opt. Soc. Am. B28(6), 1467–1474 (2011).
[CrossRef]

Q. Cheng, K. Wu, and G. P. Wang, “All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies,” Opt. Express19(23), 23240–23248 (2011).
[CrossRef] [PubMed]

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

2010 (4)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

K. Wu and G. P. Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express18(19), 19894–19901 (2010).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

K. Wu and G. P. Wang, “General insight into the complementary medium-based camouflage devices from Fourier optics,” Opt. Lett.35(13), 2242–2244 (2010).
[CrossRef] [PubMed]

2009 (4)

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical Conformal Mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt.43(4), 773–793 (1996).
[CrossRef]

1994 (1)

B. H. Kolner, “Space-Time Duality and the Theory of Temporal Imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

1992 (1)

1965 (1)

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput.19(90), 297–301 (1965).
[CrossRef]

Barbastathis, G.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Boardman, A.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Chen, H. Y.

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Cheng, Q.

Cooley, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput.19(90), 297–301 (1965).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

Favaro, A.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

Han, D. Z.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kinsler, P.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

Kolner, B. H.

B. H. Kolner, “Space-Time Duality and the Theory of Temporal Imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

Lai, Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical Conformal Mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

Liu, X.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

Lohmann, A. W.

Luo, Y.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

McCall, M. W.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

Mendlovic, D.

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ng, J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt.43(4), 773–793 (1996).
[CrossRef]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

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,” Science314(5801), 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,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Tukey, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput.19(90), 297–301 (1965).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Wang, G. P.

Ward, A. J.

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt.43(4), 773–793 (1996).
[CrossRef]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Wu, K.

Xiao, J. J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, Z.-Q.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

B. H. Kolner, “Space-Time Duality and the Theory of Temporal Imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994).
[CrossRef]

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt.43(4), 773–793 (1996).
[CrossRef]

J. Opt. (1)

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

Math. Comput. (1)

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput.19(90), 297–301 (1965).
[CrossRef]

Nat. Mater. (2)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009).
[CrossRef]

Nature (1)

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (3)

B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett.106(3), 033901 (2011).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion Optics: The Optical Transformation of an Object into Another Object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Science (4)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical Conformal Mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

R. Bracewell, The Fourier Transform and Its Applications, (McGraw Hill, 2000).

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Figures (3)

Fig. 1
Fig. 1

Scheme of temporal filters consisted of a pair of gratings, lenses and mirrors.

Fig. 2
Fig. 2

Time-dependent complex amplitude distributions of (a) an incident event, (b) an interferential event occurs during the temporal gap, and the output signal as the cloak is (c) off and (d) on. Time-dependent complex amplitude distributions of (e) an interferential event occurs during the edge of temporal gap and (f) corresponding output signal.

Fig. 3
Fig. 3

Scheme of the dispersion curves of media (a) for creating interferential events (left) and constructing conjugated temporal cloaks (right). Time-dependent complex amplitude distributions of (b) an interferential event, (c) mixed output signal of the incident event and interferential event, (d) conjugated temporal filter, and (e) output signal after filter is implemented for compensating for the interferential event, respectively.

Equations (8)

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u(t)= 1 2π + U(μ)exp(i2πμt) dμ= F 1 [U(μ)]
U(μ)= + u(t)exp(i2πμt) dt=F[u(t)]
H 1 (μ)={ exp(i2πμΔt),t> t 0 exp(+i2πμΔt),t< t 0
U'(μ)=U(μ) H 1 (μ)={ U(μ)exp(i2πμΔt), t> t 0 U(μ)exp(+i2πμΔt), t< t 0
u'(t)={ u(tΔt),t> t 0 +Δt 0, t 0 Δt<t< t 0 +Δt u(t+Δt),t< t 0 Δt
H 2 (μ)={ exp(+i2πμΔt),t> t 0 exp(i2πμΔt),t< t 0
U out (μ)=U'(μ) H 2 (μ)=U(μ) H 1 (μ) H 2 (μ)=CU(μ)
u out (t)= F 1 [ U out (μ)]=Cu(t)

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