## Design and demonstration of temporal cloaks with and without the time gap |

Optics Express, Vol. 21, Issue 1, pp. 238-244 (2013)

http://dx.doi.org/10.1364/OE.21.000238

Acrobat PDF (1096 KB)

### 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

## 1. Introduction

1. U. Leonhardt, “Optical Conformal Mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science **312**(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]

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]

9. 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]

10. 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]

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

12. M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature **481**(7379), 62–65 (2012). [CrossRef] [PubMed]

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

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

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

14. 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]

17. Q. Cheng, K. Wu, and G. P. Wang, “All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies,” Opt. Express **19**(23), 23240–23248 (2011). [CrossRef] [PubMed]

## 2. Theoretical analysis

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

19. A. W. Lohmann and D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt. **31**(29), 6212–6219 (1992). [CrossRef] [PubMed]

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

12. M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature **481**(7379), 62–65 (2012). [CrossRef] [PubMed]

12. M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature **481**(7379), 62–65 (2012). [CrossRef] [PubMed]

## 3. Numerical simulations

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]

9. 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]

10. 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]

14. 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]

17. Q. Cheng, K. Wu, and G. P. Wang, “All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies,” Opt. Express **19**(23), 23240–23248 (2011). [CrossRef] [PubMed]

## 4. Conclusions and discussions

## Acknowledgments

## References and links

1. | U. Leonhardt, “Optical Conformal Mapping,” Science |

2. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science |

3. | H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. |

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,” Science |

5. | J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. |

6. | L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics |

7. | T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science |

8. | B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic Invisibility Cloak for Visible Light,” Phys. Rev. Lett. |

9. | 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. |

10. | 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. |

11. | M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt. |

12. | M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature |

13. | A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. |

14. | K. Wu and G. P. Wang, “General insight into the complementary medium-based camouflage devices from Fourier optics,” Opt. Lett. |

15. | K. Wu, Q. Cheng, and G. P. Wang, “Fourier optics theory for invisibility cloaks,” J. Opt. Soc. Am. B |

16. | K. Wu and G. P. Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express |

17. | Q. Cheng, K. Wu, and G. P. Wang, “All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies,” Opt. Express |

18. | B. H. Kolner, “Space-Time Duality and the Theory of Temporal Imaging,” IEEE J. Quantum Electron. |

19. | A. W. Lohmann and D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt. |

20. | J. W. Goodman, |

21. | R. Bracewell, |

22. | A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. |

23. | J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput. |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: September 17, 2012

Revised Manuscript: December 2, 2012

Manuscript Accepted: December 12, 2012

Published: January 3, 2013

**Citation**

Kedi Wu and Guo Ping Wang, "Design and demonstration of temporal cloaks with and without the time gap," Opt. Express **21**, 238-244 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-238

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### References

- 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]
- H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (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. 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]
- 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]
- 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]
- M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editors,” J. Opt.13(2), 024003 (2011). [CrossRef]
- M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature481(7379), 62–65 (2012). [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]
- 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]
- K. Wu, Q. Cheng, and G. P. Wang, “Fourier optics theory for invisibility cloaks,” J. Opt. Soc. Am. B28(6), 1467–1474 (2011). [CrossRef]
- 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]
- 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. H. Kolner, “Space-Time Duality and the Theory of Temporal Imaging,” IEEE J. Quantum Electron.30(8), 1951–1963 (1994). [CrossRef]
- A. W. Lohmann and D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt.31(29), 6212–6219 (1992). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).
- R. Bracewell, The Fourier Transform and Its Applications, (McGraw Hill, 2000).
- A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000). [CrossRef]
- 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]

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