## Hiding objects and creating illusions above a carpet filter using a Fourier optics approach |

Optics Express, Vol. 18, Issue 19, pp. 19894-19901 (2010)

http://dx.doi.org/10.1364/OE.18.019894

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### Abstract

Invisibility carpet cloaks are usually used to hide an object beneath carpet. In this paper we propose and demonstrate a carpet filter to hide objects and create illusions above the filter by using a Fourier optics method. Instead of using transformation optics, we get electromagnetic parameters of the filter by optical transfer functions, which play the role of modulating the propagation of the scattering angular spectrum directly from an object above the filter. By further adding a functional layer onto the filter, we can even camouflage the object so that it appears to be a different object. The analytical results are confirmed by numerical simulations. Our method is completely different from the current coordinate transfer method and may provide another point of view to more clearly understand the mechanism of invisibility cloaks.

© 2010 OSA

## 1. Introduction

## 2. Theoretical analysis

27. 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]

28. G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. **23**(5), 658–660 (1984). [CrossRef] [PubMed]

*λ*can be read as

*F*represents the Fourier transform (FT) operator, and

*x*and

*z*directions, respectively. After propagating to a

*y*direction. For the observing plane

29. J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. **96**(11), 113511 (2010). [CrossRef]

*****means the conjugation operation. As a result, at the observing plane

*l*thick medium is

*n*; then, its TF can be read as

*n*can be a scalar or a tensor. By symmetrically putting a medium layer with thickness

*l*and refractive index

30. G. A. Zheng, X. Heng, and C. H. Yang, “A phase conjugate mirror inspired approach for building cloaking structures with left-handed materials,” N. J. Phys. **11**(3), 033010 (2009). [CrossRef]

31. J. Zhang, Y. Luo, and N. A. Mortensen, “Cloaking of levitating objects above a ground plane,” http://arxiv.org/abs/1005.3316.

*d*thick compressed medium with refractive index

## 3. Numerical simulations

*y*direction for 3 times [refer to Eq. (1)], plays the roles of compensating for the optical path, matching the impedance, and restoring the optical field of the object

*y*direction) is one-third of the radius of the circle (1/12 unit). However, the semi-major axis (

*x*direction) of the ellipse is the same as the radius of the circle, because in the

*x*direction no compression occurs (1/4 unit). To make the observed circle above the carpet centered at (0, 0), the distance of the center of the circle to the substrate should be compressed to one-third of the original. Thus the embedding ellipse is centered at (0, −5/3). The electromagnetic parameters of the ellipse can be obtained from

*x*direction, while the system is the same as Figs. 4(a) and 4(b), respectively. The figures further confirm that the object upon the carpet is camouflaged to another object.

## 4. Conclusions and discussions

32. J. Zhang, J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B.-I. Wu, “Cloak for multilayered and gradually changing media,” Phys. Rev. B **77**(3), 035116 (2008). [CrossRef]

13. S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **74**(3), 036621 (2006). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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

2. | U. Leonhardt, “Optical conformal mapping,” Science |

3. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

4. | G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A |

5. | Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express |

6. | Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. |

7. | W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics |

8. | 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 |

9. | W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. |

10. | H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. |

11. | Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B |

12. | M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostr. Fundam. Appl. |

13. | S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

14. | A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. |

15. | A. Alù and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” J. Opt. A, Pure Appl. Opt. |

16. | A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

17. | J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. |

18. | R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science |

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

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

21. | 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. |

22. | Y. Lai, J. Ng, H. Y. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. |

23. | J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today |

24. | Y. Luo, J. Zhang, H. Chen, B.-I. Wu, and L. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” PIER |

25. | J. W. Goodman, |

26. | M. Born, and E. Wolf, |

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

28. | G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. |

29. | J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. |

30. | G. A. Zheng, X. Heng, and C. H. Yang, “A phase conjugate mirror inspired approach for building cloaking structures with left-handed materials,” N. J. Phys. |

31. | J. Zhang, Y. Luo, and N. A. Mortensen, “Cloaking of levitating objects above a ground plane,” http://arxiv.org/abs/1005.3316. |

32. | J. Zhang, J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B.-I. Wu, “Cloak for multilayered and gradually changing media,” Phys. Rev. B |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(070.7345) Fourier optics and signal processing : Wave propagation

(260.2710) Physical optics : Inhomogeneous optical media

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Physical Optics

**History**

Original Manuscript: May 27, 2010

Revised Manuscript: August 3, 2010

Manuscript Accepted: August 5, 2010

Published: September 3, 2010

**Citation**

Kedi Wu and Guo Ping Wang, "Hiding objects and creating illusions above a carpet filter using a Fourier optics approach," Opt. Express **18**, 19894-19901 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19894

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### References

- A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell's equations,” J. Mod. Opt. 43, 773–793 (1996). [CrossRef]
- U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- G. W. Milton and N.-A. P. Nicorovici, “On the cloaking effects associated with anomalous localized resonance,” Proc. R. Soc. Lond. A 462(2074), 3027–3059 (2006). [CrossRef]
- Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]
- Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99(11), 113903 (2007). [CrossRef] [PubMed]
- W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]
- 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 314(5801), 977–980 (2006). [CrossRef] [PubMed]
- W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007). [CrossRef]
- H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99(6), 063903 (2007). [CrossRef] [PubMed]
- Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008). [CrossRef]
- M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostr. Fundam. Appl. 6(1), 87–95 (2008). [CrossRef]
- S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036621 (2006). [CrossRef] [PubMed]
- A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100(11), 113901 (2008). [CrossRef] [PubMed]
- A. Alù and N. Engheta, “Plasmonic and metamaterial cloaking: physical mechanisms and potentials,” J. Opt. A, Pure Appl. Opt. 10(9), 093002 (2008). [CrossRef]
- A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]
- J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008). [CrossRef] [PubMed]
- R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (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. Photonics 3(8), 461–463 (2009). [CrossRef]
- 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. Han, 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. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57(6), 37–43 (2004). [CrossRef]
- Y. Luo, J. Zhang, H. Chen, B.-I. Wu, and L. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” PIER PIER 95, 167–178 (2009). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Wiley, 2005), Chap. 3.
- M. Born, and E. Wolf, Principles of Optics (Pergamon, 1970), Chap. 8.
- 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]
- G. A. Massey, “Microscopy and pattern generation with scanned evanescent waves,” Appl. Opt. 23(5), 658–660 (1984). [CrossRef] [PubMed]
- J. Zhang, Y. Luo, and N. A. Mortensen, “Minimizing the scattering of a nonmagnetic cloak,” Appl. Phys. Lett. 96(11), 113511 (2010). [CrossRef]
- G. A. Zheng, X. Heng, and C. H. Yang, “A phase conjugate mirror inspired approach for building cloaking structures with left-handed materials,” N. J. Phys. 11(3), 033010 (2009). [CrossRef]
- J. Zhang, Y. Luo, and N. A. Mortensen, “Cloaking of levitating objects above a ground plane,” http://arxiv.org/abs/1005.3316 .
- J. Zhang, J. Huangfu, Y. Luo, H. Chen, J. A. Kong, and B.-I. Wu, “Cloak for multilayered and gradually changing media,” Phys. Rev. B 77(3), 035116 (2008). [CrossRef]

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