## Design of invisibility anti-cloak for two-dimensional arbitrary geometries |

Optics Express, Vol. 21, Issue 8, pp. 9422-9427 (2013)

http://dx.doi.org/10.1364/OE.21.009422

Acrobat PDF (1182 KB)

### Abstract

In this paper, we derive the material parameter formulae for designing an electromagnetic invisibility anti-cloak of two-dimensional arbitrary geometry, which is conformal with the cloaked object. Different shapes of electromagnetic invisibility anti-cloaks are proposed to verify the correctness and effectiveness of the proposed formulae. The simulation results show that the invisibility anti-cloak can break cloak shielding and make the external electromagnetic waves into the cloak. This is not only to realize the transfer of information, but will not affect the role of cloak of stealth.

© 2013 OSA

## 1. Introduction

*et al.*proposed a new vision-electromagnetic invisible cloak, which is based on the optical transformation [1

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. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. **8**(10), 247 (2006). [CrossRef]

5. G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. **8**(10), 248 (2006). [CrossRef]

6. 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]

7. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics **1**(4), 224–227 (2007). [CrossRef]

8. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. **90**(24), 241105 (2007). [CrossRef]

11. J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. **34**(5), 644–646 (2009). [CrossRef] [PubMed]

12. D. H. Kwon and D. H. Werner, “Transformation electromagnetics: an overview of the theory and applications,” IEEE Trans. Antennas Propag. **52**(1), 24–46 (2010). [CrossRef]

13. X. Chen, Y. Fu, and N. Yuan, “Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through Helmholtz’s equation,” Opt. Express **17**(5), 3581–3586 (2009). [CrossRef] [PubMed]

14. H. Chen, X. Luo, H. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express **16**(19), 14603–14608 (2008). [CrossRef] [PubMed]

*et al.*proposed a new concept-electromagnetic invisibility anti-cloak. An anti-cloak with a specific form of negative index anisotropic material is embedded inside the cloak, makes the external electromagnetic wave penetrate into the interior of the invisibility cloak and partially defeats the cloaking effect. This concept has been elaborated in [15

15. G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express **17**(5), 3101–3114 (2009). [CrossRef] [PubMed]

18. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking a sensor via transformation optics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **83**(1), 016603 (2011). [CrossRef] [PubMed]

15. G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express **17**(5), 3101–3114 (2009). [CrossRef] [PubMed]

## 2. Invisibility anti-cloak for two-dimensional arbitrary geometries

19. C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express **16**(17), 13414–13420 (2008). [CrossRef] [PubMed]

**A**is the Jacobi matrix of the transformation from the virtual space to the real space defined by

15. G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express **17**(5), 3101–3114 (2009). [CrossRef] [PubMed]

## 3. Full-wave simulation and analysis

20. Comsol Multiphysics” (Comsol AB), <http://www.comsol.com>.

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

## 4. Conclusion

## 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. | U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. |

4. | D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express |

5. | G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. |

6. | 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 |

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

8. | H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. |

9. | M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Desigh of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photon. Nanostruct.: Fundam. Appl. |

10. | T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express |

11. | J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. |

12. | D. H. Kwon and D. H. Werner, “Transformation electromagnetics: an overview of the theory and applications,” IEEE Trans. Antennas Propag. |

13. | X. Chen, Y. Fu, and N. Yuan, “Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through Helmholtz’s equation,” Opt. Express |

14. | H. Chen, X. Luo, H. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express |

15. | G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express |

16. | G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Analytical study of spherical cloak/anti-cloak interactions,” Wave Motion |

17. | I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B |

18. | A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking a sensor via transformation optics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

19. | C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express |

20. | Comsol Multiphysics” (Comsol AB), <http://www.comsol.com>. |

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

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(230.0230) Optical devices : Optical devices

(160.3918) Materials : Metamaterials

(260.2710) Physical optics : Inhomogeneous optical media

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Physical Optics

**History**

Original Manuscript: February 1, 2013

Revised Manuscript: March 20, 2013

Manuscript Accepted: April 2, 2013

Published: April 9, 2013

**Citation**

Long Li, Feifei Huo, Yuanming Zhang, Yang Chen, and Changhong Liang, "Design of invisibility anti-cloak for two-dimensional arbitrary geometries," Opt. Express **21**, 9422-9427 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9422

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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]
- U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006). [CrossRef]
- D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006). [CrossRef] [PubMed]
- G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys.8(10), 248 (2006). [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,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
- W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007). [CrossRef]
- H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett.90(24), 241105 (2007). [CrossRef]
- M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Desigh of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations,” Photon. Nanostruct.: Fundam. Appl.6(1), 87–95 (2008). [CrossRef]
- T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express16(22), 18545–18550 (2008). [CrossRef] [PubMed]
- J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett.34(5), 644–646 (2009). [CrossRef] [PubMed]
- D. H. Kwon and D. H. Werner, “Transformation electromagnetics: an overview of the theory and applications,” IEEE Trans. Antennas Propag. 52(1), 24–46 (2010). [CrossRef]
- X. Chen, Y. Fu, and N. Yuan, “Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through Helmholtz’s equation,” Opt. Express17(5), 3581–3586 (2009). [CrossRef] [PubMed]
- H. Chen, X. Luo, H. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express16(19), 14603–14608 (2008). [CrossRef] [PubMed]
- G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express17(5), 3101–3114 (2009). [CrossRef] [PubMed]
- G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Analytical study of spherical cloak/anti-cloak interactions,” Wave Motion48(6), 455–467 (2011). [CrossRef]
- I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “General class of metamaterial transformation slabs,” Phys. Rev. B81(12), 125124 (2010). [CrossRef]
- A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Cloaking a sensor via transformation optics,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.83(1), 016603 (2011). [CrossRef] [PubMed]
- C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express16(17), 13414–13420 (2008). [CrossRef] [PubMed]
- Comsol Multiphysics” (Comsol AB), < http://www.comsol.com >.
- S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036621 (2006). [CrossRef] [PubMed]

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