## The Anti-Cloak

Optics Express, Vol. 16, Issue 19, pp. 14603-14608 (2008)

http://dx.doi.org/10.1364/OE.16.014603

Acrobat PDF (1606 KB)

### Abstract

A kind of transformation media, which we shall call the “anti-cloak”, is proposed to partially defeat the cloaking effect of the invisibility cloak. An object with an outer shell of “anti-cloak” is visible to the outside if it is coated with the invisible cloak. Fourier-Bessel analysis confirms this finding by showing that external electromagnetic wave can penetrate into the interior of the invisibility cloak with the help of the anti-cloak.

© 2008 Optical Society of America

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**, 1780–1782 (2006). [CrossRef] [PubMed]

4. A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas **24**, 413–419 (2003). [CrossRef] [PubMed]

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**, 1780–1782 (2006). [CrossRef] [PubMed]

18. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E **72**, 016623 (2005). [CrossRef]

19. 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**, 977–980 (2006). [CrossRef] [PubMed]

8. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express **14**, 9794–9804 (2006). [CrossRef] [PubMed]

9. 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 **74**, 036621 (2006). [CrossRef]

10. Z. Liang, P. Yao, X. Sun, and X. Jiang, “The physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. **92**, 131118 (2008). [CrossRef]

11. Z. Ruan, M. Yan, C.W. Neff, and M. Qiu, “Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. **99**, 113903 (2007). [CrossRef] [PubMed]

12. H.S. Chen, B.-I. Wu, B. Zhang, and J.A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. **99**, 063903 (2007). [CrossRef] [PubMed]

11. Z. Ruan, M. Yan, C.W. Neff, and M. Qiu, “Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. **99**, 113903 (2007). [CrossRef] [PubMed]

12. H.S. Chen, B.-I. Wu, B. Zhang, and J.A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. **99**, 063903 (2007). [CrossRef] [PubMed]

6. Huanyang Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C.T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B **76**, 241104 (2007). [CrossRef]

14. R.V. Kohn, H. Shen, M.S. Vogelius, and M.I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. **24**, 015016 (2008). [CrossRef]

*r*′=

*a*to an equivalent PEC cylinder whose radius is

*r*=

*r*

_{0}. In the limit as

*r*

_{0}goes to zero, the partial cloak becomes perfect [1

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**, 1780–1782 (2006). [CrossRef] [PubMed]

*c*<

*r*′<

*a*) as depicted in Fig. 2(a),

*r*′=

*c*is coated with the anti-cloak in direct contact with the partial cloak, the total scattering cross section will be changed into that of an equivalent PEC cylinder whose radius is

*r*=

*d*. We note that there are no PEC boundary between the cloak and the anti-cloak (at

*r*′=

*a*), they are in direct contact.

11. Z. Ruan, M. Yan, C.W. Neff, and M. Qiu, “Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. **99**, 113903 (2007). [CrossRef] [PubMed]

*J*\

_{l}*H*are the

_{l}*l*-order Bessel\Hankel function of the 1st kind,

*k*

_{0}is the wave vector of the light in vacuum,

*α*and

^{in}_{l}*α*are the incident and scattering coefficients outside the cloak,

^{sc}_{l}*α*(i=1,2,3,4) are the expansion coefficients for the field in the cloak and anti-cloak. The primes are dropped for aesthetic reasons from here. From the continuous boundary conditions (at

^{i}_{l}*r*=

*b*and

*r*=

*a*) and the PEC boundary (

*E*=0 at

_{z}*r*=

*c*), we can obtain that,

*r*=

*c*coated with the anti-cloak and cloak is equivalent to a PEC cylinder with its radius

*r*=

*d*in the view of outside world.

*a*=0.1

*m*,

*b*=0.2

*m*,

*c*=0.05

*m*,

*d*=0.02

*m*,

*r*

_{0}=0.001

_{m}. We plot the parameters of the cloak and anti-cloak at different radial positions in Fig. 2(b)–(d). All the parameters of anti-cloak are negative because of the negative slope of the coordinate transformation. A plane wave is incident from left to right with the frequency 2

*GHz*. In Fig. 3(a), we plot the scattering pattern of a PEC cylinder with a radius

*r*

_{0}. The tiny PEC cylinder causes little scattering for the incoming plane wave which can be treated as almost invisible. In Fig. 3(b), we plot the scattering pattern of a PEC cylinder with a radius

*a*coated by a partial cloak. The outer radius of the cloak is

*b*. We see that the partial cloak reduces substantially the scattering of the PEC cylinder with its radius

*a*when we compare Fig. 3(a) and Fig. 3(b). When

*r*

_{0}is made as small as we like, the scattering becomes vanishing small. In Fig. 3(c), we plot the scattering pattern of a PEC cylinder with a radius

*c*coated by an anti-cloak and a partial cloak [20]. The anti-cloak is located in

*c*<

*r*<

*a*, the cloak locates in

*a*<

*r*<

*b*. Without the anti-cloak, the wave basically goes around the shielded region, but if the anti-cloak is in contact with the cloak, EM wave from outside can go into the anti-cloak to interact with the object inside. The scattering of the cloak is enlarged again to that of an equivalent PEC cylinder whose radius is

*d*. We plot the scattering pattern of the equivalent PEC cylinder in Fig. 3(d). When

*c*=

*d*, the anti-cloak together with the partial cloak becomes invisible, that means one can directly see the PEC cylinders with radius

*r*=

*c*, and the anti-cloak cancels out the effect of the partial cloak completely. For aesthetic reasons, if the electric field is larger than the maximum value in color bar in Fig. 3(c), we have replaced this overvalued field with the maximum value when plotting Fig. 3(c). If the electric field is smaller than the minimum value, we have replaced this overvalued field with the minimum value when plotting Fig. 3(c).

*r*=

*a*, the impedances are matched at this touching boundary of the cloak and anti-cloak. The electric field is very large at this touching boundary. To show this property, we plot the electric field for different angles at fix radii near

*r*=

*a*in Fig. 4. Three fixed radii are chosen,

*r*=

*a*-0.1

*r*

_{0},

*r*=

*a*and

*r*=

*a*+0.1

*r*

_{0}. We find that the electric field near

*r*=

*a*is very large.

*r*=

*a*as follow,

*H*(

_{l}*k*

_{0}

*r*

_{0}) becomes very large when

*r*

_{0}is small, that is why we obtain large electric field above.

*r*

_{0}as small as we like, we reach the conclusion that an almost perfect cloak can be defeated by an anti-cloak. In other words, the transformation media cloak is not a panacea as there exists some objects that it cannot hide. In the limit that

*r*

_{0}is exactly zero, the situation requires further mathematical analysis due to the singularity properties of the anti-cloak and cloak (

*H*(

_{l}*k*

_{0}

*r*

_{0}) diverges when

*r*

_{0}goes to zero). From a physical standpoint, we may argue as follows. Near the inner boundary of the invisibility cloak,

*µ*goes to zero and

_{r}*µ*goes to infinity and they are positive, while near the outer boundary of the anti cloak,

_{θ}*µ*goes to zero and

_{r}*µ*goes to infinity from the negative side. The positive singular values have to come from an in-phase resonance while the negative infinity comes from out-of-phase resonance. If we put them in contact, the system response is canceled out, and the cloaking effect is weaken or even destroyed. The surface mode resonance at

_{θ}*r*=

*a*is excited and contributes to the large electric field. In addition, if the losses are considered, the electric field will become finite for

*r*

_{0}is exactly zero. The cylindrical anti-cloak concept could be extended to three dimensions.

21. J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter **15**, 6345–6364 (2003). [CrossRef]

## Acknowledgments

## References and links

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

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

3. | A. Greenleaf, M. Lassas, and G. Uhlmann, “On nonuniqueness for Calderon’s inverse problem,” Math. Res. Lett. |

4. | A. Greenleaf, M. Lassas, and G. Uhlmann, “Anisotropic conductivities that cannot be detected by EIT,” Physiol. Meas |

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

6. | Huanyang Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C.T. Chan, “Extending the bandwidth of electromagnetic cloaks,” Phys. Rev. B |

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

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

9. | 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 |

10. | Z. Liang, P. Yao, X. Sun, and X. Jiang, “The physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. |

11. | Z. Ruan, M. Yan, C.W. Neff, and M. Qiu, “Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations,” Phys. Rev. Lett. |

12. | H.S. Chen, B.-I. Wu, B. Zhang, and J.A. Kong, “Electromagnetic Wave Interactions with a Metamaterial Cloak,” Phys. Rev. Lett. |

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

14. | R.V. Kohn, H. Shen, M.S. Vogelius, and M.I. Weinstein, “Cloaking via change of variables in electric impedance tomography,” Inverse Probl. |

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

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

17. | N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express |

18. | A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E |

19. | 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 |

20. | We have run simulations with a finite-element code, and obtained the same results as in Fig. 3(c). |

21. | J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(230.0230) Optical devices : Optical devices

(260.2110) Physical optics : Electromagnetic optics

(260.2710) Physical optics : Inhomogeneous optical media

**ToC Category:**

Physical Optics

**History**

Original Manuscript: August 4, 2008

Revised Manuscript: August 6, 2008

Manuscript Accepted: August 6, 2008

Published: September 3, 2008

**Citation**

Huanyang Chen, Xudong Luo, Hongru Ma, and C.T. Chan, "The Anti-Cloak," Opt. Express **16**, 14603-14608 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-19-14603

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### References

- J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). [CrossRef] [PubMed]
- U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006). [CrossRef] [PubMed]
- A. Greenleaf, M. Lassas, and G. Uhlmann, "On nonuniqueness for Calderon??s inverse problem," Math. Res. Lett. 10, 685-693 (2003).
- A. Greenleaf, M. Lassas, and G. Uhlmann, "Anisotropic conductivities that cannot be detected by EIT," Physiol. Meas 24, 413-419 (2003). [CrossRef] [PubMed]
- W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007). [CrossRef]
- H. Chen, Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, "Extending the bandwidth of electromagnetic cloaks," Phys. Rev. B 76, 241104 (2007). [CrossRef]
- H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007). [CrossRef]
- D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006). [CrossRef] [PubMed]
- 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 74, 036621 (2006). [CrossRef]
- Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008). [CrossRef]
- Z. Ruan, M. Yan, C.W. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007). [CrossRef] [PubMed]
- H. S. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic Wave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007). [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, 111105 (2007). [CrossRef]
- R.V. Kohn, H. Shen, M. S. Vogelius, and M. I. Weinstein, "Cloaking via change of variables in electric impedance tomography," Inverse Probl. 24, 015016 (2008). [CrossRef]
- G. W. Milton and N.-A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. Roy. Soc. A 462, 3027-3059 (2006). [CrossRef]
- 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, 248-267 (2006). [CrossRef]
- N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance," Opt. Express 15, 6314-6323 (2007). [CrossRef] [PubMed]
- A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E 72, 016623 (2005). [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, 977-980 (2006). [CrossRef] [PubMed]
- We have run simulations with a finite-element code, and obtained the same results as in Fig. 3(c).
- J. B. Pendry and S. A. Ramakrishna, "Focusing light using negative refraction," J. Phys.: Condens. Matter 15, 6345-6364 (2003). [CrossRef]

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