## Moving targets virtually via composite optical transformation

Optics Express, Vol. 18, Issue 5, pp. 5161-5167 (2010)

http://dx.doi.org/10.1364/OE.18.005161

Acrobat PDF (321 KB)

### Abstract

We propose a composite optical transformation to design an illusion device which can move the image of a target from one place to another place. Enclosed by such an illusion device, an arbitrary object located at one place appears to be at another place virtually. Different from the published shifted-position cloak which is composed of the left-handed materials with simultaneously negative permittivity and permeability, the illusion device proposed in this paper has positive permittivity and permeability. Hence the proposed illusion device is easier to be realized by artificial metamaterials.

© 2010 Optical Society of America

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

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

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,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

4. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. **101**, 203901 (2008). [CrossRef] [PubMed]

5. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science **323**, 366–369 (2009). [CrossRef] [PubMed]

6. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. **3**, 461–463 (2009). [CrossRef]

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

10. T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys. **10**, 115038 (2008). [CrossRef]

11. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. **8**, 639–642 (2009). [CrossRef] [PubMed]

12. W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. **93**, 221906 (2008). [CrossRef]

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

*et*al. have proposed an interesting idea of illusion optics, which makes a target with arbitrary shape and material property look like another object of some other shape and material makeup [19

19. 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**, 253902 (2009). [CrossRef] [PubMed]

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

16. T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express **16**, 18545–18550 (2008). [CrossRef] [PubMed]

21. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B **78**, 125113 (2008). [CrossRef]

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

16. T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express **16**, 18545–18550 (2008). [CrossRef] [PubMed]

21. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B **78**, 125113 (2008). [CrossRef]

*A*is enclosed with the illusion device, as shown in Fig. 1(a). Such an illusion device make any detector outside the virtual boundary (surface

*s*) observe the EM fields of a virtual car at Position

*B*(shown in Fig. 1(c)) instead of the actual one. In other words, the illusion device makes the EM-field distributions outside the virtual boundary in both the virtual and physical spaces exactly the same, regardless the direction from which the EM waves are incident. The composite coordinate transformation of the illusion device contains two sub-mappings. First, we map the first virtual space (the free space outside the car in the virtual space in Fig. 1(c)) into a smaller annulus region (the light green region in Fig. 1(b)). Second, we transform the second virtual space (light green region in Fig. 1(b)) into the physical space (dark green region in Fig. 1(a)). The electric permittivity and magnetic permeability tensors of the illusion device are calculated by

*ε*̄,

*μ*̄) and (

_{1}and ∧

_{2}are the Jacobian transformation matrices with components ∧

_{1ij}=

*∂x*′/

_{i}*∂x*and ∧

_{j}_{2ij}=

*∂x*″/

_{i}*∂x*′ corresponding to the mapping from the first virtual space to the second virtual space, and the mapping from the second virtual space to the physical space, respectively.

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

2. U. Leonhardt, “Optical conformal mapping,” Science **312**, 1777–1780 (2006). [CrossRef] [PubMed]

**E**″ = (∧

_{2}

^{T})

^{-1}(∧

_{1}

^{T})

^{-1}

**E**and

**H**″ = (∧

_{2}

^{T})

^{-1}(∧

_{1}

^{T})

^{-1}

**H**, where

**E**and

**H**are electric and magnetic fields in the first virtual space, respectively. Because the virtual boundary

*s*is mapped to itself during these two sub-mappings ∧

_{1}and ∧

_{2}, we have

**E**″

_{t}=

**E**′

_{t}=

**E**

_{t}and

**H**″

_{t}=

**H**′

_{t}=

**H**

_{t}, where the subscript

*t*indicates the transverse components along the surface

*s*. That is to say, the tangential components of the EM fields on the whole virtual boundary (

*s*) are exactly the same in both physical and virtual spaces. Hence the EM fields outside the illusion device are also exactly the same by using the uniqueness theorem. Any observers outside the illusion device will perceive the scattered fields as if they were scattered from a car at Position

*B*.

*a*

_{1}+

*a*

_{2}, 0), (0, 0) and (

*a*

_{1}, 0) are the centers of virtual and actual metallic cylinders and circular virtual region, respectively,

*x*″,

*y*″,

*z*″) and (

*x*,

*y*,

*z*) can be found from Eqs. (2)-(7) as follows,

*f*(

*x*,

*y*) to

*x*as

*f*. We have assumed that the background profile be free space, i.e.,

_{x}*ε*̄ =

*ε*

_{0}

*I*̄ and

*μ*̄ =

*μ*

_{0}

*I*̄.

*z*component of electric field, hence only

*μ″*,

_{xx}*μ″*,

_{xy}*μ″*and

_{yy}*ε″*are of interest and must satisfy the request of Eqs. (11)-(16). Therefore, the EM parameters in the eigen-basis can be expressed as

_{zz}*μ*

_{1},

*μ*

_{2}, and

*ε*are finite and positive. Also,

_{z}*μ*

_{2}is always greater than

*μ*

_{1}.

*a*

_{1}= 0.0333 m,

*a*

_{2}= 0.01667 m,

*r*

_{0}=

*r*

_{1}= 0.01 m,

*b*

_{1}=0.0433 m, and

*b*

_{2}= 0.05 m.

*μ*

_{1},

*μ*

_{2}and

*ε*are of interest. The distributions of principle components

_{z}*μ*

_{1},

*μ*

_{2}and

*ε*are illustrated in Figure 3, from which we clearly observe that all values are finite and positive. It is worth to note that these two sub-mappings in this illusion device are compressing and extending mappings, respectively, instead of the folding of geometry [17–21

_{z}17. Y. Lai, H. 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**, 093901 (2009). [CrossRef] [PubMed]

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,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

11. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. **8**, 639–642 (2009). [CrossRef] [PubMed]

*μ*

_{1}, we can make use of the split-ring resonators (SRR) [3

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,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

11. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. **8**, 639–642 (2009). [CrossRef] [PubMed]

22. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Micro. Theo. Tech. **47**, 2075 (2009). [CrossRef]

*ε*can be easily realized using the non-resonant structures such as wire or I shape [5

_{z}5. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science **323**, 366–369 (2009). [CrossRef] [PubMed]

## 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. | 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 |

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

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

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

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

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

9. | H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and Experimental Realization of a Broadband Transformation Media Field Rotator at Microwave Frequencies,” Phys. Rev. Lett. |

10. | T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” New J. Phys. |

11. | Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. |

12. | W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. |

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

14. | W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, “Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials,” Phys. Rev. E |

15. | M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. |

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

17. | Y. Lai, H. 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. |

18. | Y. Luo, J. J. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” (2009). ArXiv: 0904.1463. |

19. | 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. |

20. | U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” (2008). ArXiv: 0805.4778. |

21. | M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B |

22. | J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Micro. Theo. Tech. |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(260.2110) Physical optics : Electromagnetic optics

(160.3918) Materials : Metamaterials

(260.2710) Physical optics : Inhomogeneous optical media

**ToC Category:**

Physical Optics

**History**

Original Manuscript: December 11, 2009

Revised Manuscript: February 22, 2010

Manuscript Accepted: February 22, 2010

Published: February 25, 2010

**Citation**

Wei Xiang Jiang and Tie Jun Cui, "Moving targets virtually via composite optical transformation," Opt. Express **18**, 5161-5167 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5161

Sort: Year | Journal | Reset

### 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]
- 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]
- J. Li and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett. 101, 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, 366-369 (2009). [CrossRef] [PubMed]
- L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nat. Photonics 3, 461-463 (2009). [CrossRef]
- J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Mater. 8, 568-571 (2009). [CrossRef] [PubMed]
- H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007). [CrossRef]
- H. Chen, B. Hou, S. Chen, X. Ao,W. Wen, and C. T. Chan, "Design and Experimental Realization of a Broadband Transformation Media Field Rotator at Microwave Frequencies," Phys. Rev. Lett. 102, 183903 (2009). [CrossRef] [PubMed]
- T. Tyc and U. Leonhardt, "Transmutation of singularities in optical instruments," New J. Phys. 10, 115038 (2008). [CrossRef]
- Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, "An omnidirectional retroreflector based on the transmutation of dielectric singularities," Nat. Mater. 8, 639-642 (2009). [CrossRef] [PubMed]
- W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, "Layered high-gain lens antennas via discrete optical transformation," Appl. Phys. Lett. 93, 221906 (2008). [CrossRef]
- J. Ng, H. Y. Chen, and C. T. Chan, "Metamaterial frequency-selective superabsorber," Opt. Lett. 34, 644-646 (2009). [CrossRef] [PubMed]
- W. X. Jiang, T. J. Cui, X. Y. Zhou, X. M. Yang, and Q. Cheng, "Arbitrary bending of electromagnetic waves using realizable inhomogeneous and anisotropic materials," Phys. Rev. E 78, 066607 (2008). [CrossRef]
- M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008). [CrossRef] [PubMed]
- T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, "Superscatterer: enhancement of scattering with complementary media," Opt. Express 16, 18545-18550 (2008). [CrossRef] [PubMed]
- Y. Lai, H. 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, 093901 (2009). [CrossRef] [PubMed]
- Y. Luo, J. J. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect," (2009). ArXiv: 0904.1463.
- 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, 253902 (2009). [CrossRef] [PubMed]
- U. Leonhardt and T. G. Philbin, "Transformation optics and the geometry of light," (2008). ArXiv: 0805.4778.
- M. Yan, W. Yan, and M. Qiu, "Cylindrical superlens by a coordinate transformation," Phys. Rev. B 78, 125113 (2008). [CrossRef]
- J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Micro. Theo. Tech. 47, 2075 (2009). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.