OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11276–11281
« Show journal navigation

Virtual conversion from metal object to dielectric object using metamaterials

Wei Xiang Jiang, Hui Feng Ma, Qiang Cheng, and Tie Jun Cui  »View Author Affiliations


Optics Express, Vol. 18, Issue 11, pp. 11276-11281 (2010)
http://dx.doi.org/10.1364/OE.18.011276


View Full Text Article

Acrobat PDF (875 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose an illusion device which transforms a perfectly-electric-conducting (PEC) object into a virtual dielectric object with arbitrary material parameters. Such an illusion device has unconventional electromagnetic properties as verified by accurate numerical simulations. The presented illusion device is composed of inhomogeneous and anisotropic media with finite and positive permittivity and permeability components. Hence the designed device is possible to be realized using artificial metamaterials.

© 2010 Optical Society of America

An intuitive schematic diagram to show the proposed idea is illustrated in Fig. 1. A PEC sphere (the actual object) is enclosed by an metamaterial layer, the illusion medium layer. Such a layer of illusion medium makes any external detector perceive the scattering fields of a dielectric sphere (the virtual object) instead of the original PEC sphere. In another word, the illusion medium makes the field distribution outside the virtual boundary in both the physical and virtual spaces be exactly the same, regardless the direction of incident fields. Generally, the illusion medium has two functions, concealing the optical signature of the PEC sphere and generating the image of a dielectric sphere. After constructing a proper coordinate transformation Λ, the permittivity and permeability tensors of the illusion medium are calculated by

ε==Λε=ΛT/det(Λ),μ==Λμ=ΛT/det(Λ),
(1)

in which (ε̿, μ̿) and (ε̿, μ̿) are the constitutive tensors in the illusion space and the real space, respectively, and Λ is the Jacobian matrix with components Λij = ∂x i/∂xj, corresponding to the transformation from the illusion space to the material space. In the following discussions, we assume that the illusion objects are isotropic, i.e., ε̿ = εr I̿ and μ̿ = μr I̿. We remark that, in the design of invisibility cloaks, the virtual space is just the free space. Hence one usually selected εr = 1, μr = 1, and there were almost no scattered fields from a perfect cloak. For the illusion device, however, the virtual space may contain a lot of illusion objects as our choice. Thus the scattered fields are the same as those from the virtual objects.

Fig. 1. (color online) A simple scheme of an illusion medium layer that transforms q PEC sphere to a dielectric sphere. Left: The PEC sphere (the actual object) enclosed with the illusion medium layer in the physical space. Right: The dielectric sphere (the illusion) in the virtual space.

The cross section of an illusion medium which transforms a PEC sphere to a dielectric sphere virtually is shown in Fig. 2. The inner and outer radii of the illusion medium layer are r 1 and r 3, respectively. The radius of the dielectric sphere in the illusion space is r 0. We can construct a coordinate transformation in the spherical system as

r={k1r+r1,0rr0,k2(rr0)+r2,r0rr3,
(2)

in which k 1 = (r 2r 1)/r 0 and k 2 = (r 3r 2)/(r 3r 0). In order to demonstrate the function of the illusion device clearly, we divide the device into two layers. Based on the above transformation and Eq. (1), we can obtain the permittivity and permeability tensors as

ε==εrA,=μ==μrA,=
(3)

in which

A=={((rr1)2/k1r20001/k10001/k1)r1rr2,((rr2+k2r0)2/k2r20001/k20001/k2)r2rr3.

Equation (3) provide the full design parameters for the permittivity and permeability in the spherical illusion medium layers. Clearly, the illusion medium is composed of inhomogeneous and anisotropic metamaterials with finite and positive parameters. This kind of metamaterials have been extensively studied and fabricated in the microwave frequencies [2

2. 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]

,5

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]

,9

9. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129 (2010). [CrossRef]

,10

10. 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

22. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006). [CrossRef]

].

Fig. 2. (color online) The cross section of an illusion device which transforms a PEC sphere to a dielectric sphere virtually. (a) A PEC sphere with the illusion medium layer in the physical space. (b) A dielectric sphere in the illusion space.

Equation (3) is not only valid to the three-dimensional (3D) spherical illusion medium, but also valid to two-dimensional (2D) cylindrical illusion medium. For the sake of perspicuity, we focus our demonstration on 2D illusion devices, which are more feasible for realization. In order to validate the formula, Eq. (3), for the 2D case, we make full-wave simulations on a cylindrical illusion medium by using the finite element method (FEM). In the following simulations, we consider the case when a transverse-electric (TE) polarized plane wave is incident upon an illusion medium layer, in which there exists only z component of electric field. Then only μr, μϕ and εz are of interest and must satisfy the request of Eq. (3).

First, we consider an illusion medium layer which realizes the virtual conversion from a PEC cylinder to a dielectric cylinder. Figure 3 illustrates the numerical results of electric fields for the illusion device. The plane waves are incident horizontally from the left to the right at 2 GHz. In this example, we select r 1 = 0.4 m, r 2 = 0.6 m, r 3 = 0.8 m, and r 0 = 0.4 m. Figures 3(a) and 3(c) show the scattered patterns of a bare PEC cylinder without the illusion medium layer and a dielectric cylinder with εr = 3 and μr = 1, respectively. When enclosed by the illusion medium layer, the scattered pattern from the PEC cylinder will be changed as if there were a dielectric cylinder. This can be clearly observed by comparing the near-field pattern of the PEC cylinder coated by the illusion medium layer shown in Fig. 3(b) with that of the dielectric cylinder shown in Fig. 3(c). The near-field distributions are exactly the same outside the virtual boundary. Inside the virtual boundary, the field distributions in Figs. 3(b) and 3(c) are different.

In the above example, we have considered an illusion device which transforms a PEC cylinder to a dielectric cylinder. For the inner illusion medium layer shown in Fig. 3(b), εr = 3 and μr = 1, which generates the illusion of the dielectric cylinder; for the outer layer, εr = 1 and μr = 1, which generates the illusion of free space. Here we consider another illusion device which transforms a PEC cylinder to a dielectric hollow pipe. In such a case, we choose εr = 1 and μr = 1 in the inner layer and εr = 3 and μr = 1 in the outer layer. Figure 4(b) illustrates the electric-field distribution for such an illusion medium layer, which is very similar to that of the dielectric hollow pipe with εr = 3 and μr = 1, as shown in Fig. 4(a). In this case, the inner layer with εr = 1 and μr = 1 generates an illusion of free space inside the dielectric pipe; while the outer layer with εr = 3 and μr = 1 generates an illusion of the outer dielectric pipe. Hence the illusion medium layer renders the enclosed PEC cylinder invisible and projects the illusion of a dielectric hollow pipe as shown in Fig. 4(b).

Fig. 3. (color online) The electric-field distributions in the computational domain for (a) a PEC cylinder without the illusion medium layer; (b) a PEC cylinder with the illusion medium layer; and (c) a dielectric cylinder when the plane waves are incident horizontally from the left to the right.
Fig. 4. (color online) The electric-field distributions in the computational domain for (a) the dielectric hollow pipe; (b) the PEC cylinder with the illusion medium layer, when the plane waves are incident horizontally from the left to the right.

To calculate the permittivity and permeability of the illusion medium layers, we first consider a three-dimensional problem obtained by rotating the mirror-symmetric women model around the y-axis [24

24. P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93, 243502 (2008). [CrossRef]

]. Then we can obtain two-dimensional parameters by setting z = 0. Again, all medium parameters are finite and positive, and hence the illusion medium could be realized with the development of metamaterial technique for the complicated device. Figure 5 demonstrates the numerical simulation results of the scattered electric fields when the plane waves are incident horizontally from the left to the right at 2 GHz, in which Figs. 5(a) and 5(c) give the scattered-field distributions of the woman bronze and the dielectric woman in the computational domain, respectively, and Fig. 5(b) gives the scattered-field pattern of the woman bronze enclosed by the illusion medium layers. Comparing Figs. 5(b) and 5(c), we observe that the scattered-field patterns are completely identical outside the illusion medium layers. Thus, an observer outside the virtual boundary will see the metal woman as if a dielectric woman at the working frequency of the illusion medium.

Fig. 5. (color online) The electric-field distributions in the computational domain for (a) the bronze woman model without the illusion medium layers; (b) the bronze woman model with the illusion medium layers; and (c) a woman with material parameters εr = 3 and μr = 1, when the plane waves are incident in the horizontal direction from the left to the right.

In summary, we have presented a kind of new illusion media, which can transform a PEC object to a dielectric object by using artificial metamaterials. In such illusion devices, all principal values of the constitutive parameters are finite and positive. Hence the illusion device could be realizable using artificial structures.

Acknowledgments

This work was supported in part by the National Science Foundation of China under Grant Nos. 60990320, 60990324, 60871016, 60921063 and 60901011, in part by the National Key Preliminary Research Foundation for Weapons and Equipment, in part by the Natural Science Foundation of Jiangsu Province under Grant No. BK2008031, and in part by the 111 Project under Grant No. 111-2-05. WXJ acknowledges the support from the Graduate Innovation Program of Jiangsu Province under No. CX08B_074Z and the Scientific Research Foundation of Graduate School of Southeast University under No. YBJJ0816.

References and links

1.

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

2.

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]

3.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (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.

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]

7.

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]

8.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008). [CrossRef]

9.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129 (2010). [CrossRef]

10.

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]

11.

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]

12.

W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008). [CrossRef]

13.

W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009). [CrossRef]

14.

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]

15.

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,” Prog. Electro. Resea. - PIER 95, 167 (2009). [CrossRef]

16.

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

17.

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

18.

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

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]

20.

J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys.: Condens. Matter 148463–8479 (2002). [CrossRef]

21.

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 156345–6364 (2003). [CrossRef]

22.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006). [CrossRef]

23.

J. Pendry, “All smoke and metamaterials,” Nature 460, 579 (2009). [CrossRef]

24.

P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93, 243502 (2008). [CrossRef]

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: January 29, 2010
Revised Manuscript: April 28, 2010
Manuscript Accepted: May 11, 2010
Published: May 13, 2010

Citation
Wei Xiang Jiang, Hui Feng Ma, Qiang Cheng, and Tie Jun Cui, "Virtual conversion from metal object to dielectric object using metamaterials," Opt. Express 18, 11276-11281 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11276


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef] [PubMed]
  2. 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]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (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. 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]
  7. 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]
  8. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E 77, 066607 (2008). [CrossRef]
  9. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129 (2010). [CrossRef]
  10. 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]
  11. 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]
  12. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008). [CrossRef]
  13. W. Yan, M. Yan, and M. Qiu, “Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens,” Phys. Rev. B 79, 161101 (2009). [CrossRef]
  14. 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]
  15. 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,” Prog. Electro. Resea. - PIER 95, 167 (2009). [CrossRef]
  16. J. Ng, H. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. 34, 644–646 (2009). [CrossRef] [PubMed]
  17. T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” Opt. Express 16, 18545–18550 (2008). [CrossRef] [PubMed]
  18. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008). [CrossRef]
  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]
  20. J. B. Pendry and S. A. Ramakrishna, “Near-field lenses in two dimensions,” J. Phys.: Condens. Matter 148463–8479 (2002). [CrossRef]
  21. J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 156345–6364 (2003). [CrossRef]
  22. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006). [CrossRef]
  23. J. Pendry, “All smoke and metamaterials,” Nature 460, 579 (2009). [CrossRef]
  24. P. Zhang, Y. Jin, and S. He, “Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak,” Appl. Phys. Lett. 93, 243502 (2008). [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.

CrossCheck Deposited