Abstract

Grating cloaks are a variation of dielectric carpet (or ground-plane) cloaks. The latter were introduced by Li and Pendry. In contrast to the numerical work involved in the quasi-conformal carpet cloak, the refractive-index profile of a conformal grating cloak follows a closed and exact analytical form. We have previously mentioned that finite-size conformal grating cloaks may exhibit better cloaking than usual finite-size carpet cloaks. In this paper, we directly visualize their performance using photorealistic ray-tracing simulations. We employ a Newtonian approach that is advantageous compared to conventional ray tracing based on Snell’s law. Furthermore, we quantify the achieved cloaking quality by computing the cross-correlations of rendered images. The cross-correlations for the grating cloak are much closer to 100% (i.e., ideal) than those for the Gaussian carpet cloak.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
    [CrossRef] [PubMed]
  4. H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
    [CrossRef] [PubMed]
  5. M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63(10), 32–36 (2010).
    [CrossRef]
  6. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. 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]
  10. J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
    [CrossRef] [PubMed]
  11. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
    [CrossRef] [PubMed]
  12. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 1–6 (2010).
    [CrossRef]
  13. B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
    [CrossRef] [PubMed]
  14. J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
    [CrossRef] [PubMed]
  15. R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18(23), 24361–24367 (2010).
    [CrossRef] [PubMed]
  16. A. S. Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).
  17. G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express 14(5), 1842–1849 (2006).
    [CrossRef] [PubMed]
  18. A. J. Danner, “Visualizing invisibility: metamaterials-based optical devices in natural environments,” Opt. Express 18(4), 3332–3337 (2010).
    [CrossRef] [PubMed]
  19. T. Ergin, J. C. Halimeh, N. Stenger, and M. Wegener, “Optical microscopy of 3D carpet cloaks:ray-tracing calculations,” Opt. Express 18(19), 20535–20545 (2010).
    [CrossRef] [PubMed]
  20. J. L. Synge, Geometrical Mechanics and De Broglie Waves (Cambridge U. Press, 1954).
  21. M. Born, and E. Wolf, Principles of Optics (Pergamon, 1970).
  22. J. S. Desjardins, “Time-dependent geometrical optics,” J. Opt. Soc. Am. 66(10), 1042–1047 (1976).
    [CrossRef]
  23. J. Molcho and D. Censor, “A simple derivation and an example of Hamiltonian ray propagation,” Am. J. Phys. 54(4), 351–353 (1986).
    [CrossRef]
  24. P. S. J. Russell and T. A. Birks, “Hamiltonian optics of nonuniform photonic crystals,” J. Lightwave Technol. 17(11), 1982–1988 (1999).
    [CrossRef]
  25. C. Bellver-Cebreros and M. Rodriguez-Danta, “Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays,” Am. J. Phys. 69(3), 360–367 (2001).
    [CrossRef]
  26. Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
    [CrossRef] [PubMed]
  27. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
    [CrossRef] [PubMed]
  28. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
    [CrossRef]
  29. K. Niu, C. Song, and M.-L. Ge, “The geodesic form of light-ray trace in the inhomogeneous media,” Opt. Express 17(14), 11753–11767 (2009).
    [CrossRef] [PubMed]
  30. M. James, Pattern Recognition (John Wiley & Sons, 1988).
    [PubMed]
  31. J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
    [CrossRef]

2010 (8)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63(10), 32–36 (2010).
[CrossRef]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 1–6 (2010).
[CrossRef]

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
[CrossRef] [PubMed]

A. J. Danner, “Visualizing invisibility: metamaterials-based optical devices in natural environments,” Opt. Express 18(4), 3332–3337 (2010).
[CrossRef] [PubMed]

T. Ergin, J. C. Halimeh, N. Stenger, and M. Wegener, “Optical microscopy of 3D carpet cloaks:ray-tracing calculations,” Opt. Express 18(19), 20535–20545 (2010).
[CrossRef] [PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18(23), 24361–24367 (2010).
[CrossRef] [PubMed]

2009 (7)

K. Niu, C. Song, and M.-L. Ge, “The geodesic form of light-ray trace in the inhomogeneous media,” Opt. Express 17(14), 11753–11767 (2009).
[CrossRef] [PubMed]

J. H. Lee, J. Blair, V. A. Tamma, Q. Wu, S. J. Rhee, C. J. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express 17(22), 19328–19336 (2009).
[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]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

2008 (2)

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[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]

2006 (4)

2004 (1)

Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
[CrossRef] [PubMed]

2001 (1)

C. Bellver-Cebreros and M. Rodriguez-Danta, “Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays,” Am. J. Phys. 69(3), 360–367 (2001).
[CrossRef]

1999 (1)

1988 (1)

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[CrossRef]

1986 (1)

J. Molcho and D. Censor, “A simple derivation and an example of Hamiltonian ray propagation,” Am. J. Phys. 54(4), 351–353 (1986).
[CrossRef]

1976 (1)

Bartal, G.

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]

Bellver-Cebreros, C.

C. Bellver-Cebreros and M. Rodriguez-Danta, “Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays,” Am. J. Phys. 69(3), 360–367 (2001).
[CrossRef]

Birks, T. A.

Blair, J.

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[CrossRef] [PubMed]

Cardenas, J.

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]

Censor, D.

J. Molcho and D. Censor, “A simple derivation and an example of Hamiltonian ray propagation,” Am. J. Phys. 54(4), 351–353 (1986).
[CrossRef]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Chan, T.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
[CrossRef] [PubMed]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Chin, J. Y.

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]

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 1–6 (2010).
[CrossRef]

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]

Danner, A. J.

Desjardins, J. S.

Dolling, G.

Ergin, T.

Fan, S.

Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
[CrossRef] [PubMed]

Gabrielli, L. H.

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]

Ge, M.-L.

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Halimeh, J. C.

Hormann, C.

Ji, C.

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]

Jiao, Y.

Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
[CrossRef] [PubMed]

Lee, J. H.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

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]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Linden, S.

Lipson, M.

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]

Liu, R.

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]

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 1–6 (2010).
[CrossRef]

Miller, D. A. B.

Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
[CrossRef] [PubMed]

Mock, J. J.

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]

Molcho, J.

J. Molcho and D. Censor, “A simple derivation and an example of Hamiltonian ray propagation,” Am. J. Phys. 54(4), 351–353 (1986).
[CrossRef]

Mueller, J.

Nicewander, W. A.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[CrossRef]

Niu, K.

Park, W.

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[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]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Poitras, C. B.

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]

Rhee, S. J.

Rodgers, J. L.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[CrossRef]

Rodriguez-Danta, M.

C. Bellver-Cebreros and M. Rodriguez-Danta, “Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays,” Am. J. Phys. 69(3), 360–367 (2001).
[CrossRef]

Russell, P. S. J.

Schmied, R.

Schurig, D.

Shalaev, V. M.

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[CrossRef] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[CrossRef] [PubMed]

Smith, D. R.

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. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Song, C.

Stenger, N.

Summers, C. J.

Tamma, V. A.

Valentine, J.

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]

Wegener, M.

Wu, B.-I.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
[CrossRef] [PubMed]

Wu, Q.

Zentgraf, T.

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]

Zhang, B.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
[CrossRef] [PubMed]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

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]

Am. J. Phys. (2)

J. Molcho and D. Censor, “A simple derivation and an example of Hamiltonian ray propagation,” Am. J. Phys. 54(4), 351–353 (1986).
[CrossRef]

C. Bellver-Cebreros and M. Rodriguez-Danta, “Eikonal equation from continuum mechanics and analogy between equilibrium of a string and geometrical light rays,” Am. J. Phys. 69(3), 360–367 (2001).
[CrossRef]

Am. Stat. (1)

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1(3), 1–6 (2010).
[CrossRef]

Nat. Mater. (2)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[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]

Nat. Photonics (1)

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]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[CrossRef]

Opt. Express (8)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Y. Jiao, S. Fan, and D. A. B. Miller, “Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036612 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010).
[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]

Phys. Today (1)

M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63(10), 32–36 (2010).
[CrossRef]

Science (5)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

V. M. Shalaev, “Physics. Transforming light,” Science 322(5900), 384–386 (2008).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[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]

Other (4)

J. L. Synge, Geometrical Mechanics and De Broglie Waves (Cambridge U. Press, 1954).

M. Born, and E. Wolf, Principles of Optics (Pergamon, 1970).

A. S. Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).

M. James, Pattern Recognition (John Wiley & Sons, 1988).
[PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) False-color representation of the normalized refractive-index profile n/n min of the conformal grating cloak in the xy-plane according to Eq. (1). The normalized grating-cloak parameters are Λ = 1 and A = 3/(16π)≈0.06 (leading to n min = 0.727). The normalized height of the cloak is equal to 1.1. In Figs. 3-7, one normalized unit corresponds to 19 cm. (b) Same, but for the Gaussian conformal map with w = 0.306 and h = 0.13 (leading to n min = 0.873). The normalized height of the cloak is 1.1. Note that these parameters have been chosen such that n/n min in (a) and (b) varies in the same interval [1.0, 2.2]. This aspect allows for comparing the two setups in a meaningful manner.

Fig. 3
Fig. 3

Color images rendered by the Newtonian ray-tracing approach. The corresponding scenery is illustrated in Fig. 2. (a) Flat mirror. (b) Grating profile with Λ = 1 (or 18.9 cm) and A = 3/(16π) ≈0.06 (or 1.1 cm), without cloak. (c) As (b), but with cloak. The cloak height is 1.1 normalized units (or 20.8 cm). Its refractive-index profile is depicted in Fig. 1(a). Note that this profile contains index values below unity with minimum n min = 0.728.

Fig. 7
Fig. 7

As Fig. 6, but for a yet smaller height of the grating-cloak structure of 0.41 normalized units (or 7.8 cm).

Fig. 2
Fig. 2

Illustration of the scenery used for all photorealistic images rendered in this work. (a) This color image actually serves as the input for the following Newtonian ray-tracing calculations. (b) In these calculations, the model looks at the mirror in front of her (compare Fig. 1(a)) and observes the images shown in Figs. 3-7. The mirror (gray) is located at a distance of d = 0.5 m from the model, the cloak is shown in green.

Fig. 4
Fig. 4

As Fig. 3, but for the Gaussian conformal map with w = 0.306 and h = 0.13. The corresponding refractive-index profile is depicted in Fig. 1(b). Note that this profile contains index values below unity with minimum n min = 0.873.

Fig. 5
Fig. 5

As Fig. 3, but the refractive-index profile of the grating cloak is divided by n min (see Fig. 1(a)) such that the minimum refractive index in the cloaking profile becomes n = 1. In (a) and (b), we have added a homogeneous dielectric plate with index n = 1/n min = 1.37 and with the same height as that of the cloak (see Fig. 1(a)), i.e., 1.1 normalized units (or 20.8 cm). The cloak height is successively reduced in Figs. 6 and 7.

Fig. 6
Fig. 6

As Fig. 5, but for a smaller height of the grating-cloak structure of 0.55 normalized units (or 10.4 cm).

Tables (1)

Tables Icon

Table 1 Cross-Correlation Coefficients C: = C(0,0) According to Eq. (15) for Different Combinations of Images, f and g, As Indicated in the Two Left-Hand Side Columns for Different Horizontal Field of Views (FOV)

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

n ( x , y , z ) = 1 | 1 + W 0 ( i c k e i k ( x + i y ) ) | .
x ( ξ ) = ξ A sin ( k ξ ) y ( ξ ) = A cos ( k ξ ) ,
x ( y ) = ± ( Λ 2 π arccos ( y A ) A 2 y 2 ) + N Λ ,
y ( x ) A cos ( k x ) .
y ( x ) h e ( x / w ) 2 ,
δ t 1 t 2 L ( r , v , t ) d t = 0.
L r i d d t L v i = 0.
d v d t = d 2 r d t 2 = F m .
δ t 1 t 2 n ( r ) | v | d t = 0.
| v | n d d t ( n v | v | ) = 0 ,
d v d t = d 2 r d t 2 = | v | 2 n 2 ( n v ) v n .
n = ( ( 2 Re ( 1 + W 0 ) Im ( W 0 ) | 1 + W 0 | 2 Im ( W 0 ) ) × k | 1 + W 0 | 3 ( Im 2 ( W 0 ) Re 2 ( 1 + W 0 ) | 1 + W 0 | 2 + Re ( 1 + W 0 ) ) × k | 1 + W 0 | 3 0 ) ,
W 0 = W 0 ( i c k e i k ( x + i y ) ) .
f ( x , y ) f ( x , y ) f g ( x , y ) g ( x , y ) g .
C ( Δ x , Δ y ) : = f ( x , y ) g ( x + Δ x , y + Δ y ) d x d y f 2 ( x , y ) d x d y .

Metrics