Abstract

Many optical instruments with dielectric singularities cannot be manufactured directly. Their singularities can be transmuted through optical transformation, and equivalent physical media can be built to perform the same optical behaviors. The transformed physical media are usually anisotropic and inhomogeneous and, therefore, difficult to fabricate. In this work, several mathematical approaches are proposed to produce a transformed lens with all the elements of the material tensors to be no less than unity. This increases the ease of implementation, as natural materials may be used, which substantially widens the bandwidth of the transformed devices. Although we focus on an omnidirectional retroreflection lens as an example, the approaches developed here are universal and applicable to a wide class of devices with dielectric singularities.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
    [CrossRef]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef]
  4. 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]
  5. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  6. U. Leonhardt and T. G. Philbin, “General relativity in electric engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  7. 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]
  8. J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. 34, 644–646 (2009).
    [CrossRef]
  9. T. Tyc and U. Leonhardt, “Superantenna made of transformation media,” New J. Phys. 10, 115026 (2008).
    [CrossRef]
  10. 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]
  11. Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
    [CrossRef]
  12. P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
    [CrossRef]
  13. J. E. Eaton, “An extension of the Luneburg-type lenses,” Rept. No. 4110, Naval Research Lab, 1953.
  14. 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]
  15. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
    [CrossRef]
  16. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
    [CrossRef]
  17. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
    [CrossRef]
  18. H. Y. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
    [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]
  20. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef]
  21. 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]
  22. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef]
  23. L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
    [CrossRef]
  24. T. Tyc and U. Loenhardt, “Transmutation of singularities in optical instruments,” New J. Phys. 10, 115038 (2008).
    [CrossRef]
  25. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  26. C. W. Qiu, A. Novitsky, and L. Gao, “Inverse design mechanism of cylindrical cloaks without the knowledge of required coordinate transformation,” J. Opt. Soc. Am. A 27, 1079–1082 (2010).
    [CrossRef]
  27. R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  28. S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .
  29. Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
    [CrossRef]
  30. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
    [CrossRef]
  31. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
    [CrossRef]

2011 (1)

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

2010 (8)

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef]

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

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
[CrossRef]

C. W. Qiu, A. Novitsky, and L. Gao, “Inverse design mechanism of cylindrical cloaks without the knowledge of required coordinate transformation,” J. Opt. Soc. Am. A 27, 1079–1082 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef]

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

2009 (9)

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

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]

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]

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

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

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[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]

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

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
[CrossRef]

2008 (5)

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]

T. Tyc and U. Leonhardt, “Superantenna made of transformation media,” New J. Phys. 10, 115026 (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]

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

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

2006 (4)

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

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (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,” Science 314, 977–980(2006).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Bartal, G.

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

Brenner, P.

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

Cardenas, J.

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

Chan, C. T.

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

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]

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

Chen, H. S.

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

Chen, H. Y.

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

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

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]

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]

Cheng, X. X.

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

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, 366–369 (2009).
[CrossRef]

Cui, T. J.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (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, 366–369 (2009).
[CrossRef]

Cummer, S. A.

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]

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]

Eaton, J. E.

J. E. Eaton, “An extension of the Luneburg-type lenses,” Rept. No. 4110, Naval Research Lab, 1953.

Ergin, T.

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

Feng, Y. J.

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Gabrielli, L.

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

Gao, L.

Garcia-Vidal, F. J.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

Han, D. Z.

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]

Huidobro, P. A.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

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, 366–369 (2009).
[CrossRef]

Jiang, T.

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Justice, B. J.

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]

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
[CrossRef]

Lai, Y.

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]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[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]

T. Tyc and U. Leonhardt, “Superantenna made of transformation media,” New J. Phys. 10, 115026 (2008).
[CrossRef]

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

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

Li, J.

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

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

Lipson, M.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 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, 366–369 (2009).
[CrossRef]

Loenhardt, U.

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

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Luo, X. D.

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef]

Ma, H. R.

Ma, Y. G.

Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
[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]

Martin-Moreno, L.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

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, 366–369 (2009).
[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]

Moser, H. O.

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Nesterov, M. L.

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

Ng, J.

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]

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

Novitsky, A.

Ong, C. K.

Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
[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]

Pendry, J. B.

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

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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,” Science 314, 977–980(2006).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

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

Poitras, C.

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

Qiu, C. W.

Rahm, M.

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]

Roberts, D. A.

Schurig, D.

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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,” Science 314, 977–980(2006).
[CrossRef]

Sheng, P.

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

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
[CrossRef]

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]

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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,” Science 314, 977–980(2006).
[CrossRef]

Starr, A. F.

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]

Stenger, N.

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

Tyc, T.

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]

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

T. Tyc and U. Leonhardt, “Superantenna made of transformation media,” New J. Phys. 10, 115026 (2008).
[CrossRef]

Valentine, J.

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

Wang, N.

Wegener, M.

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

Xi, S.

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

Xiao, J. J.

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]

Xu, S.

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

Xu, X. F.

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Yang, T.

Yu, Z. Z.

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Zentgraf, T.

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

Zhang, X.

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

Zhang, Z. Q.

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]

Zhao, J. M.

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. D: Appl. Phys. (1)

Z. Z. Yu, Y. J. Feng, X. F. Xu, J. M. Zhao, and T. Jiang, “Optimized cylindrical invisibility cloak with minimum layers of non-magnetic isotropic materials,” J. Phys. D: Appl. Phys. 44, 185102 (2011).
[CrossRef]

Nano Lett. (1)

P. A. Huidobro, M. L. Nesterov, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10, 1985–1990 (2010).
[CrossRef]

Nat. Commun. (2)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef]

H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef]

Nat. Mater. (4)

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

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[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]

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

Nat. Photon. (1)

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

New J. Phys. (3)

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

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

T. Tyc and U. Leonhardt, “Superantenna made of transformation media,” New J. Phys. 10, 115026 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (4)

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]

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]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

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

Prog. Opt. (1)

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
[CrossRef]

Science (5)

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (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,” Science 314, 977–980(2006).
[CrossRef]

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]

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

Other (3)

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

S. Xu, X. X. Cheng, S. Xi, H. O. Moser, and H. S. Chen, “Low scattering broadband cylindrical invisibility cloak in free-space,” arXiv:1108.1204 .

J. E. Eaton, “An extension of the Luneburg-type lenses,” Rept. No. 4110, Naval Research Lab, 1953.

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 (8)

Fig. 1.
Fig. 1.

Index profiles for (a) the original Eaton lens and (b) the transformed lens ( n r r ) plotted as functions of the radial component.

Fig. 2.
Fig. 2.

Wave scattering patterns for (a) the original Eaton lens and (b) the transformed Eaton lens. The wavelength is 0.3 a . The left pictures are the snapshots of the electric field taken at zero phases, and the right ones are the biscattering curves obtained by collecting the far-field electromagnetic fields at different ϕ angles. In the field patterns, the incident wave beam is of a cosine distribution and illuminates the sample from the bottom left side and refracts back through the top channel. A perfectly matched layer (PML) is placed in the middle to divide these two channels.

Fig. 3.
Fig. 3.

Radial component of permeability μ r r ( R 0 ) at the transformation boundary for a selectively transformed Eaton lens (black) and the rescaled Eaton lens (red).

Fig. 4.
Fig. 4.

Wave scattering patterns for (a) a selectively transformed Eaton lens and (b) the rescaled Eaton lens at R 0 = 0.36 a .

Fig. 5.
Fig. 5.

Wave scattering patterns for a transformed Eaton lens with the index profiles (a) from Eq. (8) and (b) from Eq. (9) at A = 2 .

Fig. 6.
Fig. 6.

Wave scattering patterns for a transformed Eaton lens using Eq. (5) in (a) continuous and (b) five-layered index profiles.

Fig. 7.
Fig. 7.

Invisible lens. (a) Geometrical ray tracing for the original invisible lens and (b) material parameters for the rescaled transformed invisible lens.

Fig. 8.
Fig. 8.

Wave scattering patterns for (a) the original invisible lens, (b) the transformed lens, and (c) the rescaled lens. In the figures on the left, a Gaussian beam illuminates the samples from the top left side.

Equations (11)

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

ε i j = μ i j = g γ g i k 1 γ k j n ( R ) ,
ε i j = μ i j = diag ( n ( R ) R 2 n 0 r 2 , n 0 , n 0 ) , n 0 = n ( R ) d R d r
ε i j = μ i j = diag ( ( 1 α ) , 1 1 α , 1 1 α ) .
n ( R ) = 2 a R 1 for R < a and 1 for R a .
r ( R ) = 2 a n 0 [ arcsin R 2 a + R 2 a ( 1 R 2 a ) ] , n 0 = π 2 + 1
μ r r = n ( R ) R 2 n 0 r 2 , μ ϕ ϕ = n 0 , and ε θ θ = n 0 .
μ r r = ( R d r r d R ) 2 = 1 A 2 , μ ϕ ϕ = 1 , and ε θ θ = [ n ( R ) d R d r ] 2 .
μ r r = A 2 , μ ϕ ϕ = 1 , and ε θ θ = A 2 [ 2 ( r a ) A 2 ( r a ) 2 A 2 ] .
μ r r = 1 , μ ϕ ϕ = A 2 , and ε θ θ = 2 ( r a ) A 2 ( r a ) 2 A 2 with A 2 .
ε r r = [ n ( R ) R r ] 2 , ε ϕ ϕ = n 0 2 , and μ θ θ = 1 .
( a n R + a 2 n 2 R 2 1 ) 2 = n ,

Metrics