Abstract

Luneburg lenses are able to form perfect focus that is free of aberration. Because of the varying refractive index throughout the lens, incoming electromagnetic waves can travel in a curved path and be guided to focus at the back of the lens. The implementation of Luneburg lenses is often difficult due to the challenges in creating a medium with varying refractive index using normal materials. This problem can be overcome with the use of gradient index metamaterials. We report a two dimensional Luneburg lens made of gradient index metamaterials. It consists of 17 concentric shells with etched patterns on a printed circuit board working in microwave X band frequency. The broad properties of the Luneburg lens are then discussed.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Schurig, “An aberration-free lens with zero F-number,” New J. Phys. 10, 115034 (2008).
    [CrossRef]
  2. U. Leonhardt and T. G. Philbin, Geometry and Light: the Science of Invisibility (Dover, 2010).
  3. 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]
  4. Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
    [CrossRef]
  5. Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (2009).
    [CrossRef]
  6. R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  7. S. P. Morgan, “General solution of the Luneburg lens problem,” J. Appl. Phys. 29, 1358–1367 (1958).
    [CrossRef]
  8. J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .
  9. C. H. Walter, “Surface-wave Luneberg lens antennas,” IEEE Trans. Antennas Propag. 8, 508–515 (1960).
    [CrossRef]
  10. Y. J. Park and W. Wiesbeck, “Angular independency of a parallel-plate Luneburg lens with hexagonal lattice and circular metal posts,” IEEE Antennas Wireless Propag. Lett 1, 128–130(2002).
    [CrossRef]
  11. L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microwave Opt. Technol. Lett. 50, 378–380 (2008).
    [CrossRef]
  12. P. Hall, S. Kutuzov, and R. Dagkesamanskii, “A prototype Luneburg lens antenna,” http://www.atnf.csiro.au/projects/askap/techdocs/prototype_luneburg.pdf .
  13. Meta Group, Duke University, “Electromagnetic metamaterials,” http://people.ee.duke.edu/~drsmith/about_metamaterials.html .
  14. D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23, 391–403 (2006).
    [CrossRef]
  15. N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
    [CrossRef]
  16. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
    [CrossRef]
  17. A. Demetriadou and H. Yang, “Slim Luneburg lens for antenna applications,” Opt. Express 19, 19925–19934 (2011).
    [CrossRef]
  18. L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
    [CrossRef]
  19. N. Kundtz, “Advances in complex artificial electromagnetic media,” Ph.D. thesis (Duke University, Department of Physics, 2009).
  20. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  21. H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
    [CrossRef]

2011 (2)

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

A. Demetriadou and H. Yang, “Slim Luneburg lens for antenna applications,” Opt. Express 19, 19925–19934 (2011).
[CrossRef]

2010 (3)

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

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

2009 (2)

Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (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]

2008 (3)

D. Schurig, “An aberration-free lens with zero F-number,” New J. Phys. 10, 115034 (2008).
[CrossRef]

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microwave Opt. Technol. Lett. 50, 378–380 (2008).
[CrossRef]

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
[CrossRef]

2006 (1)

2002 (2)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Y. J. Park and W. Wiesbeck, “Angular independency of a parallel-plate Luneburg lens with hexagonal lattice and circular metal posts,” IEEE Antennas Wireless Propag. Lett 1, 128–130(2002).
[CrossRef]

2000 (1)

J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .

1960 (1)

C. H. Walter, “Surface-wave Luneberg lens antennas,” IEEE Trans. Antennas Propag. 8, 508–515 (1960).
[CrossRef]

1958 (1)

S. P. Morgan, “General solution of the Luneburg lens problem,” J. Appl. Phys. 29, 1358–1367 (1958).
[CrossRef]

Chen, Q.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

Chen, X.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
[CrossRef]

Cheng, Q.

Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (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, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Demetriadou, A.

Fusco, V. F.

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microwave Opt. Technol. Lett. 50, 378–380 (2008).
[CrossRef]

Graeme, J.

J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .

Kot, J.

J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .

Kundtz, N.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

N. Kundtz, “Advances in complex artificial electromagnetic media,” Ph.D. thesis (Duke University, Department of Physics, 2009).

Landy, N. I.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Leonhardt, U.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[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]

U. Leonhardt and T. G. Philbin, Geometry and Light: the Science of Invisibility (Dover, 2010).

Luneburg, R. K.

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

Ma, H. F.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

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

Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Ma, Y. G.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[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]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Morgan, S. P.

S. P. Morgan, “General solution of the Luneburg lens problem,” J. Appl. Phys. 29, 1358–1367 (1958).
[CrossRef]

Ong, C. K.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[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]

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
[CrossRef]

Parfitt, A.

J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .

Park, Y. J.

Y. J. Park and W. Wiesbeck, “Angular independency of a parallel-plate Luneburg lens with hexagonal lattice and circular metal posts,” IEEE Antennas Wireless Propag. Lett 1, 128–130(2002).
[CrossRef]

Pendry, J. B.

Philbin, T. G.

U. Leonhardt and T. G. Philbin, Geometry and Light: the Science of Invisibility (Dover, 2010).

Sahebdivan, S.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Schurig, D.

D. Schurig, “An aberration-free lens with zero F-number,” New J. Phys. 10, 115034 (2008).
[CrossRef]

Smith, D. R.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23, 391–403 (2006).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Tyc, T.

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[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]

Walter, C. H.

C. H. Walter, “Surface-wave Luneberg lens antennas,” IEEE Trans. Antennas Propag. 8, 508–515 (1960).
[CrossRef]

Wiesbeck, W.

Y. J. Park and W. Wiesbeck, “Angular independency of a parallel-plate Luneburg lens with hexagonal lattice and circular metal posts,” IEEE Antennas Wireless Propag. Lett 1, 128–130(2002).
[CrossRef]

Xu, H. S.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

Xue, L.

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microwave Opt. Technol. Lett. 50, 378–380 (2008).
[CrossRef]

Yang, H.

Yang, X. M.

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

Zhao, L.

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

Q. Cheng, H. F. Ma, and T. J. Cui, “Broadband planar Luneburg lens based on complementary materials,” Appl. Phys. Lett. 95, 181901 (2009).
[CrossRef]

Chin. Sci. Bull. (1)

H. F. Ma, X. Chen, X. M. Yang, H. S. Xu, Q. Chen, and T. J. Cui, “A broadband metamaterial cylindrical lens antenna,” Chin. Sci. Bull. 55, 2066–2070 (2010).
[CrossRef]

IEEE Antennas Wireless Propag. Lett (1)

Y. J. Park and W. Wiesbeck, “Angular independency of a parallel-plate Luneburg lens with hexagonal lattice and circular metal posts,” IEEE Antennas Wireless Propag. Lett 1, 128–130(2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

C. H. Walter, “Surface-wave Luneberg lens antennas,” IEEE Trans. Antennas Propag. 8, 508–515 (1960).
[CrossRef]

J. Appl. Phys. (1)

S. P. Morgan, “General solution of the Luneburg lens problem,” J. Appl. Phys. 29, 1358–1367 (1958).
[CrossRef]

J. Opt. Soc. Am. B (1)

Microwave Opt. Technol. Lett. (1)

L. Xue and V. F. Fusco, “Printed holey plate Luneburg lens,” Microwave Opt. Technol. Lett. 50, 378–380 (2008).
[CrossRef]

Nat. Commun. (1)

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

Nat. Mater. (1)

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]

New J. Phys. (2)

Y. G. Ma, S. Sahebdivan, C. K. Ong, T. Tyc, and U. Leonhardt, “Evidence for subwavelength imaging with positive refraction,” New J. Phys. 13, 033016 (2011).
[CrossRef]

D. Schurig, “An aberration-free lens with zero F-number,” New J. Phys. 10, 115034 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of permittivity and permeability of metamaterials from scattering data,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformation,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Radio Sci. Bull. (1)

J. Graeme, A. Parfitt, and J. Kot, “A case for the Luneburg lens as the antenna element for the Square Kilometre Array radio telescope,” Radio Sci. Bull. 293, 32–38 (2000); also found at http://www.atnf.csiro.au/projects/askap/techdocs/SKA_Luneburg_Paper_6%28James%29.pdf .

Rev. Sci. Instrum. (1)

L. Zhao, X. Chen, and C. K. Ong, “Visual observation and quantitative measurement of the microwave absorbing effect at X band,” Rev. Sci. Instrum. 79, 124701 (2008).
[CrossRef]

Other (5)

N. Kundtz, “Advances in complex artificial electromagnetic media,” Ph.D. thesis (Duke University, Department of Physics, 2009).

P. Hall, S. Kutuzov, and R. Dagkesamanskii, “A prototype Luneburg lens antenna,” http://www.atnf.csiro.au/projects/askap/techdocs/prototype_luneburg.pdf .

Meta Group, Duke University, “Electromagnetic metamaterials,” http://people.ee.duke.edu/~drsmith/about_metamaterials.html .

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

U. Leonhardt and T. G. Philbin, Geometry and Light: the Science of Invisibility (Dover, 2010).

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 (6)

Fig. 1.
Fig. 1.

Ray tracing of a plane wave entering a Luneburg lens. The incoming plane wave is focused at the back of the lens.

Fig. 2.
Fig. 2.

Implemented device. (a) First 11 inner shells of device: I-shaped copper with different dimensions patterned on a dielectric substrate. (b) In the completed device, the outer 5 shells have square-shaped copper patterned on the substrate. The actual device consist of only 16 shells, as the last shell is air to ensure impedance match.

Fig. 3.
Fig. 3.

Normal component of the electric field measured for a point source placed on one end of the device obtained (a) experimentally and (b) from simulations at 10 GHz. The position of the device is represented by the circle drawn. The intense blue point on one end of device shows where the point source is placed, and plane waves are generated at the other end of device.

Fig. 4.
Fig. 4.

Image plots for normal components of an electric field for six frequencies for a point source producing plane waves: (a) 8 GHz, (b) 9 GHz, (c) 10 GHz, (d) 11 GHz, (e) 12 GHz, (f) 13 GHz.

Fig. 5.
Fig. 5.

Image plot of the normal component of an electric field of a plane wave approaching the device obtained from (a) the experiment and (b) the simulation at 10 GHz. The red and blue region represents the region with the greatest amplitude. The intense, small point at the other end of the device demonstrates that the incoming plane wave is focused at the opposite end of device.

Fig. 6.
Fig. 6.

Image plots for normal components of an electric field for six frequencies for a plane wave focused at the back of the device: (a) 8 GHz, (b) 9 GHz, (c) 10 GHz, (d) 11 GHz, (e) 12 GHz, (f) 13 GHz.

Metrics