Abstract

We demonstrate both the beam-forming and imaging capabilities of an X-band (8–12 GHz) operational Lüneburg lens, one side of which has been flattened via a coordinate transformation optimized using quasi-conformal transformation optics (QCTO) procedures. Our experimental investigation includes benchmark performance comparisons between the QCTO Lüneburg lens and a commensurate conventional Lüneburg lens. The QCTO Lüneburg lens is made from a metamaterial comprised of inexpensive plastic and fiberglass, and manufactured using fast and versatile numerically controlled water-jet machining. Looking forward towards the future and advanced TO designs, we discuss inevitable design trade-offs between affordable scalable manufacturing and rigorous adherence to the full TO solution, as well as possible paths to mitigate performance degradation in realizable designs.

© 2012 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. N. Kundtz and D. R. Smith, “Experimental and theoretical advances in the design of complex artificial electromagnetic media,” Ph.D. thesis (Duke University, 2009).
  3. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9, 129–132 (2010).
    [CrossRef]
  4. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
    [CrossRef] [PubMed]
  5. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17, 16535–16542 (2009).
    [CrossRef] [PubMed]
  6. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006).
    [CrossRef] [PubMed]
  7. D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express15, 14772–14782 (2007).
    [CrossRef] [PubMed]
  8. D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  9. T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
    [CrossRef]
  10. W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (2006).
    [CrossRef]
  11. 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,” Science314, 977–980 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  27. T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  29. N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
    [CrossRef]

2011

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

2010

N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
[CrossRef]

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

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

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

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

2009

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17, 16535–16542 (2009).
[CrossRef] [PubMed]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

2008

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

2007

2006

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
[CrossRef] [PubMed]

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

1999

A. Mojammad-Djafari, N. Qaddoumi, and R. Zoughi, “A blind deconvolution approach for resolution enhancement of near-field microwave images,” Proc. SPIE3816, 274–281 (1999).
[CrossRef]

1992

W. S. Jagger, “The optics of the spherical fish lens,” Vision Res.32, 1271–1284 (1992).
[CrossRef] [PubMed]

1958

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.29, 1358–1368 (1958).
[CrossRef]

1906

J. C. M. Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions. II,” Philos. Trans. R. Soc. London205, 237–288 (1906).
[CrossRef]

1854

J. C. Maxwell, “Solutions of problems,” Cambridge Dublin Math. J.8, 188–195 (1854).

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

Basov, D. N.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1977).

Chae, B. G.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Chapler, B.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

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] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

Cummer, S. A.

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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Di Ventra, M.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Driscoll, T.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

Garnett, J. C. M.

J. C. M. Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions. II,” Philos. Trans. R. Soc. London205, 237–288 (1906).
[CrossRef]

Gaultney, D.

N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
[CrossRef]

Goldflam, M. D.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

Hunt, J.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

Jagger, W. S.

W. S. Jagger, “The optics of the spherical fish lens,” Vision Res.32, 1271–1284 (1992).
[CrossRef] [PubMed]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

Jokerst, N. M.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Khatib, O.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

Kildishev, A. V.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Kim, B. J.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Kim, H. T.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Kundtz, N.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
[CrossRef]

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

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. Express17, 16535–16542 (2009).
[CrossRef] [PubMed]

N. Kundtz and D. R. Smith, “Experimental and theoretical advances in the design of complex artificial electromagnetic media,” Ph.D. thesis (Duke University, 2009).

Landy, N.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

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

Lee, Y. W.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

Luneburg, R.

R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

Ma, H. F.

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

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Maxwell, J. C.

J. C. Maxwell, “Solutions of problems,” Cambridge Dublin Math. J.8, 188–195 (1854).

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

Mojammad-Djafari, A.

A. Mojammad-Djafari, N. Qaddoumi, and R. Zoughi, “A blind deconvolution approach for resolution enhancement of near-field microwave images,” Proc. SPIE3816, 274–281 (1999).
[CrossRef]

Morgan, S. P.

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.29, 1358–1368 (1958).
[CrossRef]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

Nguyen, V.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

Padilla, W. J.

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (2006).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

Palit, S.

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express15, 14772–14782 (2007).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
[CrossRef] [PubMed]

Perram, T.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

Qaddoumi, N.

A. Mojammad-Djafari, N. Qaddoumi, and R. Zoughi, “A blind deconvolution approach for resolution enhancement of near-field microwave images,” Proc. SPIE3816, 274–281 (1999).
[CrossRef]

Roberts, D. A.

Rye, P.

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

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

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express15, 14772–14782 (2007).
[CrossRef] [PubMed]

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 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. Express14, 9794–9804 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Smith, D. R.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

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

N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
[CrossRef]

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

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17, 16535–16542 (2009).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express15, 14772–14782 (2007).
[CrossRef] [PubMed]

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (2006).
[CrossRef]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

N. Kundtz and D. R. Smith, “Experimental and theoretical advances in the design of complex artificial electromagnetic media,” Ph.D. thesis (Duke University, 2009).

Smith, S. R.

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Smolyaninov, I. I.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Smolyaninova, V. N.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Starr, A. F.

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1977).

Zentgraf, T.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

Zhang, X.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

Zoughi, R.

A. Mojammad-Djafari, N. Qaddoumi, and R. Zoughi, “A blind deconvolution approach for resolution enhancement of near-field microwave images,” Proc. SPIE3816, 274–281 (1999).
[CrossRef]

Appl. Phys. Lett.

T. Driscoll, D. N. Basov, A. F. Starr, P. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett.88, 081101 (2006).
[CrossRef]

M. D. Goldflam, T. Driscoll, B. Chapler, O. Khatib, N. M. Jokerst, S. Palit, D. R. Smith, H. T. Kim, M. Di Ventra, and D. N. Basov, “Reconfigurable gradient index using VO2 memory metamaterials,” Appl. Phys. Lett.99, 044103 (2011).
[CrossRef]

Cambridge Dublin Math. J.

J. C. Maxwell, “Solutions of problems,” Cambridge Dublin Math. J.8, 188–195 (1854).

J. Appl. Phys.

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.29, 1358–1368 (1958).
[CrossRef]

Mater. Today

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today9, 28–35 (2006).
[CrossRef]

Materials

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010).
[CrossRef]

Nano Lett.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010).
[CrossRef] [PubMed]

Nat. Commun.

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

Nat. Mater.

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

New J. Phys.

N. Kundtz, D. Gaultney, and D. R. Smith, “Scattering cross-section of a transformation optics-based metamaterial cloak,” New J. Phys.12, 043039 (2010).
[CrossRef]

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

Opt. Express

Philos. Trans. R. Soc. London

J. C. M. Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions. II,” Philos. Trans. R. Soc. London205, 237–288 (1906).
[CrossRef]

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65, 195104 (2002).
[CrossRef]

Phys. Rev. Lett.

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84, 4184–4187 (2000).
[CrossRef] [PubMed]

Proc. SPIE

A. Mojammad-Djafari, N. Qaddoumi, and R. Zoughi, “A blind deconvolution approach for resolution enhancement of near-field microwave images,” Proc. SPIE3816, 274–281 (1999).
[CrossRef]

Science

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,” Science314, 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 1780–1782 (2006).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323, 366–369 (2009).
[CrossRef] [PubMed]

T. Driscoll, H. T. Kim, B. G. Chae, B. J. Kim, Y. W. Lee, N. M. Jokerst, S. Palit, S. R. Smith, M. Di Ventra, and D. N. Basov, “Memory metamaterials,” Science325, 1518–1521 (2009).
[CrossRef] [PubMed]

Sensors

J. Hunt, N. Kundtz, N. Landy, V. Nguyen, T. Perram, A. F. Starr, and D. R. Smith, “Broadband wide angle lens implemented with dielectric metamaterials,” Sensors11, 7982–7991 (2011).
[CrossRef] [PubMed]

Vision Res.

W. S. Jagger, “The optics of the spherical fish lens,” Vision Res.32, 1271–1284 (1992).
[CrossRef] [PubMed]

Other

R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1977).

Rozendal Associates, http://www.rozendalassociates.com/

N. Kundtz and D. R. Smith, “Experimental and theoretical advances in the design of complex artificial electromagnetic media,” Ph.D. thesis (Duke University, 2009).

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Figures (5)

Fig. 1
Fig. 1

(a) Dielectric prescription for a QCTO Lüneburg lens flattened via QCTO to FOV π steradian, and with the isotropic and nonmagnetic assumptions mentioned in text. (b) Effective medium mapping for a metamaterial consisting of a cylindrical hole matrix of fixed spacing but variable diameter. The square and circular points show finite element solutions for TE and TM polarizations, respectively. (c) Photograph of completed lens, with representative slice showing HDPE ring and FR4 core.

Fig. 2
Fig. 2

Beamforming measurements for the QCTO Lüneburg lens. Electric-field amplitude as a function of the spherical angles ϕ and θ taken at 12GHz in the Far-field (160cm) for (a) A conventional spherical 9” Lüneburg lens [22]. (b) Our QCTO-Lüneburg lens with the source feed at the center of the flattened plane. Off-center source which directs beam in θ or ϕ for (c) source feed at X+15mm (d) Y-15mm (e) X+43mm (f) Y-43mm. Note the axes are zoomed in (a) to reveal the tight symmetrical beam of the conventional Lüneburg lens. To enable quantitative performance evaluation, the directivity of each is given. (g) illustrates the capability of broadband operation by showing directivity for the conventional Lüneburg lens and our TO Lüneburg lens (center feed) across the entire X-band.

Fig. 3
Fig. 3

XZ and YZ planar slices of the beam Re[(x,y,z)], displaying both phase and beam-amplitude information. As measured from the lens front, the scan Z-range is +60cm to +70cm along the optical axis.

Fig. 4
Fig. 4

Imaging performance of the QCTO Lüneburg lens revealed through the Point Spread Function. Collimated beams, using a horn-fed conventional Lüneburg lens, are incident from various azimuthal (θ) and elevation (ϕ) angles. (a) Raw data for normal incidence θ = 0°, ϕ = 0°. (b) Data for θ = 0°, ϕ = 0° after deconvolution of the detector’s transfer function. (c–f) Deconvolved data for off-normal-azimuth beams (TE polarization) for (c) θ = 12°, (d) θ = 29°. Deconvolved data for off-normal-elevation beams (TM polarization) for (e) ϕ = 12°, (f) ϕ = 29°. On each, the white circle shows the expected position and size of a perfect diffraction-limited focus.

Fig. 5
Fig. 5

2D Eikonal ray-tracing and directivity results for different Lüneburg lens designs (a) a A conventional spherical Lüneburg lens. (b) Isotropic dielectric-only QCTO design, without any material simplifications. (c) Our fabricated Lüneburg lens, which includes a minimum dielectric cutoff, and anisotropy.

Equations (1)

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ɛ r i j = 1 | A | A i i A j j ɛ r i j , μ r i j = 1 | A | A i i A j j μ r i j , A i i = x i x i .

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