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,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
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  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,” Science 323, 366–369 (2009).
    [CrossRef] [PubMed]
  5. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 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. Express 14, 9794–9804 (2006).
    [CrossRef] [PubMed]
  7. D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 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]
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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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [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,” Sensors 11, 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,” Materials 3, 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,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 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,” Science 325, 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. Today 9, 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,” Science 314, 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. Express 14, 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 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. B 65, 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. SPIE 3816, 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. London 205, 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,” Science 325, 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]

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today 9, 28–35 (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,” Science 325, 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,” Science 323, 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,” Science 323, 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,” Science 314, 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,” Science 325, 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,” Science 325, 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. London 205, 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,” Sensors 11, 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,” Science 323, 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,” Science 325, 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,” Science 314, 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,” Materials 3, 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,” Science 325, 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,” Science 325, 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,” Sensors 11, 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]

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]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 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,” Sensors 11, 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,” Science 325, 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,” Science 323, 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. B 65, 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,” Science 323, 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,” Science 314, 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. SPIE 3816, 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,” Sensors 11, 7982–7991 (2011).
[CrossRef] [PubMed]

Padilla, W. J.

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today 9, 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,” Science 325, 1518–1521 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772–14782 (2007).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 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, 9794–9804 (2006).
[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,” Science 314, 977–980 (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,” Sensors 11, 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. SPIE 3816, 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. B 65, 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. Express 15, 14772–14782 (2007).
[CrossRef] [PubMed]

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

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

Shalaev, V. M.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials 3, 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,” Sensors 11, 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, 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]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

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

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 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]

W. J. Padilla, D. N. Basov, and D. R. Smith, “Negative refractive index metamaterials,” Mater. Today 9, 28–35 (2006).
[CrossRef]

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

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[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,” Science 314, 977–980 (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. B 65, 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,” Science 325, 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,” Materials 3, 4793–4810 (2010).
[CrossRef]

Smolyaninova, V. N.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials 3, 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. B 65, 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,” Sensors 11, 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,” Science 314, 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. SPIE 3816, 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. Today 9, 28–35 (2006).
[CrossRef]

Materials

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials 3, 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.

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

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. London 205, 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. B 65, 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. SPIE 3816, 274–281 (1999).
[CrossRef]

Science

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,” Science 325, 1518–1521 (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, 366–369 (2009).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[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,” Science 314, 977–980 (2006).
[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,” Sensors 11, 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).

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

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

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

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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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