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

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]
12. V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Broadband transformation optics devices,” Materials3, 4793–4810 (2010). [CrossRef]
13. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10, 1991–1997 (2010). [CrossRef] [PubMed]
14. J. C. Maxwell, “Solutions of problems,” Cambridge Dublin Math. J.8, 188–195 (1854).
15. R. Luneburg, Mathematical Theory of Optics (Brown University, 1944).
16. W. S. Jagger, “The optics of the spherical fish lens,” Vision Res.32, 1271–1284 (1992). [CrossRef] [PubMed]
17. D. Schurig, “An aberration-free lens with zero F-number,” New J. Phys.10, 115034 (2008). [CrossRef]
18. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun.1, 124 (2010). [CrossRef] [PubMed]
19. 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]
20. 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]
21. 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]
22. Rozendal Associates, http://www.rozendalassociates.com/
23. 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]
24. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1977).
25. 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]
26. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys.29, 1358–1368 (1958). [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]
28. 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]
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]

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.

• 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

• 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, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14, 9794–9804 (2006). [CrossRef] [PubMed]
• D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express15, 14772–14782 (2007). [CrossRef] [PubMed]

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

• 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]
• 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]
• J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312, 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,” Science314, 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,” 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).
• 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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