Abstract

Utilizing non-resonant metamaterial elements, we demonstrate that complex gradient index optics can be constructed exhibiting low material losses and large frequency bandwidth. Although the range of structures is limited to those having only electric response, with an electric permittivity always equal to or greater than unity, there are still numerous metamaterial design possibilities enabled by leveraging the non-resonant elements. For example, a gradient, impedance matching layer can be added that drastically reduces the return loss of the optical elements due to reflection. In microwave experiments, we demonstrate the broadband design concepts with a gradient index lens and a beam-steering element, both of which are confirmed to operate over the entire X-band (roughly 8-12 GHz) frequency spectrum.

© 2009 OSA

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  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  3. W. E. Kock, “Metallic delay lenses,” Bell Syst. Tech. J. 27, 58 (1948).
  4. R. W. Corkum, “isotropic artificial dielectric,” Proceedings of the IRE 40(5), 574–587 (1952).
    [CrossRef]
  5. J. Brown, and W. Jackson, “The Properties of Artificial Dielectrics at Centimetre Wavelengths,” Proc. IEE paper no.1699R vol. 102B pp. 11–21, January 1995.
  6. I. Bahl and K. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974).
    [CrossRef]
  7. Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).
  8. I. Awai, H. Kubo, T. Iribe, D. Wakamiya, and A. Sanada, “An artificial dielectric material of huge permittivity with novel anisotropy and its application to a microwave BPF,” in Microwave Symposium Digest, 2003 IEEE MTT-S International 2 1085–1088 (2003).
  9. I. Awai, S. Kida, and O. Mizue, “Very Thin and Flat Lens Antenna Made of Artificial Dielectrics,” in 2007 Korea-Japan Microwave Conference 177–180 (2007).
  10. I. Awai, “Artificial Dielectric Resonators for Miniaturized Filters,” IEEE Microw. Mag. 9(5), 55–64 (2008).
    [CrossRef]
  11. Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
    [CrossRef]
  12. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  13. J. B. Pendry and S. A. Ramakrishna, “Focusing light with negative refractive index,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
    [CrossRef]
  14. S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett. 30(10), 1204–1206 (2005).
    [CrossRef] [PubMed]
  15. 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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  16. R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
    [CrossRef] [PubMed]
  20. M. J. Minot, “Single-layer, gradient refractive index antireflection films effective from 0.35 µm to 2.5 µm,” J. Opt. Soc. Am. 66(6), 515–519 (1976).
    [CrossRef]
  21. R. Jacobson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Haas, M. Francombe, and R. Hoffman, eds. (Academic, New York, 1975), Vol. 8, p. 51.
  22. C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (1982).
  23. B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006).
    [CrossRef] [PubMed]
  24. J. Li and J. B. Pendry, “Hiding under the Carpet: a New Strategy for Cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  25. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [CrossRef] [PubMed]

2009 (1)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

2008 (3)

I. Awai, “Artificial Dielectric Resonators for Miniaturized Filters,” IEEE Microw. Mag. 9(5), 55–64 (2008).
[CrossRef]

Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the Carpet: a New Strategy for Cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

2007 (1)

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[CrossRef] [PubMed]

2006 (3)

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

2003 (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light with negative refractive index,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[CrossRef]

2002 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
[CrossRef]

1999 (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).

1982 (1)

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (1982).

1976 (1)

1974 (1)

I. Bahl and K. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974).
[CrossRef]

1952 (1)

R. W. Corkum, “isotropic artificial dielectric,” Proceedings of the IRE 40(5), 574–587 (1952).
[CrossRef]

1948 (1)

W. E. Kock, “Metallic delay lenses,” Bell Syst. Tech. J. 27, 58 (1948).

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Focusing light with negative refractive index,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[CrossRef]

Awai, I.

I. Awai, “Artificial Dielectric Resonators for Miniaturized Filters,” IEEE Microw. Mag. 9(5), 55–64 (2008).
[CrossRef]

Bahl, I.

I. Bahl and K. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974).
[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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Corkum, R. W.

R. W. Corkum, “isotropic artificial dielectric,” Proceedings of the IRE 40(5), 574–587 (1952).
[CrossRef]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Degiron, A.

Dolling, G.

Enkrich, C.

Gralak, B.

Guenneau, S.

Guo, L.

Gupta, K.

I. Bahl and K. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974).
[CrossRef]

Hasebe, N.

Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Huang, D.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Justice, B. J.

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kock, W. E.

W. E. Kock, “Metallic delay lenses,” Bell Syst. Tech. J. 27, 58 (1948).

Li, J.

J. Li and J. B. Pendry, “Hiding under the Carpet: a New Strategy for Cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Linden, S.

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[CrossRef] [PubMed]

Ma, Y.

Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
[CrossRef]

Minot, M. J.

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

Mukoh, Y.

Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).

Nojima, T.

Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the Carpet: a New Strategy for Cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett. 30(10), 1204–1206 (2005).
[CrossRef] [PubMed]

J. B. Pendry and S. A. Ramakrishna, “Focusing light with negative refractive index,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Rejaei, B.

Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Rye, P. M.

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
[CrossRef]

Schurig, D.

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(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
[CrossRef]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
[CrossRef] [PubMed]

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[CrossRef] [PubMed]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
[CrossRef]

Snedaker, C. G.

C. G. Snedaker, “New numerical thin-film synthesis technique,” J. Opt. Soc. Am. 72, 1732 (1982).

Soukoulis, C. M.

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Vier, D. C.

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

Wegener, M.

Zhao, B.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[CrossRef] [PubMed]

Zhou, J.

Zhuang, Y.

Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
[CrossRef]

Bell Syst. Tech. J. (1)

W. E. Kock, “Metallic delay lenses,” Bell Syst. Tech. J. 27, 58 (1948).

Electronics and Communications in Japan (1)

Y. Mukoh, T. Nojima, and N. Hasebe, “A reflector lens antenna consisting of an artificial dielectric,” Electronics and Communications in Japan (1), 82 (1999).

IEEE Microw. Mag. (1)

I. Awai, “Artificial Dielectric Resonators for Miniaturized Filters,” IEEE Microw. Mag. 9(5), 55–64 (2008).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

Y. Ma, B. Rejaei, and Y. Zhuang, “Radial Perfectly Matched Layer for the ADI-FDTD Method,” IEEE Microw. Wirel. Compon. Lett. 19, 431–433 (2008).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

I. Bahl and K. Gupta, “A leaky-wave antenna using an artificial dielectric medium,” IEEE Trans. Antenn. Propag. 22(1), 119–122 (1974).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light with negative refractive index,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 026606 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

J. Li and J. B. Pendry, “Hiding under the Carpet: a New Strategy for Cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

D. R. Smith, P. M. Rye, J. J. Mock, D. C. Vier, and A. F. Starr, “Enhanced diffraction from a grating on the surface of a negative-index metamaterial,” Phys. Rev. Lett. 93(13), 137405 (2004).
[CrossRef] [PubMed]

Proceedings of the IRE (1)

R. W. Corkum, “isotropic artificial dielectric,” Proceedings of the IRE 40(5), 574–587 (1952).
[CrossRef]

Science (4)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292(5514), 77–79 (2002).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 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,” Science 323(5912), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Other (5)

C. Kittel, Solid State Physics (John Wiley & Sons, New York, 1986), 6th ed., p275.

R. Jacobson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Haas, M. Francombe, and R. Hoffman, eds. (Academic, New York, 1975), Vol. 8, p. 51.

I. Awai, H. Kubo, T. Iribe, D. Wakamiya, and A. Sanada, “An artificial dielectric material of huge permittivity with novel anisotropy and its application to a microwave BPF,” in Microwave Symposium Digest, 2003 IEEE MTT-S International 2 1085–1088 (2003).

I. Awai, S. Kida, and O. Mizue, “Very Thin and Flat Lens Antenna Made of Artificial Dielectrics,” in 2007 Korea-Japan Microwave Conference 177–180 (2007).

J. Brown, and W. Jackson, “The Properties of Artificial Dielectrics at Centimetre Wavelengths,” Proc. IEE paper no.1699R vol. 102B pp. 11–21, January 1995.

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Figures (7)

Fig. 1
Fig. 1

(a) Retrieved permittivity for a metamaterial composed of the repeated unit cell shown in the inset; (b) retrieved permeability for a metamaterial composed of the repeated unit cell shown in the inset. (c) The distortions and artifacts in the retrieved parameters are due to spatial dispersion, which can be removed to find the Drude-Lorentz like resonance shown in the lower figure.

Fig. 2
Fig. 2

Retrieval results for the closed ring medium. In all cases the radius of curvature of the corners is 0.6 mm, w=0.2 mm and unit cell periodicity is 2 mm. (a) The extracted permittivity with a=1.4 mm. (b) The extracted index and impedance for several values of a. The low frequency region is shown. (c) The relationship between the dimension a and the extracted refractive index and wave impedance.

Fig. 3
Fig. 3

Refractive index distributions for the designed gradient index structures. (a) A beam-steering element based on a linear index gradient. (b) A beam focusing lens, based on a higher order polynomial index gradient. Note the presence in both designs of an impedance matching layer (IML), provided to improve the insertion loss of the structures.

Fig. 4
Fig. 4

Calculated reflected power of metamaterial impedance matching layers (IMLs) (a) An IML interface between air and a dielectric with refractive index n=1.68. (b) A dielectric slab (n=1.68) with two IML interfaces on either side, (c) Reflection calculation for a TEM wave for case (a) and its control without IML. (d) Reflection calculation on a TEM wave for case (b) and its control without IML. (e) Reflection calculation for an oblique incident TE wave. Note that the angle is measured with respect to the surface normal.

Fig. 5
Fig. 5

Fabricated sample in which the design of each metamaterial element varies with the space coordinate.

Fig. 6
Fig. 6

Field mapping measurements of the beam steering lens. The lens has a linear gradient that causes the incoming beam to be deflected by an angle of 16.2 degrees. The effect is broadband, as can be seen from the identical maps taken at four different frequencies that span the X-band range of the experimental apparatus.

Fig. 7
Fig. 7

Field mapping measurements of the beam focusing lens. The lens has a symmetric profile about the center (given in the text) that causes the incoming beam to be focused to a point. Once again, the function is broadband, as can be seen from the identical maps taken at four different frequencies that span the X-band range of the experimental apparatus.

Equations (5)

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ε e f f = ε ¯ ( f ) ( θ / 2 ) sin ( θ / 2 ) cos ( θ / 2 ) μ e f f = μ ¯ ( f ) cos ( θ / 2 ) sin ( θ / 2 ) ( θ / 2 )
ε ( ω ) = 1 f p 2 f 2 f 0 2 + i Γ f = f 2 f 0 2 f p 2 i Γ f f 2 f 0 2 + i Γ f
ε ( ω 0 ) = 1 + f p 2 f 0 2 = f L 2 f 0 2
μ ( f ) = 1 F f 2 f 2 f 0 2 + i Γ f
Re ( n ) = 4 × 10 6 | x | 3 5 × 10 4 | x | 2 6 × 10 4 | x | + 1.75

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