Abstract

A novel ring structure is proposed for double negative NIMs at visible light spectrum with high FOM (e.g. about 11 at a wavelength of 583 nm) and low loss. Besides the effective medium theory, an equivalent circuit model is also given to explain physically why our novel structure can give double negative behavior with low loss. Adapted from the original ring structure, two other types of structures, namely, disk and nanowire structures, are also given to further push double negative NIMs toward ultraviolet (UV) spectrum.

©2010 Optical Society of America

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References

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  • Publication
  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
    [Crossref] [PubMed]
  5. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
    [Crossref] [PubMed]
  6. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
    [Crossref] [PubMed]
  7. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
    [Crossref] [PubMed]
  8. S. Zhang, W. J. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. O. Osgood, “Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23(3), 434–438 (2006).
    [Crossref]
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    [Crossref] [PubMed]
  10. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
    [Crossref]
  11. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32(12), 1671–1673 (2007).
    [Crossref] [PubMed]
  12. U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
    [Crossref]
  13. S. M. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. 34(22), 3478–3480 (2009).
    [Crossref] [PubMed]
  14. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
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  15. 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(19), 195104 (2002).
    [Crossref]
  16. X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
    [Crossref] [PubMed]
  17. S. A. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express 14(15), 6778–6787 (2006).
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  18. H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
    [Crossref]
  19. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [Crossref]
  20. R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
    [Crossref] [PubMed]
  21. J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
    [Crossref] [PubMed]

2009 (1)

2008 (3)

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
[Crossref]

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[Crossref] [PubMed]

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (4)

2005 (1)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

2004 (4)

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

2002 (1)

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(19), 195104 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Aydin, K.

Bartal, G.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Brueck, S. R. J.

Cai, W.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
[Crossref]

U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32(12), 1671–1673 (2007).
[Crossref] [PubMed]

Chen, H. S.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

Chen, K. M.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

Chen, X. D.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Dolling, G.

Drachev, V. P.

Drachey, V. P.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
[Crossref]

Economou, E. N.

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Fan, W. J.

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Grzegorczyk, T. M.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Grzegorczyk, T. M. S.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Huangfu, J. T.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kafesaki, M.

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Kildishev, A. V.

Kong, J. A.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Koschny, T.

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Liu, Y. M.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Liu, Z. W.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Malloy, K. J.

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(19), 195104 (2002).
[Crossref]

Osgood, R. M.

Osgood, R. O.

Ozbay, E.

Pacheco, J.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Panoiu, N. C.

Penciu, R. S.

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Ran, L. X.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
[Crossref]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[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(19), 195104 (2002).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Shalaev, V. M.

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 (2001).
[Crossref] [PubMed]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[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(19), 195104 (2002).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Soukoulis, C. M.

R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16(22), 18131–18144 (2008).
[Crossref] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[Crossref]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[Crossref] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[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(19), 195104 (2002).
[Crossref]

Stacy, A. M.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Sun, C.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Wang, Y.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
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G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
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G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

Wu, B. I.

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Xiao, S.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
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U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32(12), 1671–1673 (2007).
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Yao, J.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Yuan, H. K.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
[Crossref]

Yuan, H.-K.

Zhang, S.

Zhang, S. A.

Zhang, X.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Zhang, X. F.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
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Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
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Zhou, J. F.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
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IEEE Trans. Microw. Theory Tech. (1)

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J. Appl. Phys. (1)

H. S. Chen, L. X. Ran, J. T. Huangfu, X. F. Zhang, K. M. Chen, T. M. S. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96(9), 5338–5340 (2004).
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J. Opt. Soc. Am. B (1)

MRS Bull. (1)

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. K. Yuan, V. P. Drachey, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921–926 (2008).
[Crossref]

Opt. Express (2)

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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(19), 195104 (2002).
[Crossref]

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

X. D. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Science (6)

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[Crossref] [PubMed]

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[Crossref]

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Figures (5)
Fig. 1
Fig. 1 (color online). (a) The geometries of the proposed NIM of ring structure. The inner radius of the silver rings is a ( = 20 nm), the outer radius is a + b ( = 55 nm), the thickness is t ( = 20 nm), the distances between rings are d x ( = 40 nm), d y ( = 20 nm) and d z ( = 20 nm), in x-, y- and z- directions, respectively. The whole structure is submerged in SiO2 ( ε = 2.25 ). (b) The real and imaginary parts of the effective refractive index and FOM (blue solid line) for 1-layer ring structure. The real part of the refractive index for the 4- (green line) and 5- (red line) layer ring structures converge from that of the 1-layer ring structure. The grey solid line is the FOM when loss increases by a factor of three as compared to that of bulk silver. (c) The real and imaginary parts of the effective permeability and permittivity for 1-layer ring structure. Double negative NIM is realized in the wavelength region from 538 nm to 598 nm. (d) The negative refraction behavior at 555 nm wavelength, indicating an effective refractive index of −0.53.

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Fig. 2
Fig. 2 (color online). The field distribution of (a) H z and (b) vectorial E field at 583 nm wavelength. (c) For the magnetic response: the left panel shows the schematic E field (dash arrows) and charge distribution (denoted by “+” or “-”), while the right panel shows the equivalent LC circuit model. (d) For the electric response: the left panel shows the schematic E field (dashed arrows) and charge distribution, while the right panel shows the equivalent LC circuit model. For the equivalent LC circuits in (c) and (d), the resistance is not plotted.

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Fig. 3
Fig. 3 The real part (solid lines) and imaginary part (dash-dotted lines) of the effective permeability plotted according to Eq. (5) (black lines) and Eq. (7) (red lines).

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Fig. 4
Fig. 4 (a) The effective refractive index after (red line) and before (green line) disturbance of the periodicity in the x direction. (b) The effective refractive index after (red line) and before (green line) disturbance of the periodicity in the y direction.

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Fig. 5
Fig. 5 The double-negative wavelength region (upper plot) and FOM (lower plot) for each sample. For each sample, hollow circles represent the upper bound and lower bound of the double negative region, while black solid circle represents the wavelength where the FOM is the largest. Insets indicate that it is ring structure for samples 1 to 5, disk structure for samples 6 to 9, and nanowire structure for samples 10 to 15.

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Tables (1)

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Table 1 Geometric parameters of the 15 samples

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Equations (7)

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I 1 ( 1 − i ω C ) + ( I 1 − I 2 ) ( − i ω L e 1 + R 1 ) + I 1 ( − i ω L m 1 ) = U 1 = i ω μ 0 H 0 S 1 ,
I 2 ( − i ω L e 2 + R 2 ) + ( I 2 − I 1 ) ( − i ω L e 1 + R 1 ) + I 2 ( − i ω L m 2 ) = U 2 = i ω μ 0 H 0 S 2 ,
I 1 = i ω μ 0 H 0 [ S 1 + Z 1 Z 1 + Z 2 + ( − i ω L m 2 ) S 2 ] 1 − i ω C + Z 1 + ( − i ω L m 1 ) − Z 1 2 Z 1 + Z 2 + ( − i ω L m 2 ) ,
I 2 = i ω μ 0 H 0 S 2 + Z 1 I 1 Z 1 + Z 2 + ( − i ω L m 2 ) ,
μ e f f = H 0 H 0 − M = H 0 H 0 − S 1 I 1 + S 2 I 2 V ,
I = i ω μ 0 H 0 S 1 1 − i ω C + Z 1 + ( − i ω L m 1 ) ,
μ e f f = H 0 H 0 − M = H 0 H 0 − S 1 I V .

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