Abstract

We fabricated silver split-ring resonators (SRRs) using nanosphere lithography and measured the LC resonance wavelength of single isolated SRRs in optical wavelength range. The SRRs’ sizes decreased when smaller polystyrene spheres were used as templates, and their LC resonance wavelength decreased to 721 nm. The LC resonance wavelength corresponding to the observed properties of the SRRs was calculated using the LC circuit model; we confirmed that the observational and calculated results agreed well. The LC resonance frequency of a miniaturized SRR with a constant shape was also calculated. For SRRs of the shape that we fabricated, the estimated short-wavelength limit was 426 nm.

© 2012 OSA

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  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]
  2. J. Zhou, Th. 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]
  3. A. Ishikawa, T. Tanaka, and S. Kawata, “Frequency dependence of the magnetic response of split-ring resonators,” J. Opt. Soc. Am. B24(3), 510–515 (2007).
    [CrossRef]
  4. K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
    [CrossRef]
  5. T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B75(20), 205102 (2007).
    [CrossRef]
  6. S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials (Amst.)1(1), 40–43 (2007).
    [CrossRef]
  7. M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
    [CrossRef] [PubMed]
  8. B. Lahiri, S. G. McMeekin, A. Z. Khokhar, R. M. De La Rue, and N. P. Johnson, “Magnetic response of split ring resonators (SRRs) at visible frequencies,” Opt. Express18(3), 3210–3218 (2010).
    [CrossRef] [PubMed]
  9. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
    [CrossRef] [PubMed]
  10. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
    [CrossRef] [PubMed]
  11. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006).
    [CrossRef] [PubMed]
  12. A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
    [CrossRef] [PubMed]
  13. J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antennas,” Adv. Mater. (Deerfield Beach Fla.)17(17), 2131–2134 (2005).
    [CrossRef]
  14. T. Okamoto, T. Fukuta, S. Sato, M. Haraguchi, and M. Fukui, “Visible near-infrared light scattering of single silver split-ring structure made by nanosphere lithography,” Opt. Express19(8), 7068–7076 (2011).
    [CrossRef] [PubMed]
  15. A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express13, 2668–2677 (2005).
  16. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
    [CrossRef]
  17. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
    [CrossRef]
  18. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
    [CrossRef]
  19. M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
    [CrossRef]

2011

2010

2009

A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
[CrossRef] [PubMed]

2007

A. Ishikawa, T. Tanaka, and S. Kawata, “Frequency dependence of the magnetic response of split-ring resonators,” J. Opt. Soc. Am. B24(3), 510–515 (2007).
[CrossRef]

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B75(20), 205102 (2007).
[CrossRef]

S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials (Amst.)1(1), 40–43 (2007).
[CrossRef]

2006

2005

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antennas,” Adv. Mater. (Deerfield Beach Fla.)17(17), 2131–2134 (2005).
[CrossRef]

A. Curry, G. Nusz, A. Chilkoti, and A. Wax, “Substrate effect on refractive index dependence of plasmon resonance for individual silver nanoparticles observed using darkfield microspectroscopy,” Opt. Express13, 2668–2677 (2005).

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

J. Zhou, Th. 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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
[CrossRef]

1999

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]

1990

M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

Busch, K.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

Chilkoti, A.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Clark, A. W.

A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
[CrossRef] [PubMed]

Cooper, J. M.

A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
[CrossRef] [PubMed]

Cumming, D. R. S.

A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
[CrossRef] [PubMed]

Curry, A.

De La Rue, R. M.

Economou, E. N.

J. Zhou, Th. 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.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Fukui, M.

T. Okamoto, T. Fukuta, S. Sato, M. Haraguchi, and M. Fukui, “Visible near-infrared light scattering of single silver split-ring structure made by nanosphere lithography,” Opt. Express19(8), 7068–7076 (2011).
[CrossRef] [PubMed]

M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
[CrossRef]

Fukuta, T.

Gerthsen, D.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

Giessen, H.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B75(20), 205102 (2007).
[CrossRef]

Glidle, A.

A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Plasmonic split-ring resonators as dichroic nanophotonic DNA biosensors,” J. Am. Chem. Soc.131(48), 17615–17619 (2009).
[CrossRef] [PubMed]

Haraguchi, M.

T. Okamoto, T. Fukuta, S. Sato, M. Haraguchi, and M. Fukui, “Visible near-infrared light scattering of single silver split-ring structure made by nanosphere lithography,” Opt. Express19(8), 7068–7076 (2011).
[CrossRef] [PubMed]

M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
[CrossRef]

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]

Ishikawa, A.

Johnson, N. P.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kafesaki, M.

J. Zhou, Th. 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]

Kawata, S.

Khokhar, A. Z.

Klein, M. W.

Koschny, T.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Koschny, Th.

J. Zhou, Th. 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]

Kreiter, M.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antennas,” Adv. Mater. (Deerfield Beach Fla.)17(17), 2131–2134 (2005).
[CrossRef]

Lahiri, B.

Linden, S.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

McMeekin, S. G.

McPeake, D.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
[CrossRef]

Meyrath, T. P.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B75(20), 205102 (2007).
[CrossRef]

Mingaleev, S. F.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

Nusz, G.

O’Brien, S.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
[CrossRef]

Okamoto, T.

Pendry, J. B.

J. Zhou, Th. 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. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
[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]

Pérez-Willard, F.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

Ramakrishna, S. A.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B69(24), 241101 (2004).
[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]

Rochholz, H.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antennas,” Adv. Mater. (Deerfield Beach Fla.)17(17), 2131–2134 (2005).
[CrossRef]

Sato, S.

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

Shintani, Y.

M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
[CrossRef]

Shumaker-Parry, J. S.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, “Fabrication of crescent-shaped optical antennas,” Adv. Mater. (Deerfield Beach Fla.)17(17), 2131–2134 (2005).
[CrossRef]

Soukoulis, C. M.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
[CrossRef] [PubMed]

J. Zhou, Th. 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]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (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]

Tanaka, T.

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

Tretyakov, S.

S. Tretyakov, “On geometrical scaling of split-ring and double-bar resonators at optical frequencies,” Metamaterials (Amst.)1(1), 40–43 (2007).
[CrossRef]

von Freymann, G.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

Wax, A.

Wegener, M.

K. Busch, G. von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep.444(3-6), 101–202 (2007).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. (Deerfield Beach Fla.)17(21), 2547–2549 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Yano, M.

M. Yano, M. Fukui, M. Haraguchi, and Y. Shintani, “In situ and real-time observation of optical constants of metal films during growth,” Surf. Sci.227(1-2), 129–137 (1990).
[CrossRef]

Zentgraf, T.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B75(20), 205102 (2007).
[CrossRef]

Zhou, J.

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Figures (7)

Fig. 1
Fig. 1

Illustration of (a) SRR and (b) equivalent LC circuit.

Fig. 2
Fig. 2

Field-emission scanning electron microscopy images of silver SRRs made with polystyrene spheres (a) 100 nm and (b) 60 nm in diameter.

Fig. 3
Fig. 3

SRR size versus the diameter of the polystyrene spheres. Circles, squares, and triangles indicate average values of outside diameter 2R, inside diameter 2r, and gap width d of the SRRs, respectively. Error bars indicate the size range for each type of SRR. Error bars for the diameter of the polystyrene spheres indicate the difference between the diameter obtained from the nominal value of the coefficient of variation and that given by the manufacturer.

Fig. 4
Fig. 4

Light scattering spectra of a single isolated SRR made with polystyrene sphere (a) 100 nm and (b) 60 nm in diameter.

Fig. 5
Fig. 5

Relationship between diameter of polystyrene spheres and experimentally observed LC resonance wavelength.

Fig. 6
Fig. 6

Measured and theoretical values of LC resonance wavelength. Solid and open circles represent LC resonance wavelengths of SRRs fabricated using polystyrene spheres 100 nm and 60 nm in diameter, respectively. Dashed line represents λLC-cal = λLC-exp.

Fig. 7
Fig. 7

Dependence of LC resonance frequency on SRR size. Red dotted line shows fLC = 704 THz (λLC = 426 nm). Blue dotted line shows fLC = 570 THz (λLC = 526 nm).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I sca (λ)= I S (λ) I BD (λ) I BB (λ) .
C= ε 0 ε g w g h d ,
J 0 0 h e z δ dz= J 0 δ(1 e h δ ).
L s = μ 0 π a 2 t ,
σ(ω)= ω p 2 ε 0 γiω ,
L kin = l eff ε 0 ω p 2 w reff t ,
λ LCcal = 2π v c ω LC =2π v c LC ,

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