Abstract

Extinction cross-section spectra of split-ring-resonator dimers have been measured at near-infrared frequencies with a sensitive spatial modulation technique. The resonance frequency of the dimer's coupled mode as well as its extinction cross-section and its quality factor depend on the relative orientation and separation of the two split-ring resonators. The findings can be interpreted in terms of electric and magnetic dipole-dipole interaction. Numerical calculations based on a Discontinuous Galerkin Time-Domain approach are in good agreement with the experiments and support our physical interpretation.

© 2010 OSA

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  1. 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]
  2. S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
    [CrossRef] [PubMed]
  3. 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), 203901–1 (2005).
    [CrossRef] [PubMed]
  4. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  5. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007).
    [CrossRef] [PubMed]
  6. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  7. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  8. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
    [CrossRef] [PubMed]
  9. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007).
    [CrossRef] [PubMed]
  10. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
    [CrossRef] [PubMed]
  11. 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]
  12. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
    [CrossRef]
  13. N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
    [CrossRef]
  14. N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
    [CrossRef]
  15. M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009).
    [CrossRef] [PubMed]
  16. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
    [CrossRef]
  17. M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
    [CrossRef]
  18. O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005).
    [CrossRef]
  19. G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
    [CrossRef]
  20. M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009).
    [CrossRef]
  21. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
    [CrossRef] [PubMed]
  25. P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
    [CrossRef] [PubMed]
  26. F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
    [CrossRef]
  27. A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
    [CrossRef] [PubMed]
  28. O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
    [CrossRef]
  29. M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
    [CrossRef]
  30. J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002).
    [CrossRef]
  31. J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
    [CrossRef]
  32. K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
    [CrossRef] [PubMed]

2009

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009).
[CrossRef] [PubMed]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009).
[CrossRef]

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009).
[CrossRef] [PubMed]

J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
[CrossRef]

K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
[CrossRef] [PubMed]

2008

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
[CrossRef] [PubMed]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

2007

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007).
[CrossRef] [PubMed]

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007).
[CrossRef] [PubMed]

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

2006

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[CrossRef]

O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

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

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
[CrossRef] [PubMed]

2005

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (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), 203901–1 (2005).
[CrossRef] [PubMed]

O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005).
[CrossRef]

2004

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]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

2003

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
[CrossRef]

2002

J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002).
[CrossRef]

1999

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]

Arbouet, A.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Arnaud, L.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Billaud, P.

O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Broyer, M.

O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

Burger, S.

M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009).
[CrossRef]

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[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), 203901–1 (2005).
[CrossRef] [PubMed]

Busch, K.

J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
[CrossRef]

K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
[CrossRef] [PubMed]

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

Christofilos, D.

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Dahmen, C.

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

Davis, T. J.

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009).
[CrossRef] [PubMed]

Decker, M.

Del Fatti, N.

O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Dolling, G.

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[CrossRef]

Edwards, D. J.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Eng, L. M.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
[CrossRef] [PubMed]

Enkrich, C.

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), 203901–1 (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]

Fan, W. J.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

Faulkner, G.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Fedotov, V. A.

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
[CrossRef] [PubMed]

Feth, N.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

Frauenglass, A.

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

Frimmer, M.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

Funston, A. M.

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009).
[CrossRef] [PubMed]

Giessen, H.

N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

Hao, T.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Hesmer, F.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Hesthaven, J. S.

J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002).
[CrossRef]

Hohenau, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

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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]

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O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
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A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

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M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
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N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
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N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
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M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007).
[CrossRef] [PubMed]

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I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

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K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
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J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
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M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

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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), 203901–1 (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]

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W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

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W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

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W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
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U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
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S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

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M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009).
[CrossRef] [PubMed]

M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009).
[CrossRef]

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007).
[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, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[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), 203901–1 (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).
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N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
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N. Liu, H. Liu, S. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

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S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

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S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

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S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

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K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
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A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009).
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O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

Niegemann, J.

J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
[CrossRef]

K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
[CrossRef] [PubMed]

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

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A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries,” Nano Lett. 9(4), 1651–1658 (2009).
[CrossRef] [PubMed]

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P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
[CrossRef] [PubMed]

Park, Y. S.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

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

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F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Rechberger, W.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical Properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

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P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
[CrossRef] [PubMed]

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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]

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A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
[CrossRef] [PubMed]

Schädle, A.

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[CrossRef]

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C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

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), 203901–1 (2005).
[CrossRef] [PubMed]

Schultz, S.

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

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

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A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
[CrossRef] [PubMed]

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N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008).
[CrossRef]

Sersic, I.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
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V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
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F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Shamonina, E.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
[CrossRef]

Smith, D. R.

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

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

Solymar, L.

O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005).
[CrossRef]

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
[CrossRef]

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C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007).
[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), 203901–1 (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]

Stannigel, K.

J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostruct. - Fundamentals Appl. 7(1), 2–11 (2009).
[CrossRef]

K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,” Opt. Express 17(17), 14934–14947 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14934 .
[CrossRef] [PubMed]

Stevens, C. J.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

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]

Su, K. H.

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

Sydoruk, O.

O. Sydoruk, O. Zhuromskyy, E. Shamonina, and L. Solymar, “Phonon-like dispersion curves of magnetoinductive waves,” Appl. Phys. Lett. 87(7), 072501–1 (2005).
[CrossRef]

Tatartschuk, E.

F. Hesmer, E. Tatartschuk, O. Zhuromskyy, A. A. Radkovskaya, M. Shamonin, T. Hao, C. J. Stevens, G. Faulkner, D. J. Edwards, and E. Shamonina, “Coupling mechanisms for split ring resonators: Theory and experiment,” Phys. Status Solidi 244(4), 1170–1175 (2007).
[CrossRef]

Vallée, F.

O. L. Muskens, N. Del Fatti, F. Vallée, J. R. Huntzinger, P. Billaud, and M. Broyer, “Single-metal nanoparticle absorption spectroscopy and optical characterization,” Appl. Phys. Lett. 88(6), 063109–1 (2006).
[CrossRef]

A. Arbouet, D. Christofilos, N. Del Fatti, F. Vallée, J. R. Huntzinger, L. Arnaud, P. Billaud, and M. Broyer, “Direct measurement of the single-metal-cluster optical absorption,” Phys. Rev. Lett. 93(12), 127401–1 (2004).
[CrossRef] [PubMed]

Verhagen, E.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

von Plessen, G.

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

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J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids - I. Time-domain solution of Maxwell's equations,” J. Comput. Phys. 181(1), 186–221 (2002).
[CrossRef]

Wegener, M.

M. Decker, S. Burger, S. Linden, and M. Wegener, “Magnetization waves in split-ring-resonator arrays: Evidence for retardation effects,” Phys. Rev. B 80(19), 193102 (2009).
[CrossRef]

M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. 34(10), 1579–1581 (2009).
[CrossRef] [PubMed]

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute Extinction Cross Section of Individual Magnetic Split-Ring Resonators,” Nat. Photonics 2(10), 614–617 (2008).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007).
[CrossRef] [PubMed]

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89(23), 231118–1 (2006).
[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), 203901–1 (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]

Wenzel, M. T.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008).
[CrossRef] [PubMed]

Wie, Q. H.

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

Wiltshire, M. C. K.

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
[CrossRef]

Young, I. R.

M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, “Dispersion characteristics of magneto-inductive waves: comparison between theory and experiment,” Electron. Lett. 39(2), 215–217 (2003).
[CrossRef]

Zhang, S.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94(3), 037402–1 (2005).
[CrossRef] [PubMed]

Zhang, W.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative Refractive Index in Chiral Metamaterials,” Phys. Rev. Lett. 102(2), 023901–1 (2009).
[CrossRef] [PubMed]

K. H. Su, Q. H. Wie, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003).
[CrossRef]

Zheludev, N. I.

A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant Gyrotropy due to Electromagnetic-Field Coupling in a Bilayered Chiral Structure,” Phys. Rev. Lett. 97(17), 177401–1 (2006).
[CrossRef] [PubMed]

Zhou, J. 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), 203901–1 (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).
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Figures (5)

Fig. 1
Fig. 1

(a) Scanning-electron micrographs of four different SRR dimers: On-top configuration, side-by-side configuration, gap-to-gap configuration, and back-to-back configuration. (b) Scheme of a usual 2D-periodic square lattice of equally oriented SRRs. The on-top configuration and the side-by-side configuration are directly related to the arrangement of SRRs in a usual 2D array (see red and blue boxes). (c) Scanning-electron micrographs of a series of SRR dimers (gap-to-gap configuration). The separation d between the two SRRs decreases from d = 210 nm (left) to d = 35 nm (right).

Fig. 2
Fig. 2

Scheme of the spatial modulation setup.

Fig. 3
Fig. 3

(a) Measured (circles) and calculated (black curve) extinction cross-section of a single SRR for normal incidence and horizontal polarization. The corresponding calculated absorption cross-section and scattering cross-section spectra are represented by the red and blue curve, respectively. The insets show a scanning electron micrograph of the single SRR and the geometry assumed in our calculations, respectively. The scale bars are 200 nm. (b) Equivalent dipole model for a SRR. The blue (red) arrow corresponds to the electric (magnetic) dipole moment. (c) Calculated electric (left) and magnetic (right) near-field distribution, respectively, for the plane intersecting the middle of the SRR.

Fig. 4
Fig. 4

Measured extinction cross-section spectra of four different sets of SRR dimers for different separations. The symbols correspond to the experimental data. The solid curves are Lorentzian fits to the experimental data. The different curves in each set are vertically displaced for clarity (see arrows). (a) Side-by-side configuration, (b) on-top configuration, (c) gap-to-gap configuration, and (d) back-to-back configuration.

Fig. 5
Fig. 5

Calculated extinction cross-section spectra of four different sets of SRR dimers. The geometries and separations of the SRRs correspond to the experiments in Fig. 4. The different curves in each set are vertically displaced for clarity (see arrows). (a) Side-by-side configuration, (b) on-top configuration, (c) gap-to-gap configuration, and (d) back-to-back configuration.

Equations (1)

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C e x t = A × R D S max ξ .

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