Abstract

We derive an analytical LC model from Maxwell's equations for the magnetic resonance of subwavelength ring resonators. Using the LC model, we revisit the scaling of split-ring resonators. Inspired by the LC model, we propose a hybrid metal-dielectric ring resonator mainly composed of high index dielectric material (e.g., TiO2) with some gaps filled with metal (e.g., Ag). The saturation frequency of magnetic response for the hybrid metal-dielectric ring resonator is much higher (up to the ultraviolet range) than that for split-ring resonators, and can be controlled by the metal fraction in the ring. The hybrid metal-dielectric ring resonator can also overcome the homogenization problem of all-dielectric magnetic resonators, and therefore can form homogenizable magnetic metamaterials at short wavelengths down to the ultraviolet range.

© 2013 OSA

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ofε and μ, ” Sov. Phys. Usp.10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  4. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  5. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
    [CrossRef] [PubMed]
  6. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
    [CrossRef] [PubMed]
  7. Y. Jin, P. Zhang, and S. He, “Squeezing electromagnetic energy with a dielecric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B81(8), 085117 (2010).
    [CrossRef]
  8. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
    [CrossRef]
  9. Y. Jin and S. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express18(16), 16587–16593 (2010).
    [CrossRef] [PubMed]
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
    [CrossRef] [PubMed]
  11. 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,” Science303(5663), 1494–1496 (2004).
    [CrossRef] [PubMed]
  12. S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science306(5700), 1351–1353 (2004).
    [CrossRef] [PubMed]
  13. S. Zhang, W. 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 (2005).
    [CrossRef] [PubMed]
  14. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett.95(20), 203901 (2005).
    [CrossRef] [PubMed]
  15. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
    [CrossRef] [PubMed]
  16. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
    [CrossRef] [PubMed]
  17. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
    [CrossRef] [PubMed]
  18. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
    [CrossRef] [PubMed]
  19. A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14(4), 1557–1567 (2006).
    [CrossRef] [PubMed]
  20. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
    [CrossRef]
  21. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
    [CrossRef] [PubMed]
  22. J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
    [CrossRef] [PubMed]
  23. U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
    [CrossRef]
  24. 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]
  25. Y. Jeyaram, S. K. Jha, M. Agio, J. F. Löffler, and Y. Ekinci, “Magnetic metamaterials in the blue range using aluminum nanostructures,” Opt. Lett.35(10), 1656–1658 (2010).
    [CrossRef] [PubMed]
  26. J. Tang and S. He, “A novel structure for double negative NIMs towards UV spectrum with high FOM,” Opt. Express18(24), 25256–25263 (2010).
    [CrossRef] [PubMed]
  27. V. A. Fedotov, T. Uchino, and J. Y. Ou, “Low-loss plasmonic metamaterial based on epitaxial gold monocrystal film,” Opt. Express20(9), 9545–9550 (2012).
    [CrossRef] [PubMed]
  28. Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
    [CrossRef] [PubMed]
  29. M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
    [CrossRef] [PubMed]
  30. 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]
  31. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
    [CrossRef]
  32. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
    [CrossRef] [PubMed]
  33. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
    [CrossRef] [PubMed]
  34. A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
    [CrossRef] [PubMed]
  35. R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
    [CrossRef] [PubMed]
  36. 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]
  37. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
    [CrossRef]
  38. All simulations in this paper were performed using finite-difference time-domain (FDTD) technique by the commercial software CST Microwave Studio.
  39. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
    [CrossRef]
  40. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express19(6), 4815–4826 (2011).
    [CrossRef] [PubMed]

2013 (2)

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

2012 (4)

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

V. A. Fedotov, T. Uchino, and J. Y. Ou, “Low-loss plasmonic metamaterial based on epitaxial gold monocrystal film,” Opt. Express20(9), 9545–9550 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (5)

2009 (2)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

2008 (4)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

2007 (3)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
[CrossRef] [PubMed]

2006 (3)

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

2005 (7)

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. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

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

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

2004 (2)

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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

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

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[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. B6(12), 4370–4379 (1972).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ofε and μ, ” Sov. Phys. Usp.10, 509 (1968).
[CrossRef]

Agio, M.

Aizpurua, J.

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Basilio, L. I.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Bossard, J. A.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Brener, I.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

Burger, S.

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

Cai, W.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

Chantada, L.

Chettiar, U. K.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

Chichkov, B. N.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Christy, R. W.

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

Clem, P. G.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

De La Rue, R. M.

Dolling, G.

Drachev, V. P.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

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]

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Ekinci, Y.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Y. Jeyaram, S. K. Jha, M. Agio, J. F. Löffler, and Y. Ekinci, “Magnetic metamaterials in the blue range using aluminum nanostructures,” Opt. Lett.35(10), 1656–1658 (2010).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

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

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

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Evlyukhin, A. B.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Fedotov, V. A.

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Frauenglass, A.

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

Froufe-Pérez, L. S.

Fu, Y. H.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

García-Etxarri, A.

García-Meca, C.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Genov, D. A.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Ginn, J. C.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Gómez-Medina, R.

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

He, S.

Hines, P. F.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

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]

Ihlefeld, J. F.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Jeyaram, Y.

Jha, S. K.

Jiang, Z. H.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Jin, Y.

Y. Jin and S. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express18(16), 16587–16593 (2010).
[CrossRef] [PubMed]

Y. Jin, P. Zhang, and S. He, “Squeezing electromagnetic energy with a dielecric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B81(8), 085117 (2010).
[CrossRef]

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]

Khokhar, A. Z.

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. 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]

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

Kuznetsov, A. I.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

Lahiri, B.

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Lin, L.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

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

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

Lippens, D.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

Löffler, J. F.

López, C.

Lorente-Crespo, M.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Luk’yanchuk, B.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

Martínez, A.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Mayer, T. S.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

McMeekin, S. G.

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

Minhas, B. K.

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Novikov, S. M.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Ortuño, R.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Ou, J. Y.

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (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]

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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[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]

Peters, D. W.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Reinhardt, C.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

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]

Sáenz, J. J.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

Sarychev, A. K.

Scheffold, F.

Schmidt, F.

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

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Sinclair, M. B.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (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]

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

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

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

Stevens, J. O.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[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]

Tang, J.

Uchino, T.

Ulin-Avila, E.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ofε and μ, ” Sov. Phys. Usp.10, 509 (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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, L.

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

Warne, L. K.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

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

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

Wendt, J. R.

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Werner, D. H.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Xiao, S.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[CrossRef] [PubMed]

Yuan, H.

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

Yuan, H. K.

Yun, S.

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Zentgraf, Th.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

Zhang, J. B.

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

Zhang, P.

Y. Jin, P. Zhang, and S. He, “Squeezing electromagnetic energy with a dielecric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B81(8), 085117 (2010).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Zhao, Q.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

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

Zhou, J. F.

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

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30(23), 3198–3200 (2005).
[CrossRef] [PubMed]

Zschiedrich, L.

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

Zywietz, U.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

IEEE Trans. Microw. Theory Tech. (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]

Mater. Today (1)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today12(12), 60–69 (2009).
[CrossRef]

MRS Bull. (1)

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical metamagnetism and negative-index metamaterials,” MRS Bull.33(10), 921–926 (2008).
[CrossRef]

Nano Lett. (2)

M. Lorente-Crespo, L. Wang, R. Ortuño, C. García-Meca, Y. Ekinci, and A. Martínez, “Magnetic hot spots in closely spaced thick gold nanorings,” Nano Lett.13(6), 2654–2661 (2013).
[CrossRef] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett.12(7), 3749–3755 (2012).
[CrossRef] [PubMed]

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

Nature (2)

J. Valentine, S. Zhang, Th. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature455(7211), 376–379 (2008).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature438(7066), 335–338 (2005).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. B (4)

Y. Jin, P. Zhang, and S. He, “Squeezing electromagnetic energy with a dielecric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B81(8), 085117 (2010).
[CrossRef]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailor ring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B65(19), 195104 (2002).
[CrossRef]

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

Phys. Rev. Lett. (9)

S. Zhang, W. 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 (2005).
[CrossRef] [PubMed]

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

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95(13), 137404 (2005).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008).
[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]

J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett.108(9), 097402 (2012).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A.106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

Sci. Rep. (2)

A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. B. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep.2, 492 (2012).
[CrossRef] [PubMed]

Z. H. Jiang, S. Yun, L. Lin, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Tailoring dispersion for broadband low-loss optical metamaterials using deep-subwavelength inclusions,” Sci. Rep.3, 1571 (2013).
[CrossRef] [PubMed]

Science (5)

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science315(5808), 47–49 (2007).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[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,” Science303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

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

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ofε and μ, ” Sov. Phys. Usp.10, 509 (1968).
[CrossRef]

Other (1)

All simulations in this paper were performed using finite-difference time-domain (FDTD) technique by the commercial software CST Microwave Studio.

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Figures (5)

Fig. 1
Fig. 1

The cross-sectional schematic diagram of the two-dimensional ring resonator in a unit cell a×a . The radius r ( r=d 1 2 b ) and thickness b of the ring are r=0.3a and b=0.2a , respectively. The permittivity of the two θ 1 ( θ 2 ) angle part of the ring is ε 1 ( ε 2 ). The background is air.

Fig. 2
Fig. 2

(a) The comparison between the effective inductance L e (solid line), the well-known kinetic inductance L k (dashed line) and the geometrical inductance L g (dotted line). (b) Determination of the magnetic resonance frequency (denoted by the circle) when dispersive effective inductance L e is used. The structure parameters are: a=100nm, r=30nm, b=20nm, θ 1 = 20 .

Fig. 3
Fig. 3

The scaling of the magnetic resonance frequency of conventional SRRs as a function of the unit cell size a. The solid lines give the simulated results while the non-solid lines are calculated with our analytical LC model. The black, red, green and blue solid lines are simulated results for SRRs with θ 1 = 10 , θ 1 = 20 , θ 1 = 30 and θ 1 = 40 , respectively. The black, green, red and blue dashed lines are the results calculated with the LC model for SRRs with θ 1 = 10 , θ 1 = 20 , θ 1 = 30 and θ 1 = 40 , respectively. The red dash-dotted line is the LC model result with the approximation L e = L k for SRRs with θ 1 = 20 .

Fig. 4
Fig. 4

(a) The scaling of the simulated (solid lines) and LC model calculated (dashed lines) magnetic resonance frequency of HRRs as a function of the unit cell size a . (b,c) The effective permeability (retrieved from simulated S parameters) of HRRs with a=100nm [denoted by the vertical dotted line in panel (a)] and θ 1 = 40 , 30 , 20 , 10 , 5 , from left to right. The Drude model of Ag is used in (b), the experimental material data of Ag from [37] is used in (c).

Fig. 5
Fig. 5

The normalized wavelength (left y-axis) and the minimum effective permeability (right y-axis) versus the scaling factor 1/a for SRRs (a) and HRRs (b). The solid lines with solid symbols are the normalized vacuum wavelength λ/a , the dashed lines with solid symbols are the normalized effective wavelength λ eff /a , the solid lines with hollowed symbols are the minimum effective permeability μ eff min . Note that the right y-axis for μ eff min is in a reversed direction.

Equations (5)

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

I=b D t =iωb ε 1 E 1 =iωb ε 2 E 2 ,
2r θ 1 E 1 +2r θ 2 E 2 =iω( Φ int + Φ ext ),
[ 1 iωC +(1F)(iω L g ) ]I=iω Φ ext ,
μ eff =1 F ' ω 2 ω 2 1 ( L g + L e ) C 1 +i ωR L g + L e ,
μ eff =1 F ' ω 2 ω 2 1 ( L g + L e ) C 2 +i ωR L g + L e ,

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