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 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  38. 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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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. Express 20(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. Today 12(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,” Nature 455(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. B 75(15), 155410 (2007).
[Crossref]

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]

2006 (3)

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. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(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,” Nature 438(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,” Science 303(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,” Science 306(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. B 65(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. B 6(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. B 75(15), 155410 (2007).
[Crossref]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(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,” Nature 455(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,” Science 303(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, 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]

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. B 6(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.

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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, 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]

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]

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

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

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,” Nature 455(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,” Nature 455(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,” Science 303(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,” Science 315(5808), 47–49 (2007).
[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]

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]

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

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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]

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

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,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(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. B 81(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,” Nature 455(7211), 376–379 (2008).
[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]

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]

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,” Nature 455(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,” Science 303(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,” Nature 438(7066), 335–338 (2005).
[Crossref] [PubMed]

Zhao, Q.

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

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(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,” Science 306(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]

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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. Today 12(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. Photonics 1(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,” Nature 455(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,” Nature 438(7066), 335–338 (2005).
[Crossref] [PubMed]

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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. B 65(19), 195104 (2002).
[Crossref]

Y. Jin, P. Zhang, and S. He, “Squeezing electromagnetic energy with a dielecric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B 81(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. B 75(15), 155410 (2007).
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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]

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]

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]

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]

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

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

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(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.

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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 ∘ .

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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 ∘ .

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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).

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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.

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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 +(1−F)(−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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