Abstract

A type of negative-index metamaterial composed of periodic arrays of SRRs is proposed and numerically investigated in the visible frequencies. Employing the high order magnetic resonance to induce negative permeability, negative refractive index is obtained between 395 THz and 430 THz with the maximum FOM=4.59. The effective permeability exhibits a rapid convergence with increasing number of metamaterial layers. Different responses from the electric and magnetic resonances to the changing geometric parameters are compared and analyzed in terms of the field distribution. Simulation results show that the high order magnetic resonance can be greatly enhanced at visible frequencies as well as effectively tuned over a wide spectral range without notably altering the coupling between unit cells.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (4)

K. Song, Q. H. Fu, and X. P. Zhao, “U-shaped multi-band negative-index bulk metamaterials with low loss at visible frequencies,” Phys. Scr. 84, 035402 (2011).
[CrossRef]

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

D. R. Chowdhury, R. Singh, M. Reiten, J. Zhou, A. J. Taylor, and J. F. O’Hara, “Tailored resonator coupling for modifying the terahertz metamaterial response,” Opt. Express 19, 10679–10685 (2011).
[CrossRef]

2010 (5)

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97, 241108 (2010).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Optical metamaterials—more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef]

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18, 12770–12778 (2010).
[CrossRef]

2009 (7)

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

C. García-Meca, R. Ortuno, F. J. Rodríguez-Fortuno, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett. 34, 1603–1605 (2009).
[CrossRef]

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, 213902 (2009).
[CrossRef]

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
[CrossRef]

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. 34, 3478–3480 (2009).
[CrossRef]

E. Tatartschuk, E. Shamonina, and L. Solymar, “Plasmonic excitations in metallic nanoparticles: resonances, dispersion characteristics and near-field patterns,” Opt. Express 17, 8447–8460 (2009).
[CrossRef]

2008 (3)

M. J. Freire, R. Marques, and L. Jelinek, “Experimental demonstration of a μ=−1 metamaterial lens for magnetic resonance imaging,” Appl. Phys. Lett. 93, 231108 (2008).
[CrossRef]

C. C. Yan, Q. Wang, S. Z. Zhuo, and Y. P. Cui, “High-transmission negative refraction of discrete rod resonators confined in a metal waveguide at visible wavelengths,” Opt. Express 16, 13818–13823 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

2007 (1)

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

2006 (5)

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

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

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef]

J. F. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, “A unifying approach to left handed material design,” Opt. Lett. 31, 3620–3622 (2006).
[CrossRef]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

2005 (3)

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95, 223902 (2005).
[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, 3356–3358 (2005).
[CrossRef]

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

2001 (1)

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

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1967 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk 92, 517–526 (1967) [Phys. Usp. 10, 509–514 (1968)].
[CrossRef]

Andryieuski, A.

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

Atwater, H. A.

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18, 12770–12778 (2010).
[CrossRef]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

Au Kong, J.

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

Burgos, S. P.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18, 12770–12778 (2010).
[CrossRef]

Cai, W.

Chen, H. S.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Chen, K.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Chen, X.

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Chettiar, U. K.

Chowdhury, D. R.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Cui, Y. P.

de Waele, R.

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18, 12770–12778 (2010).
[CrossRef]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

Dickson, W.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Dolling, G.

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

Drachev, V. P.

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

J. F. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, “A unifying approach to left handed material design,” Opt. Lett. 31, 3620–3622 (2006).
[CrossRef]

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

Enkrich, C.

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

Etrich, C.

Freire, M. J.

M. J. Freire, R. Marques, and L. Jelinek, “Experimental demonstration of a μ=−1 metamaterial lens for magnetic resonance imaging,” Appl. Phys. Lett. 93, 231108 (2008).
[CrossRef]

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, 213902 (2009).
[CrossRef]

Fu, Q. H.

K. Song, Q. H. Fu, and X. P. Zhao, “U-shaped multi-band negative-index bulk metamaterials with low loss at visible frequencies,” Phys. Scr. 84, 035402 (2011).
[CrossRef]

Garcia-Meca, C.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

García-Meca, C.

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

C. García-Meca, R. Ortuno, F. J. Rodríguez-Fortuno, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett. 34, 1603–1605 (2009).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

Giessen, H.

Grzegorczyk, T. M.

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Hagness, S. C.

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method (Artech House, 2000).

Huangfu, J. T.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Hurtado, J.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Jelinek, L.

M. J. Freire, R. Marques, and L. Jelinek, “Experimental demonstration of a μ=−1 metamaterial lens for magnetic resonance imaging,” Appl. Phys. Lett. 93, 231108 (2008).
[CrossRef]

Jeppesen, C.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kafesaki, M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

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

Kildishev, A. V.

Koenderink, A. F.

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, 213902 (2009).
[CrossRef]

Koschny, T.

J. F. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, “A unifying approach to left handed material design,” Opt. Lett. 31, 3620–3622 (2006).
[CrossRef]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

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

Kristensen, A.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
[CrossRef]

Kuhl, J.

Lavrinenko, A. V.

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

Lederer, F.

Lee, Y.

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

Linden, S.

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

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

Malureanu, R.

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

Marques, R.

M. J. Freire, R. Marques, and L. Jelinek, “Experimental demonstration of a μ=−1 metamaterial lens for magnetic resonance imaging,” Appl. Phys. Lett. 93, 231108 (2008).
[CrossRef]

Marti, J.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Martí, J.

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

C. García-Meca, R. Ortuno, F. J. Rodríguez-Fortuno, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett. 34, 1603–1605 (2009).
[CrossRef]

Marti nez, A.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Martínez, A.

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

C. García-Meca, R. Ortuno, F. J. Rodríguez-Fortuno, J. Martí, and A. Martínez, “Double-negative polarization-independent fishnet metamaterial in the visible spectrum,” Opt. Lett. 34, 1603–1605 (2009).
[CrossRef]

Menzel, C.

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

Mortensen, N. A.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
[CrossRef]

O’Hara, J. F.

Ortuno, R.

Ortuño, R.

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Park, J. W.

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

Pendry, J. B.

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

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Polman, A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

R. de Waele, S. P. Burgos, H. A. Atwater, and A. Polman, “Negative refractive index in coaxial plasmon waveguides,” Opt. Express 18, 12770–12778 (2010).
[CrossRef]

Ran, L. X.

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Reiten, M.

Rhee, J. Y.

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

Rockstuhl, C.

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97, 241108 (2010).
[CrossRef]

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef]

Rodríguez-Fortuno, F. J.

Rodríguez-Fortuño, F. J.

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

Sarychev, A. K.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[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, 213902 (2009).
[CrossRef]

Shalaev, V. M.

Shamonina, E.

Shelby, R. A.

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

Singh, R.

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

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

Solymar, L.

Song, K.

K. Song, Q. H. Fu, and X. P. Zhao, “U-shaped multi-band negative-index bulk metamaterials with low loss at visible frequencies,” Phys. Scr. 84, 035402 (2011).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Optical metamaterials—more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef]

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

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

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

J. F. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, “A unifying approach to left handed material design,” Opt. Lett. 31, 3620–3622 (2006).
[CrossRef]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

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

Taflove, A.

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method (Artech House, 2000).

Tatartschuk, E.

Taylor, A. J.

Thuy, V. T. T.

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

Tung, N. T.

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

Tuttle, G.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

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, 213902 (2009).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk 92, 517–526 (1967) [Phys. Usp. 10, 509–514 (1968)].
[CrossRef]

Wang, Q.

Wegener, M.

C. M. Soukoulis and M. Wegener, “Optical metamaterials—more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef]

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

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

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Wu, B. I.

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Xiao, S.

Yan, C. C.

Yuan, H-K.

Zayats, A. V.

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef]

Zhang, L.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

Zhang, W.

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97, 241108 (2010).
[CrossRef]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Zhao, X. P.

K. Song, Q. H. Fu, and X. P. Zhao, “U-shaped multi-band negative-index bulk metamaterials with low loss at visible frequencies,” Phys. Scr. 84, 035402 (2011).
[CrossRef]

Zhou, J.

D. R. Chowdhury, R. Singh, M. Reiten, J. Zhou, A. J. Taylor, and J. F. O’Hara, “Tailored resonator coupling for modifying the terahertz metamaterial response,” Opt. Express 19, 10679–10685 (2011).
[CrossRef]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

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

Zhou, J. F.

Zhuo, S. Z.

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, “Negative-index materials: New frontiers in optics,” Adv. Mater. 18, 1941–1952 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97, 241108 (2010).
[CrossRef]

M. J. Freire, R. Marques, and L. Jelinek, “Experimental demonstration of a μ=−1 metamaterial lens for magnetic resonance imaging,” Appl. Phys. Lett. 93, 231108 (2008).
[CrossRef]

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “Capacitance tuning of nanoscale split-ring resonators,” Appl. Phys. Lett. 95, 193108 (2009).
[CrossRef]

J. Appl. Phys (1)

N. T. Tung, V. T. T. Thuy, J. W. Park, J. Y. Rhee, and Y. Lee, “Left-handed transmission in a simple cut-wire pair structure,” J. Appl. Phys 107, 023530 (2010).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, and A. V. Lavrinenko, “The split cube in a cage: bulk negative-index material for infrared applications,” J. Opt. A: Pure Appl. Opt. 11, 114010 (2009).
[CrossRef]

Nat. Mater. (1)

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mater. 9, 407–412 (2010).
[CrossRef]

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Phy. Rev. Lett. (1)

C. Garcia-Meca, J. Hurtado, J. Marti, A. Marti nez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phy. Rev. Lett. 106, 067402 (2011).
[CrossRef]

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

F. J. Rodríguez-Fortuño, C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Modeling high-order plasmon resonances of a U-shaped nanowire used to build a negative-index metamaterial,” Phys. Rev. B 79, 075103 (2009).
[CrossRef]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).
[CrossRef]

Phys. Rev. E (1)

X. Chen, B. I. Wu, J. Au Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
[CrossRef]

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

H. S. Chen, L. X. Ran, J. T. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 057605 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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

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, 213902 (2009).
[CrossRef]

Phys. Scr. (1)

K. Song, Q. H. Fu, and X. P. Zhao, “U-shaped multi-band negative-index bulk metamaterials with low loss at visible frequencies,” Phys. Scr. 84, 035402 (2011).
[CrossRef]

Proceeding IEEE (1)

J. Valentine, S. Zhang, T. Zentgraf, and X. Zhang, “Development of bulk optical negative index fishnet metamaterials: achieving a low loss and broadband response through coupling,” Proceeding IEEE 99, 1–9 (2011).
[CrossRef]

Science (5)

C. M. Soukoulis and M. Wegener, “Optical metamaterials—more bulky and less lossy,” Science 330, 1633–1634 (2010).
[CrossRef]

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

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

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

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

Usp. Fiz. Nauk (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Usp. Fiz. Nauk 92, 517–526 (1967) [Phys. Usp. 10, 509–514 (1968)].
[CrossRef]

Other (1)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method (Artech House, 2000).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic for the unit cell of the structure. The green parts are the split rings and the red part is the dielectric spacer. The detailed geometry parameters are W=60nm, h=60nm, t=40nm, d=34nm, ax=160nm, ay=140nm, Px=200nm, and Py=180nm. The propagation of the polarized electromagnetic wave is along the z axis, and the electric field and the magnetic field are respectively in the x and y directions.

Fig. 2.
Fig. 2.

(a) Normalized magnetic field |Hy/H0| calculated at the center of dielectric spacer (b) The electric field distribution inside the upper SRR (left graph) and lower SRR (right graph) at the resonance of 221 THz (c) The same with (b) but for the resonance at 416 THz. The arrows represent the direction of the electric field. The “+” and “” stand for the positive and negative charges, respectively.

Fig. 3.
Fig. 3.

Transmission characteristics and extracted effective parameters of the structure (a) Spectra of transmission and reflection coefficients (b) Retrieved permeability (c) Retrieved permittivity (d) Retrieved refractive index. The inset of (b) shows the HOMR frequencies as a function of 1/SF. The inset of (d) shows the FOM values in the negative index region. The blue dashed line represents the zero value for the extracted parameters.

Fig. 4.
Fig. 4.

Effective permeability of the structure with different layers of SRRs in one unit cell (a) Incidence polarized parallel to x axis (b) Incidence polarized parallel to y axis. Magnified data ofRe(μ) resulted from the high order magnetic mode is depicted in the inset of (a) for clarity.

Fig. 5.
Fig. 5.

Retrieved effective (a) permeability and (b) permittivity of the structure with length h=110nm (black), h=90nm (red) and h=70nm (blue) (c) The resonance frequencies for different values of h. (d) Spatial distribution of average field Hy at the fundamental (solid line) and high order (dashed line) magnetic mode, respectively. The vertical line represents the position of the fixed boundary of the bottom arms.

Fig. 6.
Fig. 6.

(a) Evolution of HOMR frequency as a function of the gap width W. (b) Transmission spectrum of the structure with W=90nm, 100 nm, and 110 nm near the resonance frequency of the high order magnetic mode.

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