Abstract

Engineering resonances in metamaterials has been so far the main way of reaching simultaneously negative permittivity and negative permeability leading to negative index materials. In this paper, we present an experimental and numerical analysis of the infrared response of metamaterials made of continuous nanowires and split ring resonators (SRR) deposited on low-doped silicon when the geometry of the SRRs is gradually altered. The impact of the geometric transformation of the SRRs on the spectra of the composite metamaterial is measured in the 20–200 THz frequency range (i.e., in the 1.5–15µm wavelength range) for the two field polarizations under normal to plane propagation. We show experimentally and numerically that tuning the SRRs towards elementary cut wires translates in a predictable manner the frequency response of the artificial material. We also analyze coupling effects between the SRRs and the continuous nanowires for different spacings between them. The results of our study are expected to provide useful guidelines for the design of negative index metamaterials on silicon.

© 2008 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  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, 4184-4187 (2000).
    [CrossRef] [PubMed]
  3. D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  4. J. B. Pendry, "Negative refraction makes a perfect lens," Phys Rev Lett 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  5. D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys 7, 162-176 (2005).
    [CrossRef]
  6. J. B. Pendry, D. Schurig, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  8. J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
    [CrossRef]
  9. R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
    [CrossRef]
  10. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  11. 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, 203905 (2005).
    [CrossRef]
  12. 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]
  13. 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]
  14. K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metyamaterial under normal-to-plane propagation," Opt. Express 14, 8685-8693 (2006).
    [CrossRef] [PubMed]
  15. 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] [PubMed]
  16. J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15, 17881-17890 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
    [CrossRef] [PubMed]
  20. S. Tretyakov, "On geometrical scaling of split-ring resonators at optical frequencies," Metamaterials 1, 40-43, 2007.
    [CrossRef]
  21. 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, 223902 (2005).
    [CrossRef] [PubMed]
  22. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
    [CrossRef]

2008 (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

2007 (2)

S. Tretyakov, "On geometrical scaling of split-ring resonators at optical frequencies," Metamaterials 1, 40-43, 2007.
[CrossRef]

J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

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]

K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metyamaterial under normal-to-plane propagation," Opt. Express 14, 8685-8693 (2006).
[CrossRef] [PubMed]

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] [PubMed]

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

2005 (5)

D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys 7, 162-176 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (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. 30,3356-3358 (2005).
[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, 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, 203905 (2005).
[CrossRef]

2004 (3)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

2000 (3)

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, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys Rev Lett 85, 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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

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, 203905 (2005).
[CrossRef]

Cai, W.

Caliskan, M. D.

Chettiar, U. K.

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Depine, R. A.

R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

Drachev, V. P.

Economou, E. N.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (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, 223902 (2005).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Enkrich, C.

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, 203905 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Etrich, C.

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

Giessen, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (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] [PubMed]

Gundogdu, T. F.

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

Guven, K.

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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (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, 223902 (2005).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

Katsarakis, N.

Kildishev, A. V.

Konstantinidis, G.

Koschny, T.

J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

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]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Koschny, Th.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 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, 203905 (2005).
[CrossRef]

Kostopoulos, A.

Kroll, N.

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Kuhl, J.

Lakhtakia, A.

R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

Lederer, F.

Linden, 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, 203905 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Liu, N.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

Ozbay, E.

Padilla, W. J.

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, 4184-4187 (2000).
[CrossRef] [PubMed]

Penciu, R. S.

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D.R. Smith, "Controlling electromagnetic fields," Science 312, 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, 223902 (2005).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys Rev Lett 85, 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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Rockstuhl, C.

Sarychev, A. K.

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, 203905 (2005).
[CrossRef]

Schultz, S.

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, 4184-4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys 7, 162-176 (2005).
[CrossRef]

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys 7, 162-176 (2005).
[CrossRef]

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

Smith, D.R.

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

Soukoulis, C. M.

J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

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, 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, 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, 203905 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Stewart, W.J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Tretyakov, S.

S. Tretyakov, "On geometrical scaling of split-ring resonators at optical frequencies," Metamaterials 1, 40-43, 2007.
[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]

Vier, D. 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, 4184-4187 (2000).
[CrossRef] [PubMed]

Wegener, M.

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, 203905 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Yuan, H. K.

Zentgraf, T.

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]

Zhou, J.

J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic and electric excitations in split ring resonators," Opt. Express 15, 17881-17890 (2007).
[CrossRef] [PubMed]

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, 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, 223902 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 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, 203905 (2005).
[CrossRef]

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, 203905 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

IEEE Trans. Microwave 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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Phys. Condens. Matter (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys. Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Metamaterials (1)

S. Tretyakov, "On geometrical scaling of split-ring resonators at optical frequencies," Metamaterials 1, 40-43, 2007.
[CrossRef]

Microwave Opt. Technol. Lett. (1)

R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004).
[CrossRef]

Nature materials (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nature materials 7, 31-37 (2008).
[CrossRef]

New J. Phys (1)

D. Schurig and D. R. Smith, "Sub-diffraction imaging with compensating bilayers," New J. Phys 7, 162-176 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys Rev Lett (1)

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

Phys. Rev. B (1)

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. Lett. (4)

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, 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, 203905 (2005).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Science (3)

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Other (1)

HFSS, High-frequency structure simulator version 10.1 Finite-element package, Ansoft Corporation, Pittsburgh, PA (2006).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representations (top) and scanning electron microscope images (middle and bottom) of the four metamaterial structures fabricated on silicon. The top and bottom pictures show the elementary unit cell of each structure. From left to right, the length of SRR legs is reduced to the point where the SRR is transformed into a single wire piece. The middle pictures show the regularity achieved in the fabrication of the periodic arrays of nanowires and split ring resonators

Fig. 2.
Fig. 2.

Measured and simulated transmission/reflection spectra of the four structures depicted in Fig. 1. Curves in red, blue, green and black are for the 1st, 2nd, 3rd and 4th structures, respectively. - (a) and (b): transmission and reflection spectra measured for the parallel polarization (incident electric field parallel to the SRR gap). - (c) and (d): numerical simulations corresponding to (a) and (b), respectively. - (e) and (f): transmission and reflection spectra measured for the perpendicular polarization (incident electric field perpendicular to the SRR gap). - (g) and (h): numerical simulations corresponding to (e) and (f), respectively.

Fig. 3.
Fig. 3.

Magnitude of the normal electric field component (|Ez|) calculated at the bottom surface of the metallic elements for each of the resonant plasmon modes observed in the different spectra of Fig. 2. The different colours, from blue to red correspond to increasing magnitudes of the field component. Modes are classified according to the resonance order and to the polarization of the incident electric field. As expected, both the energy and the number of field nodes increase with the resonance order.

Fig. 4.
Fig. 4.

(a). Transmission spectra calculated for a periodic array of SRRs (red curve), a periodic array of continuous wires (pink dashed curve) and periodic arrays of SRRs and wires with different separations between SRRs and wires: d=130 nm (blue curve), d=50 nm (green dashed curve), d=10 nm (black dashed curve). In each case, the incident electric field is polarized parallel to the gap, the SRR dimensions and lattice period as the same as for structure 1 in Fig. 1(b): Magnitude of the normal electric field component (|Ez|) calculated at the bottom surface of the metallic elements for each of the resonant modes observed in the transmission spectra of Fig. 4(a). The different colours, from blue to red correspond to increasing magnitudes of the field component. Modes are classified according to the resonance order and to the separation d between the SRR and the closest wire.

Tables (1)

Tables Icon

Table 1: comparison between the frequency calculated from formulas (2)–(5) and that measured at the first resonance for each of the four structures studied in this work.

Equations (5)

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ε ( ω ) = 1 ω p 2 ω ( ω + i ω c )
L m = μ 0 l 4 ln 8 l w + t and C m = ε 0 ε r wt g
L eff = l ( S ω p 2 ε 0 )
C eff = ε 0 wt l
f 1 = 1 ( 2 π ( L m + L eff ) × ( C m + C eff ) )

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