Abstract

We explain the origin of the electric and particular the magnetic polarizabiltiy of metamaterials employing a fully electromagnetic plasmonic picture. As example we study an U-shaped split-ring resonator based metamaterial at optical frequencies. The relevance of the split-ring resonator orientation relative to the illuminating field for obtaining a strong magnetic response is outlined. We reveal higher-order magnetic resonances and explain their origin on the basis of higher-order plasmonic eigenmodes caused by an appropriate current flow in the split-ring resonator. Finally, the conditions required for obtaining a negative index at optical frequencies in a metamaterial consisting of split-ring resonators and wires are investigated.

© 2007 Optical Society of America

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  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  2. D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
    [CrossRef]
  3. L. Lewin, "The electrical constants of a material loaded with spherical particles," Proc. Inst. Elec. Eng.  94, 65-68 (1947).
  4. V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. Condens. Matter 17, 3717-3734 (2005).
    [CrossRef] [PubMed]
  5. V. Yannopapas, "Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres," Phys. Rev. B 75, 035112 (2007).
    [CrossRef]
  6. V. Yannopapas and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength," Phys. Rev. B 74, 193304 (2006).
    [CrossRef]
  7. W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
    [CrossRef]
  8. S. A. Schelkunoff and H. T. Friis, "Antennas: theory and practice", (New York, John Wiley & Son, 1952).
  9. J. P. 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]
  10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  11. 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, 037402 (2005).
    [CrossRef] [PubMed]
  12. N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
    [CrossRef]
  13. M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
    [CrossRef]
  14. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
    [CrossRef]
  15. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
    [CrossRef]
  16. V. V. Varadan and A. R. Tellakula, "Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
    [CrossRef]
  17. P. Markoš and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
    [CrossRef]
  18. T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
    [CrossRef]
  19. U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
    [CrossRef] [PubMed]
  20. 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]
  21. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  22. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  23. 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]
  24. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
    [CrossRef]
  25. 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, 195104 (2002).
    [CrossRef]
  26. F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
    [CrossRef]
  27. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
    [CrossRef] [PubMed]
  28. T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
    [CrossRef]
  29. 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 (1997).
    [CrossRef]
  30. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
    [CrossRef] [PubMed]
  31. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]

2007

V. Yannopapas, "Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres," Phys. Rev. B 75, 035112 (2007).
[CrossRef]

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

2006

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (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]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

V. V. Varadan and A. R. Tellakula, "Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

V. Yannopapas and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength," Phys. Rev. B 74, 193304 (2006).
[CrossRef]

2005

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. Condens. Matter 17, 3717-3734 (2005).
[CrossRef] [PubMed]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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, 037402 (2005).
[CrossRef] [PubMed]

2004

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[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]

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

2003

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

2002

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, 195104 (2002).
[CrossRef]

P. Markoš and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

2000

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]

1999

J. P. 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]

1997

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 (1997).
[CrossRef]

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

1972

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

1962

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

1947

L. Lewin, "The electrical constants of a material loaded with spherical particles," Proc. Inst. Elec. Eng.  94, 65-68 (1947).

Augustin, M.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Aydin, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

Bauerschäfer, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Bermel, P.

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, 037402 (2005).
[CrossRef] [PubMed]

Bulu, I.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Burr, G. W.

Chettiar, U. K.

Christy, R. W.

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

Dolling, G.

Economou, E. N.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

Enkrich, C.

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.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (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] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Fan, W.

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

Farjadpour, A.

Frauenglass, A.

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

Fu, L.

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

Garwe, F.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Giessen, H.

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (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] [PubMed]

Gundogdu, T. F.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

Guo, H.

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Guven, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

Holden, A. J.

J. P. 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 (1997).
[CrossRef]

Hübner, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Ibanescu, M.

Joannopoulos, J. D.

Johnson, P. B.

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

Johnson, S. G.

Kafesaki, M.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

Kaiser, S.

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

Kildishev, A. V.

Klar, T. A.

Koschny, T.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (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]

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

Kuhl, J.

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]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Lederer, F.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (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] [PubMed]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Lewin, L.

L. Lewin, "The electrical constants of a material loaded with spherical particles," Proc. Inst. Elec. Eng.  94, 65-68 (1947).

Li, L.

Linden, S.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[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, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Loa, I.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Mahdjoubi, K.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Malloy, K. 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, 037402 (2005).
[CrossRef] [PubMed]

Markoš, P.

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

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

P. Markoš and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Meyrath, T. P.

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

Minhas, B. K.

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

Moroz, A.

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. Condens. Matter 17, 3717-3734 (2005).
[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.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

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.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

Pendry, J. B.

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

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 (1997).
[CrossRef]

Pendry, J. P.

J. P. 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]

Pertsch, T.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Robbins, D. J.

J. P. 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 (1997).
[CrossRef]

Rockstuhl, C.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (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] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Rodriguez, A.

Rotman, W.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

Roundy, D.

Sauleau, R.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Schultz, S.

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

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

Schweizer, H.

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

Seetharamdoo, D.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Setzpfandt, F.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Shalaev, V. M.

Smith, D. R.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

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

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

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (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]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

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

P. Markoš and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Soukoulis, C.M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Soukoulis, M.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

Stewart, W. J.

J. P. 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 (1997).
[CrossRef]

Syassen, K.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

Tarot, A.-C.

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

Tellakula, A. R.

V. V. Varadan and A. R. Tellakula, "Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

Tünnermann, A.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

Varadan, V. V.

V. V. Varadan and A. R. Tellakula, "Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (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]

Vitanov, N. V.

V. Yannopapas and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength," Phys. Rev. B 74, 193304 (2006).
[CrossRef]

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
[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]

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] [PubMed]

Yannopapas, V.

V. Yannopapas, "Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres," Phys. Rev. B 75, 035112 (2007).
[CrossRef]

V. Yannopapas and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength," Phys. Rev. B 74, 193304 (2006).
[CrossRef]

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. Condens. Matter 17, 3717-3734 (2005).
[CrossRef] [PubMed]

Zentgraf, T.

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (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] [PubMed]

Zhang, L.

Zhang, S.

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, 037402 (2005).
[CrossRef] [PubMed]

Zhou, J.

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]

Appl. Phys. B

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, "Resonances of split-ring resonator metamaterials in the near infrared," Appl. Phys. B 84, 219-227 (2006).
[CrossRef]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, "Evaluation of gold nanowire pairs as a potential negative index material," Appl. Phys. B 84, 139-148 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. P. 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]

IRE Trans. Antennas Propag.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. 10, 82-95 (1962).
[CrossRef]

J. Appl. Phys.

V. V. Varadan and A. R. Tellakula, "Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A.-C. Tarot, "Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity," J. Appl. Phys. 98, 063505 (2005).
[CrossRef]

J. Opt. A: Pure Appl. Opt

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, M. Soukoulis, "Left-handed metamaterials: detailed numerical studies of the transmission properties," J. Opt. A: Pure Appl. Opt 7, S12-S22 (2005).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Condens. Matter

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 (1997).
[CrossRef]

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. Condens. Matter 17, 3717-3734 (2005).
[CrossRef] [PubMed]

New J. Phys.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

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, 195104 (2002).
[CrossRef]

T. P. Meyrath, T. Zentgraf, and H. Giessen, "Lorentz model for Metamaterials: Optical frequency resonance circuits," Phys. Rev. B 75, 205102 (2007).
[CrossRef]

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

V. Yannopapas, "Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres," Phys. Rev. B 75, 035112 (2007).
[CrossRef]

V. Yannopapas and N. V. Vitanov, "Photoexcitation-induced magnetism in arrays of semiconductor nanoparticles with a strong excitonic oscillator strength," Phys. Rev. B 74, 193304 (2006).
[CrossRef]

Phys. Rev. E

P. Markoš and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

T. Koschny, P. Markoš, D. R. Smith and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003).
[CrossRef]

Phys. Rev. Lett.

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]

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, 037402 (2005).
[CrossRef] [PubMed]

Phys. Status Solidi B

N. Liu, H. Guo, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, "Electromagnetic resonances in single and double split-ring resonator metamaterials in the near infrared," Phys. Status Solidi B 224, 1251-1255 (2007).
[CrossRef]

Proc. Inst. Elec. Eng

L. Lewin, "The electrical constants of a material loaded with spherical particles," Proc. Inst. Elec. Eng.  94, 65-68 (1947).

Science

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[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

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Figures (7)

Fig. 1.
Fig. 1.

Spectral response (R-reflectance, T -transmittance) of an array of SRRs as described in the text for an electric field polarization parallel (a) and perpendicular to the gap (c). The corresponding excitation geometry is schematically shown in (b) and (d), respectively. The geometrical details of a single SRR are shown in (e).

Fig. 2.
Fig. 2.

(a) Transmittance and reflectance for the two cases shown in (b). Retrieved effective refractive index (b), effective permittivity (c), and effective permeability (d) for the two possible orientations of the SRR at parallel incidence and an electric field polarized parallel to the gap. The geometry of the two configurations is shown on top of the figure.

Fig. 3.
Fig. 3.

(a) Transmittance and reflectance for the geometry shown in (b). Retrieved effective permittivity (c) and effective permeability (d) for the orientation of the SRR at parallel incidence and an electric field polarized perpendicularly to the gap.

Fig. 4.
Fig. 4.

Amplitude of the electric field component perpendicularly to the SRR surface at the three different resonance frequencies indicated in the figures. The illuminating plane wave is x -polarized and propagates in the positive z-direction. The arrows indicate the direction of current flow in the structure. Please note that this represents a snapshot. The direction will reverse with the frequency of the illumination. The direction of the currents flowing in the SRR was deduced from the FDTD simulations.

Fig. 5.
Fig. 5.

Diffraction efficiencies and retrieved effective material parameters for a medium made of SRRs (blue solid line), of thin metallic wires (red dashed line), and a combination of both (green dashed-dotted line). (a) shows the transmitted and (b) the reflected diffraction efficiency. In (c, d) the effective permittivities and in (e,f) the effective permeabilities are shown, respectively. The corresponding effective refractive indices for these values are shown in (g, h).

Fig. 6.
Fig. 6.

Transmission (a), real part of the effective permittivity (b), the permeability (c), and the refractive index (d) for a medium comprising SRRs and metallic wires as a function of the height h of the wires.

Fig. 7.
Fig. 7.

Real part of the effective refractive index if the SRR and the wire with a height of h = 80 nm in different dielectric environments. The blue solid curve shows the structure completely surrounded by air. The green dashed curve shows the structure as deposited on a substrate with n = 1.5. The red solid-dashed curve shows the real part of the effective refractive index if the background medium in the unit cell is a dielectric medium with n = 1.5 instead of air but the unit cell itself is yet surrounded by air. Finally the black dotted solid curve shows the effective index if this structure is finally deposited on a substrate. The latter structure is the structure which is technological feasible to fabricate.

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