Abstract

We present magnetic metamaterials composed of 35nm minimum feature-size gold split-ring resonators with a fundamental magnetic resonance at a wavelength of 900nm. Corresponding calculations reveal excellent agreement with the experiments and show that the limits of size scaling have been reached.

© 2006 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  3. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
    [CrossRef] [PubMed]
  4. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
    [CrossRef] [PubMed]
  5. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef] [PubMed]
  6. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
    [CrossRef] [PubMed]
  7. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
    [CrossRef]
  8. S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 6383 (2002).
    [CrossRef]
  9. S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
    [CrossRef]
  10. J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
    [CrossRef] [PubMed]
  11. A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
    [CrossRef] [PubMed]
  12. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]

2005

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

2004

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

2002

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 6383 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Economou, E. N.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Gerthsen, D.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kafesaki, M.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Koschny, T.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

McPeake, D.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

O'Brien, S.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 6383 (2002).
[CrossRef]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 6383 (2002).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Pérez-Willard, F.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

Ramakrishna, S. A.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Wegener, M.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhou, J. F.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Adv. Mater.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. F. Zhou, C. M. Soukoulis, M. Wegener, and S. Linden, Adv. Mater. 17, 2547 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

J. Phys. Condens. Matter

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 6383 (2002).
[CrossRef]

Phys. Rev. B

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, R241101 (2004).
[CrossRef]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

J. F. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Oblique-view electron micrograph of the gold SRR array. The upper inset shows a top-view image, and the black line depicts the lateral dimensions of the SRR used in the calculations. The lower inset is a corresponding perspective view, shown on the same scale as the large micrograph.

Fig. 2
Fig. 2

First row: experimental transmittance spectra for (a) horizontal and (b) vertical incident polarization (see arrows). The inset shows a top-view electron micrograph of a gold SRR. Second row: (c) and (d) exhibit corresponding calculated spectra (solid curves). To mimic the influence of inhomogeneous broadening, the dashed curve depicted in both (a) and (c) is the convolution of the solid curve in (c) with a Gaussian distribution ( HWHM = 3 % of the center frequency). The magnetic resonance frequency (see Fig. 3) is indicated by an arrow in (a).

Fig. 3
Fig. 3

Scaling behavior of the magnetic resonance frequency [compare arrow in Fig. 2a]. The SRR size is referenced with respect to the parameters of Fig. 2 (see arrow here). (i) For the circles, all geometrical parameters and the lattice constant are scaled by the same scale factor s. (ii) For the triangles, only the lateral parameters are scaled, the thickness is fixed. For the open symbols, the measured metal permittivity of gold is used in the calculations, while for the full symbols a Drude permittivity for gold is used. The solid curve corresponds to a fit using the simple formula ω L C 1 s 2 + const. , yielding ω L C max = 2 π × 373 THz ; the dashed curves are guides to the eye. The crosses are for (i), but for silver rather than for gold.

Equations (1)

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ω L C 1 s 2 + const . .

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