Abstract

We report on the fabrication, through photolithography techniques, and the detailed characterization, through direct transmission measurements, of a periodic system composed of five layers of photolithographically aligned micrometer-sized Ag split-ring resonators (SRRs). The measured transmission spectra for propagation perpendicular to the SRRs plane show a gap around 6 THz for one of the two possible polarizations of the incident electric field; this indicates the existence of a magnetic resonance, which is verified by detailed theoretical analysis. To our knowledge this is the first time that a system of more than one layer of micrometer-sized SRRs has been fabricated. The measured optical spectra of the Ag microstructure are in very good agreement with the corresponding theoretical calculations.

© 2005 Optical Society of America

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. Holden, D. Robbins, and W. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef] [PubMed]
  5. M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
    [CrossRef]
  6. K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
    [CrossRef]
  7. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
    [CrossRef]
  8. K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
    [CrossRef] [PubMed]
  9. P. Gay-Balmaz and O. J.F. Martin, J. Appl. Phys. 92, 2929 (2002).
    [CrossRef]
  10. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
    [CrossRef]
  11. S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
    [CrossRef]
  12. 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]
  13. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef] [PubMed]
  14. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
    [CrossRef]
  15. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
    [CrossRef]
  16. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]

2004 (7)

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

2003 (1)

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

2002 (3)

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[CrossRef]

P. Gay-Balmaz and O. J.F. Martin, J. Appl. Phys. 92, 2929 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2000 (2)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1996 (1)

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Aydin, K.

K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
[CrossRef] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[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]

Bayindir, M.

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[CrossRef]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. 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]

Gay-Balmaz, P.

P. Gay-Balmaz and O. J.F. Martin, J. Appl. Phys. 92, 2929 (2002).
[CrossRef]

Gregor, R. B.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

Guven, K.

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Holden, A.

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

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Kafesaki, M.

K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
[CrossRef] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

Koschny, T.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

Li, K.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

Linden, S.

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

Markoš, P.

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Martin, O. J.F.

P. Gay-Balmaz and O. J.F. Martin, J. Appl. Phys. 92, 2929 (2002).
[CrossRef]

McLean, S. J.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

McPeake, D.

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

O’ Brien, S.

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Ozbay, E.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
[CrossRef] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Parazzoli, C. G.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

Pendry, J. B.

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

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]

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

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Robbins, D.

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

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Smith, D. R.

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, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

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

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Stewart, W.

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

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Tanielian, M.

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vier, D. C.

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (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]

Youngs, I.

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Zhang, Lei

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.

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

Appl. Phys. Lett. (3)

M. Bayindir, K. Aydin, E. Ozbay, P. Markoš, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).
[CrossRef]

K. Li, S. J. McLean, R. B. Gregor, C. G. Parazzoli, and M. Tanielian, Appl. Phys. Lett. 82, 2535 (2003).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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

J. Appl. Phys. (1)

P. Gay-Balmaz and O. J.F. Martin, J. Appl. Phys. 92, 2929 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (4)

S. O’ Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, Phys. Rev. B 70, 201101(R) (2004).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Science (2)

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

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Left, single unit cell of the SRR geometry studied, in all possible EM field propagation directions and polarizations [(a)–(d)]. Right, top view photograph of the SRR metamaterial fabricated by a microlithography process.

Fig. 2
Fig. 2

Measured transmission spectra for the configurations shown in Figs. 1(c), 1(d).

Fig. 3
Fig. 3

(a) Calculated transmission versus frequency for the configurations shown in Figs. 1(c) (dashed curve) and 1(d) (solid curve). (b) Calculated transmission for the configuration in Fig. 1(a).

Fig. 4
Fig. 4

(a) Real part of the effective permittivity of the SRR metamaterial shown in Fig. 1, for propagation direction and EM field polarization those of Fig. 1(d) (solid curve) and Fig. 1(c) (dashed curve). (b) Real part of the effective permeability of the SRR metamaterial for the orientations of Fig. 1(d) (solid curve), Fig. 1(c) (dashed curve), and Fig. 1(a) (dashed–dotted curve).

Metrics