Abstract

We present a design of dielectric metamaterials exhibiting a broad range of negative effective permeability in the terahertz spectral region. The investigated structures consist of an array of high-permittivity rods that exhibit a series of Mie resonances giving rise to the effective magnetic response. The spectral positions of resonances depend on the geometrical parameters of the rods and on their permittivity, which define the resonant confinement of the electromagnetic field within the rods. The electromagnetic coupling between the adjacent rods is negligible. With a suitable aspect ratio of the rods, a broadband magnetic response can be obtained.

© 2009 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef] [PubMed]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
    [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. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef] [PubMed]
  5. V. Yannopapas and A. Moroz, J. Phys. Condens. Matter 17, 3717 (2005).
    [CrossRef] [PubMed]
  6. S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 4035 (2002).
    [CrossRef]
  7. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
    [CrossRef]
  8. Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
    [CrossRef] [PubMed]
  9. P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
    [CrossRef]
  10. H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
    [CrossRef]
  11. P. Kužel, and F. Kadlec, C. R. Phys. 9, 197 (2008).
    [CrossRef]
  12. Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
    [CrossRef]
  13. http://www.alphanov.com, retrieved October 26, 2009.
  14. http://www.ansoft.com/, retrieved October 26, 2009.
  15. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]

2009 (2)

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

2008 (3)

P. Kužel, and F. Kadlec, C. R. Phys. 9, 197 (2008).
[CrossRef]

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

2006 (1)

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
[CrossRef]

2005 (1)

V. Yannopapas and A. Moroz, J. Phys. Condens. Matter 17, 3717 (2005).
[CrossRef] [PubMed]

2004 (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]

2002 (2)

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 4035 (2002).
[CrossRef]

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

2000 (1)

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

1996 (1)

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

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
[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]

Ding, P.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Du, B.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

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]

Holden, A. J.

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

Hu, W. Q.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Huang, X.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Kadlec, C.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

Kadlec, F.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

P. Kužel, and F. Kadlec, C. R. Phys. 9, 197 (2008).
[CrossRef]

Kang, L.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Koschny, T.

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

Kužel, P.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

P. Kužel, and F. Kadlec, C. R. Phys. 9, 197 (2008).
[CrossRef]

Li, B.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Li, L.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Liang, E. J.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[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.

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

Meng, Y.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
[CrossRef]

Moroz, A.

V. Yannopapas and A. Moroz, J. Phys. Condens. Matter 17, 3717 (2005).
[CrossRef] [PubMed]

Mounaix, P.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[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]

Nemec, H.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

O'Brien, S.

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 4035 (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]

Pendry, J. B.

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 and J. B. Pendry, J. Phys. Condens. Matter 14, 4035 (2002).
[CrossRef]

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

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]

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.

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

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

Stewart, W. J.

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

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]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
[CrossRef]

Xie, Q.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Xue, Q. Z.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Yahiaoui, R.

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Moroz, J. Phys. Condens. Matter 17, 3717 (2005).
[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. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Zhang, L.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Zhang, X.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[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]

Zhao, H.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Zhao, Q.

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhou, J.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

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

Zhou, Q.

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

Q. Zhao, B. Du, L. Kang, H. Zhao, Q. Xie, B. Li, X. Zhang, J. Zhou, L. Li, and Y. Meng, Appl. Phys. Lett. 92, 051106 (2008).
[CrossRef]

C. R. Phys. (1)

P. Kužel, and F. Kadlec, C. R. Phys. 9, 197 (2008).
[CrossRef]

J. Phys. Condens. Matter (2)

V. Yannopapas and A. Moroz, J. Phys. Condens. Matter 17, 3717 (2005).
[CrossRef] [PubMed]

S. O'Brien and J. B. Pendry, J. Phys. Condens. Matter 14, 4035 (2002).
[CrossRef]

Photonics Nanostruct. Fundam. Appl. (1)

P. Ding, E. J. Liang, W. Q. Hu, L. Zhang, Q. Zhou, Q. Z. Xue, Photonics Nanostruct. Fundam. Appl. 7, 92 (2009).
[CrossRef]

Phys. Rev. B (3)

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, Phys. Rev. B 79, 241108(R) (2009).
[CrossRef]

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

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B 73, 045108 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, Phys. Rev. Lett. 101, 027402 (2008).
[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]

J. B. Pendry, A. J. Holden, W. J. 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]

Other (2)

http://www.alphanov.com, retrieved October 26, 2009.

http://www.ansoft.com/, retrieved October 26, 2009.

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Figures (3)

Fig. 1
Fig. 1

(a) Geometry of the MM structure. (b) Measured and calculated transmission amplitude spectra of the studied sample at room temperature. Mie resonances are indicated by arrows. (c) Resonant frequencies as a function of the thickness e. (d) Resonant frequencies as a function of Re ϵ of the rods. Symbols, experiment; lines, calculations. The resonance indicated by the dash–dotted curve has a nonmagnetic character.

Fig. 2
Fig. 2

Left panel, calculated spectra of effective μ for a periodic structure of alternating rods with three different widths a, b, and c. Solid curve, a = 50 μ m , b = 30 μ m , c = 20 μ m , g = 20 μ m ; dots, same values of a, b, c, but g = 2 μ m ; dashed curve, a = b = c = 30 μ m , g = 20 μ m ; e = 50 μ m for all structures. Right panel, sections of a unit cell of the MM with the spatial distribution of the resonant magnetic field. The ratios H max H inc of the maximum and incident fields are 2.6 at 0.240 THz , 2.9 at 0.334 THz , and 2.4 at 0.458 THz .

Fig. 3
Fig. 3

(a) Calculated amplitude transmittance for several widths a of STO rods ( g = 30 μ m , e = 20 μ m , tan δ = 2.5 % ) and (b) the corresponding effective μ. (c) Effective μ for a = 200 μ m and tan δ from 0.1% to 5%. (d) Spatial distribution of the resonant magnetic field inside the rods for a = 200 μ m and tan δ = 2.5 % ; the ratios H max H inc of the maximum and incident fields are 19.6 at 0.435 THz , 15.4 at 0.450 THz , 12.2 at 0.483 THz , and 8.7 at 0.527 THz .

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