Abstract

We studied a metasurface constituted as a periodic array of semiconductor split-ring resonators. The resonance frequencies of the metasurface excited by normally incident light were found to be continuously tunable in the terahertz regime through an external magnetostatic field of suitable orientation. As such metasurfaces can be assembled into 3D metamaterials, the foregoing conclusion also applies to metamaterials comprising semiconductor split-ring resonators.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).
  2. S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
    [CrossRef]
  3. V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
    [CrossRef]
  4. Negative Refraction Metamaterials: Fundamental Principles and Applications, edited by G. V. Eleftheriades and K. G. Balmain (Wiley, Hoboken, NJ, USA, 2005).
  5. C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, Hoboken, NJ, USA, 2006).
  6. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
    [CrossRef] [PubMed]
  7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies,"Science 314, 977-980 (2006)
    [CrossRef] [PubMed]
  8. T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008).
    [CrossRef]
  9. Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
    [CrossRef]
  10. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
    [CrossRef]
  11. Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
    [CrossRef]
  12. L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
    [CrossRef] [PubMed]
  13. A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
    [CrossRef] [PubMed]
  14. M. Lapine and S. A. Tretyakov, "Contemporary notes on metamaterials," IET Microw. Antennas Propag. 1, 3-11 (2007).
    [CrossRef]
  15. Polaritons: Proceedings of the First Taormina Research Conference on the Structure of Matter, edited by E. Burstein and F. De Martini (Pergamon, New York, NY, USA, 1974).
  16. Semiconductors: Physics of Group IV Elements and III-V Compounds, edited by O. Madelung (Springer, Berlin, Germany, 1982).
  17. C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, "The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach," Opt. Express 15, 8871-8883 (2007).
    [CrossRef] [PubMed]
  18. N. Miura, Physics of Semiconductors in High Magnetic Fields (Oxford University Press, Oxford, United Kingdom, 2008).

2008

T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

2007

A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
[CrossRef] [PubMed]

M. Lapine and S. A. Tretyakov, "Contemporary notes on metamaterials," IET Microw. Antennas Propag. 1, 3-11 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, "The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach," Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

2006

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

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

2005

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

2002

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).

Averitt, R. D.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Chipouline, A.

Cummer, S. A.

T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

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

Degiron, A.

Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Giessen, H.

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Hand, T. H.

T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

Harris, V. G.

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

He, P.

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

He, Y.

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

Justice, B. J.

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

Kang, L.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Kuhl, J.

Lakhtakia, A.

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).

Lapine, M.

M. Lapine and S. A. Tretyakov, "Contemporary notes on metamaterials," IET Microw. Antennas Propag. 1, 3-11 (2007).
[CrossRef]

Lederer, F.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

Li, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Liang, X.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

McCall, M. W.

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).

Mock, J. J.

A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
[CrossRef] [PubMed]

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

Padilla, W. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Pendry, J. B.

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

Pertsch, T.

Petschulat, J.

Pshenay-Severin, E.

Ramakrishna, S. A.

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Rockstuhl, C.

Schurig, D.

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

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

Smith, D. R.

A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
[CrossRef] [PubMed]

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

Starr, A. F.

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

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

Tang, H.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Taylor, A. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Tretyakov, S. A.

M. Lapine and S. A. Tretyakov, "Contemporary notes on metamaterials," IET Microw. Antennas Propag. 1, 3-11 (2007).
[CrossRef]

Vittoria, C.

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

Weiglhofer, W. S.

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

Zentgraf, T.

Zhang, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

Zhao, H.

Zhao, Q.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zhou, J.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Appl. Phys. Lett.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

IEEE Trans. Magn.

Y. He, P. He, V. G. Harris, and C. Vittoria, "Role of ferrites in negative index metamaterials," IEEE Trans. Magn. 42, 2852-2854 (2006).
[CrossRef]

IET Microw. Antennas Propag.

M. Lapine and S. A. Tretyakov, "Contemporary notes on metamaterials," IET Microw. Antennas Propag. 1, 3-11 (2007).
[CrossRef]

J. Appl. Phys.

T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008).
[CrossRef]

J. Electron. Commun.

A. Lakhtakia, M. W. McCall and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AE?? Int.J. Electron. Commun. 56, 407-410 (2002).

Nature

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 579-600 (2006).
[CrossRef]

Nature Photon.

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

Opt. Express

Rep. Prog. Phys.

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Science

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686 (2007).
[CrossRef] [PubMed]

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

Other

Negative Refraction Metamaterials: Fundamental Principles and Applications, edited by G. V. Eleftheriades and K. G. Balmain (Wiley, Hoboken, NJ, USA, 2005).

C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, Hoboken, NJ, USA, 2006).

Polaritons: Proceedings of the First Taormina Research Conference on the Structure of Matter, edited by E. Burstein and F. De Martini (Pergamon, New York, NY, USA, 1974).

Semiconductors: Physics of Group IV Elements and III-V Compounds, edited by O. Madelung (Springer, Berlin, Germany, 1982).

N. Miura, Physics of Semiconductors in High Magnetic Fields (Oxford University Press, Oxford, United Kingdom, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) A single SRR with dimensions L=36 µm, T=10 µm, D=2 µm and W=6 µm. (b) The chosen metasurface, which is a square array of SRRs printed on a substrate with a period of 60 µm. (c) Transmittance spectrum of the chosen metasurface illuminated normally by a plane wave with electric field oriented perpendicular to the gaps in the SRR. (d) Map of the magnitude of the electric field in an SRR at 1.59 THz. (e) Map of the current density in an SRR at 1.59 THz. (f) The same as (c) but when both gaps are closed in every SRR.

Fig. 2.
Fig. 2.

Faraday configuration. (a) Transmittance spectra for various values of B 0, when B 0 is aligned parallel to the wave vector of the incident plane wave and the electric field of the incident plane wave is aligned perpendicular to the gaps in each SRR. (b) Resonance frequency ω 0 as a function of B 0, with the solid line showing the exponential fit ω 0=α+βexp(-B 0/χ), where α=0.27, β=2.04, and χ=2.11.

Fig. 3.
Fig. 3.

Real part of ñ as a function of the linear frequency ω/2π and the magnitude B 0 of the applied magnetostatic field in the Faraday configuration.

Fig. 4.
Fig. 4.

First Voigt configuration. (a) Transmittance spectra for various values of B 0, when B 0 is aligned parallel to the gaps in each SRR and the electric field of the incident plane wave is aligned perpendicular to the gaps in each SRR. (b) Resonance frequency ω 0 as a function of B 0, with the solid line showing the exponential fit ω 0=α+βexp(-B 0/χ), where α=0.27, β=1.64, and χ=3.03.

Fig. 5.
Fig. 5.

Real part of ñ as a function of the linear frequency ω/2π and the magnitude B 0 of the applied magnetostatic field in the first Voigt configuration.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ε ( ω ) = ε ω p 2 ( ω 2 + i γ ω ) ,
ε xx = ε yy = ε ω p 2 ( ω 2 + i γ ω ) ( ω 2 + i γ ω ) 2 ω 2 ω c 2 ,
ε xy = ε yx = i ω ω c ω p 2 ( ω 2 + i γ ω ) 2 ω 2 ω c 2 ,
ε zz = ε ω p 2 ( ω 2 + i γ ω ) ,
ε yy = ε zz = ε ω p 2 ( ω 2 + i γ ω ) ( ω 2 + i γ ω ) 2 ω 2 ω c 2 ,
ω yz = ε zy = i ω ω c ω p 2 ( ω 2 + i γ ω ) 2 ω 2 ω c 2 ,
ε xx = ε ω p 2 ( ω 2 + i γ ω ) .
ε xx = ε zz = ε ω p 2 ( ω 2 + i γ ω ) ( ω 2 + i γ ω ) 2 ω 2 ω c 2 ,
ε zx = ε xz = i ω ω c ω p 2 ( ω 2 + ω ) 2 ω 2 ω c 2 ,
ε yy = ε ω p 2 ( ω 2 + ω ) .

Metrics