Abstract

A symmetric metamaterial superlattice is introduced accommodating a high Q-factor trapped mode. THz time-domain spectroscopy is employed to measure the transmission spectra, identifying the excitation of trapped and open-modes in the meta-resonances. A finite-difference-time-domain calculation showed that the trapped mode excitation is from the cancelation of current densities among the nearest-neighboring meta-particles. A cryogenic temperature THz measurement is carried out to examine the temperature dependence of resonance characteristics of meta-resonances. At low temperatures, the temperature-independent radiative damping is dominant for the open-mode, while the Q-factor of the trapped mode is determined by the temperature-dependent phonon scattering and temperature-independent defect scattering with the radiative damping significantly suppressed. When compared with the room temperature measurement, a 16% increase in Q-factor is observed for the trapped mode, while a 7% increase for the open-mode at the cryogenic temperature.

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References

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  1. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
    [Crossref] [PubMed]
  2. B. Kang, E. Choi, H.-H. Lee, E. Kim, J. Woo, J. Kim, T. Hong, J. Kim, and J. Wu, “Polarization angle control of coherent coupling in metamaterial superlattice for closed mode excitation,” Opt. Express 18, 11552–11561 (2010).
    [Crossref] [PubMed]
  3. R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
    [Crossref]
  4. V. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. Zheludev, “Temperature control of fano resonances and transmission in superconducting metamaterials,” Opt. Express 18, 9015–9019 (2010).
    [Crossref] [PubMed]
  5. S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in “Advances in Electromagnetics of Complex Media and Metamaterials,” S. Zouhdi and et al., ed. (Kluwer Academic Publishers, 2003), pp. 281–290.
  6. See http://www.teraview.com .
  7. See http://www.lumerical.com .
  8. B. Kang, J. Woo, E. Choi, H.-H. Lee, E. Kim, J. Kim, T.-J. Hwang, Y.-S. Park, D. Kim, and J. Wu, “Optical switching of near infrared light transmission in metamaterial-liquid crystal cell structure,” Opt. Express 18, 16492–16498 (2010).
    [Crossref] [PubMed]
  9. S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
    [Crossref]
  10. M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
    [Crossref]
  11. S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
    [Crossref]
  12. T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72, 3032 (1998).
    [Crossref]
  13. N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008).
    [Crossref]
  14. N. Ashcroft and N. Mermin, Solid State Physics (Saunders, 1976).

2010 (4)

2008 (1)

N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008).
[Crossref]

2007 (1)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

2005 (1)

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

2002 (1)

M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
[Crossref]

2001 (1)

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

1998 (1)

T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72, 3032 (1998).
[Crossref]

Ashcroft, N.

N. Ashcroft and N. Mermin, Solid State Physics (Saunders, 1976).

Bain, M.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Buckingham, R.

Chen, Y.

Choi, E.

de Groot, P.

Fedotov, V.

Fedotov, V. A.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Gamble, H. S.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Grischkowsky, D.

N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008).
[Crossref]

T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72, 3032 (1998).
[Crossref]

Gu, J.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Han, J.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Hangyo, M.

M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
[Crossref]

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

Harrison, P.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Hong, T.

Hwang, T.-J.

Ikonic, Z.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72, 3032 (1998).
[Crossref]

Kang, B.

Kelsall, R. W.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Kim, D.

Kim, E.

Kim, J.

Laman, N.

N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008).
[Crossref]

Lee, H.-H.

Lynch, S. A.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Matmon, G.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Mermin, N.

N. Ashcroft and N. Mermin, Solid State Physics (Saunders, 1976).

Morikawa, O.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

Nagashima, T.

M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
[Crossref]

Nashima, S.

M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
[Crossref]

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

Papasimakis, N.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Park, Y.-S.

Paul, D. J.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Prosvirnin, S.

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in “Advances in Electromagnetics of Complex Media and Metamaterials,” S. Zouhdi and et al., ed. (Kluwer Academic Publishers, 2003), pp. 281–290.

Prosvirnin, S. L.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Rockstuhl, C.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Shi, J. H.

Singh, R.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Takata, K.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

Tian, Z.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Townsend, P.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Tsiatmas, A.

Wang, S.

Woo, J.

Wu, J.

Zhang, J.

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

Zhang, W.

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

Zheludev, N.

Zheludev, N. I.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Zouhdi, S.

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in “Advances in Electromagnetics of Complex Media and Metamaterials,” S. Zouhdi and et al., ed. (Kluwer Academic Publishers, 2003), pp. 281–290.

Appl. Phys. Lett. (4)

R. Singh, Z. Tian, J. Han, C. Rockstuhl, J. Gu, and W. Zhang, “Cryogenic temperatures as a path toward high-q terahertz metamaterials,” Appl. Phys. Lett. 96, 071114 (2010).
[Crossref]

S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble, J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, “Temperature dependence of terahertz optical transitions from boron and phosphorus dopant impurities in silicon,” Appl. Phys. Lett. 87, 101114 (2005).
[Crossref]

T.-I. Jeon and D. Grischkowsky, “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Appl. Phys. Lett. 72, 3032 (1998).
[Crossref]

N. Laman and D. Grischkowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93, 051105 (2008).
[Crossref]

J. Appl. Phys. (1)

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Temperature dependence of optical and electronic properties of moderately doped silicon at terahertz frequencies,” J. Appl. Phys. 90, 837 (2001).
[Crossref]

Meas. Sci. Technol. (1)

M. Hangyo, T. Nagashima, and S. Nashima, “Spectroscopy by pulsed terahertz radiation,” Meas. Sci. Technol. 13, 1727 (2002).
[Crossref]

Opt. Express (3)

Phys. Rev. Lett. (1)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
[Crossref] [PubMed]

Other (4)

S. Prosvirnin and S. Zouhdi, “Resonances of closed modes in thin arrays of complex particles,” in “Advances in Electromagnetics of Complex Media and Metamaterials,” S. Zouhdi and et al., ed. (Kluwer Academic Publishers, 2003), pp. 281–290.

See http://www.teraview.com .

See http://www.lumerical.com .

N. Ashcroft and N. Mermin, Solid State Physics (Saunders, 1976).

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Figures (7)

Fig. 1
Fig. 1

Schematic drawings of (a) grating-wavy-strip [5] and (b) symmetric metamaterial superlattice are shown.

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Fig. 2
Fig. 2

(a) Optical microscope picture of symmetric metamaterial superlattice, (b) room temperature THz transmission spectra for various polarization angles, and (c) absorbance plot of THz spectra for 0° and 90° incident polarizations are shown.

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Fig. 3
Fig. 3

Current density plots of (a) Jx and (b) Jy, and (c) schematic drawing of current flows in the trapped mode are shown.

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Fig. 4
Fig. 4

Current density plots of (a) Jx and (b) Jy, and (c) schematic drawing of current flows in the open-mode are shown. The thickness of arrows in (c) is proportional to the magnitude of current densities.

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Fig. 7
Fig. 7

Temperature dependence of the Q-factor of trapped and open-mode of symmetric metamaterial superlattice is shown. The solid curve is fit to the experimental data with Eq. (1)

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Fig. 5
Fig. 5

3-dimensional plot of THz (a)&(b) amplitude transmission and (c)&(d) phase spectra for silicon substrate and symmetric metamaterial superlattice.

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Fig. 6
Fig. 6

Temperature dependence of THz transmission spectra of the symmetric metamaterial superlattice is shown.

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Equations (3)

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

Γ = Γ R + Γ D + Γ P ( T ) .
Γ closed ( f = 1.2 THz ) = 0.062 + ( 3.4 ± 0.1 ) × 10 − 5 T
Γ open ( f ≈ 2.4 THz ) = 0.26 + ( 5.6 ± 0.5 ) × 10 − 5 T

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