Abstract

Superconducting planar terahertz (THz) metamaterials (MMs), with unit cells of different sizes, are fabricated on 200 nm-thick niobium nitride (NbN) films deposited on MgO substrates. They are characterized using THz time domain spectroscopy over a temperature range from 8.1 K to 300 K, crossing the critical temperature of NbN films. As the gap frequency (fg = 2Δ0/h, where Δ0 is the energy gap at 0 K and h is the Plank constant) of NbN is 1.18 THz, the experimentally observed THz spectra span a frequency range from below fg to above it. We have found that, as the resonance frequency approaches fg, the relative tuning range of MMs is quite wide (30%). We attribute this observation to the large change of kinetic inductance of superconducting film.

© 2011 OSA

1. Introduction

The development of metamaterials (MMs), which acquire their electromagnetic properties from artificial subwavelength metallic elements rather than the composition, has led to the realization of properties and applications that cannot be obtained with natural materials [1,2]. At terahertz (THz) frequencies, the new class of MMs is viewed as efficient devices for manipulating THz waves [36]. The resonant properties of planar metamaterials could be tuned by varying the surface impedance of metallic film, such as changing the thickness of the metallic film or engineering the conductivity [7,8]. Superconducting THz MMs have recently drawn great attentions in the THz and MMs fields, due to their low ohmic loss as well as their thermal and magnetic-field tuning behaviors [913]. When the temperature is close to the transition temperature (Tc) and adjusted over even a rather narrow range, large tuning can be obtained due to the large change of effective kinetic inductance of superconducting film. This change is enhanced as the working frequency is going higher. However, these behaviors cannot be observed if the frequency of the THz wave is much higher than the gap frequency fg = 2Δ0/h, where Δ0 is the energy gap of the superconductor at 0 K, and h is the Plank constant. Thus it is expected that a wide tuning range can be obtained as the frequency is approaching fg.

Here we look at the THz transmissions through a class of electrically resonant superconducting MMs with resonance frequencies going from below fg to above it. The MMs are made from 200 nm-thick niobium nitride (NbN) films. It is shown that the resonance strengths of NbN MMs are persistently high when the frequency is below fg but drop sharply beyond fg. And the relative frequency tuning range [f(Tc)-fmin]/f(Tc) is the largest (up to 30%) as the resonance frequency approaches fg, where f(Tc) and fmin and are the resonance frequency at the critical temperature Tc and the minimum of the resonance frequency in superconducting state, respectively.

2. Experiments and discussions

The electric inductive-capacitive (ELC) resonator structure is used in our work [1416]. Figure 1(a) shows the planar geometry of a unit cell. The geometric parameters are set to be l = a, t = 0.1a, g = 0.1a, w = 0.2a, and the dimensions of each unit cell is 1.2a × 1.2a. Four samples are fabricated (denoted by S1, S2, S3 and S4) with the same structure but different values of a, a = 20, 25, 35, and 50 μm respectively. Assuming that the films are ideal conducting ones, we have found by simulations the fundamental frequencies of S1-S4 to be 1.44, 1.17, 0.84, and 0.59 THz respectively, revealing the fact that the larger the sizes of the unit cell are, the lower the resonance frequencies are [17]. For our NbN films, Δ0 calculated from previous measurements [18] is 2.45 meV, and thus fg is 1.18 THz, which is below the resonance frequency of S1. Therefore, the transmission characteristics of superconducting NbN THz MMs can be studied over a range when the resonance frequency changes from below fg to above it.

 

Fig. 1 (a) The planar geometry of single ELC structure. (b) The photo micrograph of S4, and the incident polarized electric field is parallel to the gap.

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The NbN films used in our experiments typically have Tc = 15.8 K and are deposited on 500 μm-thick MgO substrates (<100> orientation) using RF magnetron sputtering. The thickness of NbN film (d) is 200 nm for each sample. Photolithography and reactive ion etching are used to pattern the film surface periodical ELC resonator structure. The optical micrograph image of S4 is shown in Fig. 1(b). The samples are mounted in a continuous flow liquid helium cryostat, which is installed in the THz time domain spectroscopy (TDS) system. The THz transmission spectra are measured in a temperature range of 8.1-300 K using a bare MgO substrate as the reference. In the measurements, the electric fields are applied parallel to the gap of capacitor (shown in Fig. 1(b)).

Shown in Figs. 2(a) and 2(b) are the transmission spectra of S1-S4 at 18 K and 8.1 K. At 18 K, the resonance frequencies for S1-S4 are 1.47, 1.24, 0.84 and 0.60 THz respectively, which agree with the simulation. When temperature lowers to 8.1 K, these frequencies become 1.25, 1.02, 0.80 and 0.58 THz. Now, the resonance frequency of S1 remains to be larger than fg. When the samples go from normal to superconducting, all the resonance frequencies decrease. This is attributed to the occurrence of kinetic inductance in superconducting states. At 18 K, the resonance transmission minima are all around −5 dB. As temperature goes down to 8.1 K, these values are about −30 dB except for S1, in which case the minimum is −11.9 dB and MMs made of superconducting films do not seem to be superior to that made of normal metal.

 

Fig. 2 THz transmission spectra of S1-S4 (a) at 18 K and (b) at 8.1 K.

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Based on transmission-line RLC model, the power transmission coefficient at resonance frequency can be approximated as follows [19,20],

T=(1+ns1+ns+Z0/R)2,
where ns is the refractive index of substrate, Z0 is the impedance of vacuum, and R is the resistance of ELC resonator at resonance frequency. And R can be calculated by the equation, R = Rs·(3.02l/t) = 30.2Rs, where Rs is the surface resistance of smooth NbN film, and 3.02l is the equivalent length of loop [21]. From Eq. (1) we can know the deep resonant minima mean low R, or relatively low loss of the superconducting MMs. The large resonant minimum for S1 is because its resonance frequency is larger than fg. Based on BCS theory, the NbN film has a s-wave pair symmetry without nodes in the gap, and keep a constant value in all directions in momentum space [22]. As the frequency of incident photons is large than fg, almost all paired electrons are broken into quasi-particles, leading to the abrupt increase of Rs and a large decrease of depth of the resonant minimum.

Quantitatively, Rs can be calculated from the following equation [23],

Rs=Re[(jωμ0/σ)coth(djωμ0σ)],
where σ is the complex conductivity of NbN film. Then Rs is obtained through theoretic simulation in the framework of the BCS theory [18,24], and the resonant minimum as a function of the resonance frequency is plotted in Fig. 3(a) (solid line). A relative good agreement between the measurements (square dots) and the calculations is obtained. Here it is important to note that the radiation loss, which arises from the coupling of MMs to free space radiation, is not considered in the simulation [7,9,25]. In the low frequency region, the radiation loss may play an important role in the total loss, making it very difficult to obtain a deep resonant minimum. Recently, the suppression of radiation loss has been demonstrated by introducing asymmetry in split ring resonators to excite sharp Fano resonance which weakly couples to free space, or packing the unit cell at an optimal periodicity to confine electromagnetic fields in MM array [26,27].

 

Fig. 3 (a) The simulated (square dots) and measured (solid line) resonant minimum as a function of resonance frequency at 8.1 K. (b) The temperature dependence of resonance frequency normalized with the resonance frequency at 16 K for S1-S4

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The temperature dependence of the resonance frequencies for all samples is also studied. Figure 3(b) shows the normalized resonance frequency f(T)/f(16K) as a function of temperature. We have found that a large relative tuning range up to 30% can be obtained as the resonance frequency approaches to fg. And this is the largest tuning so far we can achieve. The physical reason is that the biggest change of inductance of superconducting loop happens in this case. The geometric inductance (Lg) can be calculated as follows, Lg≈μ0(πA)1/2 = μ0l(π/2)1/2, where μ0 is the permeability of vacuum and A = (l/2)1/2 is the area of small rectangle loop [21]. The kinetic inductance (Lk) is distinct for MMs in superconducting state, and it can be estimated by the formula, Lk≈μ0λcoth(d/λ)·(3.02l/t), where λ is the penetration depth of NbN film [21,23]. Thus, the normalized change of inductance can be calculated as follows,

ΔL/LLk/Lg=2.41λcoth(d/λ)/t.

When frequency is below fg, λ is almost constant, so the smaller t of S2 leads to the comparatively larger ΔL/L than S3 and S4. As resonance frequency exceeds fg, the Lk is seriously degraded due to strong absorption of photons. The above factors result in the large frequency change of S2 since its resonance frequency is closest to fg. This provides a nice method to tune the frequency by temperature.

Changing the thickness of the metal film, at the scale of the skin depth, offers an effective way to control the resonance property of THz MMs [8]. The similar tuning behavior also occurs in superconducting MMs. Remarkable enhancement of frequency tuning range by reducing the film thickness has been demonstrated in YBCO MMs [13]. According to Eq. (3), reducing d of NbN film could enhance ΔL/L. Thus, we fabricate another sample (denoted by S5) with the same structure as S2 but the NbN film is 100 nm-thick NbN film in an attempt to improve the frequency tuning property, The temperature dependent transmission spectra are measured and plotted in Fig. 4 . The resonance frequency shifts from 966 GHz at 8.1 K to 754 GHz at 13 K (indicated by arrow). The 212 GHz red-shift of resonance frequency is much wider than the red-shift of S2 (146 GHz) and the other three samples. However, as S5 goes into normal state, the resonance dip is not easy to discern because of the increased ohmic resistance as NbN film becomes thinner. What is more, such frequency tuning occurs in a quite smaller temperature range compared with MMs fabricated from metallic films on ferroelectric substrate [28], meaning faster response. Furthermore, if the ELC resonator is substituted with an improved resonator structure, which exhibits larger ΔL/L in superconducting state, we could get better tuning property. Therefore, the potential is great to boost the frequency tuning range of NbN MMs.

 

Fig. 4 Transmission spectra of S5 at various temperatures. The arrow indicates the resonance frequency of S5 at 13 K.

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3 Conclusions

In summary, we have demonstrated that the superconducting NbN MMs exhibit remarkably high resonance strength until their resonance frequencies reach fg. Moreover, the MMs with resonance frequency approaching fg have wide tuning properties due to relatively large change of inductance. And appropriate modification in resonator structure will improve the tuning capability of superconducting MMs further. We expect that our results could contribute to the applications of superconducting MMs in tunable broadband THz devices.

Acknowledgments

This work is supported by the MOST 973 Project of China (No. 2007CB310404, No. 2011CBA00107), the National Natural Science Foundation (No. 61071009), the Program for New Century Excellent Talents in University (NCET-07-0414), the Fundamental Research Funds for the Central Universities (021014360004) and the Specialized Research Fund for Doctoral Program of Higher Education (20090091110040).

References and links

1. D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef]   [PubMed]  

2. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]  

3. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef]   [PubMed]  

4. 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(7119), 597–600 (2006). [CrossRef]   [PubMed]  

5. H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

6. W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009). [CrossRef]  

7. R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008). [CrossRef]   [PubMed]  

8. R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008). [CrossRef]   [PubMed]  

9. 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(7), 071114 (2010). [CrossRef]  

10. J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010). [CrossRef]  

11. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010). [CrossRef]   [PubMed]  

12. B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010). [CrossRef]   [PubMed]  

13. H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010). [CrossRef]  

14. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]  

15. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006). [CrossRef]  

16. H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef]   [PubMed]  

17. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005). [CrossRef]   [PubMed]  

18. L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011). [CrossRef]  

19. A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008). [CrossRef]  

20. J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

21. T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, Second Edition, (Cambridge University Press, 2004), Chap. 4.

22. M. Tinkham, Introduction to superconductivity, (McGraw-Hill, 1980)

23. M. J. Lancaster, Passive Microwave Device Applications of High-Temperature superconductors, (Cambridge University Press, 2006), Chap. 1.

24. S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997). [CrossRef]  

25. T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005). [CrossRef]  

26. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011). [CrossRef]   [PubMed]  

27. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010). [CrossRef]  

28. R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011). [CrossRef]   [PubMed]  

References

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  1. D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [CrossRef] [PubMed]
  2. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [CrossRef]
  3. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
    [CrossRef] [PubMed]
  4. 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(7119), 597–600 (2006).
    [CrossRef] [PubMed]
  5. H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).
  6. W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
    [CrossRef]
  7. R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
    [CrossRef] [PubMed]
  8. R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
    [CrossRef] [PubMed]
  9. 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(7), 071114 (2010).
    [CrossRef]
  10. J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
    [CrossRef]
  11. V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010).
    [CrossRef] [PubMed]
  12. B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
    [CrossRef] [PubMed]
  13. H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
    [CrossRef]
  14. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
    [CrossRef]
  15. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
    [CrossRef]
  16. H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
    [CrossRef] [PubMed]
  17. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
    [CrossRef] [PubMed]
  18. L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
    [CrossRef]
  19. A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
    [CrossRef]
  20. J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).
  21. T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, Second Edition, (Cambridge University Press, 2004), Chap. 4.
  22. M. Tinkham, Introduction to superconductivity, (McGraw-Hill, 1980)
  23. M. J. Lancaster, Passive Microwave Device Applications of High-Temperature superconductors, (Cambridge University Press, 2006), Chap. 1.
  24. S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
    [CrossRef]
  25. T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
    [CrossRef]
  26. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011).
    [CrossRef] [PubMed]
  27. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
    [CrossRef]
  28. R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
    [CrossRef] [PubMed]

2011 (3)

2010 (7)

V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010).
[CrossRef] [PubMed]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

2009 (1)

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[CrossRef]

2008 (3)

2007 (3)

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

2006 (3)

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

2005 (2)

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
[CrossRef]

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

1997 (1)

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

Abbott, D.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[CrossRef]

Al-Naib, I. A. I.

Averitt, R. D.

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

Azad, A. K.

R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
[CrossRef] [PubMed]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
[CrossRef] [PubMed]

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
[CrossRef]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Buckingham, R.

Cao, C. H.

Cao, W.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Chen, H. T.

R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
[CrossRef] [PubMed]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[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(7119), 597–600 (2006).
[CrossRef] [PubMed]

Chen, H.-T.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Chen, J.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Chen, Y.

de Groot, P.

Economou, E. N.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Edwards, D. J.

T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
[CrossRef]

Engelbrecht, S.

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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Fedotov, V. A.

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

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(7), 071114 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (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(7), 071114 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Hao, T.

T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
[CrossRef]

He, M.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Hensen, S.

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

Highstrete, C.

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

Ji, Z. M.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Jia, Q. X.

R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
[CrossRef] [PubMed]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

Jia, X. Q.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Jin, B. B.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Kafesaki, M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Kang, L.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Koch, M.

Koschny, Th.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Lee, M.

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

Liu, X. Y.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Mi, S. B.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Müller, G.

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

O’Hara, J. F.

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
[CrossRef]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[CrossRef] [PubMed]

R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
[CrossRef] [PubMed]

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Padilla, W. J.

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

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(7119), 597–600 (2006).
[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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Pimenov, A.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Rieck, C. T.

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

Rockstuhl, C.

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

Scharnberg, K.

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Shi, J. H.

Singh, R.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011).
[CrossRef] [PubMed]

R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
[CrossRef] [PubMed]

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[CrossRef] [PubMed]

R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
[CrossRef] [PubMed]

Smirnova, E.

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
[CrossRef]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[CrossRef] [PubMed]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Smith, D. R.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

Stevens, C. J.

T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
[CrossRef]

Tao, H.

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

Taylor, A. J.

R. Singh, A. K. Azad, Q. X. Jia, A. J. Taylor, and H. T. Chen, “Thermal tunability in terahertz metamaterials fabricated on strontium titanate single-crystal substrates,” Opt. Lett. 36(7), 1230–1232 (2011).
[CrossRef] [PubMed]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
[CrossRef]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[CrossRef] [PubMed]

R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
[CrossRef] [PubMed]

H. T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[CrossRef] [PubMed]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

Tian, Z.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

Trugman, S. A.

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

Tsiatmas, A.

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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Wang, B. G.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Wang, S.

Wiltshire, M. C.

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Withayachumnankul, W.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[CrossRef]

Wu, J. B.

Wu, P. H.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Wu, Y. J.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Xing, Q.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Xu, Q. Y.

Xu, W. W.

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

B. B. Jin, C. H. Zhang, S. Engelbrecht, A. Pimenov, J. B. Wu, Q. Y. Xu, C. H. Cao, J. Chen, W. W. Xu, L. Kang, and P. H. Wu, “Low loss and magnetic field-tunable superconducting terahertz metamaterial,” Opt. Express 18(16), 17504–17509 (2010).
[CrossRef] [PubMed]

Yang, H.

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Zhang, C. H.

Zhang, J. W.

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

Zhang, W.

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19(7), 6312–6319 (2011).
[CrossRef] [PubMed]

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16(9), 6537–6543 (2008).
[CrossRef] [PubMed]

R. Singh, A. K. Azad, J. F. O’Hara, A. J. Taylor, and W. Zhang, “Effect of metal permittivity on resonant properties of terahertz metamaterials,” Opt. Lett. 33(13), 1506–1508 (2008).
[CrossRef] [PubMed]

Zhang, X.

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Zheludev, N. I.

Zhou, J.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

Act. Passive Electron. Compon. (1)

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, and A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

Appl. Phys. Lett. (5)

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008).
[CrossRef]

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(7), 071114 (2010).
[CrossRef]

J. Gu, R. Singh, Z. Tian, W. Cao, Q. Xing, M. He, J. W. Zhang, J. Han, H.-T. Chen, and W. Zhang, “Terahertz superconductor metamaterial,” Appl. Phys. Lett. 97(7), 071102 (2010).
[CrossRef]

R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Electron. Lett. (1)

T. Hao, C. J. Stevens, and D. J. Edwards, “Optimization of Metamaterials by Q factor,” Electron. Lett. 41(11), 653–654 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Tao, W. J. Padilla, X. Zhang, and R. D. Averitt, “Recent progress in electromagnetic metamaterial devices for terahertz applications,” IEEE J. Sel. Top. Quantum Electron. 99, 1–10 (2010).

IEEE Photon. J. (1)

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009).
[CrossRef]

J. Appl. Phys. (1)

L. Kang, B. B. Jin, X. Y. Liu, X. Q. Jia, J. Chen, Z. M. Ji, W. W. Xu, P. H. Wu, S. B. Mi, A. Pimenov, Y. J. Wu, and B. G. Wang, “Suppression of superconductivity in epitaxial NbN ultrathin films,” J. Appl. Phys. 109(3), 033908 (2011).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[CrossRef]

Nature (1)

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(7119), 597–600 (2006).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. B (2)

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B 75, 041102 (2006).
[CrossRef]

S. Hensen, G. Müller, C. T. Rieck, and K. Scharnberg, “In-plane surface impedance of epitaxial YBa2Cu3O7+Δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity,” Phys. Rev. B 56(10), 6237–6264 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[CrossRef] [PubMed]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the resonance in high-temperature superconducting terahertz metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[CrossRef]

Science (2)

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (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, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Other (3)

T. H. Lee, The Design of CMOS Radio-Frequency Integrated Circuits, Second Edition, (Cambridge University Press, 2004), Chap. 4.

M. Tinkham, Introduction to superconductivity, (McGraw-Hill, 1980)

M. J. Lancaster, Passive Microwave Device Applications of High-Temperature superconductors, (Cambridge University Press, 2006), Chap. 1.

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Figures (4)

Fig. 1
Fig. 1

(a) The planar geometry of single ELC structure. (b) The photo micrograph of S4, and the incident polarized electric field is parallel to the gap.

Fig. 2
Fig. 2

THz transmission spectra of S1-S4 (a) at 18 K and (b) at 8.1 K.

Fig. 3
Fig. 3

(a) The simulated (square dots) and measured (solid line) resonant minimum as a function of resonance frequency at 8.1 K. (b) The temperature dependence of resonance frequency normalized with the resonance frequency at 16 K for S1-S4

Fig. 4
Fig. 4

Transmission spectra of S5 at various temperatures. The arrow indicates the resonance frequency of S5 at 13 K.

Equations (3)

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

T = ( 1 + n s 1 + n s + Z 0 / R ) 2 ,
R s = Re [ ( j ω μ 0 / σ ) coth ( d j ω μ 0 σ ) ] ,
Δ L / L L k / L g = 2.41 λ coth ( d / λ ) / t .

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