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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 42–47
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Low-loss terahertz metamaterial from superconducting niobium nitride films

C. H. Zhang, J. B. Wu, B. B. Jin, Z. M. Ji, L. Kang, W. W. Xu, J. Chen, M. Tonouchi, and P. H. Wu  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 42-47 (2012)
http://dx.doi.org/10.1364/OE.20.000042


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Abstract

This paper reports a type of low Ohmic loss terahertz (THz) metamaterials made from low-temperature superconducting niobium nitride (NbN) films. Its resonance properties are studied by THz time domain spectroscopy. Our experiments show that its unloaded quality factor reaches as high as 178 at 8 K with the resonance frequency at around 0.58 THz, which is about 24 times that of gold metamaterial at the same temperature. The unloaded quality factor keeps at a high level, above 90, even when the resonance frequency increases to 1.02 THz, which is close to the gap frequency of NbN film. All these experimental observations fit well into the framework of Bardeen-Copper-Schrieffer theory and equivalent circuit model. These new metamaterials offer an efficient way to the design and implementation of high performance THz electronic devices.

© 2011 OSA

1. Introduction

Metamaterials (MMs) made from elements of artificial metallic structures have demonstrated exotic electromagnetic phenomena, such as artificial magnetism [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

], negative refractive index [2

2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

], super focusing [3

3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

, 4

4. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]

] and extraordinary transmission [5

5. A. Tsiatmas, A. R. Buckingham, V. A. Fedotov, S. Wang, Y. Chen, P. A. J. De Groot, and N. I. Zheludev, “Superconducting plasmonics and extraordinary transmission,” Appl. Phys. Lett. 97(11), 111106 (2010). [CrossRef]

], etc. Such phenomena are not exhibited by natural materials. They are the effect of the resonant nature of the metallic structures of the elements [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

, 6

6. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

]. However, also because of the metallic structures of the elements, the strong metallic loss will balance the amplification of evanescent wave in MMs, thus hinder the implementation of these exotic phenomena [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

, 7

7. X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68(11), 113103 (2003). [CrossRef]

]. In the microwave region, this loss is low, and the exotic electromagnetic phenomena can still be easily demonstrated. However, as the frequency is pushed higher towards to terahertz (THz), this loss often increases rapidly and has a large negative impact on the realization of exotic electromagnetic phenomena. It is highly desirable to find MMs that have lower loss at THz for practical application of such phenomena.

The degree of Ohmic loss can be measured by the quality factor Q of the resonance [8

8. R. E. Collin, Foundations for Microwave Engineering (IEEE Press, 1992).

,9

9. D. M. Pozar, Microwave Engineering (Wiley, 1998).

]. It is defined as ωWem/Pl, where ω is the working frequency, Wem is the time-averaged energy stored in the electric and magnetic fields, Pl is the energy loss per second in the system [8

8. R. E. Collin, Foundations for Microwave Engineering (IEEE Press, 1992).

,9

9. D. M. Pozar, Microwave Engineering (Wiley, 1998).

]. When Pl represents the loss in the resonant circuit only, Q gives the quality factor of the material when it is unloaded. Thus, it is called unloaded quality factor, and denoted by Qu in the sequel. When the resonant circuit is coupled to an external load, the external circuit also absorbs a certain amount of power Pc. Therefore, Pl is the sum of the loss in the resonator and Pc. In this case, the Q gives the quality factor when the resonator is loaded, thus, it is called loaded quality factor and denoted by Ql.

Recently, two approaches have been proposed to reduce the Ohmic loss and increase the quality factor Q of the resonance. The first is to cool the metallic elements to liquid nitrogen or helium temperatures [10

10. 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]

]. At the temperatures of 77 K and 10 K, an increase in the quality factor Q of the resonance by 14% and 40%, respectively, has been observed in experiments and simulations [10

10. 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]

]. The second is to replace the normal metals by superconductors, which can yield even lower Ohmic loss than the first approach. In [11

11. 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]

], we have reported a superconducting THz metamaterial made from Nb film, which demonstrates low loss behavior [11

11. 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]

]. This material was once used to show negative refractive index in the microwave region [12

12. M. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett. 87(3), 034102 (2005). [CrossRef]

]. In [13

13. 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]

15

15. 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] [PubMed]

], a superconducting THz MMs based on yttrium-barium-copper oxide (YBCO) film were also reported. However, at a temperature around 10 K and frequency at 0.5 THz, its surface resistance Rs is greater than that of copper [16

16. C. Jaekel, C. Waschke, H. G. Roskos, H. Kurz, W. Prusseit, and H. Kinder, “Surface resistance and penetration depth of YBa2Cu3O7−δ thin films on silicon at ultrahigh frequencies,” Appl. Phys. Lett. 64(24), 3326–3328 (1994). [CrossRef]

]. Besides, the theoretical studies have also shown that the surface resistance of YBCO increases with frequency more rapidly than that of Cu. The fact that the surface resistance Rs of Cu is smaller than YBCO at the working temperature of 8 K and frequency of THz regime indicates that a normal metal has an advantage over YBCO for fabricating high Q resonator at THz regime.

However, the low Ohmic loss of THz Nb MM can only be maintained below 0.7 THz due to the limitation of gap frequency fg = 0 /h, where Δ0 is the energy gap at 0 K and h is the Planck’ constant. Therefore, a superconducting film with a higher fg can be expected to work at higher frequency. In this paper, we present a low Ohmic loss superconducting THz MM made from NbN film. This film has a higher fg (≈1.2 THz) than Nb [17

17. 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]

]. Our experiments successfully demonstrated that the Qu of the MM is 178 at 0.58 THz, which is about 24 times that of gold MM in the same pattern and at the same temperature. Even at 1.02 THz, which is higher than fg of Nb film, the MM’s Qu achieved 90. The experiment data can be well explained by the Bardeen-Cooper-Schrieffer (BCS) theory and equivalent circuit model [17

17. 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

19. 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]

].

2. Experiments

Our NbN MMs use the electric-field-coupled inductor-capacitor (ELC) resonator structure [20

20. 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]

]. As shown in Fig. 1 (a)
Fig. 1 (a) Scanning electron microscopy images of superconducting THz metamaterial, where E and H represent the electric field and magnetic fields. (b) Geometry and dimensions of an individual unit cell: orange and gray parts are thin film (NbN) and substrate (MgO), respectively.
, each piece of the MMs is a square array of ELC resonators. The geometry and the notations of the dimensions of the ELC structure are shown in Fig. 1(b). Three pieces of MMs were prepared following two steps. First, a 200 nm-thick NbN film was deposited on 500 μm thick MgO substrate using RF magnetron sputtering. The superconducting transition temperature (Tc) of the NbN film is 15.8 K. Second, it was then patterned with standard photolithograph and reactive ion etching (RIE) method [21

21. J. B. Wu, B. B. Jin, Y. H. Xue, C. H. Zhang, H. Dai, L. B. Zhang, C. H. Cao, L. Kang, W. W. Xu, J. Chen, and P. H. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express 19(13), 12021–12026 (2011). [CrossRef] [PubMed]

]. A contrastive sample was also fabricated by using gold film with same thickness and pattern as Sample I. The values of dimensions of these samples of MMs are listed in Table 1

Table 1. The parameters of the ELC cells and the resonant frequencies fr (All length units are in μm.)

table-icon
View This Table
.

The NbN MMs were studied with different resonance frequency fr:

  • (a) at 0.58 THz, which is below fg of Nb,
  • (b) at 0.81 THz, which is between fg of Nb and NbN, and
  • (c) at 1.02 THz, which is close to fg of NbN.

In the experiments, THz time-domain spectroscopy (THz TDS) incorporated with a continuous flow liquid helium cryostat is used to characterized the MMs over a temperature region from 8 K to 300 K. THz transmission spectra are measured under normal incidence, using a bare MgO substrate as the reference.

3. Results and discussions

Our attention is focused on the resonance properties of the MMs in the fundamental mode. The THz power transmission spectra of Sample I are shown in Fig. 2
Fig. 2 Transmission spectra of Sample I of the NbN metamaterial at various temperatures, where the inset shows the transmission spectra of Au metamaterial at 8 K and 300 K.
, which exhibit LC resonance mode around 0.58 THz. At low temperatures, e.g. 8 K, the superconducting MM exhibits the strongest resonance, indicated by the sharp dip of THz transmission curve at 0.58 THz with the minimal power transmission of 0.00025. The resonance strength decreases as the temperature increases, indicated by the broadening and lifting of the resonance dip. As the temperature goes up close to Tc, the transmission spectrum experiences remarkable changes, but it keeps almost constant when the temperature is higher than Tc. Other two samples also show the similar behavior as the temperature varies. In contrast, as shown in the inset of Fig. 2 for the transmission spectra at 8 K and 300 K, the resonance frequency of the gold MM with the same pattern is almost temperature independent. Its power transmission minimum is about 0.05. The change of resonance properties of gold MMs with temperature is imperceptible.

Figure 3
Fig. 3 The unloaded quality factor (Qu) of NbN MMs at various temperatures when the resonance frequency is around 0.58 THz, 0.81 THz and 1.02 THz at 8 K, respectively.
shows the temperature dependence of Qu of the three NbN MMs calculated from the Eq. (1) in Ref [11

11. 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]

]. The coupling coefficient β is 2[P(ω)/P(ωr)]0.5-1, where ωr is the resonance angular frequency, P(ω) and P(ωr) are the power transmission at the frequency ω and ωr, respectively. Then, we substitute β into the Eq. (1) in Ref [11

11. 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]

]. and fit the measured resonance curves to obtain Qu. At around 8 K, the Qu value of sample I reaches as high as 178. As the temperature increases, Qu decreases, but it keeps constant with a value about 2 when temperature is above Tc. In contrast, the Qu of the gold metamaterials is only about 7.6 and temperature independent. So, the superconducting NbN MMs has a Qu that is 24 times that of gold MM. For sample II resonating at 0.81 THz, which is higher than fg of Nb film, the Qu is about 120 at 8 K. Even for sample III resonating at 1.02 THz, which is close to fg of NbN, the Qu is about 90. In summary, the NbN MMs are of Qu values much better than Nb and YBCO even at high THz frequency.

As discussed in the introduction, a high Qu indicates the low Ohmic loss of superconducting MMs at THz. It is only the first step toward a high Ql because the large coupling loss, which often manifests itself in such structure, can easily degrade it. For this reason, although our Qu of NbN MMs is high, Ql is low, which is about 3. However, we believe that the coupling loss can be greatly reduced by optimizing the structural design, for example, using an asymmetric structure as proposed by Fedotov et al. [22

22. 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(14), 147401 (2007). [CrossRef] [PubMed]

] and others [23

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

,24

24. C. Jansen, I. A. I. Al-Naib, N. Born, and M. Koch, “Terahertz metasurfaces with high Q-factors,” Appl. Phys. Lett. 98(5), 051109 (2011). [CrossRef]

].

High quality factor also implies low transmission minimum [25

25. 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]

]. In order to interpret Qu and resonance property’s temperature dependence, we simulate the transmission using the equivalent circuit model [26

26. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H. U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

]. In this model, the transmission coefficient T through samples is as follows [26

26. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H. U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

]:
T=|1+ns1+ns+Z0/Zs,eff|,
(1)
where Z0 is the impedance of vacuum, ns is the refractive index of substrate and Zs,eff is the effective surface impedance of superconducting thin film, which can be calculated from the following formula [21

21. J. B. Wu, B. B. Jin, Y. H. Xue, C. H. Zhang, H. Dai, L. B. Zhang, C. H. Cao, L. Kang, W. W. Xu, J. Chen, and P. H. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express 19(13), 12021–12026 (2011). [CrossRef] [PubMed]

, 26

26. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H. U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

,27

27. M. W. Coffey and J. R. Clem, “Unified theory of effects of vortex pinning and flux creep upon the rf surface impedance of type-II superconductors,” Phys. Rev. Lett. 67(3), 386–389 (1991). [CrossRef] [PubMed]

]:
Zs=(Rs+jXs)coth(d/δ)=jωμ0σcoth(d/δ),
(2)
where σ is the complex conductivity of superconducting film, d is the thickness of the film, δ = 1/ (jωμ0σ)1/2 is the penetration depth, and µ0 is the vacuum permeability. The complex conductivity (σ = σ1 + jσ2) can be described in the framework of the BCS theory. Its temperature dependence can be calculated assuming the normal state conductivity, Δ(0) /kBTc and γ to be 1.2 × 106 S/m, 2.0 and 40 THz, respectively [17

17. 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]

]. Here, kB is the Boltzmann constant and γ is the scattering rate. Figure 4
Fig. 4 The calculated temperature dependent complex conductivity and surface impedance of 200 nm thick NbN film at 0.6 THz.
shows the calculated temperature-dependent complex conductivity and surface impedance of 200 nm thick NbN film. It is easy to see that the real part of the conductivity that causes Ohmic loss is very small at low temperature.

It is well known that MMs can be considered as an effective medium with an effective permittivity (εeff ) and permeability (μeff). Therefore, the effective surface impedance can be described as (μeff/εeff)1/2. For the ELC resonator, μeff is equal to μ0. Moreover, εeff is proportional to the filling factor s, which is the ratio of the areas of a loop and a unit cell. So, the effective surface impedance is inversely proportional to the square root of s [28

28. J. Han, W. Zhang, W. Chen, L. Thamizhmani, A. K. Azad, and Z. Zhu, “Far-infrared characteristics of ZnS nanoparticles measured by terahertz time-domain spectroscopy,” J. Phys. Chem. B 110(5), 1989–1993 (2006). [CrossRef] [PubMed]

,29

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

]. At resonance, the reactance X is zero and R is about 0.5 [(Lloop-g)/t]Rs for each ELC unit, where Lloop is the equivalent length of current loop [20

20. 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]

,21

21. J. B. Wu, B. B. Jin, Y. H. Xue, C. H. Zhang, H. Dai, L. B. Zhang, C. H. Cao, L. Kang, W. W. Xu, J. Chen, and P. H. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express 19(13), 12021–12026 (2011). [CrossRef] [PubMed]

, 30

30. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967). [CrossRef]

]. The factor 0.5 is due to the two shunt-wound current loops. Therefore, the equivalent surface impedance is R/s1/2. The transmission coefficient at resonance can be calculated using Eq. (1).

The experimental and calculated temperature dependent transmission minimum Tmin, which is the transmission at resonance frequency, is plotted in Fig. 5
Fig. 5 Transmission minimums of the three NbN MMs at various temperatures. The line is the theoretical results and the dots are experimental results.
. The theoretical results agree with the experimental data very well. This implies that coupling of MMs to the free space could be described within the equivalent circuit model.

The discrepancy of transmission minimum at relative low temperature is due to the following physical reasons. First, the calculated values are outside the dynamic range of the THz spectroscopy. Second, the residual surface resistance of the film does not allow for further decrease at very low temperature. This leads to a saturation of transmission minimum.

4. Conclusion

In conclusion, we successfully fabricated the low loss THz MM from superconducting NbN film and demonstrated its high unloaded quality factor, which are about 24 times of the quality of gold MMs at 0.58 THz. The performance of NbN MMs remains high even at a higher frequency close to the gap frequency of NbN. We have also theoretically analyzed its THz resonance using the BCS theory and equivalent circuit model. The theoretical results agreed well with the experimental data. We hope that our results can provide a useful way to develop high-performance THz

Acknowledgments

The work is supported by the National Basic Research Program of China under Grants No. 2011CBA00107 and No. 2007CB310404, the NSFC program under contract No. 61071009 and 61027008.

References and links

1.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

2.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

3.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

4.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]

5.

A. Tsiatmas, A. R. Buckingham, V. A. Fedotov, S. Wang, Y. Chen, P. A. J. De Groot, and N. I. Zheludev, “Superconducting plasmonics and extraordinary transmission,” Appl. Phys. Lett. 97(11), 111106 (2010). [CrossRef]

6.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

7.

X. S. Rao and C. K. Ong, “Amplification of evanescent waves in a lossy left-handed material slab,” Phys. Rev. B 68(11), 113103 (2003). [CrossRef]

8.

R. E. Collin, Foundations for Microwave Engineering (IEEE Press, 1992).

9.

D. M. Pozar, Microwave Engineering (Wiley, 1998).

10.

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]

11.

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]

12.

M. Ricci, N. Orloff, and S. M. Anlage, “Superconducting metamaterials,” Appl. Phys. Lett. 87(3), 034102 (2005). [CrossRef]

13.

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]

14.

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]

15.

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] [PubMed]

16.

C. Jaekel, C. Waschke, H. G. Roskos, H. Kurz, W. Prusseit, and H. Kinder, “Surface resistance and penetration depth of YBa2Cu3O7−δ thin films on silicon at ultrahigh frequencies,” Appl. Phys. Lett. 64(24), 3326–3328 (1994). [CrossRef]

17.

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]

18.

B. B. Jin, P. Kuzel, F. Kadlec, T. Dahm, J. M. Redwing, A. V. Pogrebnyakov, X. X. Xi, and N. Klein, “Terahertz surface impedance of epitaxial MgB2 thin film,” Appl. Phys. Lett. 87(9), 092503 (2005). [CrossRef]

19.

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]

20.

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]

21.

J. B. Wu, B. B. Jin, Y. H. Xue, C. H. Zhang, H. Dai, L. B. Zhang, C. H. Cao, L. Kang, W. W. Xu, J. Chen, and P. H. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express 19(13), 12021–12026 (2011). [CrossRef] [PubMed]

22.

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(14), 147401 (2007). [CrossRef] [PubMed]

23.

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

24.

C. Jansen, I. A. I. Al-Naib, N. Born, and M. Koch, “Terahertz metasurfaces with high Q-factors,” Appl. Phys. Lett. 98(5), 051109 (2011). [CrossRef]

25.

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]

26.

S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H. U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter 49(9), 6185–6187 (1994). [CrossRef] [PubMed]

27.

M. W. Coffey and J. R. Clem, “Unified theory of effects of vortex pinning and flux creep upon the rf surface impedance of type-II superconductors,” Phys. Rev. Lett. 67(3), 386–389 (1991). [CrossRef] [PubMed]

28.

J. Han, W. Zhang, W. Chen, L. Thamizhmani, A. K. Azad, and Z. Zhu, “Far-infrared characteristics of ZnS nanoparticles measured by terahertz time-domain spectroscopy,” J. Phys. Chem. B 110(5), 1989–1993 (2006). [CrossRef] [PubMed]

29.

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

30.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys. 7(1), 37–55 (1967). [CrossRef]

OCIS Codes
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials
(300.6495) Spectroscopy : Spectroscopy, teraherz

ToC Category:
Metamaterials

History
Original Manuscript: October 10, 2011
Revised Manuscript: November 22, 2011
Manuscript Accepted: December 2, 2011
Published: December 19, 2011

Citation
C. H. Zhang, J. B. Wu, B. B. Jin, Z. M. Ji, L. Kang, W. W. Xu, J. Chen, M. Tonouchi, and P. H. Wu, "Low-loss terahertz metamaterial from superconducting niobium nitride films," Opt. Express 20, 42-47 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-42


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References

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  15. 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] [PubMed]
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  19. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature444(7119), 597–600 (2006). [CrossRef] [PubMed]
  20. 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]
  21. J. B. Wu, B. B. Jin, Y. H. Xue, C. H. Zhang, H. Dai, L. B. Zhang, C. H. Cao, L. Kang, W. W. Xu, J. Chen, and P. H. Wu, “Tuning of superconducting niobium nitride terahertz metamaterials,” Opt. Express19(13), 12021–12026 (2011). [CrossRef] [PubMed]
  22. 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(14), 147401 (2007). [CrossRef] [PubMed]
  23. R. Singh, I. A. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express19(7), 6312–6319 (2011). [CrossRef] [PubMed]
  24. C. Jansen, I. A. I. Al-Naib, N. Born, and M. Koch, “Terahertz metasurfaces with high Q-factors,” Appl. Phys. Lett.98(5), 051109 (2011). [CrossRef]
  25. 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]
  26. S. D. Brorson, R. Buhleier, J. O. White, I. E. Trofimov, H. U. Habermeier, and J. Kuhl, “Kinetic inductance and penetration depth of thin superconducting films measured by THz-pulse spectroscopy,” Phys. Rev. B Condens. Matter49(9), 6185–6187 (1994). [CrossRef] [PubMed]
  27. M. W. Coffey and J. R. Clem, “Unified theory of effects of vortex pinning and flux creep upon the rf surface impedance of type-II superconductors,” Phys. Rev. Lett.67(3), 386–389 (1991). [CrossRef] [PubMed]
  28. J. Han, W. Zhang, W. Chen, L. Thamizhmani, A. K. Azad, and Z. Zhu, “Far-infrared characteristics of ZnS nanoparticles measured by terahertz time-domain spectroscopy,” J. Phys. Chem. B110(5), 1989–1993 (2006). [CrossRef] [PubMed]
  29. R. Singh, C. Rockstuhl, and W. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett.97(24), 241108 (2010). [CrossRef]
  30. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys.7(1), 37–55 (1967). [CrossRef]

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