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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 Optical Society of America
1. Introduction
Metamaterials (MMs) made from elements of artificial metallic structures have demonstrated exotic electromagnetic phenomena, such as artificial magnetism [1], negative refractive index [2], super focusing [3, 4] and extraordinary transmission [5], 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, 6]. 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, 7]. 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 [8,9]. 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 [8,9]. 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]. 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]. The second is to replace the normal metals by superconductors, which can yield even lower Ohmic loss than the first approach. In [11], we have reported a superconducting THz metamaterial made from Nb film, which demonstrates low loss behavior [11]. This material was once used to show negative refractive index in the microwave region [12]. In [13–15], 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]. 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 = 2Δ0 /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]. 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 [17–19].
2. Experiments
Our NbN MMs use the electric-field-coupled inductor-capacitor (ELC) resonator structure [20]. As shown in Fig. 1 (a) , 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]. 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 .
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.
Table 1. The parameters of the ELC cells and the resonant frequencies fr (All length units are in μm.)
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 , 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.
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.
Figure 3 shows the temperature dependence of Qu of the three NbN MMs calculated from the Eq. (1) in Ref [11]. 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]. 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.
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.
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] and others [23,24].
High quality factor also implies low transmission minimum [25]. In order to interpret Qu and resonance property’s temperature dependence, we simulate the transmission using the equivalent circuit model [26]. In this model, the transmission coefficient T through samples is as follows [26]:
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, 26,27]: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]. Here, kB is the Boltzmann constant and γ is the scattering rate. Figure 4 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.Fig. 4 The calculated temperature dependent complex conductivity and surface impedance of 200 nm thick NbN film at 0.6 THz.
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 [28,29]. 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 [20,21, 30]. 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 . 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.
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 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.
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