## 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 (*f _{g}* = 2

*Δ*where

_{0}/h,*Δ*is the energy gap at 0 K and

_{0}*h*is the Plank constant) of NbN is 1.18 THz, the experimentally observed THz spectra span a frequency range from below

*f*to above it. We have found that, as the resonance frequency approaches

_{g}*f*, the relative tuning range of MMs is quite wide (30%). We attribute this observation to the large change of kinetic inductance of superconducting film.

_{g}© 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 [3–6]. 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 [9–13]. When the temperature is close to the transition temperature (*T _{c}*) 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

*f*, where

_{g}= 2Δ_{0}/h*Δ*is the energy gap of the superconductor at 0 K, and

_{0}*h*is the Plank constant. Thus it is expected that a wide tuning range can be obtained as the frequency is approaching

*f*.

_{g}Here we look at the THz transmissions through a class of electrically resonant superconducting MMs with resonance frequencies going from below *f _{g}* 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

*f*but drop sharply beyond

_{g}*f*. And the relative frequency tuning range

_{g}*[f(T*is the largest (up to 30%) as the resonance frequency approaches

_{c})-f_{min}]/f(T_{c})*f*, where

_{g}*f(T*and

_{c})*f*and are the resonance frequency at the critical temperature

_{min}*T*and the minimum of the resonance frequency in superconducting state, respectively.

_{c}## 2. Experiments and discussions

The electric inductive-capacitive (ELC) resonator structure is used in our work [14–16]. Figure 1(a)
shows the planar geometry of a unit cell. The geometric parameters are set to be *l* = *a*, *t* = 0.1*a*, *g* = 0.1*a*, *w* = 0.2*a*, and the dimensions of each unit cell is 1.2*a* × 1.2*a*. 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, *Δ _{0}* calculated from previous measurements [18] is 2.45 meV, and thus

*f*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

_{g}*f*to above it.

_{g}The NbN films used in our experiments typically have *T _{c}* = 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 *f _{g}*. 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.

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

where*n*is the refractive index of substrate,

_{s}*Z*is the impedance of vacuum, and

_{0}*R*is the resistance of ELC resonator at resonance frequency. And

*R*can be calculated by the equation,

*R = R*, where

_{s}·(3.02l/t) = 30.2R_{s}*R*is the surface resistance of smooth NbN film, and

_{s}*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

*f*. 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

_{g}*f*, almost all paired electrons are broken into quasi-particles, leading to the abrupt increase of

_{g}*R*and a large decrease of depth of the resonant minimum.

_{s}Quantitatively, *R _{s}* can be calculated from the following equation [23],

*σ*is the complex conductivity of NbN film. Then

*R*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].

_{s}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 *f _{g}*. 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 (

*L*) can be calculated as follows,

_{g}*L*, where

_{g}≈μ_{0}(πA)^{1/2}= μ_{0}l(π/2)^{1/2}*μ*is the permeability of vacuum and

_{0}*A =*(

*l/2*)

*is the area of small rectangle loop [21]. The kinetic inductance (*

^{1/2}*L*) is distinct for MMs in superconducting state, and it can be estimated by the formula,

_{k}*L*, where

_{k}≈μ_{0}λcoth(d/λ)·(3.02l/t)*λ*is the penetration depth of NbN film [21,23]. Thus, the normalized change of inductance can be calculated as follows,

When frequency is below *f _{g}*,

*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

*f*, the

_{g}*L*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

_{k}*f*. This provides a nice method to tune the frequency by temperature.

_{g}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.

## 3 Conclusions

In summary, we have demonstrated that the superconducting NbN MMs exhibit remarkably high resonance strength until their resonance frequencies reach *f _{g}*. Moreover, the MMs with resonance frequency approaching

*f*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.

_{g}## 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).

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