We report the extraordinary terahertz (THz) transmission through subwavelength hole array in superconducting NbN film. As the temperature drops below the superconducting transition temperature, the transmission spectra experience distinct changes. The extraordinary transmission is greatly enhanced in superconducting state due to the enhancement of surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs). We have also observed temperature-dependent resonance frequency shift, which mainly depends on the coupling between SPPs and LSPs.
©2011 Optical Society of America
Extraordinary transmission, or enhanced transmission through metal subwavelength hole arrays at light frequencies, has attracted great interest due to potential engineering applications [1–3]. The enhanced transmission is attributed to the interaction between the electromagnetic wave and surface plasmon polaritons (SPPs). It strongly depends on the dielectric constant of metal; and large ratio of the real to imaginary dielectric constants (-εrm/εim) is favorable to the propagation of SPPs [3,4]. In terahertz (THz) region, this kind of transmission has been demonstrated in metal films [5,6]. However, in this frequency region metals are highly conductive, and the ratio of -εrm/εim is less than 1; thus the explanation is not based on SPPs, which most people believe do not exist due to the above reasons, but based on the formation of SPP-like surface waves, or spoof surface plasmons, on the structured metal surfaces .
For subwavelength hole arrays fabricated in high-temperature superconducting (HTSC) films, previous authors have observed plasmonic properties and strong extraordinary transmission at millimeter-wave frequencies ; while at THz frequencies, such enhancement is also demonstrated and can be made use of to control the transmission .
If we switch from HTSC films to low-temperature ones, such as Nb and NbN, we shall have lower real conductivities and thus lower absorptions, from which the propagation of SPPs will benefit a lot [3,10]. In this letter, the THz extraordinary transmissions through subwavelength hole arrays in superconducting NbN films are discussed. We demonstrate that the transmission is greatly strengthened and the resonance frequency changes with temperature as the NbN films go into superconducting state. This enhanced extraordinary transmission arises from the enhancements of SPPs and localized surface plasmons (LSPs). The temperature dependence of the resonance frequency mainly comes from the coupling between SPPs and LSPs. Our results open up a new way to control extraordinary transmission both in frequency and in amplitude, while in the previous work the THz extraordinary transmissions have been dynamically controlled by modifying the conductivity of the substrates using electronic or thermal methods [11,12].
2. Experiments and discussions
Used to make the samples are 200 nm-thick NbN films, deposited on 400 μm-thick MgO substrates (twin polished, <100> orientation) using RF magnetron sputtering. The typical critical temperature (Tc) of a film is 15.8 K. Rectangular or circular subwavelength holes are patterned photolithographically in the film to form an array. The samples are mounted on the cold stage in a continuous flow liquid helium cryostat, which is installed in the THz time domain spectroscopy (TDS) system. THz transmission spectra are measured in a temperature range of 8.2-300 K, using a bare MgO substrate as the reference.
Shown in Fig. 1(a) is Sample 1, an array with rectangular subwavelength holes where the long side is a = 100 μm, the short side b = 30 μm and the period P = 120 μm (for Sample 2, also with rectangular holes but not shown here, b = 15 μm). The polarization of the electric field is chosen to be parallel to the short side of the rectangle hole. Sample 3, shown in Fig. 1(b), is an array with circular holes where the diameter is d = 80 μm and the period is P = 120 μm. The size of each sample above is 10 mm × 10 mm.
Figure 2 shows the transmission spectra of Sample 1 from 300 K (bottom) to 8.2 K (top). The resonance around 600 GHz corresponds to the SPPs [ ± 1, 0] mode for hole array at NbN-MgO interface. The transmission spectra do not change much with the temperature when it is higher than Tc. As the temperature is further reduced so that the NbN film goes into superconducting state, the transmission experiences remarkable changes. The magnitude of the peak increases with decreasing temperature, indicating that the resonance gradually enhances, while the resonance frequency suddenly drops to minimum on the normal to superconducting transition and then gradually increases as temperature lowers further.
The magnitudes of the transmission peak and the temperature-dependent resonance frequencies for sample 1 and 2 are displayed in Fig. 3(a) and 3(b). For Sample 1, the transmission maximum increases from 49.0% at 19 K to 89.8% at 8.2 K, and the transmission intensity normalized to the area occupied by the holes reaches 4.3 at 8.2 K taking into account that 20.8% of the sample area is occupied by the holes. The maximum resonance frequency shift is about 68 GHz, about 11% of resonance frequency at 19 K. Sample 2 shares the same temperature-dependent features except difference in amplitude.
In order to understand how the properties of SPPs change when the sample goes from superconducting to normal, we deduce the temperature-dependent dielectric function of a NbN film (15 nm-thick) by measuring its transmission spectra with a THz-TDS system. The dielectric constant at 0.6 THz is plotted in Fig. 4(a) . Obviously, in superconducting state, the -εrm/εim value is much larger than it is in normal state. Thus, the internal damping of NbN film for SPPs should be much weaker in superconducting state than in normal state. The internal damping can be evaluated by the propagation length (δsp) on smooth surfaces without structures, which is approximated as follows Fig. 4(b). It shows that δsp greatly increases from 0.078 m at T = 1.18Tc to 1.8 m at T = 0.58Tc. As a result, the propagation of SPPs suffers less internal damping in superconducting state than in normal state because of the increased -εrm/εim, and SPP-enhanced transmission improves much from this low internal damping . At this point it is important to note that the data in Fig. 3 are taken with a sample where NbN film is 200 nm-thick, while in Fig. 4 the film is 15 nm-thick. The thickness difference between the films, as well as the possible quality difference, may quantitatively cause some discrepancy but the measurement results do qualitatively provide us with some direct evidences of how the superconductivity of the NbN film affect the transmission.
For SPP-enhanced transmission, the thickness of the metal film is also an important factor. The transmission peak gets enhanced as the thickness of the film is increased towards the skin depth . In normal state, the skin depth of NbN at 600 GHz is about 593 nm (conductivity is 1.2 × 106 S/m from our measurement), the thickness of NbN film is about one third of the skin depth. When temperature is below 0.9Tc, the skin depth approaches penetration depth (λ), which represents the distance that electromagnetic wave could penetrate into the superconductor [15,16]. Based on our measurements, the penetration depth at 9 K is 369 nm. Thus the NbN film thickness is 54.2% of the skin depth, indicating that the relative optical thickness is remarkably increased in superconducting state. Therefore, the optically thicker NbN film in superconducting state also contributes to the enhanced extraordinary transmission.
On the other hand, the LSPs greatly affect the intensity and frequency of the transmission resonance [17,18]. The equivalent circuit model was first used in analyzing frequency selective surfaces , and then was applied to studying the transmission property of single subwavelength hole . As shown in Fig. 5 , the carriers are driven by electric field to move along the edges parallel to the polarization direction, so these edges provide inductance (Lg) and resistance (R) in series, and the edges orthogonal to polarization direction can be equivalent to capacitor (C). Besides, the inertial mass of superconductor carriers in alternating electric fields is manifested by kinetic inductance (Lk). Thus, each hole can be equivalent to an LC resonator whose impedance is Z = L/RC, where L = Lg + Lk. If we use transmission line as the analog of the THz pulse propagation path, the transmission line is shunted by this LC resonator. The derived transmission coefficient is as follows 
According to the Fano model, the resonance frequency shift arises from the coupling between SPP-enhanced transmission and non-SPP transmission, for example, LSP-enhanced transmission [21,22]. The stronger the coupling is, the more red-shift of the resonance frequency appears. We attribute the change of coupling strength to the effect of superconductor’s kinetic inductance (Lk). When temperature decreases below Tc, the emergent Lk lowers the cut-off frequency of the subwavelength hole, which delimits the propagating and non-propagating regimes of the incident electromagnetic wave. As a consequence, the coupling between SPP-enhanced and LSP-enhanced transmission intensifies, and a distinct red-shift of the resonance frequency occurs around Tc . Besides, the temperature dependence of Lk can be used to explain why the resonance frequency goes up gradually when the temperature further decreases. In fact, for a superconducting film with a finite thickness d, Lk can be approximated as Lk≈μ0λcoth(d/λ), where μ0 is permeability of vacuum, and λ is the penetration depth . According to the two-fluid theory, λ decreases as temperature lowers down due to increased density of superconductor carriers . As the temperature decreases further, Lk gradually reduces with decreasing λ. Thus, the cut-off frequency of the hole increases, and the coupling between LSP-enhanced and SPP-enhanced transmissions becomes weaker and weaker.
As mentioned earlier, an input polarization along the short side of a rectangular hole is optimal in the sense that the oscillation of LSPs around the hole is the strongest among all possible input orientations . In the case of a circular hole, however, there is no such optimal polarization and the oscillation of LSPs around the hole is less strong, which inevitably leads to quantitatively different switching behavior at resonance. In order to look at this in greater details, we have measured the transmission spectra of Sample 3 which is an array of circular holes in NbN film as shown in Fig. 1(b). Figure 6(a) shows the measured transmission spectra in the temperature region of 8.2-300 K. In normal state, the transmission maximum is lower than that of Samples 1 and 2. Meanwhile, the red-shift of resonance from the SPPs [ ± 1,0] mode (the calculated mode frequency is 815.4 GHz based on formula 1 from reference ) is much smaller, that is consistent with the experiment results in optical regime . In the LC resonator model, the equivalent capacitance is much smaller for a circular hole and the resonance strength of LSPs is much weaker, both compared with the case for a rectangular hole. It results in much weaker coupling strength and smaller resonance frequency red-shift according to Fano model .
On normal to superconducting transition, a switching process similar to that of Samples 1 and 2 occurs, as shown in Fig. 6(b). With circular holes, the contribution of superconductivity to enhancing the transmission efficiency is also evident as shown by the fact that the transmission maximum increases by a factor of 1.4 from 19 K to 8.2 K. Meanwhile, the maximum resonance frequency shift is less than 2%, much smaller than 11% for Sample 1. The smaller frequency shift could be attributed to weaker coupling between LSPs and SPPs. In superconducting state, the emergent Lk does lower the cut-off frequency of hole and enhances the coupling strength. However, considering that the oscillation of LSPs remains to be very weak as stated above, the enhancement of coupling strength is quite limited . As a result, the switching of resonance frequency is greatly degraded.
In conclusion, we have demonstrated that the enhanced THz transmission through subwavelength hole array in NbN film and the resonance frequency can be tuned by the temperature, thus manifesting the role superconductivity plays. The enhancement of resonance strength is attributed to the enhancement of SPPs and LSPs in superconducting state. And the change in coupling between LSPs and SPPs determines the red-shift of the resonance frequency. The enhanced transmission and tuning feature show good prospect in THz electronic devices.
This work is supported by the MOST 973 Project (No.2007CB310404, No.2011CBA00107) of China, the National Natural Science Foundation (Grant no. 61071009, 61027008), the Program for New Century Excellent Talents in University (NCET-07-0414) and the Specialized Research Fund for doctoral program of higher education (20090091110040).
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