Epitaxial YBa₂Cu₃O_7-δ (YBCO) high-temperature superconducting films with δ=0.05 and thicknesses of 50, 100, and 200 nm were prepared using pulsed laser deposition on (100) LaAlO₃ (LAO) substrates with dimensions of 10 mm×10 mm×0.5 mm, over which the thickness variation is <3%. The transition temperature was determined to be T_c=90 K by the ac susceptibility measurement, with a transition width of ∼0.5 K. Square arrays of electric split-ring resonators (SRRs) [41], with a unit cell microscopic image shown in the inset to Figure 1, were fabricated from the YBCO films through conventional photolithographic methods and wet chemical etching using 0.01% H₃PO₄ solution for several minutes. However, we would like to point out that other types of SRR could also be used, i.e., the results in this work do not depend on the choice of geometry of SRRs. Under normal incidence, the YBCO films and metamaterials were characterized at a temperature of 20 K using an optical-pump THz-probe (OPTP) spectrometer [16, 42] incorporated with a continuous flow liquid helium cryostat. The output near infrared laser beam (50 fs, 3.2 mJ/pulse at 800 nm with a 1-kHz repetition rate) was split into two parts with one being used for THz generation-detection and the other for optical excitation (pump) of the YBCO films or metamaterial samples. The pump beam has a beam diameter of ∼1 cm, much larger than the focused THz spot diameter of ∼3 mm at the sample, providing mostly uniform excitation over the YBCO films and metamaterials. This, however, makes it difficult to precisely measure the sample temperature, due to laser heating under high fluence photoexcitation, because the temperature sensor has to be located at the copper sample holder rather than directly touching the top of sample to avoid the direct exposure to the pump laser. Variation of pump-probe time delay was realized using a motion stage to change the pump beam optical path. For various pump powers and pump-probe time delays, THz pulses transmitting through the YBCO films and metamaterials, as well as a blank LAO substrate as the reference, were measured in the time-domain, i.e., recording the time-varying electric field of the impulsive THz radiation. The transmission amplitude and phase spectra were directly obtained by performing fast Fourier transformation of the time-domain signal and normalized to that of the reference. The complex conductivity of the YBCO films was extracted from the measured transmission amplitude and phase spectra through the inversion of Fresnel equations [43].

Figure 1

Dynamics of the 100-nm-thick YBCO metamaterial upon femtosecond near infrared photoexcitation. The transmitted THz peak signal was measured as a function of pump-probe time delay at 20 K for 50 and 300 mW photoexcitation powers. Position I indicates that the THz probe pulse has lower transmission due to the strong resonant response of the metamaterial sample when it arrives about 5 ps earlier than the optical pulse. At positions II, III and IV the THz pulse arrives after the optical excitation with different pump-probe time delays. Inset: a microscopic image of one unit cell of the 100-nm-thick YBCO metamaterial. For all measurements the normally incident THz radiation has the electric field polarized along one of the SRR arms (either in x or y direction).

Figure 1 shows the transmitted THz peak signal through a 100-nm-thick YBCO metamaterial at 20 K as a function of time delay between the near infrared pump and THz probe pulses, for two example optical pump fluences of 0.05 and 0.3 mJ/cm², or powers of 50 and 300 mW, respectively. At low temperatures, the highly superconducting YBCO film results in strong resonant response in the metamaterial structure, which causes a lower transmission of THz radiation. The near infrared photons break the superfluid Cooper pairs in the superconducting YBCO films and create the quasiparticles which dramatically reduce the conductivity and metamaterial resonance, and therefore increase the transmitted THz signal starting from the pump-probe time zero shown in Figure 1. The ∼2 ps rise time is mainly due to time duration of the THz pulses, which limits the time resolution. When the pump-probe time delay increases, the transmitted THz signal decreases due to the recombination of quasiparticles to form Cooper pairs. Under low fluence excitation, the relaxation time is approximately 5 ps, and there is a clearly observable second peak ∼7 ps after the main transmission peak arising from reflected laser pulses at the back surface of the substrate. Increasing the pump fluence causes a larger relaxation time and results in a much longer tail, most likely due to thermal effects. We have also carried out similar measurements for bare YBCO films, and the results are very similar to those shown in Figure 1.

The amplitude spectra of THz transmission through the 100-nm-thick metamaterial sample were then measured at 20 K for various photoexcitation fluences at four time delays indicated by the arrows in Figure 1. In the absence of a pump pulse, the metamaterial exhibits a strong resonant response, as shown by the red curves in Figures 2A–2D with a resonant transmission minimum of 10% or power transmission of 1%, which is comparable to that in metamaterial samples fabricated from gold with the same thickness. This also facilitates the use of high-temperature superconductors in metamaterials replacing noble metals with additional tuning capability. Figure 2A shows the resonant transmission spectra for various pump powers when THz pulses pass through the metamaterial sample a few picoseconds before the optical pump pulses (time position I in Figure 1). The small resulting change indicates that the excitation in the YBCO metamaterial has relaxed nearly completely during the time interval of 1 ms between the optical pump pulses. Immediately following the femtosecond photoexcitation (time position II), the metamaterial resonance is significantly weakened and red-shifted with increasing pump power, as shown in Figure 2B. The resonance disappears at a pump power of 100 mW. Increasing the pump-probe time delay results in recovery of metamaterial resonance strength due to carrier relaxation, as revealed in Figures 2C and 2D for positions III and IV, respectively, both of which are before the arrival of the reflected optical pulse from the back surface of the substrate. With the same pump power, the resonance strength increases and its frequency shifts back when the time delay increases. However, when the pump power is high, e.g., 500 mW, the thermal effects last much longer and the metamaterial resonance does not recover within the time delay of tens picoseconds in our measurements, which is consistent with the dynamics measurements shown in Figure 1.

Figure 2

THz transmission amplitude spectra of YBCO metamaterials for various pump powers. The spectra shown in A–D are for the 100-nm-thick YBCO metamaterial at the respective pump-probe time positions I–IV. E and F, THz transmission amplitude spectra for YBCO metamaterials with 50 and 200 nm thicknesses, respectively, measured at the pump-probe time position III.

It has been shown that the resonance tuning in superconducting metamaterials through change of temperature is strongly dependent on the film thickness [34]. We also fabricated identical metamaterial structure from YBCO films with two other thicknesses of 50 and 200 nm. Measured at the pump-probe time delay position III, the pump power dependent resonant transmission spectra are shown in Figures 2E and 2F. These spectra reveal that increasing YBCO film thickness results in a higher resonance frequency, stronger resonance strength, smaller frequency tuning range, and requiring higher pump power in tuning the resonance. In the absence of a pump pulse, the resonance frequency is 0.460, 0.553, and 0.612 THz, and the resonance transmission minimum is 0.28, 0.11, and 0.03, respectively, for the YBCO metamaterials with thickness of 50, 100, and 200 nm. For the 50-nm-thick YBCO metamaterial, 100 mW pump laser power is sufficient to completely switch off the resonance; while for the 200-nm-thick YBCO metamaterial, even 1000 mW pump laser power is insufficient to switch off the resonance.

The complex conductivity plays an essential role in the resonance tuning in high-temperature superconducting metamaterials [34]. Figure 3 shows the complex conductivity at 0.55 THz of the 100-nm-thick YBCO film, measured at 20 K as a function of pump power at four different pump-probe time delays shown in Figure 1. When there is no optical pump, the imaginary part is about one order of magnitude higher than the real part. For time position I, there is little change in the conductivity, shown in Figure 3A, with increasing pump power, which confirms that the 1 ms time interval of the laser pulses is sufficient for nearly-complete thermal relaxation. Shown in Figure 3B for the pump-probe time position II, the imaginary conductivity dramatically decreases by orders of magnitude as the superfluid Cooper pairs are broken into quasiparticles by the near infrared photons, while the real conductivity does not exhibit a significant change (at most a factor of 2) as it arises from the Drude response of quasiparticles. Shown in Figures 3C and 3D for the pump-probe time positions III and IV, respectively, the imaginary conductivity increases with increasing pump-probe time delay, which allows for recovery of the superfluid.

Figure 3

Experimentally measured complex conductivity at 20 K as a function of pump power for the 100-nm-thick bare YBCO film. A–D, Real and imaginary parts of the complex conductivity are retrieved at 0.55 THz for pump-probe time positions I–IV, respectively.

There have been a few discussions that surface resistance and kinetic inductance contribute to resonance tuning in superconducting metamaterials [29, 34]. The surface impedance (in Ω/Square) of a superconducting film can be calculated from the measured complex conductivity [34]:

where the “∼” indicates a complex value, Z₀=377 Ω is the vacuum impedance, n₃=4.8 is the LAO substrate refractive index, is the complex refractive index of the YBCO film, is the measured complex conductivity, is the complex propagation constant where c₀ is the light velocity in vacuum, and d is the thickness of the superconducting film. The surface resistance R_S and reactance X_S=ωL_S are shown in Figure 4 as a function of pump power for the 100-nm-thick YBCO film, which are calculated at 0.55 THz and at different pump-probe time delays. The surface resistance R_S, which represents the loss, increases rapidly with pump power; while the surface reactance X_S increases first with lower pump power, reaches a maximum value, and then drops with further increasing pump power. As we compare the results in Figures 3 and 4, it is interesting to find that the maximum surface reactance, and therefore the maximal frequency tuning, occurs at a pump power where the real and imaginary parts of the complex conductivity are equal. However, this is not really surprising since it can be easily verified using Eq. (1).

Figure 4

Calculated surface impedance as a function of pump power for the 100-nm-thick bare YBCO film. A–D, The surface resistance and reactance are calculated using the experimental conductivity shown in Figure 3 for the respective pump-probe time positions I–IV.

At resonance, the SRR reactance is absent and the surface resistance of the SRR layer can be calculated from the YBCO surface resistance, R=[(A-g)/w]R_S, where A=64 μm is the circumference of the SRR current loop, g=4 μm is the split gap width, and w=4 μm is the strip width of the SRR. By treating the SRR layer as a shunt resistor in a transmission line, the resonant transmission minimum can then be calculated for the pump-probe time positions I–IV, with the results shown in Figures 5A–5D, respectively. Compared to the experimental results, which are also shown in Figure 5, there is good agreement, i.e., both the experiments and calculations reveal an increase in resonant transmission minimum (decreasing resonance strength) with pump power.

Figure 5

Experimentally measured and theoretically calculated transmission minimum and resonance frequency. A–D, Resonant transmission minimum, and E–H, resonance frequency as a function of pump power for the 100-nm-thick YBCO metamaterial sample at the pump-probe time positions I–IV, respectively.

The frequency of the fundamental resonance in SRRs is typically given by , where L and C are the loop inductance and gap capacitance, respectively. However, when the ohmic loss is significant, the resistance R in an equivalent circuit of SRR has to be considered [34]:

In superconducting SRRs, the inductance L includes two contributions: Faraday inductance L_F which is determined and can be estimated by the geometry and dimensions of the SRR [44], and kinetic inductance L_k=[(A-g)/w](X_S/ω) which is associated with the kinetic energy in superconducting charge carriers. The capacitance C can be derived using Eq. (2) from simulated resonance frequency when assuming perfect conducting SRR, i.e., L=L_F, R=0, and therefore With all these derived parameters, we can calculate the resonance frequency of the YBCO metamaterial as a function of pump power, as shown in Figures 5E–5H for the pump-probe time positions I–IV, respectively. It is again compared to the experimental results with good agreement. Here we have limited our discussion to 80 mW pump power due to the diminishing metamaterial resonance strength for further increasing pump power over 100 mW. Upon photoexcitation, both the resistance and inductance increase, and the overall effect is a reduction of resonance frequency. With increasing the pump-probe time delay both the resonance strength and frequency recover due to the reformation of Cooper pairs on an ultrafast timescale.

Certainly, the complex conductivity in YBCO films is frequency dependent, in contrast to the assumption of frequency-independent conductivity taken at the resonance frequency in the above model calculations. However, this assumption does not affect the validity of this model because the change of conductivity is not significant in the relatively small frequency range around the resonance. Finally, the above model can also explain the thickness dependent YBCO metamaterial resonance and tuning shown in Figure 6. Although the thickness may affect the conductivity of the superconducting films, in all of our measurements the variation is <50%, even with the measurement error taken into account. For simplicity, we can assume thickness independent conductivity. According to Eq. (1), reducing the film thickness d results in a larger surface resistance R_S and consequently smaller resonance strength, i.e., a larger resonant transmission minimum, as verified in Figure 6A. Reducing the film thickness d increases the surface reactance X_S as well, and consequently results in a higher kinetic inductance L_K, although it also negligibly increases the Faraday inductance L_F [44]. For thin YBCO metamaterials, the kinetic inductance L_K could be comparable or even larger than the Faraday inductance L_F. Additionally, the change of L_K can be as large as L_K,20K/2 upon photoexcitation. As such, the overall effect is a lower resonance frequency, which could be predominantly caused by the increasing kinetic inductance, and a wider tuning range of the resonance frequency, as shown in Figure 6B, for reduced YBCO metamaterial thickness. The different pump power requirements for tuning of the resonant frequency in YBCO metamaterials of varying thicknesses may result from the limited penetration depth of the pump laser.

Figure 6

Experimentally measured resonance tuning for YBCO metamaterials of different thickness. A, Resonant transmission minimum, and B, resonance frequency as a function of pump power for the YBCO metamaterials of 50, 100, 200 nm thicknesses, measured at the pump-probe time position III.

We have shown the ultrafast resonance tuning behavior in high-temperature superconducting THz metamaterials through femtosecond near infrared photoexcitation. Increasing the pump power results in a reduced resonance strength and red-shifting of frequency. Under low fluence photoexcitation, the relaxation time is ∼5 ps; further increasing the pump fluence also introduces significant thermal effects with a much longer relaxation time. The dynamics of the metamaterial resonance follows that of the superconducting films. Using experimentally measured complex conductivity of the superconducting films, we are able to reproduce such behavior through calculations by including the ohmic resistance and kinetic inductance. The theoretical calculations reveal that the increasing SRR resistance upon increasing photoexcitation fluence is responsible for the reduction of the resonance strength, and both the resistance and kinetic inductance contribute to the shifting of the resonance frequency. We have also shown that the nanoscale thickness of the superconducting films plays an important role in the frequency tuning range and requirement of optical pump fluence. Thinner superconducting metamaterials require lower pump fluences to switch the resonance and result in a larger frequency tuning range. While the demonstrated metamaterial resonance tuning is not practical at optical frequencies due to the superconducting energy gap, such ultrafast dynamical resonance tuning would be useful in realizing multifunctional microwave and THz metamaterial and plasmonic devices by further design and materials integration.