Observation of tunable nonlinear effects in an analogue of superconducting composite right/left hand filter

Artificial structures with negative permittivity or permeability have attracted significant attention in the science community because they provide a pathway for obtaining exotic electromagnetic properties not found in natural materials. At the moment, the great challenge of these artificial structures in microwave frequency exhibits a relatively large loss. It is well-known that superconducting thin films have extremely low surface resistance. Hence, it is a good candidate to resolve this constraint. Besides, the reported artificial structures with negative permittivity or permeability are mainly focusing on linear regime of wave propagation. However, any future effort in creating tunable structures would require knowledge of nonlinear properties. In this work, a tunable superconducting filter with composite right/left-hand transmission property is proposed and fabricated. Its nonlinear effects on temperature and power are studied by theoretical analysis and experiments.

Scientific RepoRts | 5:14846 | DOi: 10.1038/srep14846 achieve a nonlinear response in metamaterials was realized by either engineering the elements of a metamaterial with a nonlinear component 31 or employing a nonlinear host medium 4 . In those approaches the nonlinear response is obtained on the level of individual elements. Recently, many works on controlling metamaterial properties mechanically [32][33][34][35] or thermally 36,37 have been reported. In those methods, the nonlinear response mainly emerges from mutual interaction.
Here, a high-temperature superconducting (HTS) switchable filter as an analogue of right/left metamaterials is proposed and fabricated. Nonlinear effects of the HTS composite right/left hand (CRLH) filter on temperature and power are studied by theoretical analysis and experiments. In this work, we show experimentally that the off and on states of this switchable filter can be transformed by the temperature. Furthermore, an interesting exotic electromagnetic property that this artificial device at left-hand frequency is discovered experimentally to have improved power handling capability.

Results
The HTS CRLH filter and its circuit model. Geometry and dimensions of the HTS CRLH filter are shown in Fig. 1a. From this figure, the proposed CRLH filter consists of two symmetrically interdigital structures (indicated by L 4 and L 5 ) and two capacitive patches (indicated by L 1 , 2W 1 , L 3 and W 3 ) connected by a narrow microstrip line (indicated by L 2 and W 2 ). This CRLH filter is fed by a pair of 50-Ω transmission lines. The patterns indicated by yellow color are covered by superconducting thin-film materials.
In our work, HTS circuit is electrically connected using Sub Miniature version A (SMA) connectors. Its schematic diagram is depicted in Fig. 1b. This HTS circuit is fabricated on a 2-in-diameter 0.5-mm-thick MgO wafer with double-sided YBa 2 Cu 3 O 7−x (YBCO) films, which was sourced from THEVA Company, Germany. One diagram of substrate and depletion region near the split gap is shown in Fig. 1c. One photograph of the fabricated HTS device is given in Fig. 1d. It is composed of a HTS circuit, a pair of SMA connectors and a metal shield box.
This HTS CRLH filter is designed to operate at ultra-high-frequency (UHF) band and is characterized from 1.43 to 2.13 GHz. Its − 3 dB bandwidth is 40%. Its overall size is 15 mm × 16.9 mm (about 0.229 λ g by 0.258 λ g , where λ g is the guided wavelength at center frequency of passband). Measured results (at the critical temperature Tc = 77 K) are illustrated in Fig. 2. Measured in-band insertion loss is less than 0.22 dB and return loss is greater than 12.7 dB. It shows a good transmission performance. In order to interpret behaviors of the proposed HTS CRLH device, a circuit model is built up and shown in Fig. 3. C L and L R represent the coupling capacitance and parasitic inductance of interdigital structure (indicated by L 4 and L 5 ), respectively. L L is the distributed inductances of narrow microstrip lines (indicated by L 2 and W 2 ). C R and C G are the distributed capacitances of wide microstrip lines (indicated by (L 1 , W 1 ) and (L 3 , W 3 ), respectively). R s is the surface resistance of high-temperature superconductor thin film. R s is set to zero when operating temperature is less than Tc. The values of RLC lumped-elements in this circuit model are correlated with the relevant dimensions of HTS circuit in Fig. 1a. Relative calculation formulas for extracting the circuit parameters are given in Methods.
By using circuit network analysis, the complex propagation constant γ of this circuit model can be obtained as follows: where parameter A is a matrix element of ABCD-matrix (see Methods). p is the total length of CRLH filter. It is a small constant. α is attenuation factor and β is propagation constant. Complex propagation constant γ of the fabricated HTS CRLH filter is shown in Fig. 4. In general, the bigger attenuation factor α, the greater electromagnetic wave is attenuated. If attenuation factor α = 0, a pass-band of the proposed CRLH filter can be presented since γ(ω) = jβ(ω) is an imaginary number. Otherwise, a stop-band occurs in the frequency range when attenuation factor α ≠ 0. Compared with Fig. 2, it can be found in Fig. 4 that α ≠ 0 and a stop-band occurs within the frequency ranges of 1-1.42 GHz and 2.16-3 GHz. Nevertheless, α = 0 and a pass-band occurs within the frequency ranges 1.42-2.16 GHz.
On the other hand, it also can be found that the group velocity v g < 0 (v g = ∂ω/∂β) within the frequency range of 1.42-1.69 GHz and v g > 0 within the frequency range of 1.69-2.16 GHz. The phase velocity v p > 0 (v p = ω/β) over the pass-band frequency range. In the frequency range of 1.42-1.69 GHz, v g and v p are antiparallel (v g v p < 0). Generally, the group velocity v g is associated with the direction of power flow and the phase velocity v p is associated with the direction of phase propagation. So, in this frequency   Fig. 1a. p is the length of CRLH filter. Z is impedance and Y is admittance. region of 1.42-1.69 GHz, the direction of power flow is opposite to phase propagation and the HTS CRLH filter shows a left-hand (LH) performance, an analogue to a left-hand metamaterial. However, in the frequency range of 1.69-2.16 GHz, v g and v p are parallelled (v g v p > 0). The directions of power flow and phase propagation are the same. So, the resonator shows a right-hand (RH) performance.
From the analyses above, it can be concluded that this HTS filter exhibits a composite right/left-hand (CRLH) transmission performance over the passband range. In the frequency range of 1. Nonlinear effect results on operating temperature. To further clarify microwave properties of HTS CRLH filter and make the most of superconducting properties, it is essential to understand the temperature dependence of frequency responses. Figure 6 shows the experimental frequency responses at different operating temperatures. As can be seen, the fabricated HTS CRLH filter has a steady performance when operating temperature is less than the critical temperature Tc (77 k). On the other hand, the bandpass performance from 1.42 to 2.16 GHz deteriorates when operating temperature is greater than the critical temperature Tc. This is attributed to the improved surface resistance (R s ). Generally, the relation between R s and temperature appears to be nonlinear and is shown in Methods. In superconducting  technology, surface resistance R s is extremely low when operating temperature is less than the critical temperature Tc (77 k). However, when operating temperature increases to above the critical temperature Tc, surface resistance (R s ) of the HTS film is improved dramatically. The enlarged surface resistance (R s ) will improve attenuation factor α, as shown in Fig. 7. In addition, from Fig. 6, it also can be found that the HTS CRLH filter has both bandpass performance (temperature < 77 K) and bandstop performance (temperature > 100 K). This HTS device is a good candidate for the applications of superconductor switch. Off and on states of this CRLH filter can be transformed by changing the operating temperature.
Nonlinear effect results on input power. For high reliable communication systems, such as digital telecommunication systems, nonlinear responses are an outstanding problem 38 . In the nonlinear regime, spurious signals are generated within passband, undermining device performance. Thus, evaluation of this characteristic is very important for HTS CRLH filter. To investigate nonlinearity of this filter, third-order intermodulation distortion (IMD3) is analyzed and measured. As a significant measurement of power handling capability, the third-order intercept point (IP3) is computed, which is defined as input power at which extrapolations of the fundamental and generated signal curves intersect. Figure 8 exhibits the input power versus output power at 77 K. Two-tone fundamental signals (1.57985 GHz and 1.58015 GHz signals for the left-hand frequency @1.58 GHz while 1.89985 GHz and 1.90015 GHz for the right-hand frequency @1.9 GHz) are input to the measured passband. IP3 of the left-hand and right-hand frequency are 42 and 33 dBm, respectively. It shows a good power handling capability. Based on the experiment results 39 , it can be found that the higher the frequency goes, the bigger the value of IP3 becomes. However in this experiment, it is interestingly found that IP3 at 1.58 GHz (left-hand frequency) is 9 dB more than that at 1.9 GHz (right-hand frequency). This means that the former can handle 8 times power as that of the latter. This experimental result reveals that the proposed HTS CRLH filter at left-hand frequency has better power handling capability. The mechanism at left-hand frequencies (ε < 0 and μ < 0) can slow electromagnetic wave, thereby increasing the interaction time with nonlinear

Discussion
In this paper, we have fabricated and characterized a CRLH filter from high-temperature superconducting YBCO films. This device has composite right/left-hand property, similar to the right/left-hand metamaterials. Its nonlinear effects on temperature and power are studied by theoretical analysis and experiments. In this work, a circuit model is built to describe and interpret the performance of this device. Surface resistance of YBCO films is taken into account to analyze the effects of temperature sensitivity. Modeling calculations are in good agreement with experimental observations and electromagnetic simulations. Also, we can find that this HTS filter is a good candidate for the applications of superconductor switch under different temperature conditions. Off and on states can be transformed by switching operating temperature. Besides, metamaterials have many exotic electromagnetic properties such as the reversal of Doppler effect 40,41 , the reversal of Vavilov-Cerenkov radiation 42 and the zero index of refraction 43 , which can also be found in our structure. In this work, another exotic electromagnetic property that the left-hand frequency has better power handling capability than the right hand frequency is discovered experimentally. This finding could contribute to the research field which is in need of improving the power handling capability.

Methods
Fabrication and measurement processes. In this work, HTS CRLH filter was fabricated on a 2-in-diameter 0.5-mm-thick MgO wafer with double-sided YBCO films, which was sourced from THEVA, Germany. For filter patterning, a photoresist mask was prepared by photolithography, and the front-side YBCO film was etched by ion-beam milling to form the circuit structure. Filter laminate was then carefully assembled into brass housing. It was measured by an Agilent network analyzer N5230 at temperature of 77 K. Full 2-port calibration for reflection and transmission measurements is performed at room temperature. Fig. 3. To analyze equivalent circuit model in Fig. 3, ABCD matrix method is used. By multiplication of the unit ABCD matrices in an orderly fashion, ABCD matrix of this network is expressed as follows:

Circuit network analysis. Circuit model of the proposed HTS CRLH filter is shown in
. L L is the distributed inductances of narrow microstrip lines. L L can be obtained by 44 : where w, l and t represent the length, width, and thickness of high-impedance microstrip line and h is the height of substrate. C R and C G are the distributed capacitances of wide microstrip lines. These values can be calculated by 1 : Based on the two-fluid model and BCS (Bardeen-Cooper-Schrieffer) theory, the surface resistance can be calculated by 45 : where u 0 is vacuum permeability, σ 1 is the real part of conductivity and λ(T) is magnetic penetration depth. The relation between R s and temperature (T) appears to be nonlinear 46 .  (6) can be simplified as:

N-cell
For an N-cell ladder network, the bigger N is, the more complex the electromagnetic coupling become. This strong electromagnetic coupling will change intrinsic characteristics of unit cell. To eliminate the electromagnetic coupling effects and focus on studying the characteristic of unit cell, a CRLH filter with two unit cells is proposed and fabricated.