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Abstract
In a quasi-optical system, the high temperature superconducting terahertz detector often suffers from a fundamental problem of low coupling efficiency with the terahertz signal, especially for the detector based on YBa2Cu3O7-δ (YBCO) bicrystal Josephson junction (JJ) due to a small normal-state resistance. Here, we developed a bowtie loaded meander antenna to enhance coupling efficiency. Differing from the conventional characterization confining on vector network analyzers, we applied three methods to evaluate the antenna, including the measurements of the maximal size of the first order Shapiro step under per incident power, the coupling efficiency between the antenna and the junction, and voltage responsivity. Furthermore, with simulation analysis, we propose that the inductive reactance of the YBCO bicrystal JJ is around 60 ohms under terahertz irradiation at 210 GHz, thus, the reactance is comparable as that of the antenna.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High temperature superconducting (HTS) YBa2Cu3O7-δ (YBCO) grain boundary Josephson junction (GBJJ) has a high critical temperature and a large energy gap, resulting in a high cutoff frequency [1]. Therefore, it has a preferable high-frequency response and becomes a promising candidate for terahertz (THz) applications, such as source [2–3], detection [4–10] and mixing of terahertz signals [11–16]. Due to the limited source power and severe atmospheric attenuation [17] at THz bands, the enhancement of THz coupling efficiency absorbs increasingly more attention. Thus, it is essential to avoid the RF matching problem for future applications. One way is to shrink the size of the junction, which can enhance the sensitive of the device. Nevertheless, the micro-fabrication technique becomes dramatically difficult for the THz bands.
Another promising path is to develop a suited antenna. Normally, the broadband antennas in balanced self-complementary structures [18] have an input impedance of 188 Ω in free space, for instance the log-periodic antennas [9,19–21] and spiral antennas [10,22–24]. Nevertheless, the normal-state resistances of YBCO GBJJs are often as low as 1-40 Ω, being considerably less than that of the antennas. Such an impedance mismatch between the antenna and the junction will cause a power loss [22], therefore, it is essential to reduce the impedance of the antenna. For the highly sensitive YBCO GBJJs, narrow-band antennas exhibit low input impedances, being preferred to conventional broadband antennas. Du et al., integrated ring-slot antennas with an input impedance of ∼30 Ω for YBCO step-edge JJs (typically 1-10 Ω), and the THz coupling efficiency has been enhanced to 600 GHz [7–8]. Nakajima et al., [6] and Gao et al., [16] applied slot antennas with the input impedances of ∼13 Ω to YBCO GBJJs by coplanar waveguide (CPW) feeding. The half-wavelength slot antennas have relatively low feed-point impedance, while the CPWs have a limited bandwidth as a detector. To solve this issue, Yamada et al., proposed an extra Au layer as a full-wavelength slot antenna to prevent the limited bandwidth from CPW [25], while inducing an additional fabrication procedure. On the other hand, since the YBCO bicrystal JJ can induce reactance in the zero-voltage region, based on the resistively shunted junction (RSJ) model [26], a conjugate impedance matching of the JJ should be seriously considered, although there is no any report demonstrating about this issue. Feeding an antenna with CPW can be used to improve the conjugate impedance matching, the shape of the ground, however, has to be modified as well, resulting in a complexity in the design. Alternatively, the antenna with a low impedance fed by a coplanar strip (CPS) is a promising method to be applied on THz bands. Furthermore, another measurement complication is from the expensive vector network analyzer (VNA) at the THz bands, which dramatically restricts the characterization for THz antennas, especially for the antenna with a low impedance.
In this work, we propose a bowtie loaded meander antenna (BLMA) fed by CPS for HTS YBCO bicrystal JJ. The meander acts as traveling wave antenna at one wavelength, and the bowtie is loaded at the end of the meander to enhance the radiation. The YBCO bicrystal JJ was found to be coupled by the BLMA, based on the characterization from the Josephson effects, but not just from VNA analysis. The impedance of the YBCO bicrystal JJ is also simulated to understand the experimental results.
2. On-chip layout design
Figures 1(a)–1(c) show the geometry of the presented on-chip layout, comprised of electrodes, direct current (DC) bias lines, choke filter [27] and the BLMA integrated with an YBCO bicrystal JJ. The structure is designed on a magnesium oxide (MgO) substrate with the relative permittivity of 9.6 and a thickness of 0.5 mm. A high-resistivity silicon (Si, relative permittivity of 11.9) hyper-hemispherical lens [28,29] with a hemisphere radius ${R_{\textrm{Lens}}}$ of 4.5 mm and the extended cylinder length ${L_\textrm{h}}$of 0.7 mm is attached to the back of the MgO substrate to focus the THz signals on the substrate surface where the JJ (antenna port in the simulation) locates. As for the BLMA, the surface current distribution was presented in [30]. As most current is distributed on the meander, the meander at a greater than guided wavelength ${\lambda _\textrm{g}}$ (${\lambda _\textrm{g}} = {\lambda _0}/\sqrt {({1 + {\varepsilon_r}} )/2} $, ${\lambda _0}$ is the wavelength in free space) dominates the radiation in the form of a resonant and travelling wave. At the end of the meander, a bowtie is loaded to be a part of resonant radiator in order to reduce the feed-point impedance. Here, the total length of the meander is 656 µm with a feed gap of 6 µm and the following geometrical parameters: $t$=4 µm, $g$=16 µm and $h$=60 µm. The loaded bowtie has an arm length of $l$ = 135 µm and width of $w$ = 515 µm. DC bias lines are connected to the bowtie where the current distribution is weakest in order to minimize the alternating current (AC) power leaking out from the antenna. Besides, a choke filter with a bandgap structure [31] is inserted to the DC bias lines to prevent the AC power from leaking into the CPSs. The relevant parameters with $d$=32 µm, ${l_0}$=246 µm, ${w_0}$=15 µm, ${l_1}$=165 µm, ${w_1}$=90 µm, ${l_2}$=${l_3}$=90 µm and ${l_4}$=${l_5}$=135 µm, are optimized at 210 GHz using the software Computer Simulation Technology (CST) Microwave Studio. The high or low characteristic impedance of the transmission line changes alternately, resulting in reflections at every section with the lengths of ∼${\lambda _\textrm{g}}$/4. Thus, as clearly seen in Fig. 1(d), the current leaked from the antenna is effectively blocked by the choke filter. At the other ends, the bias lines are connected to four electrodes so as to eliminate the influence of contact resistance in the four-terminal measurement.
Fig. 1. (a)-(c) Geometry of the on-chip layout based on an YBCO bicrystal JJ THz detector (structure parameters: ${L_\textrm{h}}$=0.7 mm, ${R_{\textrm{Lens}}}$ = 4.5 mm, $t$=4 µm, $g$=16 µm, $h$=60 µm, $l$=135 µm, $w$=515 µm, d=32 µm, ${l_0}$=246 µm, ${w_0}$=15 µm, ${l_1}$=165 µm, ${w_1}$=90 µm, ${l_2}$=${l_3}$=90 µm, ${l_4}$=${l_5}$=135 µm). (d) Current distribution on the BLMA and the choke filter at 210 GHz. (e) The dependence of simulated input impedance of the on-chip antenna on the frequency.
The input impedance of the on-chip antenna is shown in Fig. 1(e), obtained with the CST software. Within 100-500 GHz, the on-chip antenna resonates at frequencies of 350 GHz and 478 GHz, where the imaginary parts of impedances are zero. The resistance is 21 Ω at 350 GHz, even can be as low as 11 Ω at 478 GHz. However, when the antenna is integrated with an inductive detector (YBCO bicrystal JJ), the input impedance of the antenna should be capacitive to satisfy conjugate matching. That is to say, the antenna resonates in the regions of 110-350 or 373-478 GHz. In this case, the detector can have the best performance.
3. Fabrication and characterization setup
Based on the systematic electromagnetic design and analysis, a HTS YBCO JJ THz detector chip was fabricated and packaged into a holder, shown in Fig. 2(a). 80-nm thick YBCO film covered with a 20 nm in situ Au film was deposited via pulsed laser deposition on a bicrystal MgO substrate with a misorientaion angel of 24°. The YBCO film has a critical current density Jc of 2.5 MA cm-2 and a critical temperature Tc of 85.7 K. The detector was patterned by a standard photolithography and Ar-ion beam etching on a 10×3 mm2 bicrystal MgO substrate. The JJ is in shape of 6-µm-long and 2-µm-wide bridge crossing the GB, embedded into the BLMA, as seen in the zoomed photo. The Si hyper-hemispherical lens, inserted into a holder, is attached to the back of the MgO substrate with cryogenic glue. The DC bias lines on the detector chip are connected to the DC bias pins through gold wires and silver epoxy. A RF filter module composed of resistors and capacitors on the DC bias pins is applied to isolate the DC and RF signals.
Fig. 2. (a) Detector chip on a sample holder with packaged modules. (b) 3D view of the quasi-optical system on a GM cryocooler. Schematic diagrams of (c) measurement setups for IVCs and (d) protective circuit.
Measurements are carried out in a Gifford-McMahon (GM) cryocooler or a Dewar at the bath temperature around 4.2 K. Figure 2(c) shows the schematic diagram of our autonomous measuring system for current-voltage characteristics (IVCs). The THz signal is generated by a low frequency signal through a commercial modular amplifier/multiplier chain (AMC) Tx series (an amplifier and 16-order frequency multiplier) from Virginia Diodes Inc. (VDI). Limited by the amplifier and multipliers, the optimal frequency range of the THz source for antenna characterization is 205-230 GHz. The AMC is driven by an Agilent N5183A MXG Analog Signal Generator, and the THz beam propagates along the quasi-optical link to the holder with the Si lens facing to the window of the GM cryocooler. The quasi-optical system, on the top of the GM cryocooler, consists of two parabolic mirrors, the displacement tables, and a fixed panel, seen in Fig. 2(b) in a 3D view, to focus the THz beam. The JJ is biased by a homemade current source, driven by a trigger voltage from a data acquisition (DAQ) card controlled by the LabVIEW software. Meanwhile, the DAQ card record the current across the junction and the voltage amplified by a low noise amplifier (LNA). A protective circuit is set up between the current source and the detector to prevent the junction from being destroyed by a large current pulse. Figure 2(d) shows the schematic diagram of the protective circuit. The junction is protected when the single-pole single-throw (SPST) switches S1 and S2 are closed, and the slide rheostat R is shorted. Conversely, the measurement state will be launched when the SPST switches are open, and the rheostat sliding head is placed on the location of the greatest resistance.
Figure 3 shows the schematic diagram of measurement setup for voltage responsivity. The THz signal is generated from a commercial VDI AMC 336 driven by an Agilent E8257D PSG Analog Signal Generator and propagates along the quasi-optical link to the detector module in a Dewar. Two wire-gird polarizers (one rotatable and the other fixed) are used to guarantee a small signal measurement so that the detector operates at its linearity region. The lock-in amplifier SR830 records the voltage response of the JJ detector with the modulation frequency of 1 kHz. Meanwhile, the THz signal is calibrated by a Golay cell (optoacoustic detector) with the modulation frequency of 20 Hz. Keithley 6221 DC and AC current source is used to give a bias current to the JJ. Both IVCs and voltage responsivity of the detector can be plotted automatically by our home-made measuring system using the LabVIEW software.
4. Experimental results and discussion
Figure 4(a) shows the measured IVCs of the JJ detector irradiated by a beam of THz wave at 219 GHz at different signal power levels. When the detector is unpumped (with zero power), the IVC shows the superconducting state ($V = 0$), the finite-voltage state (linear region), and the state of transition between them, with the critical current ${I_\textrm{c}}$ of ∼1.5 mA and the normal-state resistance Rn of 0.42 Ω. When the detector is pumped, ${I_\textrm{c}}$ is suppressed and Shapiro steps [32] come out. The voltages ${V_n}$ where the Shapiro steps appear are related to the incident frequency ${f_\textrm{s}}$ and satisfy the Josephson voltage-frequency relationship ${V_n} = n{\Phi _0}{f_\textrm{s}}$ ($n$ is an integer, and ${\Phi _0}$ is the magnetic flux quantum, $1/{\Phi _0} \equiv \; $2$e/h\, = $ 483.6 GHz/mV) [33]. As the incident frequency is 219 GHz, the first order Shapiro step is at the voltage of 0.45 mV. Furthermore, the current heights ${I_n}$ of Shapiro steps are related to the incident THz power introduced to the JJ, which can be estimated by the equation of ${I_n}/{I_\textrm{c}} = {J_n}({2e{V_{\textrm{RF}}}/h{f_\textrm{s}}} )$, where ${J_n}$ is an $n$th order Bessel function and ${V_{\textrm{RF}}}$ is the RF voltage (that is the THz signal voltage here). This relationship is evident in Fig. 4(b), which displays the dependence of DC current on the square root of the incident THz signal power at frequency of 219 GHz. The dynamic resistance (differential resistance dV/dI) distribution is also presented with different color. The zero resistances, which appear with blue regions in the graph, are where Shapiro steps locate. The dynamic resistances change significantly at the turning edges of the Shapiro steps with white color. From the picture, current step heights can be easily read out by the heights of blue regions at any incident power. With the increase of incident power, the number of steps increases. When the detector is pumped with 25 mW at 219 GHz, the number of steps has attained to 12. Data from 205-230 GHz has been all collected by our autonomous measuring system.
Fig. 4. (a) Measured IVCs and (b) differential resistance (color scale) of the detector irradiated by a beam of THz wave at 219 GHz with different power.
In order to characterize the antenna intuitively, the maximal sizes of first order Shapiro steps with the incident THz signal power per mW at different frequencies are plotted in Fig. 5(a), as shown with a red squared line. We measure the maximal first order Shapiro step size $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}$ (${I_{\textrm{c}0}}$ is the critical current when JJ is unpumped) then to be divided by the incident THz power ${P_{\textrm{in}}}$. To verify this new method, the coupling efficiency η between the JJ and the antenna, defined as ${P_{\textrm{RF}}}/{P_{\textrm{in}}}$ (${P_{\textrm{RF}}}$ is the power introduced to the junction) [25], is calibrated. ${P_{\textrm{RF}}}$ can be evaluated from equations of ${P_{\textrm{RF}}} = ({1/2} )V_{\textrm{RF}}^2/{R_n}$ and ${I_0}/{I_\textrm{c}} = {J_0}({2e{V_{\textrm{RF}}}/h{f_\textrm{s}}} )$, where ${I_0}$ is the current step-height at zero voltage. As seen with a blue dotted line in Fig. 5(a), the coupling efficiencies are consistent with the maximal sizes of the first order Shapiro steps under per incident power ($\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$). In other words, two methods fit each other well. The amplitude of the η are higher than that of the $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$, except at the frequency of 210 GHz. Actually, the real amplitude of $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$ at 210 GHz should be smaller because the $\Delta {I_{1\textrm{max}}}$ cannot be measured, resulting from the limitation of the device. In addition, we roughly study the approximate half size of the maximal first order Shapiro step under per incident power $({\sim} 0.5\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}})/{P_{\textrm{in}}}$, depicted in Fig. 5(b). From the graph, we confirm that 210 GHz is a well-matched frequency.
Fig. 5. (a) Measured maximal current heights of the first order Shapiro steps under per incident power and coupling efficiencies; (b) Half of the maximal first order Shapiro current heights under per incident power; (c) Voltage responsivities compared to maximal first order Shapiro current heights under per incident power at different frequencies.
Figure 5(c) shows the measured voltage responsivity (${V_{\textrm{rp}}}/{V_{\textrm{in}}}$), compared to the $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$. The voltage responsivity here is defined as a ratio of detector voltage response ${V_{\textrm{rp}}}$ to the incident voltage ${V_{\textrm{in}}}$ of the THz signal. In the experiment, the JJ detector is biased at 1.57 mA (a bit higher than ${I_\textrm{c}}$ to maximize the dynamic resistance) to get maximum ${V_{\textrm{rp}}}$. ${V_{\textrm{in}}}$ is calibrated by a Golay cell. The frequencies related to maximum voltage responsivity are accordant with those in $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$. The deviation of frequency within 2 GHz is expected as the Josephson linewidth is ∼2 GHz. However, the frequencies corresponding to the maximal amplitude are different in Fig. 5(c). The maximal amplitude of $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$ is at 210 or 212 GHz and sub-maximal amplitude is at 219 GHz, while the maximal amplitude of ${V_{\textrm{rp}}}/{V_{\textrm{in}}}$ is at 229 and then 219 GHz and sub-maximal amplitude is at 225 GHz and then 210 GHz. We check the THz power distribution from the source of VDI AMC 336, the frequencies of 219 GHz and 229 GHz are just at the troughs of the power distribution. Thus, it is reasonable that the maximal voltage responsivities exist at 219 and 229 GHz, caused by being divided minimum power. As the incident power required for the maximal sizes of the first order Shapiro steps is of the same order, we consider the result of measuring the $\Delta {I_{1\textrm{max}}}/{I_{\textrm{c}0}}/{P_{\textrm{in}}}$ to characterize the designed antenna is more reliable.
Checking the input impedance of the on-chip antenna in Fig. 1(e), the input impedances are 21-j60 Ω at 210 GHz and 23-j54 Ω at 219 GHz. From the perspective of impedance matching, the coupling efficiency between the antenna and JJ can be computed with standard antenna theory [34] as η $= 1 - {|{{S_{11}}} |^2} = 1 - {|{({Z_d} - Z_a^\ast )/({Z_d} + Z_a^\ast )} |^2}$, where ${Z_d}$ is the impedance of the JJ and $Z_a^\ast $ is the conjugate impedance of the antenna. As the JJ detector has better responses at ∼210 and 219 GHz, the conjugate impedances of the antenna must be close to the impedance of JJ, resulting in higher coupling efficiencies. With the increase of frequency in range of 219-230 GHz, the resistance of the antenna decreases and the reactance increases. However, the detector has no higher response than that at 219 GHz. We believe, the reactance of the JJ is around 55 Ω at 219 GHz and 60 Ω at 210 GHz. In addition, both of the reactance is positive, consistent with our knowledge of the inductive bicrystal JJ. Extra work about the JJ harmonic mixer coupled with a BLMA has been reported in [35]. The experiment indicates that the mixer coupled with this novel antenna has a superior performance to that coupled with a log-periodic antenna at 210 GHz. Our future work will focus on the exact value of the reactance of the JJ detector by adjusting the input reactance of the antenna.
5. Conclusion
We have developed an antenna to match the impedance of YBCO bicrystal JJ THz detector and proposed a new reliable method to characterize it. Integrated with the bowtie loaded meander antenna, the YBCO bicrystal JJ THz detector has been fabricated. Experiments have shown that the designed bowtie loaded meander antenna has the best coupling efficiency at ∼210 GHz by measuring the maximal size of the first order Shapiro step under per incident power. Two other ways of calculating the coupling efficiency between the antenna and JJ and measuring the voltage responsivity, have been applied as well to verify this new method. The characterization of THz antenna is no longer limited to the expensive vector network analyzer. Moreover, combining the simulation and experiments, we have evaluated that the reactance of YBCO bicrystal JJ is around 60 ohms at ∼210 GHz. The evaluated imaginary part of the impedance can be a reference in future design about impedance matching in HTS circuits at THz bands.
Funding
National Natural Science Foundation of China (61501222, 61521001, 61571219, 61727805); National Key Research and Development Program of China (2016YFA0301801, 2018YFA0209002).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. J. Chen, H. Myoren, K. Nakajima, and T. Yamashita, “THz mixing properties of YBa2Cu3O7-δ grain boundary Josephson junctions on bicrystal substrates,” Phys. C 293(1-4), 288–291 (1997). [CrossRef]
2. K. Y. Constantinian, G. A. Ovsyannikov, I. V. Borisenko, and P. Yagoubov, “Voltage-tunable YBCO Josephson mixer, operating in self-pumping mode at 750-970 GHz,” Phys. C 372-376, 420–422 (2002). [CrossRef]
3. K. Y. Constantinian, G. A. Ovsyannikov, I. V. Borisenko, and P. Yagoubov, “Observation of a voltage-tunable sun-mm wave response from a YBCO Josephson device, operating in self-pumping mode,” Supercond. Sci. Technol. 14(12), 1005–1008 (2001). [CrossRef]
4. Y. V. Kislinskii, K. Y. Constantinian, I. V. Borisenko, G. A. Ovsyannikov, and P. Yagoubov, “Submillimeter wave signal detection by bicrystal YBCO Josephson junctions at liquid nitrogen temperatures,” Phys. C 372-376, 436–439 (2002). [CrossRef]
5. G. A. Ovsyannikov, I. V. Borisenko, K. Y. Constantinian, Y. V. Kislinski, A. A. Hakhoumian, N. G. Pogosyan, T. Zakaryan, N. F. Pedersen, J. Mygind, N. Uzunoglu, and E. Karagianni, “Bandwidth and noise of submillimeter wave cuprate bicrystal Josephson junction detectors,” IEEE Trans. Appl. Supercond. 15(2), 533–536 (2005). [CrossRef]
6. K. Nakajima, N. Ebisawa, H. Sato, J. Chen, T. Yamashita, and Y. Sawaya, “Millimeter-wave sensitivity of YBCO grain boundary Josephson junctions coupled with coplanar waveguide-fed slot dipole antennas,” IEEE Trans. Appl. Supercond. 15(2), 549–551 (2005). [CrossRef]
7. J. Du, A. D. Hellicar, L. Li, S. M. Hanham, N. Nikolic, J. C. Macfarlane, and K. E. Leslie, “Terahertz imaging using a high-Tc superconducting Josephson junction detector,” Supercond. Sci. Technol. 21(12), 125025 (2008). [CrossRef]
8. J. Du, A. D. Hellicar, K. E. Leslie, N. Nikolic, S. M. Hanham, J. C. Macfarlane, and C. P. Foley, “Towards large scale HTS Josephson detector arrays for THz imaging,” Supercond. Sci. Technol. 26(11), 115012 (2013). [CrossRef]
9. D. Y. An, J. Yuan, N. Kinev, M. Y. Li, Y. Huang, M. Ji, H. Zhang, Z. L. Sun, L. Kang, B. B. Jin, J. Chen, J. Li, B. Gross, A. Ishii, K. Hirata, T. Hatano, V. P. Koshelets, D. Koelle, R. Kleiner, H. B. Wang, W. W. Xu, and P. H. Wu, “Terahertz emission and detection both based on high-Tc superconductors: Towards an integrated receiver,” Appl. Phys. Lett. 102(9), 092601 (2013). [CrossRef]
10. P. Thoma, J. Raasch, A. Scheuring, M. Hofherr, K. Il’in, S. Wünsch, A. Semenov, H.-W. Hübers, V. Judin, A.-S. Müller, N. Smale, J. Hänisch, B. Holzapfel, and M. Siegel, “Highly responsive Y–Ba–Cu–O thin film THz detectors with picosecond time resolution,” IEEE Tran,” Appl. Supercond. 23(3), 2400206 (2013). [CrossRef]
11. J. Du, A. R. Weily, X. Gao, T. Zhang, C. P. Foley, and Y. J. Guo, “HTS step-edge Josephson junction terahertz harmonic mixer,” Supercond. Sci. Technol. 30(2), 024002 (2017). [CrossRef]
12. J. Du, C. M. Pegrum, X. Gao, A. R. Weily, T. Zhang, Y. J. Guo, and C. P. Foley, “Harmonic mixing using a HTS step-edge Josephson junction at 0.6 THz frequency,” IEEE Trans. Appl. Supercond. 27(4), 1–5 (2017). [CrossRef]
13. X. Gao, T. Zhang, J. Du, A. R. Weily, Y. J. Guo, and C. P. Foley, “A wideband terahertz high-T superconducting Josephson-junction mixer: electromagnetic design, analysis and characterization,” Supercond. Sci. Technol. 30(9), 095011 (2017). [CrossRef]
14. X. Gao, J. Du, T. Zhang, Y. J. Guo, and C. P. Foley, “Experimental investigation of a broadband high-temperature superconducting terahertz mixer operating at temperatures between 40 and 77 K,” J. Infrared, Millimeter, Terahertz Waves 38(11), 1357–1367 (2017). [CrossRef]
15. X. Gao, T. Zhang, J. Du, and Y. J. Guo, “Design, modelling and simulation of a monolithic high-Tc superconducting terahertz mixer,” Supercond. Sci. Technol. 31(11), 115010 (2018). [CrossRef]
16. X. Gao, J. Du, T. Zhang, and Y. J. Guo, “High-Tc superconducting fourth-harmonic mixer using a dual-band terahertz on-chip antenna of high coupling efficiency,” IEEE Trans. Terahertz Sci. Technol. 9(1), 55–62 (2019). [CrossRef]
17. Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830 (2011). [CrossRef]
18. Y. Muslliake, “Self-complementary antennas,” IEEE Antennas Propag. Mag. 34(6), 23–29 (1992). [CrossRef]
19. C. Brendel, J. M. Scholtyssek, F. Ludwig, and M. Schilling, “HTS Josephson junction cantilever with integrated near field THz antenna,” IEEE Trans. Appl. Supercond. 21(3), 319–322 (2011). [CrossRef]
20. J. Chen, E. Kobayashi, K. Nakajima, T. Yamashita, and J. Zmuidzinas, “Characterization of planar log-periodic antennas at low temperatures using Josephson junctions,” in Proc. Asia-Pacific Microw. Conf. (APMC), Singapore, pp.348–351 (1999).
21. O. Y. Volkov, Y. Y. Divin, V. N. Gubankov, I. I. Gundareva, and V. V. Pavlovskiy, “Terahertz characterization of external resonant systems by high-Tc Josephson junctions,” IEEE Trans. Appl. Supercond. 21(3), 306–310 (2011). [CrossRef]
22. P. Probst, A. Semenov, M. Ries, A. Hoehl, P. Rieger, A. Scheuring, V. Judin, S. Wünsch, K. Il’in, N. Smale, Y.-L. Mathis, R. Müller, G. Ulm, G. Wüstefeld, H.-W. Hübers, J. Hänisch, B. Holzapfel, M. Siegel, and A.-S. Müller, “Nonthermal response of YBa2Cu3O7-δ thin films to picosecond THz pulses,” Phys. Rev. B 85(17), 174511 (2012). [CrossRef]
23. M. Malnou, C. Feuillet-Palma, C. Ulysse, G. Faini, P. Febvre, M. Sirena, L. Olanier, J. Lesueur, and N. Bergeal, “High-Tc superconducting Josephson mixers for terahertz heterodyne detection,” J. Appl. Phys. 116(7), 074505 (2014). [CrossRef]
24. J. Gou, T. Zhang, J. Wang, and Y. Jiang, “Spiral antenna-coupled microbridge structures for THz application,” Nanoscale Res. Lett. 12(1), 91 (2017). [CrossRef]
25. H. Yamada, T. Hayasaka, G. Toya, A. Saito, S. Ohshima, and K. Nakajima, “YBCO grain boundary Josephson junction coupled with a slot dipole antenna for terahertz wave detectors,” J. Phys.: Conf. Ser. 507(4), 042048 (2014). [CrossRef]
26. F. Auracher and T. V. Duzer, “rf impedance of superconducting weak links,” J. Appl. Phys. 44(2), 848–851 (1973). [CrossRef]
27. I. Ederra, R. Gonzalo, B. Martinez, B. E. J. Alderman, P. G. Huggard, A. Murk, L. Marchand, and P. Maagt, “Design and test of a 0.5 THz dipole antenna with integrated Schottky diode detector on a high dielectric constant ceramic electromagnetic bandgap substrate,” IEEE Trans. Terahertz Sci. Technol. 3(5), 584–593 (2013). [CrossRef]
28. D. B. Rutledge and M. S. Muha, “Imaging antenna arrays,” IRE Trans. Antennas Propag. 30(4), 535–540 (1982). [CrossRef]
29. D. P. Neikirk, D. B. Rutledge, M. S. Muha, H. Park, and C.-X. Yu, “Far-infrared imaging antenna arrays,” Appl. Phys. Lett. 40(3), 203–205 (1982). [CrossRef]
30. M. Yu, Z. N. Chen, W. W. Xu, Y. C. Xu, H. F. Geng, T. Hua, and P. H. Wu, “Impedance matching of bow-tie antenna for high temperature superconducting YBCO Josephson junction mixer,” in Proc. 42nd Int. Conf. Infr., Millim. THz Waves (IRMMW-THz), Cancun (2017).
31. K. Han, T. K. Nguyen, I. Park, and H. Han, “Terahertz Yagi-Uda antenna for high input resistance,” J. Infrared, Millimeter, Terahertz Waves 31, 441–454 (2009). [CrossRef]
32. S. Shapiro, “Josephson currents in superconducting tunneling: the effect of microwaves and other observations,” Phys. Rev. Lett. 11(2), 80–82 (1963). [CrossRef]
33. P. Mangin and R. Kahn, Superconductivity (Springer, Cham) p 248 (2017).
34. C. A. Balanis, Antenna Theory (John Wiley & Sons, Inc., Hoboken, New Jersey) (2005).
35. M. Yu, H. F. Geng, X. Gao, T. Hua, W. Chen, J. X. Shi, W. W. Xu, Z. N. Chen, H. B. Wang, J. Chen, and P. H. Wu, “Grain boundary Josephson junction harmonic mixer coupled with a bowtie loaded meander antenna with zero-bias operation,” IEEE Trans. Appl. Supercond. 29(8), 1–4 (2019). [CrossRef]
