## 2 Materials and Methods
### Antenna Optimization  
The bow-tie antenna is composed of a two-part bow-tie shape, designed to reduce the reflection coefficient. It is characterized by broad-band impedance [15; 20]. The performance of the detection systems is analyzed by electromagnetic simulations, carried out using High-Frequency Structure Simulator (HFSS) software by ANSYS. We begin with the analysis of the conventional design, in which the Josephson junction is placed in the gap between the two poles of the antenna [12; 25]. Optimal results were obtained for a pole width of 115.5 \(\upmu\)m and a length of 144.3 \(\upmu\)m, with a separation between the two antenna poles, a gap width, of a 4.2 \(\upmu\)m. The efficiency of such systems deteriorates rapidly at very high frequencies, due to impedance mismatch between the antenna and the junction. Figure 2 shows the simulation results of the reflection coefficient S\({}_{11}\) as a function of frequency. The simulation renders a bandwidth of about 4 GHz, at 3.57:1 voltage standing wave ratio (VSWR), showing a power ratio of up to 0.874 for the power supplied to the antenna, i.e., an efficiency of 87.4% not including ohmic losses. The reflectivity obtained is around \(-\)11 dB at the central frequency of 148 GHz. We propose a new structure in which the junction is placed between the ends of two matching strips, as outlined in Figure 3. This structure is intended to enable, with proper optimization of the strip dimensions, high impedance matching at high frequencies between the antenna input impedance \(Z_{in}\) and the junction impedance \(Z_{JI}\). Figure 4 shows the structure of a two-pole antenna, as designed and built in the simulation software. The poles consist of a 250 nm thick Au layer on top of a 330 nm thick YBCO layer and 0.5 mm thick MgO substrate. Other parameters included in the simulations are the dielectric constant of the MgO substrate, \(\varepsilon_{r}\) = 9.8, and the loss tangent, tan\(\delta\), approximately 10\({}^{-4}\) at 77 K [36; 37]. The antenna dimensions were modified in order to obtain a high gain and a low reflection coefficient. Optimal results were obtained for a pole width of 75.5 \(\upmu\)m and a length of 74 \(\upmu\)m. The separation between the two antenna poles, the gap width, is 4.2 \(\upmu\)m.  
Figure 5 shows the results of simulations for the reflection coefficient S\({}_{11}\), as a function of frequency, with matching strips 4.6 \(\upmu\)m wide each, for various values of length (L in Figure 3). In order to evaluate the junction equivalent impedance \(Z_{Jl}\), we used typical parameters for bicrystal Josephson junctions [31, 38]. The light velocity ratio \(\overline{c}/c\) is estimated to be around 0.03 [8, 31] with a relative  
Figure 4: Structure of bow-tie antenna in HFSS software. Figure 3: Geometry of bow-tie antenna. L is the length of the matching impedance strips and W its width. The junction is placed between the bottom ends of the strips (purple rectangle). Figure 2: Reflection coefficient, S\({}_{11}\), for conventional bow-tie antenna, as function of frequency. dielectric constant, \(\varepsilon_{rs}\), of 5 for the YBCO [38]. The junction width \(w\) was set to 4.2 \(\upmu\)m. Inserting these values into Equation (3), one obtains \(Z_{J\!I}=\frac{1}{0.03}\left(\frac{l}{4.2\cdot 10^{-6.5}}\right)\).377 \(\Omega\). Thus, for \(l\cong 3.5\) nm, \(Z_{J\!I}\cong 2\)\(\Omega\). The lowest reflection coefficient was obtained for an antenna with \(L=108\)\(\upmu\)m. The simulation renders a bandwidth of \(\sim\)4 GHz, at 2.615:1 VSWR, with an efficiency of up to 99.75%, not including ohmic losses. For this structure, the calculated reflection coefficient is \(-26\) dB at the central frequency of 155 GHz. Simulation results presented in Figure 5 were performed assuming a known value of the junction impedance: \(Z_{J\!I}\). However, it should be pointed out that according to Equation (6), this impedance is most sensitive to the exact value of the length of the junction \(l\).