# Detection of On-Chip Generated Weak Microwave Radiation Using Superconducting Normal-Metal SET
## 3 Experimental Setup and Results
### Periodic Modulation of the Source Power  
The power tunability of the source was investigated using critical current modulation, \(I_{\mathrm{C}}(\Phi_{\mathrm{ext}})=I_{\mathrm{C}}(0)|\cos(\pi\Phi_{\mathrm{ ext}}/\Phi_{0})|\), by applying the external magnetic field to the SQUID. The suppression of the Josephson supercurrent resulted in the reduction and, finally at \(\Phi_{\mathrm{ext}}=\Phi_{0}/2\), the vanishing of the detector response, as is shown in Figure 7, over the frequency range of interest and for a change in the magnetic flux from 0 up to \(\Phi_{0}/2\) (\(B\approx 0\div 2.5\) mT). By further increasing the  
Figure 6: **(a)** The detector response as a function of the frequency of the microwave irradiation generated at \(V_{\parallel}<V_{\mathrm{max}}\). The signal delivered over the transmission line (green curve) is compared to that over the capacitive coupling (red dashed curve). The stronger response in the sample with the capacitive coupling appears due to the larger value of critical current, \(I_{\mathrm{C}}\sim 48\) nA, than in that with the transmission line, \(I_{\mathrm{C}}\sim 32\) nA; **(b)** An _1-V_ curve measured in the same voltage range for one of the Josephson sources. Those peculiarities which coincide with observed peaks in the detector responses are marked by black arrows.  
magnetic field up to a value \(B\approx 20\,\mathrm{mT}\), we observed a quasi-periodic modulation of the detector response (Figure 8) with a period \(\Delta\Phi_{\mathrm{ext}}\approx\Phi_{0}\). We consider this behavior to be a direct confirmation of the detector response being caused by the microwave signal generated by the Josephson source.  
Figure 8 also shows a reduction in the height of the maximum detector current with increasing the applied magnetic flux. This behavior was observed even in spite of a true periodic modulation of the critical current. Taking into account a quadratic dependence of the emitted power on the resulting critical current and field-dependent losses in the transmission line, we were able to fit this decay by introducing phenomenologically an exponential prefactor and assuming the dependence as: \(I_{\mathrm{NISIN}}\propto l_{\mathrm{C}}^{2}(\Phi_{\mathrm{ext}})^{-2\pi\Phi_ {\mathrm{ext}}/\Phi_{0}}\). The result of fitting is depicted in Figure 8 with a red dotted curve  
Figure 8: Normalized detector response as a function of the magnetic flux (green curve). The red dotted curve is a phenomenological fit including an exponential decay expression shown in the figure.  
Figure 7: The detector response to the increase in the magnetic flux from 0 up to the value \(\Phi_{0}/2\). The gradual decay of the response is a result of decreasing the source critical current (see inset) and, therefore, the radiation power to a vanishing value.  
using a value of 0.26 for the dimensionless coefficient \(\alpha\). The power losses in the transmission line are evaluated at \(B\approx 20\,\mathrm{mT}\) being on the level of \(\sim 0.01\) dB/\(\upmu\)m. We attribute the appearance of appreciable losses in the superconducting microstrip line to the formation of the mixed state in Al film related to the penetration of the magnetic field applied perpendicular to the film surface [34; 35]. According to our estimations made for the present layout of the coplanar wave guide, the observed level of signal damping corresponds to an effective unit length flux flow resistance up to \(r_{100\;\mathrm{GHz}}\sim\)0.7 \(\Omega/\upmu\)m at \(B\approx 20\,\mathrm{mT}\). The obtained value is on the scale with DC unit length resistance \(r_{\mathrm{DC}}\sim 0.5\)\(\Omega/\upmu\)m, measured under the same conditions, and shares the same order with the normal state resistance of Al, \(r_{\mathrm{n}}\sim\) (0.1-1) \(\Omega/\upmu\)m.