## 3 Experimental Results
### Measurement Results  
We evaluated the sensitivity of the [PERSON] detector according to its NEP, based on the relation \(\frac{NEP}{\sqrt{\Delta V}}=\sqrt{6}\Big{(}\frac{h_{0 RF}}{2 eR_{c}L}\Big{)}^{2 }\sqrt{4k_{B}TR_{n}}\). \(R_{n}\) is the normal resistance, \(I_{c}\) is the critical current in the presence of the RF radiation, and \(\omega_{RF}\) is the radiation frequency. The coupled power voltage responsivity \(\eta(V)\) was derived from \(\eta(V)=\frac{\Delta V}{P_{RF}}\) where \(P_{RF}\) is the amplitude of the RF power coupled into the junction. \(P_{RF}\) can be estimated from the amplitude of the RF current, \(I_{RF}=\frac{h_{0 RF}\sqrt{\frac{\Delta V}{\Delta V}}}{eR_{c}L}\)[7; 8; 9]. \(I_{c0}\) is the unsuppressed critical current, without RF radiation. \(\hbar\) is Planck constant divided by \(2\pi\), and \(e\) is the electron charge. \(\Delta V=R_{d}(V)\Delta I\), where \(\Delta I\) is the change in the junction current due to the RF signal. \(R_{d}(V)\) is the dynamic resistance, \(\Delta V/\Delta I\). Figure 14 shows the measured I-V and dI/dV characteristics for the antenna with a 4.6 \(\upmu\)m wide matching strip. The data was taken at 60 K without a Si lens. The unsuppressed critical current is \(I_{c0}\approx 1\) mA and the normal resistance \(R_{n}\approx 3.5\)\(\Omega\). The top curve shows the junction response to the RF signal at 155 GHz, showing a critical current \(I_{c}\approx 0.75\) mA. The estimated electrical NEP for the detector is ~\(4\times 10^{-12}\) W\(\cdot\)Hz\({}^{-1/2}\). The RF current, \(I_{RF}\), is estimated to be ~0.1 mA, thus the voltage responsivity is \(\eta(V)\approx 33\) kV\(\cdot\)W\({}^{-1}\). The Shapiro step at 0.32 mV is due to the presence of an electromagnetic radiation at ~155 GHz. The dI/dV characteristics (bottom curve Figure 14) shows the RF response of the junction to signals at various frequencies. The measured narrow bandwidth high peak at 155 GHz, as well as the poor performance at other frequencies, are a clear indication of the high accuracy of our simulations. The high frequency selectivity of the detector system is demonstrated clearly by the set of peaks, shown in the bottom figure. Figure 13: Measurement setup block diagram. Figure 15 show the I-V and dI/dV characteristics of the same antenna, measured at 60 K, but with a Si lens. The top curve presents the junction response to an RF signal at 148.2 GHz, showing a critical current of \(I_{c}\approx 0.4\) mA. The estimated NEP is \(\sim\)1 \(\times\) 10\({}^{-13}\) W\(\cdot\)Hz\({}^{-1/2}\). The RF current, \(I_{RF}\), can be estimated as \(\sim\)0.3 mA, thus the voltage responsivity is \(\eta(V)\approx\) 55 kV\(\cdot\)W\({}^{-1}\). The Shapiro step at 0.31 mV is due to the presence of electromagnetic radiation at \(\sim\)148 GHz. These results are clearly superior to typical NEP and \(\eta(V)\) values reported for sensitive detection systems at 60 K, namely around 1 \(\times\) 10\({}^{-12}\) W\(\cdot\)Hz\({}^{-1/2}\) and 10 kV\(\cdot\)W\({}^{-1}\), respectively [13; 25; 42]. Once again, the high peak at 148 GHz in the dI/dV characteristics (bottom curve Figure 15) demonstrates the high agreement between simulation and experimental results. One can see that using Si lens the center frequency of the matched antenna has shifted, as predicted by the electromagnetic simulations. Figure 16 shows the measured I-V and dI/dV characteristic of the second antenna implemented with matching strips width of 5.4 \(\upmu\)m. The measurements were taken at 60 K, with a Si lens. The unsuppressed measured critical current is \(I_{c0}\approx\) 1.93 mA, a relatively high value for a bicrystal junction. The normal resistance is R\({}_{n}\approx\) 3.8 \(\Omega\). This higher critical current reduces the sensitivity of the detector. The measured peak at 155 GHz agrees extremely well with the theoretical results shown in Figure 11, proving that the impedance matching between the antenna and the junction was not affected.