## 3 Conversion Gain Results
The frequencies of the two input signals are \(f_{1}=1\) GHz and \(f_{2}=2\) GHz, the sampling frequency is \(f_{s}=15.6\) GHz and the harmonics of the sampling signal at \(H_{n}=nf_{s}\). Figure 9: Electrical spectrum of the up-converted signal, which represents the electrical power in dBm as a function of frequency in GHz, at \(nf_{s}\pm f_{m}\) at the SOA-MZI output for the standard modulation in the counter-direction. The frequencies of the two input signals are \(f_{1}=1\) GHz and \(f_{2}=2\) GHz, the sampling frequency is \(f_{s}=15.6\) GHz and the harmonics of the sampling signal at \(H_{n}=nf_{s}\). To describe the efficiency of the frequency up-conversion process, it is convenient to define the conversion efficiency as the ratio of the electrical power of the mixed signals at mixing frequencies \(nf_{s}+f_{m}\) at the SOA-MZI output to the one of an input IF signal computed at the IF frequencies \(f_{m}\) for the standard and differential modulations in co- and counter-directions. As seen in Figure 11, the IF1 signal at \(f_{1}\) at the data input is up-converted at \(nf_{s}\pm f_{1}\) at the SOA-MZI output. For the standard modulation in the co-direction, the conversion gain obtained at \(nf_{s}+f_{1}\), shown in Figure 11 decreases from 43.3 dB at \(f_{s}+f_{1}=16.6\) GHz related to the first harmonic \(H_{1}=f_{s}\) of the sampling signal to 21.8 dB at \(10f_{s}+f_{1}=157\) GHz related to the tenth harmonic \(H_{10}=10f_{s}\). Besides, the use of the principle of the differential modulation improved the conversion gain considerably at higher mixing frequencies, which reached 31.8 dB at 157 GHz for the differential modulation, while it was 21.8 dB at the same frequency for the standard one. We should also mention that the conversion gain attenuated 2 dB over the entire mixing frequencies for both modes in the counter-direction due to its lower cut off frequency compared to the ones in the co-direction. Additionally, positive conversion gains were obtained for all mixing frequencies in all cases due to the gains of the SOAs in SOA-MZIs and the mixing frequency that was related to the harmonics of the sampling signal, which possess close amplitudes. Because of the SOA-MZI low pass behavior, the conversion gain degraded a lot at the high mixing frequencies. Regardless of that, the modulation principle for the differential mode played a role in amplifying the electrical power at the high mixing frequencies. In reality, it was difficult to obtain the same harmonic power or the same replica power due to the low pass behavior of the SOA-MZI. Figure 10: Electrical spectrum of the up-converted signal, which represents the electrical power in dBm as a function of frequency in GHz, at \(nf_{s}\pm f_{m}\) at the SOA-MZI output for the differential modulation in the counter-direction. The frequencies of the two input signals are \(f_{1}=1\) GHz and \(f_{2}=2\) GHz, the sampling frequency is \(f_{s}=15.6\) GHz and the harmonics of the sampling signal at \(H_{n}=nf_{s}\). For up-converted signals at \(nf_{s}\pm f_{2}\) at the SOA-MZI output, the conversion gain obtained at \(nf_{s}+f_{2}\), seen in Figure 12, showed the same behavior as the one related to the sampled signal at \(nf_{s}+f_{1}\). However, the conversion gain of the sampled signal related to the channel two for the four cases degraded more than the one related to the channel one. This discrepancy is linked to different amplifications of both subcarriers at \(f_{1}\) and \(f_{2}\) due to the SOAs: the gain difference between the low frequency subcarrier at 1 GHz and the one at 2 GHz was about 3 dB for both configurations. It is worth noting that the range of mixing frequency was not the same for both up-converted signals. As seen in Figure 12, conversion gain decreased from 43 dB at \(f_{s}+f_{2}=17.6\) GHz to 21 dB at \(10f_{s}+f_{2}=158\) for the standard modulation mode in the co-direction. In addition, it also decreased from 41 dB at 17.6 GHz to 19 dB at 158 GHz for the same mode in the counter-one.