## 3 Conversion Gain Results
The two optical carriers injected at the UP for the standard modulation and at UP and LP for the differential modulation were intensity modulated by a sinewave signal at the frequencies \(f_{1}=1\) GHz for the IF1 signal and \(f_{2}=2\) GHz for the IF2 signal. In both cases, the  
Figure 6: Block diagram of the simulation setup of frequency mixing for counter-direction schema. (a) Standard modulation mode, (b) Differential modulation mode. mean optical power of each optical carrier was \(-12\) dBm. The electrical power of the corresponding photo-detected signal was \(-35.8\) dBm for the IF1 signal and \(-36.4\) dBm for the IF2 one. The peak power of the sampling signal was adjusted to be \(-1\) dBm in the co-direction and \(-3\) dBm in the counter-direction at the MP. The sampled signal at the SOA-MZI output was optically filtered at \(\lambda_{s}\) before being photodetected, amplified and displayed on an ESA. In order to validate the principle of the standard and differential modulations in the co- and counter-directions, we presented the electrical spectrum of the sampled signals at the SOA-MZI output, modulated at \(f_{1}=1\) GHz and \(f_{2}=2\) GHz. These spectrums are shown in Figures 7 and 8 for the standard and differential modulations in the co-direction, respectively, and in Figures 9 and 10 for the both modes in the counter-direction, respectively. Regarding this, we can compare the mixed signals in order to observe the electrical powers of mixed signals for the four cases and compute the conversion gain. It is observed that the input signals were up-converted at mixing frequencies \(nf_{s}\pm f_{1}\) related to channel one and \(nf_{s}\pm f_{2}\) related to channel two for both configurations. The harmonics power of the sampling signal transposed at \(\lambda_{s}=1550\) nm showed that high frequencies contain close amplified power compared to the low ones, regardless of the SOA-MZI low-pass behavior for the four cases. The difference between the tenth and the first harmonic was only \(7\) dB for the standard and differential modulation in the co-direction, while it was \(9\) dB for both cases in the counter-direction. For the differential modulation, the up-converted signals were amplified considerably at the higher mixing frequencies compared to the ones for the standard modulation in co- and counter-directions. The mixed signals are attenuated with an average value of \(2\) dB in the case of counter-direction compared to the ones for the co-direction for the whole mixing frequencies. In all cases, we can observe that the up-converted signals involve up to the tenth harmonic of the sampling signal. Hence, the highest frequency range in this case becomes \(10f_{s}+f_{2}=158\) GHz, which is the highest mixing frequency. Figure 7: Electrical spectrum of the up-converted signal, which represents the electrical power in dBm as a function of frequency in GHz, at mixing frequencies \(nf_{s}\pm f_{m}\) at the SOA-MZI output for the standard modulation mode in the co-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 \(H_{n}=nf_{s}\). In conclusion, the use of the principle of the differential modulation in both directions enhanced the characteristics of the mixed signals. This may lead to bolstering the quality of the optical transmission system. It is important to highlight that we could obtain a frequency mixing at the higher frequency range for the differential modulation compared to the standard one. In order to fairly compare between them, the electrical spectrums of the mixed signals were stopped at the mixing frequency of \(10f_{s}+f_{2}=158\) GHz for the four cases. Figure 8: 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 co-direction.