## 3 Setup Characterization Used in a VPI Simulator  
The setup used in a VPI simulator of electro-optical up-converter is shown in Figure 2. In our study, two IF signals with the same characteristics are entered at the electoral port of each SOA that is biased at the value of the 350-mA bias current. Moreover, the SOA electrical port is adapted to 50 \(\Omega\). The IF signals are intensity modulated by a subcarrier in the electrical domain at \(f_{IF}=0.5\) GHz. The modulation power of the data signal is 13 dBm. The signal is generated by an optical pulse clock (OPC) having a wavelength of 1550 nm at a sampling frequency of 19.5 GHz. The electrical spectrum of this sampling signal shows a variety of harmonics at \(H_{n}=nf_{s}\). This signal is an SOA-MZI input through its MP by using plenty of contrasting optical signal mode fibers. In order to achieve frequency shifting, the mean optical power of the OPC signal is managed to be \(-1\) dBm. Figure 1: Electro-optical shifting based on a sampling SOA–MZI using the modulation of differential schema. MP: Middle Port, OP: Output Port, OC: Optical Coupler, and Att: Attenuator. At the outer port of the used SOA-MZI, the optical filter (OF) adjusted at 1550 nm is used in order to remove unwanted signals. Then, the sampled signal is passed through a photodiode (PD) to obtain a photo-detected signal after sampling. This PD has a 300 GHz bandwidth and a sensitivity of 0.85 A/W. The photo-detected signal is amplified by a 33 dB-gain low-noise amplifier (LNA) and subsequently propounded on an electrical spectrum analyzer (ESA) to procure the spectrum of the signal to be mixed or used in the BER_EL-M-QAM module to demodulate the data with a view to finding its EVM. The used PD for photo-detection in a VPI simulator corresponds to a uni-traveling carrier (UTC) PD [9]. The use of the VPI simulator assists us in applying plenty of simulations that imitate the actual work [26]. In order to validate the electro-optical differential modulation principle, we propound the electrical spectrum of the signal to be mixed at the outer port of the used SOA-MZI, as seen in Figure 3. It is validated that the data signals are mixed at requested frequencies \(nf_{s}\pm f_{IF}\). The harmonic powers of the OPC signal decrease slightly with the position of harmonics \(n\). The difference between the tenth harmonic \(H_{10}=10f_{s}\) and the first one \(H_{1}=f_{s}\) is about 8 dB. This degradation is a result of the dynamic behavior of the used SOA-MZI [11, 15] that cannot be avoided. Moreover, the mixed signals are amplified considerably at high mixing frequencies, as observed in the electro-optical differential modulation. Hence, the highest frequency range is \(10f_{s}+f_{IF}=195.5\) GHz. In conclusion, differential modulation enhances the characteristics of the sampled signals [16, 17]. To evaluate the sampling mixer efficiency for electro-optical deferential modulation, the conversion gain \(G_{c}\) is obtained. It is savvived as the difference of electrical powers in dBm between the signal to be mixed at \(nf_{s}+f_{IF}\) and the data signal at \(f_{IF}\). As apparent in Figure 4, the electro-optical differential modulation considerably improves \(G_{c}\). It reaches 24 dB at the frequency of 195.5 GHz, which corresponds to the maximum frequency of the signal to be mixed. The variation between the initial \(G_{c}\) and the final one is 14 dB. Moreover, conversion gains that have positive values are obtained for all mixing frequencies related to \(H_{n}\) due to SOAs gains. Because of the SOA-MZI dynamic behavior, \(G_{c}\) degrades at frequencies that have top values. Regardless of that, the principle of differential modulation plays a significant function in the augmentation of the electrical power of the signal to be mixed at the top frequencies. In fact, it is tricky to acquire similar power levels of the harmonics as well as the identical replica of the electrical power of the  
Figure 2: Mixing setup used in a VPI simulator counted on the modulation of the differential mode.