## 2 Principle of Standard and Differential Modulation Modes  
SOA-MZI is a mature optical device. The optical sampling is performed by using the XPM effect in a SOA-MZI used as an optical switch. SOA-MZIs possess some attractive features of low power requirements, compactness, high extinction ratios [30; 31], and noise reduction [32]. In addition, the possibility of using the same experimental setup based on the SOA-MZI [22] to implement up- and down-conversions makes the scheme a very versatile choice. The large data bandwidth is fundamentally related to the carrier lifetime of SOAs [33]. The architecture of the real SOA-MZI used in simulations by the VPI simulator is given in Figures 1 and 2, which is already proposed in our previously published work [34; 35]. One SOA was located in each arm of the MZI. The phase shifters located in the upper and lower arms helped to provide a phase optimization for both output arms. With this SOA-MZI structure, the input signals traveled in the same direction, as seen in Figure 1, but they may travel in the counter-direction, as displayed in Figure 2, since the SOAs can be operated bi-directionally. Figure 1a explains the principle of operation for the standard modulation. The sampling signal with a sampling frequency \(f_{s}\) at the wavelength \(\lambda_{s}\) is separated into two identical copies at the middle port (MP) to the upper and lower arms. Besides, the two data signals at carrier frequencies \(f_{m}\) are simultaneously injected at the upper port (UP), where \(m\) ranges from 1 to 2. In this case, any data signal causes a phase shift in the upper copy of the sampling signal. This results in a continuous variation of the amplified sampling signal that appears at the upper and lower outputs, i.e., in a modulation of the sampling signal by the data signal. Hence, the sampled signal at the SOA-MZI output after filtering at \(\lambda_{s}\) was replicated from \(f_{m}\) to mixing frequencies \(nf_{s}\pm f_{m}\), where \(n\) ranges from 1 to 10. It is worth noting that if sundry ten IF signals are injected at the same time at UP, we can obtain the same results with many up-converted signals at \(nf_{s}\pm f_{m}\), where \(m\), in this case, ranges from one to ten. The proposed differential modulation, which is a pioneering work to the best of our expertise, is depending on a XPM of two input optical signals in the MZI built using SOAs as shown in Figure 1b. In this architecture, the first data signal at the frequency \(f_{1}\) at the UP is injected into the upper arm and the second data signal at \(f_{2}\) at the LP is entered at the lower arm. As the principle of the standard modulation, the same sampling signal that corresponds to ultra-short clock pulses is coupled into the MP of the MZI and split into the upper and lower arms simultaneously by using an optical coupler (OC). These signals modulate the gain of both SOAs where their carrier densities and refractive indexes are modulated. In addition, the sampling signal in the upper arm is modulated by the first data signal and the same signal is modulated by the second data signal in the lower arm. The presence of the data signal affects the phase of the sampling signal due to the XPM. Figure 1: SOA-MZI in the co-direction configuration. Att: Attenuator, OC: Optical Coupler, MP: Middle Port, OP: Output Port, UP: Upper Port, and LP: Lower Port. (**a**) Standard modulation mode, (**b**) Differential modulation mode. Then, a phase shift occurs on the sampling signal in the upper arm as the standard modulation. However, another phase shift appears on the same signal in the lower arm. Thus, this causes a phase modulation of the sampling signal propagating in both SOAs according to the input signals. At the SOA-MZI output port (OP), the signal from both SOAs interfered in order to obtain the mixed signal. This signal was considerably improved compared to the one in the standard modulation due to the enhanced amplified sampling signal in both arms that preserves the same harmonic power whatever the harmonic rank \(n\) is.