# All-Optical Simultaneous Frequency Metamorphose Contingent on a Three Parallel SOA-MZIs Copula
## 4 Simultaneous Up-Conversion Characterization  
To revise the performances of the concurrent mixing to higher frequencies developed on three parallel SOA-MZIs, we have appraised the conversion gain (CG) in the electrical domain obtained after photo-detecting. The CG is specified as the squared modulus of the ratio between the modulated power at frequencies \(nf_{s}+f_{m}\) at the external port of the SOA-MZI (\(p_{Out,nf_{s}+f_{m}}\)) and the modulated power (\(p_{m}\)) at \(f_{m}\) at the input port of the used SOA-MZI. \[CG_{nf_{s}+f_{m}}=\left|\frac{p_{Out,nf_{s}+f_{m}}}{p_{m}}\right|^{2} \tag{3}\]  
As we have observed in the technique of the simultaneous mixing to higher frequencies dependent on the three parallel SOA-MZIs linkage, the mixed signal has many replicas at frequencies \(nf_{s}+f_{m}\). Therefore, the CGs can be calculated in Equations (4)-(6) for each replica at \(nf_{s}+f_{1}\), \(nf_{s}+f_{2}\), and \(nf_{s}+f_{3}\), respectively, as follows:\[CG_{nf_{s}+f_{1}} = \left|-K\frac{\frac{1}{\tau}\sqrt{\frac{2p_{nf_{s}}}{G_{\text{LNA} }R}}}{1-j\omega_{1}\tau_{d}}\right|^{2} \tag{4}\] \[CG_{nf_{s}+f_{2}} = \left|-K\frac{\frac{1}{\tau}\sqrt{\frac{2p_{nf_{s}}}{G_{\text{LNA} }R}}}{1-j\omega_{2}\tau_{d}}\right|^{2}\] (5) \[CG_{nf_{s}+f_{3}} = \left|-K\frac{\frac{1}{\tau}\sqrt{\frac{2p_{nf_{s}}}{G_{\text{LNA} }R}}}{1-j\omega_{3}\tau_{d}}\right|^{2} \tag{6}\]  
The CGs parade a low-pass frequency behavior, with the corner frequency occurring at \(f_{c}=1/2\pi\tau_{d}\)[15, 18]. The increment of the radian frequency \(\omega_{nf_{s}}\) from \(\omega_{f_{s}}\) to \(\omega_{5f_{s}}\) guides to a slight decline in the electrical power of the harmonic as well as the electrical power of the replicas, where \(\omega_{f_{s}}\) is extremely higher than \(\omega_{c}=2\pi f_{c}\), while \(\omega_{m}\) is subordinate \(\omega_{c}\). In this case, the CG never persuades the dynamic response of the SOA-MZI for the standard modulation constitution [13, 14] attributable to the amplification of the sampled control signal when the optical filter is filtered at the wavelength \(\lambda_{s}\). The CG of each replica of the mixed signal derived from the parallel SOA-MZIs link was computed using the equations mentioned previously. Then, it is achieved by simulations carried out by applying a VPI Transmission Maker [19] with a focus on comparing the simulation results with the theoretical ones. The data signal is up-converted simultaneously from \(f_{1}=\)0.5 GHz to \(5f_{s}+f_{1}=98\) GHz, \(f_{2}=\)1 GHz to \(5f_{s}+f_{2}=98.5\) GHz, and \(f_{3}=\)1.5 GHz to \(5f_{s}+f_{3}=99\) GHz. In addition, the CG is calculated for a variety of target frequencies \(nf_{s}\pm f_{m}\) associated with the harmonics of the sampling signal. The CGs are chosen in the following results at \(nf_{s}+f_{m}\). The system built in the VPI software in order to identify the CG is propounded in Figure 3 for the three parallel SOA-MZIs linkage. In addition, the spectrum of the high frequency signal after sampling is provided through an electrical spectrum analyzer (ESA) after light-sensing by a photodiode (PD) and augmentation by a low-noise amplifier (LNA) with the intention to calculate the CG and approve the technique of the jointly high frequency signals interpreted above. The pulsed signal is galvanized from an optical pulse clock (OPC), which coincides with the Pritel model, which was previously adopted in the experimental work [6], at a sampling frequency \(f_{s}\) equal to 19.5 GHz and provides a 2 ps pulse width duration of the optical pulse train at full width at half maximum (FWHM). The wavelength of the OPC is 1550 nm. The peak of the pulsed control signal is controlled to be \(-1\) dBm as explained in the changeless characteristics of the employed SOA-MZI. The OPC corresponds to a sampling signal that has harmonics at frequencies \(nf_{s}\). The three OPCs displayed in Figure 3 have identical structures, physical parameters, and operating points. These optical devices are used at the middle port for each SOA-MZI.