## 1 Introduction  
Millimeter-wave systems have received great importance thanks to augmented data rates [1]. Moreover, a variety of mixing appliances have evolved to generate radio frequency (RF) signals with a \(1.5\) THz frequency [2; 3]. Furthermore, radio over fiber (RoF) systems have achieved main merits, such as: good optical transmission with little losses, small weight, and spacious bandwidth. They can be implemented in a wireless fidelity (WiFi), radar systems [4], and cellular communications. Optical mixers have some major attributes that play a substantial role in order to achieve frequency mixing with good performances, especially their nonlinear implementation, such as the four-wave mixing (FWM) or the cross-phase modulation (XPM) phenomena [4] and the physical characteristics. Mach-Zehnder modulators (MZMs) that achieve high-performance characteristics [4; 5] and electro-absorption modulators (EAM) based on the cross-absorption modulation (XAM) situation [6; 7] can be used for frequency conversion. Furthermore, photodiodes (PDs), especially uni-traveling carrier PDs (UTC-PDs), can also be employed for frequency mixing because of their response to nonlinear currents [8; 9]. Semiconductor optical amplifiers (SOAs) rely on their nonlinearity such as cross-gain modulation (XGM) [10] and XPM [11; 12; 13; 14; 15; 16; 17; 18; 19; 20] can also be used for shifting at the same time in the layout of a detached apparatus or implemented in an interferometric structure such as an SOA-Mach-Zehnder Interferometer (SOA-MZI). SOA-MZIs can achieve good performance, such as a frequency range up to \(100\) GHz [19]. All-optical mixing based on a sampling SOA-MZI [11; 12; 13; 14; 15; 16; 17] has achieved excellent characteristics such as high positive conversion gain for both experimental and simulation studies. The used SOA-MZI combined with an optical pulse source that uses a mode-locked laser in order to generate an optical pulse train can be used up and down conversion simultaneously with good efficiency. Frequency up-conversion by an all-optical sampling concept based on a photonic SOA-MZI is one of the main technologies for producing an optical radio frequency (RF) signal that is the sampled signal, which is converted to an electrical one through a PD at a receiver at a range of frequencies, for RoF transmission systems, in order to enhance the efficiency performance of this optical system. Various setups for the frequency up-conversion have been elucidated by utilizing nonlinear behaviors of the SOA-MZI in real and simulation studies [11, 12, 13, 14, 15, 16, 17]. At the same time, these architectures offered a very large bandwidth with respect to the mixing of the IF signal to be up-converted. In this paper, the use of electro-optical sampling in a differential SOA-MZI of the modulation schema is well implemented and attained very good performance characterizations. Frequency mixing can also be achieved by modulating the SOA electrical port in both arms of the SOA-MZI. Then, this gives rise to modulating the SOAs carrier density for a differential schema [20, 21, 22, 23]. Previously, the technique of an electro-optical up-converter based on the Reflective SOA (RSOA) has been demonstrated [23]. An IF (intermediate frequency) signal that loads of quadratic phase shift keying (QPSK) data have been up-converted to 15 GHz with a good quality signal corresponding to an error vector magnitude (EVM) less than 6% at a bit rate of 3 Mbit/s [23]. Some novel converter systems built on a generalized proportional integral observer (GPIO) based dynamic prescribed performance sliding mode control (DPPSMC) approach is developed to realize high-quality output voltage [24]. This leads to escalation in the transient effects of the converter system. The switching frequency is limited to 5 kHz due to the experiment hardware limitation. These types of converters, called nonlinear switch systems, have been broadly used in communication apparatus and computer systems.