# Analysis and Reduction of Nonlinear Effects in Optical Fiber Frequency Transfer
## 1 Introduction  
In recent years, the achievement of precision levels at \(10^{-18}\) and the remarkable stability of optical clocks have played a significant role in various research domains, including navigation, fundamental physics, applied research, chronometric geodesy, and the quest for dark matter [1; 2; 3; 4; 5; 6]. The evolution of optical clocks has given rise to high-precision optical frequency transfer methods. Fiber optic links have demonstrated exceptional performance in transmitting optical frequencies with instabilities as low as \(10^{-20}\) over distances spanning hundreds to thousands of kilometers [7; 8; 9; 10; 11; 12; 13]. To accomplish remote optical clock frequency comparisons and enable long-distance frequency reference distribution, there has been significant interest and comprehensive research focused on high-precision optical frequency transfer through communication fibers [7; 8; 9; 10]. However, the transmission of signals in optical fibers is affected by nonlinear effects, including Brillouin scattering, Raman scattering, and Rayleigh scattering, which can cause additional noise in the optical fiber link, thereby affecting transmission performance [14; 15; 16; 17; 18]. Nonlinear effects not only introduce noise into the optical fiber frequency transfer system but also result in a form of nonlinear loss of the signal, thus limiting the increase in input fiber power and reducing the optical signal-to-noise ratio of the optical fiber frequency transfer system, thereby severely constraining the improvement of transmission system performance [19; 20; 21; 22]. Simultaneously, when the laser power injected intothe optical fiber exceeds the threshold power of the scattering, the scattering occurs [19; 23]. Scattering primarily affects the system by causing crosstalk between channels and energy loss in the channels. The Brillouin frequency shift is approximately 10-11 GHz at 1550 nm. When the channel spacing of the system matches the Brillouin frequency shift, it leads to crosstalk between the channels [24]. Additionally, because scattering causes some channel power to be transferred to noise, it affects power amplification. Although there have been numerous studies on the threshold power of Brillouin scattering and Raman scattering in the context of laser and optical fiber sensing [20; 24; 25; 26; 27; 28], there is a relative scarcity of research on fiber optical frequency transfer, particularly in long-distance and high-precision transmission [7; 11; 12; 13]. Existing studies primarily focus on estimating the threshold power for generating Brillouin scattering and Raman scattering using the optical fiber length while neglecting other important parameters, such as the attenuation coefficient and the gain coefficient. With the growing demand for large-scale scientific research projects, like the \"high precision ground-based timing system\" in the national major scientific and technological infrastructure plan [12; 13], it becomes crucial to investigate the impact of multiple parameters on the threshold power for generating Brillouin scattering and Raman scattering. This is because the parameters of optical fibers used in long-distance transmission differ from those in laboratory settings. For instance, the attenuation coefficient of optical fibers in the field is influenced by various factors, such as vibration and temperature, which differs from the attenuation coefficient in the laboratory and affects the estimation of the threshold power for generating Brillouin scattering and Raman scattering. Therefore, it is imperative to conduct a detailed study on the influence of multiple parameters on the threshold power for generating Brillouin scattering and Raman scattering in the context of long-distance and high-precision field optical fiber frequency transfer. In this study, we comprehensively investigate nonlinear effects in optical fiber frequency transfer through theoretical and simulation calculations.