# Analysis and Reduction of Nonlinear Effects in Optical Fiber Frequency Transfer
## 4 Experimental Verification
### Raman Scattering  
As shown in Figure 9, we compare the calculated results with the experimental results of the threshold power for generating the Raman scattering, including the threshold power \(P_{crit-R-F}\) for forward Raman scattering and the threshold power \(P_{crit-R-B}\) for backward Raman scattering. The experimental results of the threshold power for generating the Raman scattering are cited in ref. [36]. Figure 8: Comparison of calculated and experimental values of the threshold power for generating the Brillouin scattering. The attenuation coefficient \(\alpha\) and the effective mode area \(A_{eff}\) are 0.2 dB/km and 1.0 \(\times\) 10\({}^{-10}\) m\({}^{2}\), respectively. The gain coefficient \(\gamma_{\mathcal{B}}\) of the Brillouin scattering is 5.0 \(\times\) 10\({}^{-11}\) m/W. (**a**) Comparison of calculated and experimental values of the threshold power for generating the Brillouin scattering as a function of the optical fiber length \(L\). (**b**) The experimental measurement results of the input optical power and the output optical power when the fiber length is 120 km. The threshold power \(P_{crit-R-F}\) for forward Raman scattering is investigated. The experimental and calculated values show good agreement, with an overall difference of approximately 10%. Notably, the largest difference between the calculated and experimental values is observed at a fiber length of 2.2 km, reaching about 22%. Conversely, the smallest difference is observed at a fiber length of 3.2 km, which is approximately 0.3%. Additionally, for fiber lengths ranging from 0.2 km to 0.8 km, the calculated value exceeds the experimental value. However, at fiber lengths of 1.1 km and 4.1 km, the calculated value is lower than the experimental value. For instance, at a fiber length of 0.2 km, the experimental and calculated values are approximately 14.3 W and 16.9 W, respectively. When the fiber length is 4.1 km, the experimental value and calculated value are about 1.7 W and 1.4 W, respectively. The experimental results and calculated values for the threshold power \(P_{crit-R-B}\) for backward Raman scattering show good agreement, which is similar to the threshold power \(P_{crit-R-F}\). Generally, the difference between the experimental results and calculated values of \(P_{crit-R-B}\) is approximately 2% lower than that of \(P_{crit-R-F}\). When the fiber length is 2.2 km, the difference between the calculated value and the experimental value is the largest (around 20.6%). On the other hand, when the fiber length is 3.2 km, the difference between the calculated value and the experimental value is the smallest (approximately 2.5%). These two points resemble the behavior observed in the threshold power \(P_{crit-R-F}\). Additionally, when the fiber length ranges from 0.2 km to 0.8 km, the experimental value is lower than the calculated value. However, for fiber lengths of 3.3 km and 4.1 km, the calculated value is lower than the experimental value. For instance, at a fiber length of 0.8 km, the experimental value and calculated value are approximately 5.7 W and 6.6 W, respectively. Similarly, at a fiber length of 4.1 km, the experimental value and calculated value are approximately 2.0 W and 1.7 W, respectively. Through the experimental method, researchers have investigated the effects of various parameters on the threshold power for generating Brillouin scattering and Raman scattering [34; 35; 36; 37; 38; 39; 40]. These parameters include optical fiber length [34; 35; 36; 40], input pump powers [38], and special types of optical fibers, such as photonic crystal fiber [39] and three-layer fiber [37]. For example, [PERSON] et al. conducted a study on the threshold power for generating Brillouin scattering in photonic crystal fiber. They propose an approach to calculate this threshold and find that their results align well with experimental and simulation data. Similarly, [PERSON] et al.