# Intramode Brillouin Scattering Properties of Single-Crystal Lithium Niobate Optical Fiber
## 3 Results
Figure 4 shows the BFS characteristics of the L\({}_{0n}\) acoustic mode for the nine LP\({}_{mn}\)-LP\({}_{mn}\) pump and Stokes mode pair interactions. In Figure 4, \(v_{B}\) varies in the range of 20.7-21.3 GHz, and the \(v_{B}\) of the BGS peak of each mode decreases with the optical mode order and increases with the acoustic mode order. The specific variation in \(v_{B}\) can be qualitatively explained by the smaller ERI of the higher-order optical modes and the larger acoustic velocity of the higher-order acoustic modes. Since the pump and Stokes mode interferograms are symmetric in intra-modal SBS, the BGS peaks can be attributed to symmetric acoustic modes such as L\({}_{01}\), L\({}_{02}\), L\({}_{03}\), L\({}_{04}\) and L\({}_{05}\)[35]. Figure 5 shows the Brillouin gain characteristics of the L\({}_{0n}\) acoustic mode for the nine LP\({}_{mn}\)-LP\({}_{mn}\) pump and Stokes mode pair interactions. Figure 5 shows the relative amplitudes of the BGS peaks for each mode in multimode stimulated Brillouin scattering. In the case of each LP\({}_{mn}\)-LP\({}_{mn}\) mode pair, the Brillouin gain value of the L\({}_{01}\) acoustic mode under the LP\({}_{01}\)-LP\({}_{01}\) pump and Stokes mode pair is the largest, reaching 1.7525 m\({}^{-1}\).W\({}^{-1}\). The maximum peak (L\({}_{01}\) acoustic mode) is several orders of magnitude larger than the other peaks, except for LP\({}_{21}\), LP\({}_{31}\), and LP\({}_{41}\) modes. The amplitude difference between the two main peaks is small, which is in the same order of magnitude. Figure 4: BFS characteristics of L\({}_{0n}\) acoustic mode in the case of nine LP\({}_{mn}\) -LP\({}_{mn}\) mode pairs. Figure 6 shows the total Lorentzian curve of each LP\({}_{mn}\)-LP\({}_{mn}\) mode pair BGS for the nine LP\({}_{mn}\)-LP\({}_{mm}\) pump and Stokes mode pair interactions. It can be seen from Figure 6 that in the lithium niobate optical fiber, the BFS varies in the range of 20.7-21.3 GHz, and the highest Brillouin gain coefficient of each LP\({}_{mn}\)-LP\({}_{mn}\) mode pair is in the range of 4.9036E-1(LP\({}_{31}\))-1.7525 (LP\({}_{01}\)) inside. The order of magnitude (GHz) of its own BFS is very high; in distributed sensing, the influence of changes in external parameters on BFS is usually mostly mostly in the range of 100 MHz. The LP\({}_{01}\), LP\({}_{02}\), and LP\({}_{03}\) modes present a single main peak or a single main peak plus a small peak with a large difference in BFS. the LP\({}_{21}\), LP\({}_{31}\) and LP\({}_{41}\) modes present two comparable peaks with a small difference in BFS, and the LP\({}_{11}\), LP\({}_{12}\), and LP\({}_{22}\) modes present a single main peak plus a small peak with a large difference in BFS. In the case of intram  
Figure 5: Brillouin gain characteristics of the L\({}_{0 tt}\) acoustic mode in the case of nine LP\({}_{mn}\) -LP\({}_{mn}\) mode pairs. Figure 6: In the case of nine LP\({}_{mn}\)-LP\({}_{mm}\) mode pairs, the total Lorenz curve of each LP\({}_{mn}\) -LP\({}_{mn}\) mode pair to BGS. mode provides the largest Brillouin gain, and according to the Lorentz peak distribution, we divide the nine modes into three groups: LP\({}_{01}\), LP\({}_{02}\), and LP\({}_{03}\) modes as the first group, LP\({}_{21}\), LP\({}_{31}\), and LP\({}_{41}\) modes as the second group, LP\({}_{11}\), LP\({}_{12}\), and LP\({}_{22}\) modes as the third group. The gain coefficient of the first group is generally higher, and the highest Brillouin gain coefficient of the second and third groups is about 50% of the LP\({}_{01}\) mode. This is attributable to the BGS cleavage observed in Figure 2.