# Intramode Brillouin Scattering Properties of Single-Crystal Lithium Niobate Optical Fiber
## 3 Results  
Based on the above theory, we measured the BSBS that can realize multiple modes when the lithium niobate crystal is used as the core. We analyzed nine intramode forms. The optical modes of the nine intramode forms were LP\({}_{01}\), LP\({}_{11}\), LP\({}_{21}\), LP\({}_{02}\), LP\({}_{31}\), LP\({}_{12}\), LP\({}_{41}\), LP\({}_{22}\), and LP\({}_{03}\). The ERI parameters corresponding to the nine modes are listed in Table 2. It can be seen from Table 2 that with the increase in the optical mode order, the ERI gradually decreases. Therefore, when lithium niobate is used as the core material, the effective refractive index corresponding to each optical mode is close to that of the lithium niobate material. Figure 2a-i shows the simulated SBS BGS of nine LP\({}_{01}\)-LP\({}_{01}\), LP\({}_{11}\)-LP\({}_{11}\), LP\({}_{21}\)-LP\({}_{21}\), LP\({}_{02}\)-LP\({}_{02}\), LP\({}_{31}\)-LP\({}_{31}\), LP\({}_{12}\)-LP\({}_{12}\), LP\({}_{41}\)-LP\({}_{41}\), LP\({}_{22}\)-LP\({}_{22}\), and LP\({}_{03}\)-LP\({}_{03}\) pump and Stokes mode pairs. The BGS was calculated using Equation (6) and indicates the optical mode profile distribution for each mode pair and the acoustic mode profile distribution for each peak. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Mode** & **LP\({}_{01}\)** & **LP\({}_{11}\)** & **LP\({}_{21}\)** & **LP\({}_{02}\)** & **LP\({}_{31}\)** & **LP\({}_{12}\)** & **LP\({}_{41}\)** & **LP\({}_{22}\)** & **LP\({}_{03}\)** \\ \hline
**Effective refractive index** & 2.2413 & 2.2358 & 2.2281 & 2.2254 & 2.2189 & 2.2132 & 2.208 & 2.1991 & 2.1963 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optical mode parameters. Figure 2 shows the BGS of the LP\({}_{mn}\)-LP\({}_{mn}\) pump and Stokes mode pairs; each curve corresponds to an acoustic mode L\({}_{mn}\), and the spontaneous Brillouin spectrum of each acoustic mode is Lorentzian due to the exponential decay of the acoustic wave shape. We performed an appropriate Lorentzian curve fit for each peak in the BGS, and each BGS could fit a different number (1-5) of Lorentzian curves. It is worth noting that for BGS of all LP\({}_{mn}\)-LP\({}_{mn}\) pump and Stokes mode pairs, among all L\({}_{mn}\) acoustic modes corresponding to BGS, the peak value of L\({}_{0n}\) acoustic mode (m = 0) is dominant in all cases. This may be due to the fact that these acoustic modes are symmetric in intramodal SBS [31]. Another noteworthy point is the acoustic mode corresponding to the largest peak in all BGS, and the acoustic mode corresponding to the largest peak, is L\({}_{01}\). This can be explained by the larger gain of the multimode SBS induced by the LP\({}_{01}\) mode. The BFS is calculated by substituting \(n_{i}\) and \(n_{j}\) in Equation (4), and the acoustic mode velocity versus BFS for the intra-mode case is plotted in Figure 3.  
Figure 3: (**a**) The relationship between the BFS of the mode and the velocity of acoustic for the nine intramodes. (**b**) The acoustic mode profile under the LP\({}_{21}\)-LP\({}_{21}\) mode pair is shown as an inset, corresponding to the relationship between the velocity of acoustic and the BFS of the ten acoustic modes. Figure 3a shows the relationship between acoustic mode velocity and BFS for the nine interacting LP\({}_{mn}\)-LP\({}_{mn}\) pump and Stokes mode pairs. The line of each color represents an LP\({}_{mn}\)-LP\({}_{mn}\) optical mode pair, and each data point shape represents an L\({}_{0n}\) acoustic mode. Under the same acoustic mode (L\({}_{mn}\)), the lower-order optical mode corresponds to a larger BFS value. Under the optical mode pair (LP\({}_{mn}\)-LP\({}_{mn}\)), higher-order acoustic modes correspond to larger BFS values. Figure 3b demonstrates the intramode interaction corresponding to the pump and Stokes propagating in the LP\({}_{21}\) mode, showing the acoustic mode profiles of the symmetric and antisymmetric mode groups and their BFS values (data points denoted by stars sign). Obviously, higher-order acoustic modes correspond to larger BFS values.