# Intramode Brillouin Scattering Properties of Single-Crystal Lithium Niobate Optical Fiber
###### Abstract  
Ordinary step-type fiber usually has only one obvious Brillouin scattering gain peak with a low gain coefficient, resulting in a poor sensing performance. As a promising material for nonlinear photonics, lithium niobate can significantly improve the Brillouin gain due to its higher refractive index when replaced with the core material. Furthermore, the higher-order acoustic modes make the Brillouin gain spectrum exhibit multiple scattering peaks, which could improve the performance of sensors. In this study, we simulated the Brillouin scattering properties of different modes of intramode in step-index lithium niobate core fibers. We analyzed the intramode-stimulated Brillouin scattering properties of different pump-Stokes pairs for nine LP modes (LP\({}_{01}\), LP\({}_{11}\), LP\({}_{21}\), LP\({}_{02}\), LP\({}_{31}\), LP\({}_{12}\), LP\({}_{41}\), LP\({}_{22}\), and LP\({}_{03}\)) guided in fiber. The results show that both the effective refractive index and Brillouin scattering frequency shift are decreased with the increase in the nine mode orders, and the values of which are 2.2413 to 2.1963, and 21.17 to 20.73 GHz, respectively. The typical back-stimulated Brillouin scattering gain is obtained at 1.7525 m\({}^{-1}\)-\(W^{-1}\). These simulation results prove that the Brillouin gain of the LiNbO\({}_{3}\) optical fiber structure can be significantly improved, which will pave the way for better distributed Brillouin sensing and for improving the transmission capacity of communication systems. multimode is extremely important, and by analyzing the mode overlap of various optical and acoustic modes, the fiber BGS of any specific fiber design can be numerically calculated. With advances in fabrication and materials technology, many microdevices and nanomaterials have been used to enhance the SBS effect in various aspects, including optical fibers, photonic crystal fibers, and integrated photonic devices. Structural and material properties can lead to different Brillouin scattering properties, resulting in acoustic frequency shifts and gain value fluctuations, and even excitation of higher-order acoustic modes. Effectively enhanced SBS effects require strict material selection and structural design [21]. In 2013, [PERSON] et al. [22] experimentally measured the BGS peaks of four optical mode pairs in a circular-core step-index fiber. They found that intramodal SBS (coupling between the same modes) was stronger than the corresponding intermodal SBS (coupling between different modes). In the same year, [PERSON] et al. [23] conducted an experimental study on the BGS of different mode pairs in circular-core dual-mode fibers and measured the corresponding Brillouin gains. The experimental results show that the BGS is dependent on the optical mode pairs involved, which all lay the foundation for distributed sensing in FMFs. In 2015, [PERSON] et al. [24] designed a temperature and strain optical fiber sensor based on the intramode SBS characteristics of FMF, and obtained temperature and strain errors of 0.8 \({}^{\circ}\)C and 20.1 \(\upmu\epsilon\), respectively. In 2016, [PERSON] et al. [25] studied temperature and strain Brillouin sensors based on SBS in the fundamental mode in an inverse parabolic FMF. The errors of temperature and strain were 0.85 \({}^{\circ}\)C and 17.4 \(\upmu\epsilon\), respectively. In the same year, [PERSON] et al. [26] studied a Brillouin sensor based on graded index distribution FMF. The error of temperature and strain were 1.8 \({}^{\circ}\)C and 4 \(\upmu\epsilon\), respectively. In 2019, [PERSON] et al. [27] studied temperature and strain sensing based on intramode SBS characteristics in an elliptical core FMF, and obtained temperature and strain errors of 0.28 \({}^{\circ}\)C and 5.81 \(\upmu\epsilon\), respectively, but the system was complex. In 2021, [PERSON] et al. [28] published a technical review of the recent developments in distributed Brillouin sensors for FMF platforms, with the highest intra-modal gain of 0.47 m\({}^{-1}\).W\({}^{-1}\).