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The Brillouin sensing technology in multimode optical fibers has received much attention due to its ability to simultaneously transmit multiple parameters, such as temperature and strain, and its higher information capacity and transmission efficiency. Additionally, lithium niobate possesses excellent electro-optical properties, so it shows potential application value in the sensing field and is expected to provide higher sensitivity and precision. Owing to the maturity of manufacturing processes, current research on fiber optic sensing focuses on silicon-based materials, however, there are fewer studies of fibers in which lithium niobate is used as the core material, thereby underestimating its application potential. In this work, the Brillouin scattering effects in lithium niobate optical fibers are investigated numerically. We simulate the intra-mode backward Brillouin scattering characteristics of the first five orders of LP modes in micrometer-sized lithium niobate fibers by means of finite-element simulation to explore its intrinsic law. First of all, the relationship between the Brillouin frequency shift and gain for the first five optical mode interactions is analyzed in detail. The results show that in the case of intra-mode backward stimulated Brillouin scattering, the peak of Brillouin frequency shift exhibits a significant redshift ranging from 20.63 GHz to 18.747 GHz. The Brillouin gain coefficient decreases from 13.503 m–1·W–1 to 4.0115 m–1·W–1 with the increase of mode order, in which mode LP01 having the strongest gain intra modal interaction means the best sensing sensitivity. In addition, compared with ordinary silica fiber, the lithium niobate fiber has Brillouin gain increased by about 5 orders of magnitude, which means that fibers with lithium niobate as the core can have higher sensing sensitivity. In addition, it is found that although there are significant differences in the Brillouin frequency shift values of each optical mode under intra modal interactions, the sound velocity of their corresponding acoustic modes is always consistent under the same acoustic mode. In data processing, it is noticed that this is because as the mode order changes, the corresponding effective refractive index decreases to ensure that each acoustic mode of the material always has the same sound velocity. These findings provide a foundation for further studying the lithium niobate fiber sensors with electro-optic properties. 
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Keywords:
- stimulated Brillouin scattering /
- lithium niobate /
- micron fibers /
- simulation
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图 1 后向布里渊散射效应物理过程示意图
Figure 1. Schematic diagram of the physical process of the backward Brillouin scattering effect.
图 2 LiNbO3光纤结构原理图及光学声学模式分布图 (a) LiNbO3光纤结构原理图; (b) 光学模式分布图; (c) 声学模式分布图
Figure 2. Schematic diagram of LiNbO3 optical fiber structure and distribution diagram of optical acoustic mode: (a) Schematic diagram of LiNbO3 optical fiber structure; (b) optical pattern distribution; (c) acoustic pattern distribution.
图 3 不同模式内布里渊增益谱以及SiO2光纤与LiNbO3光纤增益谱对比图 (a) LP01-LP01模式; (b) LP11-LP11模式; (c) LP21-LP21模式; (d) LP02-LP02模式; (e) LP31-LP31模式; (f) SiO2光纤与LiNbO3光纤增益谱对比图
Figure 3. Gain spectrum within Brillouin in different modes and comparison of gain spectra between SiO2 and LiNbO3 fibers: (a) LP01-LP01 mode; (b) LP11-LP11 mode; (c) LP21-LP21 mode; (d) LP02-LP02 mode; (e) LP31-LP31 mode; (f) comparison of gain spectra between SiO2 and LiNbO3 fibers.
图 4 5个LPmn -LPmn的Pump-Stokes模式对相互作用的BGS的总洛伦兹曲线以及BFS和相对增益关系 (a) BGS的总洛伦兹曲线; (b) Pump-Stokes模式对中最高峰对应的BFS和增益关系
Figure 4. Total Lorentz curves of BGS for the interaction of the pump-Stokes mode pairs of 5LPmn -LPmn as well as the BFS and relative gain relationship: (a) Total Lorentz curves of BGS; (b) the BFS and gain relationship for the highest peak of the pump-Stokes mode pairs.
图 5 声模速度与BFS的关系以及声模频率差关系 (a) 5个pump-Stokes模式对之间BFS与声速的关系; (b)模态间的频率差关系
Figure 5. Relationship between the velocity of the sound model and the BFS and the relationship between the frequency difference of the sound mode: (a) BFS and sound velocity between five Pump-Stokes mode pairs; (b) frequency difference relationship between modalities.
表 1 光纤结构和材料参数[29]
Table 1. Fiber structure and material parameters.
Parameters Values Core Clading Radius/μm 3 — Refractive index 2.213 1 Mass density/(kg·m–3) 4700 1.29 Longitudinal acoustic
velocity/(m·s–1)7318 340 Photo-elastic coefficients p11 = –0.02, p12 = 0.08,
p44 = 0.12Transmission loss at
1550 nm /(dB·cm–1)0.89 
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[1] Hayashi N, Mizuno Y, Nakamura K, Zhang C, Jin L, Set S Y, Yamashita S 2020 Jpn. J. Appl. Phys. 59 088002
Google Scholar
[2] Wang L, Zhou B, Shu C, He S L 2013 IEEE Photonics J. 5 6801808
Google Scholar
[3] Catalano E, Vallifuoco R, Zeni L, Minardo A 2022 IEEE Sens. J. 22 6601
Google Scholar
[4] Zeng Z, Peng D, Zhang Z Y, Zhang S J, Ni G M, Liu Y 2020 IEEE Photonics Tech. L. 32 995
Google Scholar
[5] Coscetta, A, Minardo A, Zeni L 2020 Sensors 20 5629
Google Scholar
[6] Gao S, Wen Z R, Wang H Y, Baker C, Chen L, Cai Y J, Bao X Y 2023 J. Lightwave Tech. 41 4359
Google Scholar
[7] Peng J Q, Lu Y G, Zhang Z L, Wu Z N, Zhang Y Y 2021 IEEE Photonics Tech. L. 33 1217
Google Scholar
[8] Ba D X, Chen C, Fu C, Zhang D Y, Lu Z W, Fan Z G, Dong Y K 2018 IEEE Photonics J. 10 1
Google Scholar
[9] Liu P K, Lu Y A, Zhang W J, Zhu M 2024 Opt. Commun. 563 130571
Google Scholar
[10] Ippen E P, Stolen R H 1972 Appl. Phys. Lett. 21 539
Google Scholar
[11] Kobyakov A, Sauer M, Chowdhury D 2009 Adv. Opt. Photonics 2 1
Google Scholar
[12] Hill K O, Kawasaki B S, Johnson D C 1976 Appl. Phys. Lett. 28 608
Google Scholar
[13] Essiambre R J, Kramer G, Winzer P J, Foschini G J, Goebel B 2010 J. Lightwave Technol. 28 662
Google Scholar
[14] Dong Y K 2021 Photonic Sens. 11 69
Google Scholar
[15] Feng C, Schneider T 2021 Sensors 21 1881
Google Scholar
[16] Eggleton B J, Poulton C G, Pant R 2013 Adv. Opt. Photonics 5 536
Google Scholar
[17] Yang Y H, Wang J Q, Zhu Z X, Xu X B, Zhang Q, Lu J J, Zeng Y, Dong C H, Sun L Y, Guo G C, Zou C L 2024 Sci. China Phys. Mec. 67 214221
Google Scholar
[18] Rodrigues C C, Zurita R O, Alegre T P, Wiederhecker S G 2023 J. Opt. Soc. Am. B 40 56
Google Scholar
[19] Otterstrom N T, Behunin R O, Kittlaus E A 2018 Science 360 1113
Google Scholar
[20] Kittlaus E A, Shin H, Rakich P T 2016 Nat. Photonics 10 463
Google Scholar
[21] Gyger F, Liu J Q, Yang F, He J J, Raja A S, Wang R N, Bhave S A, Kippenberg T J, Thevenaz L 2020 Phys. Rev. Lett. 124 013902
Google Scholar
[22] Xiang C, Guo J, Jin W, Wu L, Peters J, Xie W Q, Chang L, Shen B Q, Wang H M, Yang Q F, Kinghorn D, Paniccia M, Vahala K J, Morton P A, Bowers J E 2021 Nat. Commun. 12 6650
Google Scholar
[23] Botter R, Ye K X, Klaver Y, Suryadharma R, Daulay O, Liu G J, van den Hoogen J, Kanger L, van der Slot P, Klein E, Hoekman M, Roeloffzen C, Liu Y, Marpaung D 2022 Sci. Adv. 8 2196
Google Scholar
[24] Morrison B, Casas-Bedoya A, Ren G, Vu K, Liu Y, Zarifi A, Nguyen T G, Choi D Y, Marpaung D, Madden S J, Mitchell A, Eggleton B J 2017 Optica 4 847
Google Scholar
[25] Choudhary A, Morrison B, Aryanfar I, Shahnia S, Pagani M, Liu Y, Vu K, Madden S, Marpaung D, Eggleton B J 2017 J. Lightwave Tech. 35 846
Google Scholar
[26] Florea C M, Bashkansky M, Dutton Z, Sanghera J, Pureza P, Aggarwal I 2006 Opt. Express 14 12063
Google Scholar
[27] Balram K C, Davanço M I, Song J D, Srinivasan K 2016 Nat. Photonics 10 346
Google Scholar
[28] Kim Y H, Song K Y 2021 Sensors 21 2168
Google Scholar
[29] Feng L Y, Liu Y, He W J, You Y J, Wang L Y, Xu X, Chou X J 2022 Applied Sciences 12 6476
Google Scholar
[30] Lin J, Bo F, Cheng Y, Xu J J 2020 Photonics Res. 8 1910
Google Scholar
[31] Eggleton B J, Poulton C G, Rakich P T, Steel M J, Bahl G 2019 Nat. Photonics 13 664
Google Scholar
[32] Cao M, Huang L, Tang M, Mi Y A, Ren W H, Ning T G, Pei L, Ren G B 2022 Opt. Commun. 507 127612
Google Scholar
[33] Florez O, Jarschel P F, Espinel Y A V, Cordeiro C M B, Alegre T P M, Wiederhecker G S, Dainese P 2016 Nat. Commun. 7 11759
Google Scholar
[34] Rakich P T, Reinke C, Camacho R, Davids P, Wang Z 2012 Phys. Rev. X. 2 011008
Google Scholar
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