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Stimulated Brillouin scattering (SBS) in a few-mode fiber (FMF) is of significance for the distributed temperature and strain sensing. An FMF with M-shaped refractive index distribution (M-FMF) is proposed in order to improve the performance of simultaneous temperature and strain sensing based on SBS. Propagation of four optical modes is supported by the M-FMF, so that the Brillouin gain spectrum (BGS) can be obtained by both intra-mode and inter-mode SBS. The BGSs produced by the interactions of LP01-LP01 mode pair, LP01-LP11 mode pair, and LP11-LP11 mode pair are analyzed, respectively. Meanwhile, the temperature and strain sensing performance based on the BGS of LP01-LP11 mode pair are studied in detail. Considering a common step-index FMF, only one obvious scattering peak is usually present in the BGS obtained from the interaction between different optical mode pairs, therefore, it is inconvenient to achieve multi-parameter sensing measurement. In this paper, the BGS of LP01-LP11 mode pair has two scattering peaks, which are contributed by the acousto-optic coupling between the acoustic modes L1n (n = 1, 2) and the optical modes LP01 and LP11. The two Brillouin scattering peaks have large gain values of 0.1004 m–1·W–1 and 0.0463 m–1·W–1, respectively. More importantly, the gain difference between two Brillouin scattering peaks is small, and the frequency interval is 75 MHz, which can be applied to simultaneous temperature and strain sensing. The influences of the refractive index and the fiber core radius on the BGS of LP01-LP11 mode pair are studied. By selecting the optimal structure parameters, we discuss the effect of temperature and strain on the BGS of LP01-LP11 mode pair. The errors for simultaneous temperature and strain measurement are reduced to 0.23 ℃ and 5.67 με. Compared with other reported results, our obtained temperature and strain sensitivity are high and sensing errors are low in the considered M-FMF. In other words, based on the BGS of LP01-LP11 mode pair, the performance of temperature and strain sensing are improved in the M-FMF. This work is of great significance for studying intra-mode and inter-mode SBS in an FMF. Moreover, the results also provide a guideline for further improving the performance of simultaneous temperature and strain sensing.
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Keywords:
- M-shaped few mode fiber /
- stimulated Brillouin scattering /
- Brillouin gain spectrum /
- sensing /
- temperature and strain
[1] Essiambre R J, Kramer G, Winzer P J, Foschini G J, Goebel B 2010 J. Lightwave Technol. 28 662
Google Scholar
[2] Randel S, Ryf R, Sierra A, Winzer P J, Gnauck A H, Bolle A C, Essiambre R J, Peckham D W, McCurdy A, Lingle R 2011 Opt. Express 19 16697
Google Scholar
[3] Smith S P, Zarinetchi F, Ezekiel S 1991 Opt. Lett. 16 393
Google Scholar
[4] Cowie G J, Yu D, Chieng Y T 1997 J. Lightwave Technol. 15 1198
Google Scholar
[5] Li B W, Wei X M, Wang X, Wong K K Y 2014 IEEE Photonics Technol. Lett. 26 2387
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[6] Alahbabi M N, Cho Y T, Newson T P 2004 Opt. Lett. 29 26
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[7] Zadok A, Zilka E, Eyal A, Thévenaz L, Tur M 2008 Opt. Express 16 21692
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[8] 刘玉 2012 硕士学位论文 (陕西: 西北大学)
Liu Y 2012 M.S. Dissertation (Shanxi: Northwest University) (in Chinese)
[9] Herráez M G, Song K Y, Thévenaz L 2006 Opt. Express 14 1395
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[10] Loayssa A, Benito D, Garde M J 2000 Opt. Lett. 25 1234
Google Scholar
[11] Preussler S, Schneider T 2015 Opt. Eng. 55 031110
Google Scholar
[12] Ballmann C W, Meng Z K, Traverso A J, Scully M O, Yakovlev V V 2017 Optica 4 124
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[13] Krug B, Koukourakis N, Czarske J W 2019 Opt. Express 27 26910
Google Scholar
[14] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photonics 2 1
Google Scholar
[15] Koyamada Y, Sato S, Nakamura S, Sotobayashi H, Chujo W 2004 J. Lightwave Technol. 22 631
Google Scholar
[16] Nikles M, Thevenaz L, Robert P A 1997 J. Lightwave Technol. 15 1842
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[17] Zou L F, Bao X Y, Afshar S, Chen L 2004 Opt. Lett. 29 1485
Google Scholar
[18] Horiguchi T, Kurashima T, Tateda M 1989 IEEE Photonics Technol. Lett. 1 107
Google Scholar
[19] Mocofanescu A, Wang L, Jain R, Shaw K D, Gavrielides A, Peterson P, Sharma M P 2005 Opt. Express 13 2019
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Google Scholar
[22] Afshar S, Kalosha V P, Bao X Y, Chen L 2005 Opt. Lett. 30 2685
Google Scholar
[23] Liu A P 2007 Opt. Express 15 977
Google Scholar
[24] Li H L, Zhang W, Huang Y D, Peng J D 2011 Chin. Phys. B 20 104211
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Google Scholar
Wang X, Qin Z J, Xiong X M, Zhang W T 2019 Laser Optoelect. Prog. 56 162901
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Google Scholar
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图 1 SI-FMF中
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ 模式对的BGS (插图为SI-FMF的结构分布)Figure 1. The BGS of
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ mode pair in SI-FMF (Inset: The structure of SI-FMF).
图 2 M-FMF的结构分布以及光学模式的模场分布 (a) M-FMF的结构分布; (b)
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ ; (c)${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ ; (d)${\rm{L}}{{\rm{P}}_{{\rm{21}}}}$ ; (e)${\rm{L}}{{\rm{P}}_{{\rm{02}}}}$ Figure 2. The structure of M-FMF and the field distribution of optical modes in M-FMF: (a) The structure of M-FMF: (b)
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ ; (c)${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ ; (d)${\rm{L}}{{\rm{P}}_{{\rm{21}}}}$ ; (e)${\rm{L}}{{\rm{P}}_{{\rm{02}}}}$ .
图 3 不同光学模式对的BGS (a)
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}\text-{\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ ; (b)${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ ; (c)${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ Figure 3. The BGS of different optical mode pairs: (a)
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}\text-{\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ ; (b)${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ ; (c)${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ .
图 4 M-FMF的结构对
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ 模式对BGS的影响 (a) n1; (b) n2; (c) r1; (d) r2Figure 4. The BGS of
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ mode pair in M-FMF versus: (a) n1; (b) n2; (c) r1; (d) r2.
图 5
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ 模式对激励的声学模式的位移场分布 (a)${{\rm{L}}_{{\rm{11}}}}$ ; (b)${{\rm{L}}_{{\rm{12}}}}$ Figure 5. The displacement field distribution of acoustic mode excited by the interaction of
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ mode pair: (a)${{\rm{L}}_{{\rm{11}}}}$ ; (b)${{\rm{L}}_{{\rm{12}}}}$ .
图 6
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ 模式对的BGS随温度和应变的变化 (a) BGS随温度的变化; (b) BGS随应变的变化Figure 6. The BGS of
${\rm{L}}{{\rm{P}}_{{\rm{01}}}}$ -${\rm{L}}{{\rm{P}}_{{\rm{11}}}}$ mode pair versus: (a) Temperature; (b) strain.
图 7 声学模式
${{\rm{L}}_{{\rm{11}}}}$ 和${{\rm{L}}_{{\rm{12}}}}$ 对应散射峰的BFS随温度和应变的变化 (a) BFS随温度的变化关系; (b) BFS随应变的变化关系Figure 7. The BFS corresponding to
${{\rm{L}}_{{\rm{11}}}}$ and${{\rm{L}}_{{\rm{12}}}}$ acoustic modes versus: (a) Temperature; (b) strain.表 1 不同光学模式对与声学模式之间相互耦合的声光有效面积(单位: μm2)
Table 1. Acousto-optic effective area by the coupling between different optical mode pairs and acoustic modes (in μm2).
LP01-LP01 LP01-LP11 LP11-LP11 m = 0 m = 1 m = 0 m = 2 Lm1 251.63 208.71 156.24 180.74 Lm2 162.48 449.52 1.65 × 103 1.09 × 103 Lm3 2.12 × 105 4.54 × 104 3.82 × 103 1.11 × 104 
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表 2 不同研究报道中基于SBS的温度应变系数和误差
Table 2. The coefficients and errors of temperature and strain based on SBS in different literatures.
Fiber $C_T^1$/MHz·℃–1 $C_T^2$/MHz·℃–1 $C_S^1$/MHz·℃–1 $C_S^2$/MHz·℃–1 δT/℃ δS/με M-FMF 4.3400 3.9315 0.19373 0.17715 0.23 5.67 M-SMF[25] 1.5187 1.1642 0.06640 0.05280 0.47 12.30 SSMF[26] 1.1900 1.1500 0.06228 0.05009 0.93 19.48 SMF[27] 1.1900 1.1190 0.03560 0.04030 0.90 28.80 IPGIF[37] 0.74323 0.9016 0.04202 0.03825 0.85 17.40 GIFMF[38] 5.2700 4.300 0.23700 0.18900 1.80 41.00 c-core FMF[39] 1.0169 0.9909 0.05924 0.04872 1.20 21.90 e-core FMF[40] 1.2420 1.2780 0.06130 0.03640 0.37 7.61
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[1] Essiambre R J, Kramer G, Winzer P J, Foschini G J, Goebel B 2010 J. Lightwave Technol. 28 662
Google Scholar
[2] Randel S, Ryf R, Sierra A, Winzer P J, Gnauck A H, Bolle A C, Essiambre R J, Peckham D W, McCurdy A, Lingle R 2011 Opt. Express 19 16697
Google Scholar
[3] Smith S P, Zarinetchi F, Ezekiel S 1991 Opt. Lett. 16 393
Google Scholar
[4] Cowie G J, Yu D, Chieng Y T 1997 J. Lightwave Technol. 15 1198
Google Scholar
[5] Li B W, Wei X M, Wang X, Wong K K Y 2014 IEEE Photonics Technol. Lett. 26 2387
Google Scholar
[6] Alahbabi M N, Cho Y T, Newson T P 2004 Opt. Lett. 29 26
Google Scholar
[7] Zadok A, Zilka E, Eyal A, Thévenaz L, Tur M 2008 Opt. Express 16 21692
Google Scholar
[8] 刘玉 2012 硕士学位论文 (陕西: 西北大学)
Liu Y 2012 M.S. Dissertation (Shanxi: Northwest University) (in Chinese)
[9] Herráez M G, Song K Y, Thévenaz L 2006 Opt. Express 14 1395
Google Scholar
[10] Loayssa A, Benito D, Garde M J 2000 Opt. Lett. 25 1234
Google Scholar
[11] Preussler S, Schneider T 2015 Opt. Eng. 55 031110
Google Scholar
[12] Ballmann C W, Meng Z K, Traverso A J, Scully M O, Yakovlev V V 2017 Optica 4 124
Google Scholar
[13] Krug B, Koukourakis N, Czarske J W 2019 Opt. Express 27 26910
Google Scholar
[14] Kobyakov A, Sauer M, Chowdhury D 2010 Adv. Opt. Photonics 2 1
Google Scholar
[15] Koyamada Y, Sato S, Nakamura S, Sotobayashi H, Chujo W 2004 J. Lightwave Technol. 22 631
Google Scholar
[16] Nikles M, Thevenaz L, Robert P A 1997 J. Lightwave Technol. 15 1842
Google Scholar
[17] Zou L F, Bao X Y, Afshar S, Chen L 2004 Opt. Lett. 29 1485
Google Scholar
[18] Horiguchi T, Kurashima T, Tateda M 1989 IEEE Photonics Technol. Lett. 1 107
Google Scholar
[19] Mocofanescu A, Wang L, Jain R, Shaw K D, Gavrielides A, Peterson P, Sharma M P 2005 Opt. Express 13 2019
Google Scholar
[20] Floch S L, Cambon P 2003 J. Opt. Soc. Am. A 20 1132
Google Scholar
[21] 王振宝, 邵碧波, 张磊, 闫燕, 杨鹏翎, 陈绍武 2011 激光与光电子学进展 48 090603
Google Scholar
Wang Z B, Shao B B, Zhang L, Yan Y, Yang P L, Chen S W 2011 Laser Optoelect. Prog. 48 090603
Google Scholar
[22] Afshar S, Kalosha V P, Bao X Y, Chen L 2005 Opt. Lett. 30 2685
Google Scholar
[23] Liu A P 2007 Opt. Express 15 977
Google Scholar
[24] Li H L, Zhang W, Huang Y D, Peng J D 2011 Chin. Phys. B 20 104211
Google Scholar
[25] Dong Y, Ren G B, Xiao H, Gao Y X, Li H S, Xiao S Y, Jian S S 2017 IEEE Photonics Technol. Lett. 29 1955
Google Scholar
[26] Xing C, Ke C J, Guo Z, Yang K Y, Wang H Y, Zhong Y B, Liu D M 2018 Opt. Express 26 28793
Google Scholar
[27] Xiao S Y, Dong Y, Xiao H, Ren G B, Jian S S 2018 IEEE Sens. J. 18 1087
[28] Song K Y, Kim Y H, Kim B Y 2013 Opt. Lett. 38 1805
Google Scholar
[29] Song K Y, Kim Y H 2013 Opt. Lett. 38 4841
Google Scholar
[30] Ke W W, Wang X J, Tang X 2014 IEEE J. Sel. Top. Quantum Electron. 20 305
Google Scholar
[31] Minardo A, Bernini R, Zeni L 2014 Opt. Express 22 17480
Google Scholar
[32] Song K Y, Kim Y H 2014 Optical Fiber Communications Conference San Francisco, CA, USA, March 9–13, 2014 pW3D.6
[33] 张燕君, 高皓雷, 付兴虎, 田永胜 2017 66 024207
Google Scholar
Zhang Y J, Gao H L, Fu X H, Tian Y S 2017 Acta Phys. Sin. 66 024207
Google Scholar
[34] 王旭, 秦祖军, 熊显名, 张文涛 2019 激光与光电子进展 56 162901
Google Scholar
Wang X, Qin Z J, Xiong X M, Zhang W T 2019 Laser Optoelect. Prog. 56 162901
Google Scholar
[35] Lü H B, Zhou P, Wang X L, Jiang Z F 2015 J. Lightwave Technol. 33 4464
Google Scholar
[36] Zou W W, He Z Y, Hotate K 2009 Opt. Express 17 1248
Google Scholar
[37] Xu Y P, Ren M Q, Lu Y, Lu P, Lu P, Bao X Y, Wang L X, Messaddeq Y, Larochelle S 2016 Opt. Lett. 41 1138
Google Scholar
[38] Zhou X, Guo Z, Ke C J, Liu D M 2016 IEEE Photonics Conference(IPC) Waikoloa, HI, October 2–6, 2016 p817
[39] Li A, Wang Y F, Hu Q, Shieh W 2015 Opt. Express 23 1139
Google Scholar
[40] Fang J, Milione G, Stone J, Peng G Z, Li M J, Ip E, Li Y W, Ji P N, Huang Y K, Huang M F, Murakami S, Shieh W, Wang T 2019 Opt. Lett. 44 1096
Google Scholar
[41] Weng Y, Ip E, Pan Z Q, Wang T 2015 Opt. Express 23 9024
Google Scholar
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