Abstract

We propose a bend-insensitive distributed Brillouin optical fiber sensing by using a singlemode-multimode-singlemode optical fiber structure for the first time to the best of our knowledge. The sensing fiber is a graded-index multimode fiber (GI-MMF) sandwiched by two standard single-mode fibers (SMFs) with central-alignment splicing at the interface between GI-MMF and SMF to excite the fundamental mode in GI-MMF. The sensing system can resist a minimal bend radius of 1.25mm while maintain the measurement performance, with which the measured coefficients of strain and temperature are 421.6MHz/% and 0.826MHz/°C, respectively. We also demonstrate that the higher-order modes excited in GI-MMF can be easily influenced by bending, so that exciting the fundamental mode is essential for bend-insensitive distributed sensing.

© 2015 Optical Society of America

1. Introduction

In recent years, Brillouin optical time-domain analysis (BOTDA) in single mode fiber (SMF) has been widely studied in the research field of structural health monitoring (SHM) of civil infrastructures such as buildings, bridges, highway pavements and dams [1,2 ]. BOTDA, a two-end access of analysis system, features a high signal noise ratio (SNR) and accuracy by virtue of stimulated Brillouin scattering (SBS) since a seed Stokes launched in the other end of the fiber can largely enhance Brillouin scattering interaction [3]. Several techniques have been developed to improve the performance (sensing length and spatial resolution) of BOTDA sensing system, such as pulse code technique [4], Raman amplification [5] and differential pulse pair (DPP) [6]. However, in practical SHM engineering applications, a major concern is that, due to harsh construction environment, it may introduce a significant deformation and subsequently a large loss at a local point of the sensing fiber so that the Brillouin signal would be sharply reduced, which will considerably deteriorate the performance of the system of BOTDA.

With the steady increasing number of subscribers of fiber-to-the-home (FTTH), a low bending loss fiber is widely developed [7]. There are mainly three kinds of bend-tolerance fibers: hole-assisted fibers [8], trenched bend-insensitive fiber (BIF) [9] and special microstructure photonics crystal fibers (PCF) [10,11 ]. The basic principle of these fibers is to introduce a trench-index profile around the fiber core to suppress the bending induced optical signal loss. However, the structures of these proposed bend-tolerance fibers are complicated and the fabricating cost is relatively high. Besides, the minimal target bend radius of these designed fibers is 5mm which is inferior to that of our proposed singlemode-multimode-singlemode (SMS) fiber structure of 1.25mm. Therefore, they are less ideal considering from the perspective of long distance distributed sensing for a practical SHM application. Another alternative candidate is the polymer optical fiber (POF) which features extreme small bend radius (~2mm) and very large strain scale (>50%) [12,13 ]. While in the recent research we found that in the multi-mode POF, there exist considerable mode coupling [14], which will result in certain amount of sensing error, and the high loss (up to 250dB/km) of POF at the wavelength of 1.55μm is also a huge disadvantage for it to achieve long-distance sensing.

In this paper, we propose a configuration of SMS fiber structure to achieve a bend-insensitive distributed sensing in BOTDA system for the first time to the best of our knowledge, which features low cost, simple structure, and suitable for long-distance sensing. The SMS structure has been proposed in the micro bend sensor [15,16 ] and index sensing [17]. However, all of them are single-point sensing, and there is no study of SMS structure under macro-bending conditions in distributed long-distance sensing, which is of great importance in practical SHM engineering applications. In our scheme, the proposed SMS structure is formed by sandwiching a silica graded index multimode fibers (GI-MMF) by two standard SMFs, where both ends of the GI-MMF fiber are central aligning spliced to the SMFs to ensure that the fundamental mode excited in the GI-MMF. The limit bend radius is as low as 1.25mm, with which the measured coefficients of strain and temperature of the GI-MMF are 421.6MHz/% and 0.826MHz/°C, respectively. In addition, we also demonstrate that higher order modes excited in the GI-MMF of the SMS structure can be easily influenced by the macro-bending, so that exciting the fundamental mode in GI-MMF is essential for bend-insensitive distributed sensing.

2. Principle

In a bent single mode fiber, there are two dominant power-loss mechanisms when subjected to a single small-radius bend: transition loss and pure bend loss [18]. Transition loss occurs at the junctions between the straight and bent fiber segments where the mode fields are not identical [19,20 ]; pure bend loss happens in the curving region where the phase velocity of outer part of evanescent field of the fundamental mode becomes equal to the speed of light in the cladding [21], which will induce light wave propagating in a tangential path to the dissociation point and radiate away. It has been shown that the key factor for the difference in macro bend property between SMF and SMS structure is pure bend loss [15], which can be divided into three distinctive regions: 1) a guided wave region that is in the core of a fiber; 2) an evanescent wave region that plays a dominating role in the loss of a bent fiber; 3) a radiation wave region, which is the real loss induced by bending. Compared to the SMF, the effective index of the fundamental mode of GI-MMF is a little higher, as well as the propagation constant of fundamental mode of GI-MMF is a little higher. While considering the same bend radius for the two fibers, phase constants of fundamental modes in both fibers decrease with the same rate that changes much slowly compared to the effective index difference between MMF’s and SMF’s fundamental mode. Hence, the evanescent wave of the fundamental mode of GI-MMF is much wider than that of SMF, which makes its bend-insensitive character a significant improvement. That is to say, under the same bending conditions, guide wave in SMF will be ahead of that of GI-MMF to reach the third region of radiation wave to radiate outwards and produce a loss.

When light wave propagates along a fiber, acoustic waves (phonons) will be excited, which will induce the periodic density fluctuations in the fiber through electrostriction mechanism. The backscattered Stokes light suffers a Doppler shift called Brillouin frequency shift (BFS), which is given by [22]

νB=2neffυAλP
where neffis the effective core refractive index, υA is the acoustic velocity, and λP is the wavelength of the pump wave in vacuum. This is known as the spontaneous Brillouin scattering. If the frequency of introduced downshifted probe wave equals to the frequency of Stokes, SBS would happen and the higher-frequency pump would convert part of its energy to the lower-frequency probe through acoustic wave field. This is known as SBS in SMF.

In a multimode fiber, with varying launching conditions of both pump and probe beams, SBS interaction involves among many optical modes and acoustic wave modes, and each pair of counter-propagating optical modes may interact through an acoustic mode travelling along the same direction of the pump wave, contributing to the overall Brillouin Gain Spectrum (BGS) with a factor of the overlap integral between the three modes [23]. The fact that BGS of GI-MMF is strongly depending on the pump and probe modal contents has been demonstrated numerically and experimentally [24]. For the lateral offset splicing, SBS interaction would involve in a lot of higher-order modes and a set of acoustic wave modes. Hence, BGS would be broadened [25,26 ] and the sensing accuracy would be decreased. Higher-order optical modes are unstable and easy to couple to other modes, which would degrade the sensing performance of BOTDA. When encountering a bending, higher-order optical modes are more unstable and more easily to couple to other optical modes, which would aggravate sensing performance of BOTDA. So, it is important to both excite the fundamental mode of the pump and probe to reduce sensing error and resist bending. In addition, unlike the step-index multimode fiber, the GI-MMF provides a relative stable condition for the fundamental optical mode to propagate a long distance, which is determined by the loss of the GI-MMF.

3. Experiment setup

The experimental setup is illustrated in Fig. 1 . The output of an optical fiber laser is split into two arms by a 50/50 coupler providing two waves, i.e. pump and probe. An arbitrary function generator is used to drive a high extinction ratio (>45 dB) electro-optic modulators to generate the pump pulse. A polarization scrambler is used to randomly change the polarization state of the pump pulse to reduce polarization-fading induced fluctuation on the signal by averaging a large number of signal traces, where 5000 times averaging is used in our experiment. Before launched into the SMS structure, the pump pulse is amplified by an Erbium doped fiber amplifier (EDFA 1). For the probe beam, the output of laser is modulated by an EOM, which is driven by a microwave generator to acquire the carrier-suppressed two sidebands modulation by adjusting the bias voltage of the modulator; after amplified by EDFA 2, the probe beam is launched into the SMS structure. The lower sideband of the probe beam is extracted by a narrowband FBG filter and then is converted into an electrical signal with a photo detector and monitored by an oscilloscope, and then a BGS can be obtained by scanning frequency offset between the pump and the probe in the vicinity of BFS.

 

Fig. 1 Experimental setup. C, coupler; PC, polarization controller; EOM, electro-optic modulator; DC, direct current; AFG, arbitrary function generator; MG, microwave generator; PS, polarization scrambler; EDFA, erbium-doped fiber amplifier; SMS, singlemode-multimode-singlemode fiber; FBG, fiber Bragg grating; PD, photo detector; OSC, Oscilloscope.

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All of the optical paths are composed of silica SMFs except for the GI-MMF (Yangtze Ltd.) in SMS structure, of which the numerical aperture, length, core size and core refractive index are 0.275, 50m, 62.5μm and ~1.4841, respectively. Noted that the width of the pump pulse used in the experiment is 10ns corresponding to a 1-m spatial resolution in a silica fiber. The peak power of pulse pump is 1.5W and the power of probe is 100mW, which lead to a relative high signal intensity. As is shown in the inset of Fig. 1, both ends of GI-MMF are centrally spliced to a standard single mode fiber by arc fusion to excite the fundamental mode in the GI-MMF.

4. Experimental results

We simulate the practical conditions by purposely introducing a single loop to SMF to illustrate how bending reduce the Brillouin signal of SMF. The loop is introduced at the position of 30m of a 50-m SMF and the frequency offset between the pump and probe is set at 10.866GHz, which is the BFS of SMF at room temperature. As shown in Fig. 2(a) , several typical Brillouin signals with bend radii at 3mm, 4.5mm, 5.5mm, 6.5mm, 7.5mm, 10mm and 12.5mm are chosen for analysis, SMF begins to decrease from the radius of 12.5mm and exhibits an obvious signal loss at the radius of 10mm; with further reducing the bend radius, the signal decreases continuously and completely disappears at the bend radius of 3mm. This result indicates that the SMF sensing performance is easily influenced by bending, which would produce a huge loss on Brillouin signal at the bending point and shorten the sensing range of long distributed system of BOTDA. For comparison, we also introduce a single loop to GI-MMF of the SMS structure at about the position of 26m with different radii varying from 1.25mm to 12.5mm by a step of 0.5mm with the same condition. The frequency offset between the pump and probe is set at 9.846GHz, which is the BFS of GI-MMF at room temperature. The measured Brillouin signals with bend radii of 1.25mm, 2.5mm, 5mm, 7.5mm, 10mm, 12.5mm are shown in Fig. 2(b), respectively. It can be seen that the Brillouin signals have little loss for all of the bend radii, even at the minimal bend radius of 1.25mm, illustrating that the proposed SMS structure can effectively resist signal loss induced by extreme bending. The comparison indicates that the proposed SMS structure can effectively resist macro bending, which would considerably reduce the Brillouin signal in SMF. The weak intensity variation of the whole Brillouin signals for different bend radii is induced by the power fluctuation of the pump and probe.

 

Fig. 2 Measured Brillouin signals with different bend radii for (a) SMF and (b) GI-MMF of the SMS structure.

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It can be seen that in the Fig. 2(b), the signal experiences a very small loss after bending, which indicates that there is a few lower-order modes excited in the MMF even with central alignment splicing, while the main content of optical modes is fundamental mode, which is the critical feature of the proposed SMS structure. Noted that even at the minimal bend radius of 1.25mm, the whole signal along the GI-MMF of SMS structure has little loss comparing to the entirety signal amplitude, which indicates that SMS structure can resist even smaller bend radius. However, due to the ability of material resistance of silica to macro bending, it is hard to impose bending radius of 1mm or even smaller on the fiber. So, 1.25mm is the minimal effective bend radius applied on the proposed SMS structure.

A criterion for discussion is to set for ten turns of winding at a specified radius. Here, 10 loops is imposed on the GI-MMF of the SMS structure with bend radii varied from 2mm to 5mm by a step of 1mm to further investigate the bend-resisting ability of the proposed SMS structure. As shown in Fig. 3 , the Brillouin signals have little loss before and after the bending point and the amplitude of each signal also has little difference. These results show that the method of the fundamental mode excited in GI-MMF can effectively resist macro bend radius. Note that there are only the fundamental mode and a few lower-order modes in the GI-MMF due to the fact that the higher-order modes are so sensitive to curvature that they would easily radiate out during the process of convolving [15] and hence producing a loss after the bending region of the Brillouin signal. The small dips of the signal at the bend point is due to the strain loading arising when 10 loops are introduced to the GI-MMF, which will cause BFS deviation and a signal loss at the bending point.

 

Fig. 3 10 loops imposed on the GI-MMF of SMS structure with bend radii varied from 2mm to 5mm by a step of 1mm.

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Under the condition of applying the bend radius of 1.25mm at the position of ~25m, the strain is applied to a 2.06m-long GI-MMF of SMS structure at the room temperature. The measured distributed BFS curves are shown in Fig. 4(a) , where the stretched step is 2mm corresponding to a strain step of 0.097% and the maximum strain is 1.165%. Figure 4(b) shows the excellent linear relationship between BFS and strain. The BFS variation sensitivity to strain is 421.6MHz/%, which is slightly lower than that of SMF. The three-dimensional diagram of BFS of applying the maximal strain of 1.165% with bend radius of 1.25mm is shown in Fig. 4(c), it can be seen that after the strain region, the signal experience a small loss but still relative high intensity for detection. These results indicate that the proposed SMS structure can effectively measure stain under the condition of extreme bending. The Brillouin gain spectra at point A, B and C in Fig. 4(a) are plotted in Fig. 4(d), and the bending point is between point A and B. The solid curves show the Lorentzian fits. It is clearly shown that full width at half maximum (FWHM) of BGS is ~100MHz before and after the bend point, as well as in the maximal strain region. Normally, in a SMF the BGS is ~80MHz for a 10ns rectangular pump pulse, while in the MMF the BGS broadens to ~100MHz for a 10ns rectangular pump pulse. The broadened BGS in MMF would reduce temperature/strain accuracy. For centrally alignment excited SBS interaction in the GI-MMF, there are many acoustic wave modes involved in, each acoustic mode has its own velocity and individually contributes to the overall BGS, which will give rise to FWHM of the BGS to broaden [24]. Besides, the fact that 10ns pump pulse used in the experiment equals to lifetime of phonon has also broadened the BGS.

 

Fig. 4 Measured results of a stretched 2.06m-long segment of a 50-m GI-MMF while a bend radius of 1.25mm is applied at the position of ~25m: (a) distributed BFS curves for different strain, (b) linear relationship between BFS and strain, (c) 3D BGS with a strain of 1.165%, (d) Brillouin gain spectra at point A, B and C in (a).

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The temperature property of the proposed SMS setup is also investigated with the same condition. A 2.5m-long GI-MMF is put in the high-low temperature test chamber (temperature fluctuation ± 1°C, temperature range −40°C-150°C) and the temperature is varied from 30 °C to 80 °C with a step of 10°C. The distributed BFS curves are shown in Fig. 5(a) and the linear relationship between BFS and temperature is shown in Fig. 5(b). The BFS shift sensitivity to temperature is 0.826MHz/°C, which is slightly lower than that of SMF. The measured strain and temperature coefficients of the fundamental mode of MMF are ~20% lower than that of SMF, which would reduce its sensing sensitivity.

 

Fig. 5 (a) Distributed data of BFS of SMS structure, (b) linear relationship between BFS and temperature

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Let us discuss the interaction between higher-order modes and bending. Higher-order modes in GI-MMF of the SMS structure are excited by intentionally applying a lateral offset splicing between the interface of SMF and MMF on the probe beam, as shown in Fig. 6 , where 10μm and 15μm are used for analysis. The BFS is measured for 10 times, respectively. In Fig. 6(a), the BFSs have a variation of 20MHz, indicating that there are a few higher-order modes excited in the fiber; while for the 15µm lateral offset splicing, as shown in Fig. 6(b), the variation of the BFSs is as high as 127MHz, indicating more higher-order modes are excited in the GI-MMF [27]. With the fact of each optical mode have their own BFS, we can find that higher-order modes in a GI-MMF are unstable and more likely to couple to other modes even without bending. The BFS showed a status of ups and downs would result in sensing error of BOTDA in a practical application. When higher-order modes experience a bending, more higher-order modes would be excited and subsequently BFS of GI-MMF varies in turn. What’s more, higher-order modes would easily break their propagation path to radiate outwards during the bending region [15], so that they are not suitable for bend-insensitive sensing. For the proposed SMS structure to achieve bend-insensitive sensing, it is vital to make central alignment splicing at both interfaces between SMF and GI-MMF to excite the fundamental mode, which can effectively alleviate the loss induced by bending and maintain the sensing performance.

 

Fig. 6 BFSs of the GI-MMF with lateral offset splicing at the interface of SMF and MMF on the probe beam for (a) 10μm and (b) 15μm

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5. Conclusion

In conclusion, we reported a bend-insensitive distributed Brillouin sensor by using Brillouin optical time-domain analysis (BOTDA). The sensor is formed by sandwiching a silica graded index multimode fibers (GI-MMF) by two standard single mode fibers (SMFs) with central- alignment splicing at the interface between GI-MMF and SMF to excite fundamental mode. The limit bend radius has been investigated, with which the measured strain and temperature coefficients are 421.6MHz/% and 0.826MHz/°C, respectively. We also demonstrated that higher order modes excited in the GI-MMF of the SMS structure are easily influenced by bending, so that exciting fundamental mode is essential for bend insensitive-distributed sensing.

Acknowledgment

The authors would like to acknowledge the financial support from the National High Technology Research and Development Program of China 863 Program 2014AA110401, the National Key Technology Research and Development Program of the Ministry of Science and Technology of China 2014BAG05B07, National Key Scientific Instrument and Equipment Development Project 2013YQ040815, the National Natural Science Foundation of China 61205073 and 61308004, Foundation for Talents Returning from Overseas of Harbin 2013RFLXJ013, China Postdoctoral Science Foundation 2013M530155, LBH-TZ0406, Scientific Research Fund of Heilongjiang Provincial Education Department 12531093, and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, China 2013GZKF031303.

References and links

1. Y. Xu, P. Lu, Z. Qin, J. Harris, F. Baset, P. Lu, V. R. Bhardwaj, and X. Bao, “Vibration sensing using a tapered bend-insensitive fiber based Mach-Zehnder interferometer,” Opt. Express 21(3), 3031–3042 (2013). [CrossRef]   [PubMed]  

2. Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012). [CrossRef]   [PubMed]  

3. T. Horiguchi and M. Tateda, “Optical-fiber-attenuation investigation using stimulated Brillouin scattering between a pulse and a continuous wave,” Opt. Lett. 14(8), 408–410 (1989). [CrossRef]   [PubMed]  

4. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. 35(2), 259–261 (2010). [CrossRef]   [PubMed]  

5. F. Rodríguez-Barrios, S. Martín-López, A. Carrasco-Sanz, P. Corredera, J. D. Ania-Castañón, L. Thévenaz, and M. González-Herráez, “Distributed Brillouin fiber sensor assisted by first-order Raman amplification,” J. Lightwave Technol. 28(15), 2162–2172 (2010). [CrossRef]  

6. W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008). [CrossRef]   [PubMed]  

7. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. 23(11), 3494–3499 (2005). [CrossRef]  

8. K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003). [CrossRef]  

9. G. Ren, Z. Lin, S. Zheng, and S. Jian, “Resonant coupling in trenched bend-insensitive optical fiber,” Opt. Lett. 38(5), 781–783 (2013). [CrossRef]   [PubMed]  

10. B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013). [CrossRef]  

11. Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013). [CrossRef]  

12. N. Hayashi, Y. Mizuno, and K. Nakamura, “Brillouin gain spectrum dependence on large strain in perfluorinated graded-index polymer optical fiber,” Opt. Express 20(19), 21101–21106 (2012). [CrossRef]   [PubMed]  

13. N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:. [CrossRef]  

14. Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014). [CrossRef]   [PubMed]  

15. D. Donlagic and B. Culshaw, “Propagation of the fundamental mode in curved graded index multimode fiber and its application in sensor systems,” J. Lightwave Technol. 18(3), 334–342 (2000). [CrossRef]  

16. D. Donlagic and B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded index multimode fiber,” J. Lightwave Technol. 17(10), 334–342 (1999). [CrossRef]  

17. P. Wang, G. Brambilla, M. Ding, Y. Semenova, Q. Wu, and G. Farrell, “High-sensitivity, evanescent field refractometric sensor based on a tapered, multimode fiber interference,” Opt. Lett. 36(12), 2233–2235 (2011). [CrossRef]   [PubMed]  

18. R. C. Gauthier and C. Ross, “Theoretical and experimental considerations for a single-mode fiber-optic bend-type sensor,” Appl. Opt. 36(25), 6264–6273 (1997). [CrossRef]   [PubMed]  

19. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976). [CrossRef]  

20. W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978). [CrossRef]  

21. W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976). [CrossRef]  

22. R. W. Boyd, Nonlinear Optics (Academic, 2008), Chap. 9.

23. W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

24. A. Minardo, R. Bernini, and L. Zeni, “Experimental and numerical study on stimulated Brillouin scattering in a graded-index multimode fiber,” Opt. Express 22(14), 17480–17489 (2014). [CrossRef]   [PubMed]  

25. A. Fotiadi and E. A. Kuzin, “Stimulated Brillouin scattering amplification in multimode optical fibers,” in Conference on Lasers and Electro Optics, CLEO, paper CThL40, (1997). [CrossRef]  

26. V. Lambin Iezzi, S. Loranger, A. Harhira, R. Kashyap, M. Saad, A. Gomes, and S. Rehman, “Stimulated Brillouin scattering in multi-mode fiber for sensing applications,” in Fibre and Optical Passive Components (WFOPC), 7th Workshop, pp. 1–4, (2011). [CrossRef]  

27. Y. Mizuno and K. Nakamura, “Core alignment of butt coupling between single-mode and multimode optical fibers by monitoring Brillouin scattering signal,” J. Lightwave Technol. 29(17), 2616–2620 (2011). [CrossRef]  

References

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  1. Y. Xu, P. Lu, Z. Qin, J. Harris, F. Baset, P. Lu, V. R. Bhardwaj, and X. Bao, “Vibration sensing using a tapered bend-insensitive fiber based Mach-Zehnder interferometer,” Opt. Express 21(3), 3031–3042 (2013).
    [Crossref] [PubMed]
  2. Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
    [Crossref] [PubMed]
  3. T. Horiguchi and M. Tateda, “Optical-fiber-attenuation investigation using stimulated Brillouin scattering between a pulse and a continuous wave,” Opt. Lett. 14(8), 408–410 (1989).
    [Crossref] [PubMed]
  4. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. 35(2), 259–261 (2010).
    [Crossref] [PubMed]
  5. F. Rodríguez-Barrios, S. Martín-López, A. Carrasco-Sanz, P. Corredera, J. D. Ania-Castañón, L. Thévenaz, and M. González-Herráez, “Distributed Brillouin fiber sensor assisted by first-order Raman amplification,” J. Lightwave Technol. 28(15), 2162–2172 (2010).
    [Crossref]
  6. W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
    [Crossref] [PubMed]
  7. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. 23(11), 3494–3499 (2005).
    [Crossref]
  8. K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
    [Crossref]
  9. G. Ren, Z. Lin, S. Zheng, and S. Jian, “Resonant coupling in trenched bend-insensitive optical fiber,” Opt. Lett. 38(5), 781–783 (2013).
    [Crossref] [PubMed]
  10. B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
    [Crossref]
  11. Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
    [Crossref]
  12. N. Hayashi, Y. Mizuno, and K. Nakamura, “Brillouin gain spectrum dependence on large strain in perfluorinated graded-index polymer optical fiber,” Opt. Express 20(19), 21101–21106 (2012).
    [Crossref] [PubMed]
  13. N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:.
    [Crossref]
  14. Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
    [Crossref] [PubMed]
  15. D. Donlagic and B. Culshaw, “Propagation of the fundamental mode in curved graded index multimode fiber and its application in sensor systems,” J. Lightwave Technol. 18(3), 334–342 (2000).
    [Crossref]
  16. D. Donlagic and B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded index multimode fiber,” J. Lightwave Technol. 17(10), 334–342 (1999).
    [Crossref]
  17. P. Wang, G. Brambilla, M. Ding, Y. Semenova, Q. Wu, and G. Farrell, “High-sensitivity, evanescent field refractometric sensor based on a tapered, multimode fiber interference,” Opt. Lett. 36(12), 2233–2235 (2011).
    [Crossref] [PubMed]
  18. R. C. Gauthier and C. Ross, “Theoretical and experimental considerations for a single-mode fiber-optic bend-type sensor,” Appl. Opt. 36(25), 6264–6273 (1997).
    [Crossref] [PubMed]
  19. D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976).
    [Crossref]
  20. W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
    [Crossref]
  21. W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
    [Crossref]
  22. R. W. Boyd, Nonlinear Optics (Academic, 2008), Chap. 9.
  23. W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).
  24. A. Minardo, R. Bernini, and L. Zeni, “Experimental and numerical study on stimulated Brillouin scattering in a graded-index multimode fiber,” Opt. Express 22(14), 17480–17489 (2014).
    [Crossref] [PubMed]
  25. A. Fotiadi and E. A. Kuzin, “Stimulated Brillouin scattering amplification in multimode optical fibers,” in Conference on Lasers and Electro Optics, CLEO, paper CThL40, (1997).
    [Crossref]
  26. V. Lambin Iezzi, S. Loranger, A. Harhira, R. Kashyap, M. Saad, A. Gomes, and S. Rehman, “Stimulated Brillouin scattering in multi-mode fiber for sensing applications,” in Fibre and Optical Passive Components (WFOPC), 7th Workshop, pp. 1–4, (2011).
    [Crossref]
  27. Y. Mizuno and K. Nakamura, “Core alignment of butt coupling between single-mode and multimode optical fibers by monitoring Brillouin scattering signal,” J. Lightwave Technol. 29(17), 2616–2620 (2011).
    [Crossref]

2014 (4)

N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:.
[Crossref]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

A. Minardo, R. Bernini, and L. Zeni, “Experimental and numerical study on stimulated Brillouin scattering in a graded-index multimode fiber,” Opt. Express 22(14), 17480–17489 (2014).
[Crossref] [PubMed]

2013 (4)

Y. Xu, P. Lu, Z. Qin, J. Harris, F. Baset, P. Lu, V. R. Bhardwaj, and X. Bao, “Vibration sensing using a tapered bend-insensitive fiber based Mach-Zehnder interferometer,” Opt. Express 21(3), 3031–3042 (2013).
[Crossref] [PubMed]

G. Ren, Z. Lin, S. Zheng, and S. Jian, “Resonant coupling in trenched bend-insensitive optical fiber,” Opt. Lett. 38(5), 781–783 (2013).
[Crossref] [PubMed]

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
[Crossref]

2012 (2)

2011 (2)

2010 (2)

2008 (1)

2005 (1)

2003 (1)

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

2000 (1)

1999 (1)

D. Donlagic and B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded index multimode fiber,” J. Lightwave Technol. 17(10), 334–342 (1999).
[Crossref]

1997 (1)

1989 (1)

1978 (1)

W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

1976 (2)

W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
[Crossref]

D. Marcuse, “Field deformation and loss caused by curvature of optical fibers,” J. Opt. Soc. Am. 66(4), 311–320 (1976).
[Crossref]

Ania-Castañón, J. D.

Bao, X.

Baset, F.

Behera, B. L.

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Bernini, R.

Bhardwaj, V. R.

Bolognini, G.

Brambilla, G.

Carrasco-Sanz, A.

Chen, L.

Corredera, P.

Culshaw, B.

D. Donlagic and B. Culshaw, “Propagation of the fundamental mode in curved graded index multimode fiber and its application in sensor systems,” J. Lightwave Technol. 18(3), 334–342 (2000).
[Crossref]

D. Donlagic and B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded index multimode fiber,” J. Lightwave Technol. 17(10), 334–342 (1999).
[Crossref]

Datta, R.

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Di Pasquale, F.

Ding, M.

Dong, Y.

Donlagic, D.

D. Donlagic and B. Culshaw, “Propagation of the fundamental mode in curved graded index multimode fiber and its application in sensor systems,” J. Lightwave Technol. 18(3), 334–342 (2000).
[Crossref]

D. Donlagic and B. Culshaw, “Microbend sensor structure for use in distributed and quasi-distributed sensor systems based on selective launching and filtering of the modes in graded index multimode fiber,” J. Lightwave Technol. 17(10), 334–342 (1999).
[Crossref]

Farrell, G.

Gambling, W. A.

W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
[Crossref]

Gauthier, R. C.

González-Herráez, M.

Guan, N.

Harris, J.

Hatsumura, H.

W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Hayashi, N.

N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:.
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Brillouin gain spectrum dependence on large strain in perfluorinated graded-index polymer optical fiber,” Opt. Express 20(19), 21101–21106 (2012).
[Crossref] [PubMed]

Himeno, K.

Hogari, K.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

Horiguchi, T.

Jian, S.

Jin, S.

Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
[Crossref]

Ke, W. W.

W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

Li, W.

Li, Y.

Lin, Z.

Lu, P.

Lu, Z.

Maity, A.

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Marcuse, D.

Martín-López, S.

Matsumura, H.

W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
[Crossref]

Matsuo, S.

Minakawa, K.

N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:.
[Crossref]

Minardo, A.

Mizuno, Y.

Nakajima, K.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

Nakamura, K.

Payne, D. N.

W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
[Crossref]

Qin, Z.

Ragdale, C. M.

W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Ren, G.

Rodríguez-Barrios, F.

Ross, C.

Sankawa, I.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

Semenova, Y.

Soto, M. A.

Tajima, K.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

Tang, X.

W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

Tateda, M.

Thévenaz, L.

Varshney, S. K.

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Wada, A.

Wang, P.

Wang, X. J.

W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

Wang, Z.

Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
[Crossref]

Wu, Q.

Xu, P.

Xu, Y.

Zeni, L.

Zhang, H.

Zhao, C.

Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
[Crossref]

Zheng, S.

Zhou, J.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

N. Hayashi, K. Minakawa, Y. Mizuno, and K. Nakamura, “Brillouin frequency shift hopping in polymer optical fiber,” Appl. Phys. Lett. 105(9), 021103 (2014), doi:.
[Crossref]

Electron. Lett. (2)

W. A. Gambling, H. Hatsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fiber,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

W. A. Gambling, D. N. Payne, and H. Matsumura, “Radiation from curved single-mode fibers,” Electron. Lett. 12(21), 567–569 (1976).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

W. W. Ke, X. J. Wang, and X. Tang, “Stimulated Brillouin scattering model in multi-mode fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 901610 (2014).

IEEE Photonics Technol. Lett. (1)

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photonics Technol. Lett. 15(12), 1737–1739 (2003).
[Crossref]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

B. L. Behera, A. Maity, S. K. Varshney, and R. Datta, “Theoretical investigations of trench-assisted large mode-area low bend loss and single-mode microstructured core fibers,” Opt. Commun. 307, 9–16 (2013).
[Crossref]

Opt. Express (5)

Opt. Fiber Technol. (1)

Z. Wang, C. Zhao, and S. Jin, “Design of a bending-insensitive single-mode photonic crystal fiber,” Opt. Fiber Technol. 19(3), 213–218 (2013).
[Crossref]

Opt. Lett. (4)

Other (3)

A. Fotiadi and E. A. Kuzin, “Stimulated Brillouin scattering amplification in multimode optical fibers,” in Conference on Lasers and Electro Optics, CLEO, paper CThL40, (1997).
[Crossref]

V. Lambin Iezzi, S. Loranger, A. Harhira, R. Kashyap, M. Saad, A. Gomes, and S. Rehman, “Stimulated Brillouin scattering in multi-mode fiber for sensing applications,” in Fibre and Optical Passive Components (WFOPC), 7th Workshop, pp. 1–4, (2011).
[Crossref]

R. W. Boyd, Nonlinear Optics (Academic, 2008), Chap. 9.

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Figures (6)

Fig. 1
Fig. 1 Experimental setup. C, coupler; PC, polarization controller; EOM, electro-optic modulator; DC, direct current; AFG, arbitrary function generator; MG, microwave generator; PS, polarization scrambler; EDFA, erbium-doped fiber amplifier; SMS, singlemode-multimode-singlemode fiber; FBG, fiber Bragg grating; PD, photo detector; OSC, Oscilloscope.
Fig. 2
Fig. 2 Measured Brillouin signals with different bend radii for (a) SMF and (b) GI-MMF of the SMS structure.
Fig. 3
Fig. 3 10 loops imposed on the GI-MMF of SMS structure with bend radii varied from 2mm to 5mm by a step of 1mm.
Fig. 4
Fig. 4 Measured results of a stretched 2.06m-long segment of a 50-m GI-MMF while a bend radius of 1.25mm is applied at the position of ~25m: (a) distributed BFS curves for different strain, (b) linear relationship between BFS and strain, (c) 3D BGS with a strain of 1.165%, (d) Brillouin gain spectra at point A, B and C in (a).
Fig. 5
Fig. 5 (a) Distributed data of BFS of SMS structure, (b) linear relationship between BFS and temperature
Fig. 6
Fig. 6 BFSs of the GI-MMF with lateral offset splicing at the interface of SMF and MMF on the probe beam for (a) 10μm and (b) 15μm

Equations (1)

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ν B = 2 n e f f υ A λ P

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