Open Access
Add to BibSonomy
Abstract
The local temperature and longitudinal strain at spatial resolution of 0.5% of the pulse-width equivalent length along a nonuniform As2Se3-PMMA tapered fiber is investigated by a Brillouin gain-profile tracing method. This scheme uses a 20 ns pump pulse with the pulse-width equivalent length longer than the fiber under test (FUT) of 50 cm nonuniform As2Se3-PMMA tapered fiber. The whole interaction process of long pump pulse is investigated including pump pulse entering the FUT, overlapping completely with FUT and leaving the FUT. The evolution of Brillouin gain spectrum (BGS) along the nonuniform fiber is formed by the subtraction of frequency-domain BGS of two adjacent sensing points in the trailing edge (where the pump pulse leaves the FUT) of the BOTDA spectrum. The trailing part is preferred due to the pre-amplified acoustic field by the long pumping pulse. Then the local responses of temperature and wide-range longitudinal strain with high spatial resolution of 1.1 cm along the nonuniform As2Se3-PMMA tapered fibers are investigated. The change of the local temperature and strain shifts the BGS that is different along the nonuniform fibers, which forms the distributed measurement. The spatial resolution, the fiber length of the detected section in the proposed method, is 1.1 cm for the local temperature and longitudinal strain measurement, which is 0.5% of the pulse-width equivalent length and is limited by the sampling rate of data acquisition and the fall-time of the pump pulse.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Tapered optical fibers are used in different applications such as structural health monitoring [1] and refractive index sensing of surrounding environment [2,3]. The chalcogenide-PMMA tapered fibers are investigated extensively due to the high intrinsic nonlinearity of chalcogenide fibers, enhanced nonlinearity by the tapering structure, high robustness of PMMA and also the special thermo/strain performance of these materials and structures. The As$_{2}$Se$_{3}$-PMMA tapered fibers are excellent for strain and temperature sensors due to high thermo-coefficient of As$_{2}$Se$_{3}$ core and PMMA cladding, low stiffness of taper structure and thermal forces on As$_{2}$Se$_{3}$ cores by the PMMA cladding. There are many interesting applications achieved with varied diameter of As$_{2}$Se$_{3}$-PMMA tapers, such as temperature and strain sensors with high sensitivities [4,5] and also temperature-insensitive strain measurement devices [6]. The Brillouin frequency shift in As$_{2}$Se$_{3}$-PMMA tapered fibers can be widely tuned with the wire diameter and the polymer cladding substantially broadens the Brillouin linewidth [7]. Specialty fibers such as chalcogenide-PMMA tapers have been investigated extensively for point sensing applications based on BOTDA [8–11], but the local response to temperature and longitudinal strain of these fibers has not been reported. Nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber has a changing core size along the fiber length, which is significantly different from single-mode fibers with equal core size in BOTDA measurement and the investigation of the As$_{2}$Se$_{3}$-PMMA tapered fibers with a nonuniform structure will bring many novel applications, such as distributed multi-parameter sensing.
BOTDA has been used for civil structural health monitoring due to the ability of distributed sensing of strain and temperature [12–16]. It is well known that the spatial resolution in a conventional BOTDA is determined by the spatial coverage of the pulse width (usually larger than the acoustic lifetime of $10$ ns)and a shorter pulse width represents a higher spatial resolution [17–19]. The spatial resolution of a conventional BOTDA in single-mode fibers is limited to 1 m, making it unsuitable for applications where higher spatial resolution is needed such as crack detection in composite materials and corrosion monitoring of metal material [20,21]. Much attention has been drawn to improve the spatial resolution of the BOTDA system [15,22–24]. For example, a differential pulse-width pair BOTDA system was developed to achieve $15$ cm spatial resolution, which employs the differential waveform subtraction at each scanned Brillouin frequency between the pulse pair obtained by injecting a $50/49$ ns pulse pair to the sensing fiber [25]. In 2010, Sperber et al. proposed a Brillouin gain-profile tracing method and the desired spatial mapping of the Brillouin response is extracted by taking the derivative of the probe signal with $2$ cm spatial resolution [26]. The advantage of gain-profile tracing is that a long pulse is utilized to pre-excite the acoustic wave and the high spatial resolution is achieved by the short fall-time of the pump pulse and high sampling DAQ through the conversion of the time domain data to spatial domain, which is adequate for the local temperature and strain measurement along fibers.
In this paper, the distributed local temperature and strain sensing with $1.1$ cm spatial resolution based on the Brillouin gain-profile tracing method is investigated. A $20$ ns pump pulse is utilized and the pulse-width equivalent length is longer than the fiber under test (FUT) of a $50$ cm nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber. The BOTDA spectra of the nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber is recorded, and the subtraction of BGS at two adjacent sensing points in the trailing edge of the measured BOTDA spectra forms the BGS of the corresponding fiber section. When temperature or strain changes around the FUT, the corresponding BGS shift provides the position information and by calculating the frequency shifts the temperature or strain changes are demodulated.
2. Fabrication procedure of nonuniform As$_{2}$Se$_{3}$-PMMA tapered fibers
The nonuniform As$_{2}$Se$_{3}$-PMMA tapered fibers are fabricated following an adiabatic tapering process combining the high intrinsic nonlinearity of As$_{2}$Se$_{3}$ fibers, enhanced nonlinearity by the tapering structure, high robustness of PMMA and also the special thermo/strain performance of these materials and structures [4,27,28]. Figure 1(a) depicts the core diameter as a function of the position along the tapered As$_{2}$Se$_{3}$-PMMA fiber with the As$_{2}$Se$_{3}$ core diameter linearly changing from $3.5\,\mathrm {\mu }$m to $1.5\,\mathrm {\mu }$m within the $50$ cm long taper section. Figure 1(b) shows the calculated SBS frequency as a function of the core diameter of As$_{2}$Se$_{3}$-PMMA tapered fiber ranging from $1.5\,\mathrm {\mu }$m to $3.5\,\mathrm {\mu }$m.
Fig. 1. (a) Core diameter as a function of position along the tapered As$_{2}$Se$_{3}$-PMMA fiber. (b) The calculated SBS frequency as a function of the core diameter ranging from $1.5\,\mathrm {\mu }$m to $3.5\,\mathrm {\mu }$m.
3. Theoretical analysis
In the conventional BOTDA schematic used in the literature, the pump pulse is usually much shorter than the FUT. However, when the pulse width equivalent fiber length of the pump pulse is longer than the FUT, the situation is different. Figure 2 presents the Brillouin gain-profile tracing process in $5$ steps. Figure 2(a) shows the first step where pump pulse does not overlap with the FUT. The Stokes light cannot be amplified due to the lack of the gain medium and the time trace observed in the oscilloscope is the unamplified DC light. Figure 2(b) shows the second step where the pump pulse overlaps in part of the FUT. While the pump pulse moves, the overlapped fiber section increases. The signal is recorded point by point in the time trace and the number of the recorded points is determined by sampling rate of the data acquisition. The signal at each point in the time trace, called the leading part, represents the Stokes light amplified by the corresponding fiber section overlapped by the pump pulse. Figure 2(c) shows the third step where the pump pulse overlaps over the whole fiber section. The signal at each point in the time trace represents the amplified Stokes light by the whole fiber gain medium and the amplitude keeps the same. Figure 2(d) shows the fourth step where the fiber length overlapped by the pump pulse is decreasing, which acquires the trailing part of the signal. When pump pulse leaves the fiber, the signal at each point in the time trace is returned to DC value, which is the last step shown in Fig. 2(e). Figure 2(f) summarizes the $5$ steps showing the overlapped fiber section changes as the points in the time trace. The time axis is labeled as position count and each point in the position count axis has its corresponding BGS of the fiber section overlapped by the pump pulse. Theoretically, both leading part in Fig. 2(b) and trailing part in Fig. 2(d) should work for obtaining the distributed property along the FUT. However, the gain of the leading part is weak due to the short interaction length while that of the trailing part is strong due to the pre-amplified acoustic field by the long pumping pulse. Then the signals in the trailing part (the situation in Fig. 2(d)) should be chosen for the distributed measurement using the proposed method in this paper.
Fig. 2. BOTDA schematic under long-pulse pumping condition. (a)-(e) The $5$ steps where long-pumping pulse interacts with the short FUT. The inset shows the overlapped section with pump pulse as a function of time. (f) A summary of the $5$ steps showing the overlapped fiber section changes as the points in the time trace. The line BA stands for the chalcogenide taper with high SBS gain: A stands for the end with a larger diameter and B stands for the end with a smaller diameter.
The Brillouin frequency shift $v_{B}$ in optical fibers is given by [29]
where $n_{eff}^{p}$ is the effective refractive index at the pump wavelength, $\lambda _{p}$ is the pump wavelength and $V_{L}$ is the longitudinal acoustic velocity. The imposed longitudinal strain changes the values of $n_{eff}^{p}$ and $V_{L}$ and then the SBS frequency shift $v_{B}$ is changed by $\Delta v_{B}$ given byFig. 3. Simulated results of (a) strain and (b) temperature sensitivity as a function of As$_{2}$Se$_{3}$ core diameter.
4. Experimental results
Figure 4 shows the BOTDA experimental setup utilized for distributed strain and temperature measurement in a nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber. Light launched by a laser source with a $3$ kHz linewidth is split by a $50:50$ coupler into two arms. The light in the upper arm is modulated by an EOM driven by a pulse generator to create a pulse with pulse width of $20$ ns and goes into the FUT through a $500$ m SMF as the pump light from the end with the larger diameter (end A). The pulse width of $20$ ns is chosen to completely cover the $50$ cm long FUT to achieve the long-pumping pulse condition. The light in the lower arm is modulated by EOM2 driven by a RF source that sweeps the radio frequency to produce two sidebands. The sideband with a shorter wavelength is filtered out and the one with a longer wavelength is launched into the FUT as the Stokes light from the end with the smaller diameter (end B). The Stokes light is amplified by the pump light due to the SBS effect following the process described in Fig. 2 and recorded by an oscilloscope with a sampling rate of $10$ GHz.
Fig. 4. Experimental setup of BOTDA. EOM: Electro-Optic Modulator; EDFA: Erbium Doped Fiber Amplifiers; SMF: single-mode fiber; FUT: Fiber Under Test; RF source: Radio-Frequency source; PD: Photo Detector.
Figure 5(a) shows the measured BOTDA spectra of the $50$ cm long nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber. The time axis is labeled as position count and each point in the position count axis has its corresponding BGS of the fiber section overlapped by the pump pulse, as described in Fig. 2. The number of points in the position count axis is determined by the sampling rate of the oscilloscope in the BOTDA measurement. To see more detailed information, the BGS is normalized at each position count, which is shown in Fig. 5(b).
Fig. 5. Experimental results of the measured BOTDA spectra of the $50$ cm long nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber: (a) the real measured data, (b) the normalized data.
Three examples are given to show the schematic of the proposed method. In the data processing process, the low amplitude signal is filtered out. Figure 6(a1) shows the measured BGS of position count $195$ (blue) and $196$ (red) corresponding to the case in Fig. 2(b). The overlapped fiber section of position count $196$ is longer than that of position count $195$, which means the SBS gain range of position count $196$ is larger than that of position count $195$ due to the nonuniform distribution of the fiber core diameter. The subtraction of the BGS of position count $196$ and $195$ is fitted by a Lorentz function, which is shown in Fig. 6(a2). Figure 6(b1) shows the measured BGS of position count $250$ (blue) and $251$ (red) corresponding to the case in Fig. 2(c). The overlapped fiber sections of position count $250$ and $251$ are the same, which means the BGS of position count $250$ is the same with that of position count $251$. The subtraction of the BGS of position count $251$ and $250$ is a DC value of zero shown in Fig. 6(b2). Figure 6(c1) shows the measured BGS of position count $305$ (blue) and $306$ (red) corresponding to the case in Fig. 2(d). The overlapped fiber section of position count $306$ is shorter than that of position count $305$, which means the SBS gain range of position count $306$ is smaller than that of position count $305$. The subtraction of the BGS of position count $306$ and $305$ is fitted by a Lorentz function shown in Fig. 6(c2). Comparing the amplitude of BGS in Figs. 6(a2) and (c2), the signals in the trailing part shows a larger contrast and narrower linewidth due to the pre-amplified acoustic wave by the long pumping pulse and is preferred for the proposed method. The subtraction of the BGS of two adjacent position counts in the trailing part in Fig. 5 ranging from $265$ to $310$ is recorded to get the BGS of the corresponding fiber section and the distributed performance of strain and temperature can be calibrated by measuring the frequency shift of the troughs in the BGS.
Fig. 6. The BGS of position count (a1) $195$ (blue) and $196$ (red), (b1) $250$ (blue) and $251$ (red), and (c1) $305$ (blue) and $306$ (red); the difference of BGS between position counts (a2) $196$ and $195$, (b2) $251$ and $250$, and (c2) $306$ and $305$.
Figure 7(a) presents an example that the BGS evolves as the change of longitudinal strain at the fiber section that corresponds to the subtraction of the BGS of position count $290$ and $289$ when a longitudinal strain is imposed on two sides of the FUT. The trough of the BGS shifts linearly with the change of the imposed strain ranging from $0$ to $10$ m$\mathrm {\varepsilon }$. To analyze the local strain performance along the whole fiber, the subtraction of the BGS of two adjacent position counts in the trailing part in Fig. 5 ranging from $265$ to $310$ is recorded. The local strain performance is obtained by relating the BGS to the fiber position shown in Fig. 1(b) and analyzing the evolution of BGS as the change of the strain. The spatial resolution is defined by the equivalent fiber length of $1$ position count, which is equal to $1.1$ cm. Figure 7(b) shows the local strain performance by monitoring the fiber section of $1.1$ cm along the $50$ cm tapered fiber.
Fig. 7. (a) An example: the measured BGS evolution as the change of strain at the fiber section that corresponds to the subtraction of the BGS of position count $290$ and $289$; (b) the Brillouin frequency shift under longitudinal strain of $10$ m$\mathrm {\varepsilon }$ by monitoring the fiber section of $1.1$ cm along the $50$ cm tapered fiber. Note: Although each point in Fig. 7(b) represents the Brillouin frequency shift at fiber section that corresponds to the subtraction of the BGS of position count $n$ and $n-1$, the $x$-axis is labeled as position count $n$. For example, $266$ in the $x$-axis corresponds to the fiber section where BGS of position count $266$ subtracts that of position count $265$.
Figure 8 presents that the BGS evolves as the change of temperature at the fiber section that corresponds to the subtraction of the BGS of position count (a) $272$ and $271$ and (b) $281$ and $280$, respectively when temperature is imposed by a cylindrical heater wrapped in two turns by the FUT. The diameter of the heater is $2$ cm and then the length of the heating section is $12.56$ cm. The fiber section corresponding to the subtraction of the BGS of position count $272$ and $271$ in Fig. 8(a) is within the heating section and the trough shifts linearly with the change of the imposed temperature while the fiber section corresponding to the subtraction of position counts of $281$ and $280$ in Fig. 8(b) is not wrapped on the heater and then the trough doesn’t shift. Similar to the strain measurement, to analyze the local temperature performance along the whole fiber, the subtraction of the BGS of two adjacent position counts in the trailing part in Fig. 5 ranging from $265$ to $310$ is recorded and the spatial resolution is defined by the equivalent fiber length of $1$ position count, which is equal to $1.1$ cm in this case. Figure 9 shows the local temperature performance by monitoring the fiber section of $1.1$ cm along the $50$ cm tapered fiber. The slope of the Brillouin frequency shift from position count $277$ to $283$ in Fig. 9 appears due to the nonuniform distribution of the imposed temperature and the induced strain when setting up the FUT and the heater. Position count ranging from $285$ to $296$ corresponds to the the heating section of $12.56$ cm and the Brillouin frequency shift varies because fiber sections with different core diameters have different temperature response.
Fig. 8. Measured evolution of the BGS as the change of temperature at the fiber sections that correspond to the subtraction of the SBS gain spectra of position count (a) $281$ and $280$ and (b) $272$ and $271$, respectively.
Fig. 9. Measured Brillouin frequency shift when the temperature change is $30$$^{\circ}\textrm{C}$ along the $50$ cm tapered fiber.
There are two limiting parameters for the spatial resolution with the gain-profile tracing method: the sampling rate of data acquisition ($S_{ac}$) and the fall-time of the pump pulse ($t_{fall}$). The spatial resolution is defined by
with the distance determined by the sampling rate of data acquisition $\Delta z_{S_{ac}}=v_{g}/S_{ac}$ and the distance determined by the fall-time of the pump pulse $\Delta z_{t_{fall}}=\left (v_{g}/2\right )t_{fall}$ [26], where $v_{g}$ is the optical group velocity. In the experiment, the sampling rate of data acquisition $S_{ac}$ is $10$ GHz and the fall-time of the pump pulse $t_{fall}$ is $100$ ps, which leads to the spatial resolution in theory of $\Delta z_{resolvable}=\Delta z_{S_{ac}}=1.06$ cm.As shown in Fig. 7 and Fig. 9, the local performance of longitudinal strain and temperature are investigated by monitoring the Brillouin frequency shift. And the local strain and temperature imposed on the local sections can be calibrated using the recorded Brillouin frequency shift divided by the simulated sensitivity of strain and temperature as a function of As$_{2}$Se$_{3}$ core diameter shown in Fig. 3.
In the distributed temperature and strain measurement of a nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber, the sensing length can be enhanced by adjusting the pulse width and the peak power of the pump pulse and the bandwidth of the obtained BGS can also be monitored to provide extra degree of freedom and accuracy for the measurement. For example, the bandwidth of the BGS in Fig. 7(a) and Fig. 8(a) also evolve as the change of the temperature and strain. Monitoring the change of the bandwidth will gain more potential novel applications such as non-destructive distributed measurement of fiber diameter and dual-parameter distributed sensing.
5. Conclusion
We have demonstrated a distributed temperature and strain sensor based on a nonuniform As$_{2}$Se$_{3}$-PMMA tapered fiber with centimeter spatial resolution using the Brillouin gain-profile tracing method. The method uses the subtraction of BGS of two adjacent position counts to form the differential BGS at each fiber location. The sensing length can be enhanced by adjusting the pulse width and the peak power of the pump pulse and the spatial resolution can be further improved if higher sampling rate of the oscilloscope and pump pulse with sharper falling edge are used in the measurement. The distributed performance of the nonuniform As$_{2}$Se$_{3}$-PMMA tapers will bring out the realization of novel sensors and devices.
Funding
Canada Research Chairs (Fiber Optics and Photonics Program (75-67138)); Natural Sciences and Engineering Research Council of Canada (06071-RGPIN-2015); Natural Science Foundation of Shandong Province (ZR2021QA019); National Natural Science Foundation of China (12104265).
Acknowledgments
The authors are thankful to Coractive Inc. for providing the As$_{2}$Se$_{3}$ multimode fiber.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. Korposh, S. W. James, S.-W. Lee, and R. P. Tatam, “Tapered optical fibre sensors: Current trends and future perspectives,” Sensors 19(10), 2294 (2019). [CrossRef]
2. C. Huang, H. Sun, H. Liang, L. Cheng, L. Chen, X. Bao, and B.-O. Guan, “Refractive index sensing based on brillouin scattering in a micro fiber,” Appl. Phys. Express 12(8), 082013 (2019). [CrossRef]
3. A. Minardo, L. Zeni, R. Bernini, E. Catalano, and R. Vallifuoco, “Quasi-distributed refractive index sensing by stimulated brillouin scattering in tapered optical fibers,” J. Lightwave Technol. 40(8), 2619–2624 (2022). [CrossRef]
4. S. Gao, C. Baker, L. Chen, and X. Bao, “Simultaneous measurement of temperature and strain in a dual-core as 2 se 3-pmma taper,” IEEE Photonics Technol. Lett. 30(1), 79–82 (2018). [CrossRef]
5. S. Gao, C. Baker, L. Chen, and X. Bao, “High-sensitivity temperature and strain measurement in dual-core hybrid tapers,” IEEE Photonics Technol. Lett. 30(12), 1155–1158 (2018). [CrossRef]
6. S. Gao, C. Baker, L. Chen, and X. Bao, “Approach for temperature-insensitive strain measurement using a dual-core as 2 se 3-pmma taper,” Opt. Lett. 43(7), 1523–1526 (2018). [CrossRef]
7. J.-C. Beugnot, R. Ahmad, M. Rochette, V. Laude, H. Maillotte, and T. Sylvestre, “Reduction and control of stimulated brillouin scattering in polymer-coated chalcogenide optical microwires,” Opt. Lett. 39(3), 482–485 (2014). [CrossRef]
8. H. Wang, S. Gao, C. Baker, Y. Wang, L. Chen, and X. Bao, “Stimulated brillouin scattering in a tapered dual-core as 2 se 3-pmma fiber for simultaneous temperature and strain sensing,” Opt. Lett. 45(12), 3301–3304 (2020). [CrossRef]
9. H. Wang, S. Gao, C. Baker, Y. Wang, L. Chen, and X. Bao, “Wide-range strain sensor based on brillouin frequency and linewidth in an as 2 se 3-pmma hybrid microfiber,” Opt. Express 28(15), 22933–22945 (2020). [CrossRef]
10. H. Wang, C. Baker, L. Chen, and X. Bao, “Stimulated brillouin scattering in high-birefringence elliptical-core as 2 se 3-pmma microfibers,” Opt. Lett. 46(5), 945–948 (2021). [CrossRef]
11. B. Saxena, C. Baker, X. Bao, and L. Chen, “High birefringent brillouin frequency shifts in a single-mode as 2 se 3-pmma microtaper induced by a transverse load,” Opt. Lett. 44(19), 4789–4792 (2019). [CrossRef]
12. R. Di Sante, “Fibre optic sensors for structural health monitoring of aircraft composite structures: Recent advances and applications,” Sensors 15(8), 18666–18713 (2015). [CrossRef]
13. H.-F. Pei, J. Teng, J.-H. Yin, and R. Chen, “A review of previous studies on the applications of optical fiber sensors in geotechnical health monitoring,” Measurement 58, 207–214 (2014). [CrossRef]
14. X. Ye, Y. Su, and J. Han, “Structural health monitoring of civil infrastructure using optical fiber sensing technology: A comprehensive review,” The Sci. World J. 2014, 1–11 (2014). [CrossRef]
15. Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-spatial-resolution fast botda for dynamic strain measurement based on differential double-pulse and second-order sideband of modulation,” IEEE Photonics J. 5(3), 2600407 (2013). [CrossRef]
16. B. Wang, B. Fan, D. Zhou, C. Pang, Y. Li, D. Ba, and Y. Dong, “High-performance optical chirp chain botda by using a pattern recognition algorithm and the differential pulse-width pair technique,” Photonics Res. 7(6), 652–658 (2019). [CrossRef]
17. X.-H. Jia, H.-Q. Chang, K. Lin, C. Xu, and J.-G. Wu, “Frequency-comb-based botda sensors for high-spatial-resolution/long-distance sensing,” Opt. Express 25(6), 6997–7007 (2017). [CrossRef]
18. L. Shen, Z. Zhao, C. Zhao, H. Wu, C. Lu, and M. Tang, “Improving the spatial resolution of a botda sensor using deconvolution algorithm,” J. Lightwave Technol. 39(7), 2215–2222 (2021). [CrossRef]
19. M. A. Soto, M. Taki, G. Bolognini, and F. Di Pasquale, “Simplex-coded botda sensor over 120-km smf with 1-m spatial resolution assisted by optimized bidirectional raman amplification,” IEEE Photonics Technol. Lett. 24(20), 1823–1826 (2012). [CrossRef]
20. M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with rayleigh scatter,” Appl. Opt. 37(10), 1735–1740 (1998). [CrossRef]
21. R. Feced, M. Farhadiroushan, V. A. Handerek, and A. J. Rogers, “A high spatial resolution distributed optical fiber sensor for high-temperature measurements,” Rev. Sci. Instrum. 68(10), 3772–3776 (1997). [CrossRef]
22. 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]
23. M. A. Soto, S. Le Floch, and L. Thévenaz, “Bipolar optical pulse coding for performance enhancement in botda sensors,” Opt. Express 21(14), 16390–16397 (2013). [CrossRef]
24. A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-spatial resolution dpp-botda by real-time balanced detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014). [CrossRef]
25. 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]
26. T. Sperber, A. Eyal, M. Tur, and L. Thévenaz, “High spatial resolution distributed sensing in optical fibers by brillouin gain-profile tracing,” Opt. Express 18(8), 8671–8679 (2010). [CrossRef]
27. C. Baker and M. Rochette, “Highly nonlinear hybrid asse-pmma microtapers,” Opt. Express 18(12), 12391–12398 (2010). [CrossRef]
28. C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express 1(6), 1065–1076 (2011). [CrossRef]
29. G. P. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century (Springer, 2000), pp. 195–211.
30. W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photonics Technol. Lett. 19(18), 1389–1391 (2007). [CrossRef]
31. S. Chaki and G. Bourse, “Guided ultrasonic waves for non-destructive monitoring of the stress levels in prestressed steel strands,” Ultrasonics 49(2), 162–171 (2009). [CrossRef]
