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Abstract
A Brillouin gain fluctuation elimination scheme based on a hybrid polarization pulling and pushing effect (HPPP) is proposed and experimentally demonstrated in a Golay-coded Brillouin optical time domain analysis (BOTDA) fiber sensor. The analysis reveals that, due to the non-negligible probe state of polarization (SOP) deviation caused by the polarization pulling or pushing effect, the effectiveness of eliminating Brillouin gain fluctuation by using polarization switch is significantly degraded. Nevertheless, when probe Stokes and anti-Stokes components separately interact with orthogonal polarization pumps, the SOP evolution of the probe Stokes component due to the polarization pulling is totally identical to the SOP evolution of the probe anti-Stokes component caused by the polarization pushing. Based on this characteristic of the SOP evolutions, a novel HPPP method is proposed to eliminate the gain fluctuation. Experimental results demonstrate that the gain fluctuation falls to one-eighth of that of the conventional gain-only scheme by using this proposed HPPP method.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Brillouin optical time domain analysis (BOTDA) fiber sensor is highly attractive for multiple applications such as geotechnical engineering and structural health monitoring since it offers the ability to accurately measure temperature and strain along the fiber [1–4]. Based on the stimulated Brillouin scattering (SBS) process between a pulsed pump and a counter-propagating frequency-sweeping continuous-wave (CW) probe, Brillouin gain spectrum (BGS) can be detected and further utilized to extract Brillouin frequency shift (BFS) which exhibits a linear relationship with the temperature and strain. Unfortunately, with the increase of sensing distance, the power of the pulsed pump and CW probe are exponentially decayed due to inherent fiber loss, which degrades signal-to-noise ratio (SNR) and thus deteriorates measurement accuracy. Therefore, sometimes raising the power of the pump or the probe is quite necessary to achieve higher measurement certainty. However, the power increment has a certain limit due to the presence of various nonlinear effects and non-local effect [5–10]. Thus, many other methods are proposed to further enhance the SNR, such as distributed Raman or Brillouin amplification [11,12], balanced or coherent detection [13–15], one or two-dimensional signal processing [16–19] and optical pulse coding [20–30]. Particularly, owning to the capacity of boosting the SNR by a factor of $\sqrt L /2$ (L denotes coding length) and easily implementing by replacing the single pulse in the conventional BOTDA fiber sensor by the coding sequences, classical unipolar unicolor Simplex or Golay coding scheme have been intensively investigated and widely applied to achieve high-quality measurements [21–25,28,29]. For instance, the sensing distance is extended to 120 km by combining Simplex-coding method with linear gain optical preamplifier [23]; high spatial resolution coded BOTDA sensors can be realized by numerous methods, such as combining Simplex-coding with the differential pulse-width pairs (DPP) scheme, combining Golay-coding with phase shift pulse method and hybrid Golay-DPP coding scheme [24,25,28].
Although the results refined from the above references represent nice demonstrations, it is still quite challenging to obtain a high-performance unipolar unicolor coded BOTDA sensor. Recent study has pointed out that the performance of such sensor is severely limited by several detrimental effects [29]. Among them, non-ignorable polarization pulling caused by ultra-high accumulated Brillouin gain largely deteriorates the effectiveness of polarization switching method on eliminating Brillouin gain fluctuation and thus results in the SNR degradation of the sensor [29–37]. Meanwhile, polarization scrambling seems to be a more effective way to eliminate the gain fluctuation, but it may offer lower measuring stability [36].
In this paper, a new Brillouin gain fluctuation elimination scheme based on hybrid polarization pulling and pushing effect (HPPP) in Golay-coded BOTDA sensor is presented. The analysis points out that state of polarization (SOP) deviation of the probe wave caused by polarization pulling or pushing effect degrades the effectiveness of eliminating the gain fluctuation in Golay-coded BOTDA by using polarization switch (PSW). As a result, the conventional Brillouin gain- or loss-based Golay-coded BOTDA sensor is suffered from the gain fluctuation. On the other hand, when Stokes and anti-Stokes components of the probe wave separately interact with orthogonal polarization pumps, the SOP evolution of the probe Stokes component caused by the polarization pulling is totally identical to the SOP evolution of the anti-Stokes component caused by the polarization pushing. This means that although the SOPs of the probe Stokes and anti-Stokes components are deviated from the initial SOP, they always align to each other. Therefore, the gain fluctuation can be eliminated by employing the HPPP method which based on superposing the Brillouin gain in the Stokes component with the absolute value of Brillouin loss in anti-Stokes component. Experimental results demonstrate that this proposed HPPP scheme reduces the gain fluctuation by ∼8 times. Moreover, an about 0.5 MHz measurement certainty with a 2 m spatial resolution over 39.12 km sensing range is achieved by the HPPP Golay-coded BOTDA sensor.
2. Principle
The Brillouin interaction between the pump and the probe depends on the degree of parallelism of their SOPs, meanwhile, the weak birefringence property of the standard single-mode fiber leads the degree of parallelism to vary randomly along the fiber [3,31]. As a result, the Brillouin gain fluctuation appears [3,31]. For eliminating the gain fluctuation, the PSW is commonly adopted [3,13,15,27–29,31,32,35–37]. Specifically, the use of PSW requires to sequentially measure Brillouin gain traces twice with relatively orthogonal polarization pumps (x- and y-polarization). Then, a gain trace with the maximal total mixing efficiency (i.e., a Brillouin gain trace without fluctuation) can be obtained by superposing the two Brillouin gain traces. Here, an important condition for the effective gain fluctuation elimination is that the probe SOPs should remain unchanged during the two sequential measurements. However, due to non-negligible probe SOP deviation caused by the polarization pulling and pushing, this condition is unable to be satisfied in the Golay-coded BOTDA sensor, which further results in the gain fluctuation as described below.
As shown on the left in Fig. 1(a), in the SBS process, the x-polarization (X-pol) pump pulse-coded sequence not only amplifies the counter-propagating lower frequency probe Stokes component constantly, but also attracts the SOP of the probe Stokes component (blue solid lines with arrow in Fig. 1(a)) towards the SOP of the pump (red solid lines with arrow in Fig. 1(a)) consecutively. This SOP evolution of the probe Stokes component is given by Eq. 1 [33]:
Fig. 1. Schematic illustration of the Brillouin gain fluctuation caused by (a) polarization pulling and (b) polarization pushing effects; (c) Brillouin gain fluctuation elimination based on the HPPP method. D: detection, including photoelectric detection, analog-to-digital conversion and logarithmic normalization. P: processing, including superposing and Golay-decoding. Linear Ac. GB: linear accumulated Brillouin gain; GB: Brillouin gain.
The first term in the right indicates the probe SOP evolution resulting from fiber birefringence and $\vec{\beta }(z)$ describes the fiber birefringence in Stokes space. The second term in the right illustrates the polarization pulling force which draws the SOP of probe Stokes component towards the SOP of the X-pol pump. Pp is pump power and γ0 [W⋅m]-1 is the Brillouin gain per unit length per a unit of pump power. Ŝs-S(z) and Ŝp-X(z) are the normalized Stokes vectors which describe the SOPs of the probe Stokes component and the X-pol pump, respectively.
On the other hand, when the Stokes component of the probe interacts with a relatively orthogonal polarization pump (i.e., the y-polarization (Y-pol) pump), the SOP of the probe Stokes component (blue dotted lines with arrow in Fig. 1(a)) is drawn towards the SOP of the Y-pol pump (red dotted lines with arrow in Fig. 1(a)), as described in Eq. 2. For clarity, the normalized Stokes vector of the Y-pol pump Ŝp-Y is replaced by -Ŝp-X [31]. It can be found that, since the SOP evolutions (i.e., the Eq. 1 and 2) are totally different in the sequential measurements with orthogonal polarization pumps, the SOPs of the probe Stokes component are deviated from the initial SOP (i.e., the SOP without the effect of polarization pulling. black solid lines with arrow in Fig. 1(a)) in different ways and became misaligned. As a result, at the receiver side, after optically filtering, photoelectrical detection, analog-to-digital conversion and logarithmical normalization [29] of the probe Stokes components in the sequential measurements, the obtained linear accumulated Brillouin gain traces related to the orthogonal polarization pumps are no longer complementary due to the non-complementary mixing efficiencies [31], as shown in the middle of Fig. 1(a). The purple and red gain traces in the middle of Fig. 1(a) are obtained from the probe Stokes components marked by purple and red circles as shown on the left in Fig. 1(a). Accordingly, after the trace superposing and Golay-decoding process, the decoded Brillouin gain trace is suffered from the gain fluctuation due to the degraded total mixing efficiency [31], as illustrated on the right in Fig. 1(a). Therefore, the use of PSW is unable to effectively eliminate the gain fluctuation in the Brillouin gain based Golay-coded BOTDA (i.e., the Gain-only).
Similarly, another sort of SOP evolution also happens in the higher-frequency probe anti-Stokes component. Instead of being drawn towards the SOP of the pump, such a SOP evolution is now dominated by a means of polarization pushing [33–35,37] which can be expressed as:
It seems that the gain fluctuation is unable to be eliminated by using the common PSW in the Golay-coded BOTDA. However, from Eq. 1 and 4 (or equivalently, in Eq. 2 and 3), we can find an interesting relationship between the pulling and pushing effect: when the Stokes and anti-Stokes components of the probe separately interact with orthogonal polarization pumps, the SOP evolution of the probe Stokes component caused by the polarization pulling is totally identical with the SOP evolution of the anti-Stokes component caused by the polarization pushing. It means that although the probe Stokes and anti-Stokes components have deviated from the initial SOP, they always align to each other when they separately interact with the orthogonal polarization pumps, as illustrated on the left in Fig. 1(c). As a result, the linear accumulated Brillouin gain traces obtained from the probe Stokes and anti-Stokes components are complementary due to the complementary mixing efficiencies [31], as shown in the middle of Fig. 1(c). Therefore, the Brillouin gain fluctuation can be eliminated by superposing the Brillouin gain in the probe Stokes component with the absolute value of Brillouin loss in the probe anti-Stokes component (i.e. using the HPPP), as shown on the right side in Fig. 1(c). It should be note that, before the trace superposing and Golay-decoding in the Fig. 1, the linear accumulated Brillouin gain traces related to the probe Stokes and anti-Stokes components must be extracted by employing the logarithmic normalization [29], which is one of the keys to effectively eliminate the gain fluctuation by using the HPPP scheme. In addition, the power of the probe should be properly adjusted to avoid high-order non-local effect [29] and coded trace distortion [23] which potentially degrade the efficiency of the HPPP on the gain fluctuation elimination at the end of the fiber.
3. Experimental setup
Figure 2 depicts a Golay-coded BOTDA setup which is deployed to experimentally demonstrate the effectiveness of this proposed HPPP method on the gain fluctuation elimination. A CW light with a linewidth of 100 kHz is emitted by an external cavity laser (ECL) and then split into two branches by a 50:50 coupler. In the lower branch, the CW light is firstly amplified by a high-power erbium-ytterbium co-doped fiber amplifier (EYDFA) and then gated to an acousto-optic modulator (AOM) to generate Golay-coded pump pulse sequence. The AOM is driven by an arbitrary function generator (AFG) which is used to generate Golay-code with a length of 256-bits. Effective pulse width of each bit and duty cycle of the Golay-code are 20 ns and 10%, respectively. The AOM has over 60 dB extinction ratio and 30 dBm average optical power handling, which makes the Golay-coded BOTDA sensor have higher SNR and potentially higher Brillouin gain. The PSW is used to eliminate the gain fluctuation. In the upper branch, a carrier-suppressed double sideband probe wave is generated by an electro-optical modulator which is operated at null transmission point and driven by a microwave generator. Due to 200 MHz frequency upshift introduced by the AOM, sweeping frequencies of this microwave generator include two ranges: 1). 10.584 GHz to 10.784 GHz for Brillouin gain and 2). 10.984 GHz to 11.184 GHz for Brillouin loss. And the sweeping step is 4-MHz. Then, the probe light with a fixed power -18.5 dBm is injected into a 39.12 km fiber under test (FUT) with the BFS around 10.88 GHz at room temperature. After that, the probe wave is sent to the receiver side by a circulator.
Fig. 2. Experimental setup of the proposed scheme. ECL: external cavity laser; EYDFA: erbium-ytterbium co-doped fiber amplifier; AFG: arbitrary function generator; AOM: acousto-optic modulator; PSW: polarization switch; FUT: fiber under test; PC: polarization controller; EOM: electro-optical modulator; MG: microwave generator; EDFA: erbium-doped fiber amplifier; WDM: wavelength division multiplexing demultiplexer; OSW: optical switch; PD: photodiode; OSC: oscilloscope; Ac. GB: accumulated Brillouin gain; Ac. LB: accumulated Brillouin loss.
At the receiver side, the probe wave is firstly pre-amplified by an erbium-doped fiber amplifiers (EDFA). Then, the probe Stokes and anti-Stokes components are separated by a wavelength division multiplexing demultiplexer and further sent to an optical switch (OSW). For implementing our proposed HPPP method, the probe Stokes and anti-Stokes components are separately and sequentially outputted by the OSW. Finally, the OSW output signal is detected by a photodiode (PD) with a bandwidth of 350-MHz. The electrical signal is then analog-to-digitally converted by an oscilloscope (OSC) with a sampling rate of 100 MSa/s.
4. Experimental results
Figure 3(a) illustrates the decoded Brillouin gain traces around the BFS with a peak Brillouin gain ∼1.5% when different schemes (i.e. conventional Gain-only, loss-only and HPPP) are employed. The decoded Brillouin gain trace is averaged 1024 times. It can be seen that, due to the polarization pulling or pushing effect, strong Brillouin gain fluctuation appears in the conventional Gain-only or Loss-only scheme. Meanwhile, it can be observed from the detail shown in Fig. 3(a1) and 3(a2) that the Brillouin gain variations of the two schemes along the sensing fiber are complementary, which indicates that the mixing efficiency factors are complementary in the two schemes. This result matches well with the theorical analysis in the principle section and demonstrates that the probe SOP evolutions caused by the polarization pulling and pushing are indeed the same and the probe Stokes and anti-Stokes components are strictly aligned. Therefore, as illustrated in the Fig. 3(a), this proposed HPPP method eliminates the gain fluctuation effectively. In order to observe the evolution of the gain fluctuation more clearly, standard deviation (STD) values of the Brillouin gain along the fiber are calculated by using a moving window with a length of 800 and shown in Fig. 3(b). It can be found that maximal Brillouin gain fluctuation is reduced from ∼0.31% to ∼0.04%.
Fig. 3. Comparisons of (a) the decode Brillouin gain around the BFS and (b) evolution of Brillouin gain fluctuation along the sensing range when different schemes are used. The details of the decode Brillouin gain from (a1) 5.05 km to 5.25 km and (a2) 19.9 km to 20.1 km.
Moreover, to further verify the gain fluctuation elimination, the peak Brillouin gain distribution of the BGS distribution is estimated. Figure 4(a) illustrates the measured BGS distribution when this proposed HPPP method is used. The estimated peak Brillouin gain distribution along the fiber is shown in Fig. 4(b). It can be seen that, in cases of the Gain-only and Loss-only, the peak gains randomly vary along the fiber. Additionally, when this proposed HPPP method is employed, the gain fluctuation significantly decreases. The results agree with the analysis in the principle section and the result in Fig. 3, which demonstrates that this proposed HPPP method can effectively eliminate the gain fluctuation.
Fig. 4. (a) Measured BGS distribution and (b) estimated peak Brillouin gain distribution along the fiber.
As demonstrated above, the HPPP method is effective in achieving the elimination of the gain fluctuation. Subsequently, we investigate the measurement certainty of the Golay-coded BOTDA incorporating the HPPP. The BGS distributions along the fiber are consecutively measured for 10 times. Then, Lorentz curve fitting is performed to estimate the BFS distributions corresponding to the 10 BGS distributions. Figure 5(a) illustrates one of the estimated BFS distributions. By calculating the STD value of the 10 BFSs at each location, the measurement uncertainty along the fiber is shown in Fig. 5(b). It can be seen that the measurement uncertainty is ∼0.5-MHz. In addition, from Fig. 5(b), the STD values increase with the increasing distance, it can be deduced that this is induced by the SNR reduction due to fiber attenuation.
Fig. 5. (a) The BFS distribution and (b) measurement certainty along the whole sensing range when the HPPP method is employed.
Finally, to verify the spatial resolution of this HPPP-based Golay-coded BOTDA system, a 12 m fiber section at the far end of the fiber is heated, while the rest of the fiber is kept at room temperature. The temperature variation at the hotspot is 25°C. By subtracting the BFSs before and after heating, the relative BFS distribution at the far end of the fiber is shown in Fig. 6. A ∼27.5 MHz BFS difference at the hotspot can be clearly observed. The spatial resolution is estimated from the 10% to 90% response to the temperature variation and found to be 2 m.
Fig. 6. Detection of a 12 m hotspot at the end of the fiber when the HPPP method is used. The BFS difference induced by 25°C temperature variation and the spatial resolution are ∼27.5 MHz and 2 m, respectively.
5. Conclusion
In summary, we have proposed a novel HPPP method to eliminate the Brillouin gain fluctuation caused by polarization pulling and pushing effects in Golay-coded BOTDA. This method relies on that, when the Stokes and anti-Stokes components of the probe separately interact with orthogonal polarization pumps, the SOP evolutions induced by the polarization pulling and pushing effects are identical. Thus, the Brillouin gain fluctuation elimination can be achieved by employing the HPPP which superposes the Brillouin gain with the absolute value of Brillouin loss. Experimental results are identical to the theorical analysis, which indicates that this proposed scheme can effectively eliminate the gain fluctuation caused by the polarization pulling and pushing effects. Compared with our previous polarization division multiplexing pulse coding method [36], the HPPP is a passive method to eliminate the gain fluctuation, and its implement is potentially easier and more flexible. In addition, although the Golay coding is employed in the theorical analysis and experimental demonstration, the HPPP method is universal and can be applied to all kinds of unipolar unicolor coding schemes which suffered from the gain fluctuation due to the polarization pulling and pushing effects, such as Simplex coding scheme [29].
Funding
National Natural Science Foundation of China (61735015).
References
1. T. Horiguchi and M. Tateda, “BOTDA-nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989). [CrossRef]
2. M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013). [CrossRef]
3. A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 81–103 (2016). [CrossRef]
4. H. Zhang, D. Zhou, B. Wang, C. Pang, P. Xu, T. Jiang, D. Ba, H. Li, and Y. Dong, “Recent progress in fast distributed Brillouin optical fiber sensing,” Appl. Sci. 8(10), 1820 (2018). [CrossRef]
5. S. M. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE 7753, 77539V (2011). [CrossRef]
6. M. Alem, M. A. Soto, and L. Thévenaz, “Analytical model and experimental verification of the critical power for modulation instability in optical fibers,” Opt. Express 23(23), 29514–29532 (2015). [CrossRef]
7. A. Minardo, R. Bernini, and L. Zeni, “A simple technique for reducing pump depletion in long-range distributed Brillouin fiber sensors,” IEEE Sens. J. 9(6), 633–634 (2009). [CrossRef]
8. L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013). [CrossRef]
9. A. Domínguez-López, X. Angulo-Vinuesa, A. López-Gil, S. Martín-López, and M. González-Herráez, “Nonlocal effects in dual-probe-sideband Brillouin optical time domain analysis,” Opt. Express 23(8), 10341–10352 (2015). [CrossRef]
10. A. Domínguez-López, Z. Yang, M. A. Soto, X. Angulo-Vinuesa, S. Martín-López, L. Thévenaz, and M. González-Herráez, “Novel scanning method for distortion-free BOTDA measurements,” Opt. Express 24(10), 10188–10204 (2016). [CrossRef]
11. M. A. Soto, G. Bolognini, and F. D. Pasquale, “Optimization of long range BOTDA sensors with high resolution using first-order bidirectional Raman amplification,” Opt. Express 19(5), 4444–4457 (2011). [CrossRef]
12. J. Urricelqui, M. Sagues, and A. Loayssa, “Brillouin optical time-domain analysis sensor assisted by Brillouin distributed amplification of pump pulses,” Opt. Express 23(23), 30448–30458 (2015). [CrossRef]
13. A. Domínguez-López, A. López-Gil, S. Martín-López, and M. González-Herráez, “Signal-to-noise ratio improvement in BOTDA using balanced detection,” IEEE Photonics Technol. Lett. 26(4), 338–341 (2014). [CrossRef]
14. Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, H. He, and Y. Zhang, “Precise Brillouin gain and phase spectra measurements in coherent BOTDA sensor with phase fluctuation cancellation,” Opt. Express 24(5), 4824–4833 (2016). [CrossRef]
15. N. Guo, L. Wang, H. Wu, C. Jin, H. Y. Tam, and C. Lu, “Enhanced coherent BOTDA system without trace averaging,” J. Lightwave Technol. 36(4), 871–878 (2018). [CrossRef]
16. M. Farahani, M. Wylie, E. Castillo-Guerra, and B. Colpitts, “Reduction in the number of averages required in BOTDA sensors using wavelet denoising techniques,” J. Lightwave Technol. 30(8), 1134–1142 (2012). [CrossRef]
17. M. A. Soto, J. A. Ramírez, and L. Thévenaz, “Intensifying the response of distributed optical fiber sensors using 2D and 3D image restoration,” Nat. Commun. 7(1), 10870 (2016). [CrossRef]
18. M. A. Soto, J. A. Ramırez, and L. Thévenaz, “Optimizing image denoising for long-range Brillouin distributed fiber sensing,” J. Lightwave Technol. 36(4), 1168–1177 (2018). [CrossRef]
19. S. Zaslawski, Z. Yang, M. A. Soto, and L. Thévenaz, “Impact of Fitting and Digital Filtering on Signal-to-Noise Ratio and Brillouin Frequency Shift Uncertainty of BOTDA Measurements,” in 26th International Conference on Optical Fiber Sensors, OSA Technical Digest (Optical Society of America, 2018), paper ThE27.
20. M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long-range complementary correlation optical time-domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989). [CrossRef]
21. M. A. Soto, G. Bolognini, and F. Di Pasquale, “Analysis of pulse modulation format in coded BOTDA sensors,” Opt. Express 18(14), 14878–14892 (2010). [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, G. Bolognini, and F. Di Pasquale, “Long-range simplex-coded BOTDA sensor over 120 km distance employing optical preamplification,” Opt. Lett. 36(2), 232–234 (2011). [CrossRef]
24. M. A. Soto, M. Taki, G. Bolognini, and F. Di Pasquale, “Optimization of a DPP-BOTDA sensor with 25 cm spatial resolution over 60 km standard single-mode fiber using Simplex codes and optical pre-amplification,” Opt. Express 20(7), 6860–6869 (2012). [CrossRef]
25. M. S. D. B. Zan and T. Horiguchi, “A dual Golay complementary pair of sequences for improving the performance of phase-shift pulse BOTDA fiber sensor,” J. Lightwave Technol. 30(21), 3338–3356 (2012). [CrossRef]
26. 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]
27. S. L. Floch, F. Sauser, M. Llera, and E. Rochat, “Novel Brillouin optical time-domain analyzer for extreme sensing range using high-power flat frequency-coded pump pulses,” J. Lightwave Technol. 33(12), 2623–2627 (2015). [CrossRef]
28. Z. Li, Z. Yang, L. Yan, M. A. Soto, and L. Thévenaz, “Hybrid Golay-coded Brillouin optical time-domain analysis based on differential pulses,” Opt. Lett. 43(19), 4574–4577 (2018). [CrossRef]
29. Z. Yang, Z. Li, S. Zaslawski, L. Thévenaz, and M. A. Soto, “Design rules for optimizing unipolar coded Brillouin optical time-domain analyzers,” Opt. Express 26(13), 16505–16523 (2018). [CrossRef]
30. R. Liao, M. Tang, C. Zhao, H. Wu, S. Fu, D. Liu, and P. P. Shum, “Harnessing oversampling in correlation-coded OTDR,” Opt. Express 27(2), 1693–1705 (2019). [CrossRef]
31. M. O. Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994). [CrossRef]
32. K. Hotate, K. Abe, and K. Y. Song, “Suppression of signal fluctuation in Brillouin optical correlation domain analysis system using polarization diversity scheme,” IEEE Photonics Technol. Lett. 18(24), 2653–2655 (2006). [CrossRef]
33. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef]
34. Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19(27), 25873–25880 (2011). [CrossRef]
35. M. A. Soto, M. Tur, A. Lopez-Gil, M. Gonzalez-Herraez, and L. Thévenaz, “Polarization pulling in Brillouin optical time-domain analyzers,” Proc. SPIE 10323, 103239L (2017). [CrossRef]
36. Y. Zhou, L. S. Yan, Z. Li, W. Pan, and B. Luo, “Polarization division multiplexing pulse coding for eliminating the effect of polarization pulling in Golay-coded BOTDA fiber sensor,” Opt. Express 26(15), 19686–19693 (2018). [CrossRef]
37. Y. Zhou, L. S. Yan, Z. Li, X. P. Zhang, W. Pan, and B. Luo, “Hybrid polarization pulling and pushing effects for eliminating Brillouin gain fluctuation in Golay-coded BOTDA sensor,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2019), paper M2J.3.
