## Abstract

A new technology for Brillouin optical correlation domain analysis (BOCDA) based on chaotic laser is proposed, analyzed and demonstrated. The numerical simulation shows that the stimulated acoustic field has the secondary spurious peaks, which are the result of a weak amplitude autocorrelation of the chaotic signal occurring at the delay time of the external cavity, i.e., time delay signature (TDS). These secondary spurious peaks deteriorate the Brillouin gain spectrum and decrease the performance of the chaotic BOCDA system. The effect of the injection current and feedback strength on the TDS suppression is theoretically analyzed. By optimizing the two free parameters, chaotic laser sources operate in a TDS suppression region. Ultimately, a 3.2 km long single-mode fiber with a spatial resolution of 7.4 cm is experimentally demonstrated. The uncertainty of the local Brillouin frequency shift is ± 1.2 MHz.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The distributed sensing technology has been extensively applied in the field of civil engineering, environmental monitoring, the aerospace industry and smart grids. Distributed fiber sensing based on Brillouin scattering has attracted a great interest owing to its unique capabilities to perform long-range distributed strain and temperature measurement.

Brillouin scattering-based fiber sensing can be mainly classified into two types: time domain systems and correlation domain systems. The time domain systems including Brillouin optical time domain reflectometry (BOTDR) [1] and analysis (BOTDA) [2, 3] have obvious advantages in the measurement range, where the pulse signal is commonly used to perceive the temperature/strain along the fiber. The ultra-long measurement range of the time domain system has been extended to above 120 km based on optical pulse coding [4], distributed amplification [5, 6] or a combination of both [7]. However, because of the inherent limitation of the phonon lifetime, the best spatial resolution is typically 1 m [8]. Numerous techniques, such as differential pulse-width pair BOTDA [9–11], dark pulse [12] and Brillouin echoes [13], have been proposed to improve the spatial resolution at the cost of the sensing distance.

The key advantage of the correlation domain systems inclusive of Brillouin optical correlation domain reflectometry (BOCDR) [14] and analysis (BOCDA) [15] is high spatial resolution, where the continuous lightwave with the sinusoidal frequency modulation is usually utilized as the sensing signal. However, the above correlation domain systems suffer from a trade-off between the measurement range and the spatial resolution [16]. To overcome the trade-off problem, the continuous lightwaves phase-modulated by a binary pseudorandom bit sequence (PRBS) [17, 18] or Golomb codes [19, 20] are employed as the sensing signals in the correlation domain system. The further scaling of the spatial resolution would require higher modulation rates, which can give rise to the high cost of the whole system. Moreover, external electro-optic modulators towards 100 GHz are seldom available. Recently, the BOCDA system based on the direct output amplified spontaneous emission (ASE) having the low coherence has been demonstrated with the improved spatial resolution [21]. The chaotic laser is another type of light with a reduced level of coherence, which has been successfully applied in the BOCDR [22] and BOCDA [23] systems. However, there are residual side peaks near the main peak of the autocorrelation trace, which are resulted by a weak amplitude autocorrelation of the chaotic signal occurring at the delay time of the external cavity [24, 25]. The residual peaks in the autocorrelation trace are referred to as the time delay signature (TDS) [26]. The TDS-induced off-peak stimulated Brillouin scattering (SBS) amplification contributes an additional noise mechanism, which can largely limit the performance of the chaotic correlation domain system.

In this paper, by controlling the injection current and feedback strength of the external cavity semiconductor laser, chaotic light sources operate in a suppression region of the TDS. Chaotic outputs serving as the sensing signals of the BOCDA system are then utilized to perceive the temperature along the sensing fiber. The improved performance of the chaotic BOCDA system is achieved with a sensing distance of 3.2 km and a spatial resolution of 7.4 cm.

## 2. Principle

In the chaotic BOCDA system, the generation of chaotic light serving as the pump and probe waves can be theoretically described by the following Lang-Kobayashi rate equations [27]:

*E* and *N* are the slowly varying complex electrical field amplitude and the carrier density in the semiconductor laser cavity, respectively. *α, G, N*_{0}, *τ _{p}, τ_{n}, V, q* are the linewidth enhancement factor, the differential gain coefficient, the carrier density at transparency, the photon lifetime, the carrier lifetime, the active region volume and the charge quantity, respectively.

*I*is the pump current density of the semiconductor laser.

*ω*is the output angular frequency of the semiconductor laser and

*τ*is the external cavity round-trip time.

And the feedback rate *k* of the optical feedback semiconductor laser is defined as follows:

*r*

_{0}and

*r*represent amplitude reflectivity of the laser exit facet and the external reflection mirror respectively.

*τ*

_{in}is the round-trip time of light in laser cavity. All the involved laser parameters and their values used in our numerical model are from [28].

Afterwards, the chaotic pump and probe waves are injected into a sensing fiber from both ends, respectively. The interference of two chaotic pump and probe waves results in a traveling acoustic wave through the mechanism of electrostriction. Because of the photo-elastic effect, the acoustic wave is associated with refractive index variations, which is known as the chaotic Brillouin dynamic grating [24, 25]. The amplitude of the corresponding acoustic wave is proportional to the temporal cross correlation between the complex envelopes of the chaotic pump and probe waves given as [21]:

*A*(

*t*) is the complex envelope of the chaotic pump/probe wave,

*v*is the group velocity of light in the fiber, and

_{g}*τ*is the acoustic wave lifetime. The position-dependent temporal offset

_{B}*θ*(

*z*) is defined as

*θ*(

*z*) = (2

*z*-

*L*)/

*v*, where

_{g}*L*is the fiber length.

The expectation value of the acoustic field magnitude at position *z* (for *t* » *τ _{B}*) is

*C*(

*θ*(

*z*)) is the cross correlation function between chaotic pump and probe waves. In particular, when

*θ*(

*z*) = 0,

*C*(

*θ*(

*z*)) is taken as the autocorrelation function (ACF) of the chaotic pump/probe wave. The acoustic wave would be confined within the correlation peak width, which is theoretically determined by the coherence length of the chaotic light source.

Figure 1 illustrates the distribution of the acoustic wave field *Q*(*z*, *t*). The three-dimensional and two-dimensional projection distributions of the acoustic wave field *Q*(*z*, *t*) as a function of the time and space are further shown in Fig. 1(a) and 1(b), respectively. Taking the duration of calculation into consideration, the length of the simulated fiber is chosen as 30 m, which has already provided useful insight to the generated acoustic wave field. At the center (*z* = *L*/2) of the sensing fiber, the acoustic wave is steadily and permanently generated in the correlation peak of approximate 1 cm width, which is the theoretical spatial resolution of the chaotic BOCDA system. Besides, we can see that around the main correlation peak, the secondary spurious peaks are distributed symmetrically on both sides. The distance between the secondary spurious and main correlation peaks is exactly equal to the external feedback delay of *τ* = 115 ns. The secondary spurious peaks result from the autocorrelation of a weak amplitude periodic signal contained in the chaotic light. Actually, the periodic signal is induced by the optical round trip in the external cavity feedback. The SBS amplification in the secondary spurious peaks contributes an additional noise mechanism. Therefore, to improve the performance of the chaotic BOCDA system, the suppression of the secondary spurious peaks should be considered.

In fact, the suppression of the secondary spurious peaks is to reduce the TDS of chaotic laser signals. As we know, the external cavity semiconductor generates the chaotic light by controlling the free parameters, such as the injection current and feedback strength. Therefore, the TDS of chaotic laser signals is suppressed by optimizing these two free parameters. The analytic model that covers the effect of the free parameters on the TDS suppression is established by utilizing the Eq. (1) - (3) and Eq. (6). The *C*(*θ*(*z*)) in Eq. (6) is used as the ACF by taking *θ*(*z*) = 0, since the TDS is caused not by the correlation function itself but by the delay time of the external cavity. Figure 2 illustrates the map of the TDS distribution of the output chaos from the external cavity semiconductor, where *I / I*_{th} and *k* vary from 1 to 1.6 and from 4 to 24 GHz, respectively. Two typical scenarios for the external feedback delays of *τ* = 1.2 ns and *τ* = 115 ns are selected, and the distributions of the correlation coefficients (*C*) at these two feedback delays are shown in Fig. 2(a) and 2(b) respectively. One of both delays is in the vicinity of the laser relaxation oscillation period (approximate 0.25 ns) and the other is much larger than this period. For the short feedback delay, the TDS can be effectively suppressed or even completely eliminated under the moderate feedback rate, when the injection current is set such that the relaxation oscillation period approaches this delay [26]. With respect to the long feedback delay, the TDS suppression region with *C*<0.2 has a large proportion of the whole area. Especially, the optimal region (0<*C*<0.1) with the feedback rate from 12 to 16 GHz and the injection current from 1.35 *I*_{th} to 1.6 *I*_{th} is theoretically obtained to suppress the TDS. This indicates that the higher the injection current, the easier the TDS is suppressed under the appropriate feedback rate. Therefore, the analytic model may provide a theoretical guidance for the optimal choice of the two free parameters in experiment.

## 3. Experimental setup

The experimental setup of the chaotic BOCDA system is illustrated in Fig. 3. The dashed box in Fig. 3 shows the chaotic laser source consisting of the distributed-feedback laser diode (DFB-LD) without light isolators and a fiber feedback loop. The threshold current and center wavelength of the DFB-LD are 22 mA and 1550 nm, respectively. The fiber feedback loop is composed of an optical circulator (OC1), a 3 dB optical coupler (50: 50), a variable attenuator (VA), and a polarization controller (PC1). By adjusting the polarization state and feedback strength of the external feedback light, and the injection current, the DBF-LD can generate the chaotic light. And the output chaotic light is split into Brillouin pump and probe signal branches with the same center frequency of *ν*_{0} by a 20:80 fiber coupler. The upper as the probe wave (80%) is modulated in a suppress-carrier, double-sideband format by the electro-optic amplitude modulator (EOM), which is driven by a microwave signal generator. The modulation frequency is in the vicinity of the Brillouin shift *ν _{B}* of fiber under test (FUT). The probe wave through a programmable optical delay generator (PODG), a polarization scrambler (PS) and an isolator (ISO2) is launched into a FUT. The PODG and EDFA1 are utilized to control the position of the correlation peak and boost up the probe wave to 7 dBm, respectively. The PS is inserted for suppressing the polarization dependence of the SBS interaction. And the lower as the pump wave (20%) through a polarization controller (PC3) and an erbium-doped optical fiber amplifier (EDFA2) is injected into the opposite end of the FUT. The EDFA2 is employed to boost up the pump power to 27 dBm. After undergoing the SBS amplification by the chaotic pump wave along the FUT, the chaotic probe wave is filtered by the optical band-pass filter via the optical fiber circulator (OC2). The optical power of the filtered Stokes wave is recorded by a digital optical power meter (OPM) with an integrating sphere sensor. The structure of the FUT is made up of a 3.2 km single-mode fiber (G.655), in which a 60 m fiber near 3 km is placed in a fiber thermostat.

DFB-LD, distributed-feedback laser diode; OC1, OC2, optical circulator; PC1, PC2, PC3, polarization controller; VA, variable attenuator; ISO1, ISO2, isolator; EDFA1, EDFA2, erbium-doped optical fiber amplifier; EOM, electro-optic modulator; RF, radio frequency; PODG, programmable optical delay generator; PS, polarization scrambler; FUT, fiber under test; OPM, optical power meter.

## 4. Experimental results

Firstly, we experimentally analyze the effect of the injection current and feedback strength on the TDS suppression of the chaotic semiconductor laser. The feedback strength is scaled with the feedback ratio *k* mentioned before and defined as the ratio of the power of the feedback light to the output of the laser. The chosen external cavity length is approximately 11.5 m and the corresponding external feedback delay *τ* is 115 ns. Figure 4 shows the distribution map of the correlation coefficient (*C*) at *τ =* 115 ns for the direct output chaotic light in the operation parameter space of the injection current and feedback strength. We can see that the evolution of the TDS could be roughly divided into three regions, i.e., 0.1<*C*<0.2, 0.2<*C*<0.3 and 0.3<*C*<0.5. Especially, the TDS suppression region with 0.1<*C*<0.2 accounts for a large proportion of the whole area, as shown in Fig. 2(b). Moreover, we experimentally find that the higher the injection current, the easier the TDS suppression, which is in accordance with the previous theoretical analysis. Therefore, the TDS can be effectively suppressed by optimizing the two parameters of the injection current and feedback strength.

Then we compare the output characteristics of chaotic laser source under the different operating points of the above parameter space. Here, three representative operating points, i.e., O (34, 0.112), P (29, 0.139) and Q (24, 0.156) are arbitrarily chosen from three TDS distribution regions shown in Fig. 4, respectively. The output chaotic characteristics corresponding to the operating points of O, P and Q are shown in Fig. 5(a)-5(c), respectively. From the optical spectra, electrical power spectra and time series of chaotic laser signals, we can visually see that there are no obvious differences for these three cases. However, the corresponding Lyapunov exponents, which are used to quantitatively measure asymptotic expansion and contraction rates in a dynamical system [29], are 0.0819, 0.0511 and 0.0123, respectively. This means that the outputs from the chaotic laser source have different chaotic states under the different operating points. Figure 5(a4)-5(c4) further display the ACF curves of the chaotic laser signals. As shown in Fig. 4(c4), the ACF trace under the operating point Q has nine side peaks separately at *τ*, 2*τ*,…9*τ* with gradually reduced height. The SBS amplification in these correlation peaks contributes an additional noise mechanism. In comparison, the ACF trace under the operating point O has half of the shortened peaks. This indicates that the performance of the chaotic BOCDA system will be improved by selecting an appropriate operating point.

The outputs from the chaotic laser source under the above three operation points O, P and Q, are served as the pump and probe waves respectively. They are then injected into the FUT, with the chaotic pump entering in one end and the probe light entering in the other end. When the chaotic pump and probe waves meet at some location of the FUT, the chaotic probe wave is subject to SBS amplification. The Brillouin gain spectrum (BGS) is achieved by recording the average power of the filtered chaotic Stokes probe versus the modulation frequency. The Brillouin gain spectra obtained by averaging 20 repeating measurements are shown in Fig. 6. Figure 6(a)-6(c) correspond to the operation points O, P and Q, respectively. The blue line represents the correlation peak located at 1.6 km of the FUT with the ambient temperature of 25 °C. The red line represents the correlation peak located in hot spot section (i.e., at the middle of the 60-m heated fiber) with the temperature of 55 °C. We can see that the better suppression of the chaotic TDS, the lower background of the obtained BGS. Based on the BGS, the signal-to-background ratio (SBR) defined as the amplitude ratio of the signal peak to the background peak [30] is experimentally measured to quantitatively evaluate the equality of the extracted BGS. With the optimization of the chaotic state, i.e., the chaotic TDS suppression, the SBR is increased from 1.12 dB to 2.44 dB when the temperature is 25 °C. Similarly, for the temperature of 55 °C, the BGS under the operation point O significantly improves compared with that under the operation point Q. At the same time, we find that as to the operation point Q, the BGS with the correlation peak in the heated section is clearly worse than the one with the correlation peak outside the heated section. This is because there are some TDS-induced side-lobes (1~3*τ*) in the heated fiber and other side-lobes (>3*τ*) outside this fiber, when the correlation peak is located at the middle of the 60-m heated fiber. The side-lobes are located in the fiber sections of different temperature, which gives rise to the inhomogeneous off-peak amplifications. This eventually leads to the deterioration of the BGS. However, with regard to the operation point O, all side-lobes are in the heated fiber due to the TDS suppression, when the correlation peak is located in the heated section. Therefore, the Brillouin gain spectra are almost same regardless of the correlation peak in or outside the heated section, which ensures that the chaotic BOCDA system is able to perceive a change in temperature. Thus, it is vital to select the appropriate chaotic state with the TDS suppression to improve the BGS of the chaotic BOCDA system.

Next, the output from the chaotic laser source under the operation point O is used to perceive the temperature of the FUT. Figure 7(a) shows a three-dimensional plot of the BGS measured along the FUT, where the linewidth of the BGS is stabilized at 45 MHz. Obviously, the Brillouin frequency shift (BFS) at the hot spot section is clearly distinguished. In the experiment, the temperature of the fiber thermostat is set to 55°C and the room temperature is maintained constant at 25 °C. And there is about 37 MHz BFS at the hot spot section. This value of the BFS matches well with the real temperature of 30 °C. Figure 7(b) plots the measured distribution of the BFS along the FUT. And the spatial resolution of the chaotic BOCDA system can be measured by the average value of 10% ~90% of the rise and fall time equivalent length in meter for the hot spot section [31], where the rise and fall time equivalent length are 6.2 cm and 8.5 cm, respectively. Therefore, the spatial resolution can reach approximate 7.4 cm along the 3.2 km FUT when a 60-m long section is heated. The experimentally obtained spatial resolution is nearly consistent with the above theoretically expected one. In fact, the approximate 100 resolution points are addressed in practice, although about 45,000 potential resolution points can be achieved. In Fig. 7(a), we can see that in the meters 2700, 2900 and 3200 there is Brilouin gain along a big interval of frequencies due to the fiber inhomogeneity.

Besides, in our measurement on the temperature-dependence of BGS and BFS (as shown in Fig. 5 of [23]), the temperature of the fiber thermostat is changed from 25 to 55 °C in succession. Several representative temperature points like 25, 29, 34, 39, 45, 50 and 55 °C are selected. At each temperature point, the BGS is obtained by averaging 20 repeating measurements. Supposed that the center frequency of each measured BGS, i.e., the BFS, is denoted as *f _{i}* (

*i*= 1, 2, …, 20). The standard deviation

*δ*of the BFS is calculated according to the equation below:

_{f}*n*= 20 is the times of the measurement. Among these representative temperature points, the maximum standard deviation of the BFSs is taken as the measurement uncertainty of the BFS. Therefore, the largest value of uncertainty of the local BFS is ± 1.2 MHz with the temperature coefficient of 1.24 MHz/°C [23].

## 5. Discussions

As in all BOCDA setups, the Brillouin interaction is spatially confined to the correlation length of the source. High spatial resolution therefore mandates the use of sources with comparatively low coherence. Multiple methods for controlling the coherence of sources in BOCDA were proposed, such as frequency modulation by sine waves, phase or direct modulation by PRBSs, and the filtered ASE sources. The sine-based BOCDA suffers from a trade-off between the measurement range and the spatial resolution. To resolve this problem, more elaborate sine-based schemes are proposed and however considerably increase the system complexity. For the PRBS-based BOCDA, the external phase modulation causes the high cost of the whole system and the direct current modulation leads to a deteriorated spatial resolution due to the bandwidth limitation of the direct modulation. In our scheme, a new kind of chaotic laser source is employed in BOCDA, which can resolve the difficulties of the above sine-based and PRBS-based BOCDA.

The chaotic BOCDA system has similar sensing mechanism with the ASE-based BOCDA system due to the noise-like characteristic of the chaotic laser. However, compared with the ASE, the chaotic laser has higher spectral density and in the same bandwidth has higher output power, which gives rise to the longer sensing distance of the chaotic BOCDA system. In addition, the coherence length of the chaotic laser is adjustable by controlling the feedback strength [32]. This causes that the submillimeter spatial resolution is easier achieved in the chaotic BOCDA system. Moreover, with the TDS suppression, the other residual side-lopes of the chaotic autocorrelation trace like the “coding noise” of PRBS, will take effect in the off-peak amplification. To overcome this problem, the temporal gating technique will be employed in the future work based on a recently reported phase-measuring time-gated BOCDA [33]. Thus, the further extended sensing distance equal to or even larger than the one of the phase-measuring time-gated BOCDA system, will be obtained in the chaotic BOCDA system with no loss of the spatial resolution.

At present, it is necessary in the BOCDA system to acquire one correlation peak for each monitored fiber point, regardless of ASE-based BOCDA, PRBS-based BOCDA or chaotic BOCDA. This leads to the comparatively long measurement time of the BOCDA system. As far as our scheme is concerned, the total time taken to measure each resolution point is approximate 20 minutes including averaging. To largely decrease the measurement time for each resolution point, the data acquisition card based on the field programmable gate-array (FPGA) and the Microsoft Foundation Class (MFC) programming will be employed to measure the BGS in the next study. Besides, to avoid the inconvenience of the variable optical delay line in utilization, chaotic correlation optical time domain reflectometry technology will be further explored to address the resolution points along the FUT [23].

## 6. Conclusions

In conclusion, Brillouin optical correlation domain analysis system based on chaotic laser is proposed and demonstrated for distributed fiber sensing. The utilization of the chaotic laser with the low coherence ensures the high spatial resolution. The location of a correlation peak is scanned by a variable optical delay line to map the temperature along the FUT. The stimulated acoustic field induced by the interference of two chaotic pump and probe waves is numerically generated and theoretically analyzed. The generated acoustic field has the secondary spurious peaks, which deteriorate the Brillouin gain spectrum and decrease the performance of the chaotic BOCDA system. By selecting appropriate injection current and feedback strength, the chaotic laser source can operate in a TDS suppression region. Under this condition, the optimized chaotic BOCDA system is achieved with a 3.2 km long sensing distance and a spatial resolution of 7.4 cm.

## Funding

National Natural Science Foundation of China (NSFC) (61527819, 61705157); Shanxi Province Natural Science Foundation under Grant (2015011049); Research Project Supported by Shanxi Scholarship Council of China under Grant (2016-036, 2017-052); Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi and Program for Sanjin Scholar.

## References and links

**1. **K. Shimizu, T. Horiguchi, Y. Koyamada, and T. Kurashima, “Coherent self-heterodyne detection of spontaneously Brillouin-scattered light waves in a single-mode fiber,” Opt. Lett. **18**(3), 185 (1993). [CrossRef] [PubMed]

**2. **T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers,” Opt. Lett. **15**(18), 1038–1040 (1990). [CrossRef] [PubMed]

**3. **J. Hu, X. Zhang, Y. Yao, and X. Zhao, “A BOTDA with break interrogation function over 72 km sensing length,” Opt. Express **21**(1), 145–153 (2013). [CrossRef] [PubMed]

**4. **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] [PubMed]

**5. **M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification,” J. Opt. Soc. Am. B **22**(6), 1321–1324 (2005). [CrossRef]

**6. **X. H. Jia, Y. J. Rao, C. X. Yuan, J. Li, X. D. Yan, Z. N. Wang, W. L. Zhang, H. Wu, Y. Y. Zhu, and F. Peng, “Hybrid distributed Raman amplification combining random fiber laser based 2nd-order and low-noise LD based 1st-order pumping,” Opt. Express **21**(21), 24611–24619 (2013). [CrossRef] [PubMed]

**7. **M. A. Soto, X. Angulovinnuesa, S. Martinlopez, S. H. Chin, J. D. Aniacastañon, P. Corredera, E. Rochat, M. Gonzalezherraez, and L. Thévenaz, “Extending the Real Remoteness of Long-Range Brillouin Optical Time-Domain Fiber Analyzers,” J. Lightwave Technol. **32**(1), 152–162 (2013). [CrossRef]

**8. **A. Fellay, L. Thévenaz, M. Facchini, M. Nikles, and P. Robert, “Distributed sensing using stimulated Brillouin scattering: towards ultimate resolution,” in *12th International Conference on Optical Fiber Sensors*, Vol. **16** of 1997 OSA Technical Digest Series (Optical Society of America, 1997). [CrossRef]

**9. **Y. Dong, X. Bao, and W. Li, “Differential Brillouin gain for improving the temperature accuracy and spatial resolution in a long-distance distributed fiber sensor,” Appl. Opt. **48**(22), 4297–4301 (2009). [CrossRef] [PubMed]

**10. **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]

**11. **J. L. Xu, Y. K. Dong, Z. H. Zhang, S. L. Li, S. Y. He, and H. Li, “Full scale strain monitoring of a suspension bridge using high performance distributed fiber optic sensors,” Meas. Sci. Technol. **27**(12), 124017 (2016). [CrossRef]

**12. **A. W. Brown, B. G. Colpitts, and K. Brown, “Dark-pulse Brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Lightwave Technol. **25**(1), 381–386 (2007). [CrossRef]

**13. **L. Thévenaz and S. F. Mafang, “Distributed fiber sensing using Brillouin echoes”, in *19th International Conference on Optical Fiber Sensors*, 2008 OSA Technical Digest Series (Optical Society of America, 2008), 70043N. [CrossRef]

**14. **Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Express **16**(16), 12148–12153 (2008). [CrossRef] [PubMed]

**15. **K. Hotate and T. Hasegawa, “Measurement of Brillouin Gain Spectrum Distribution along an Optical Fiber Using a Correlation-Based Technique-Proposal, Experiment and Simulation,” IEICE Trans. Electron. **84**(3), 405–412 (2000).

**16. **Y. Mizuno, Z. He, and K. Hotate, “Measurement range enlargement in Brillouin optical correlation-domain reflectometry based on temporal gating scheme,” Opt. Express **17**(11), 9040–9046 (2009). [CrossRef] [PubMed]

**17. **A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. **6**(5), L1–L5 (2012). [CrossRef]

**18. **A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. **5**(5), 1–8 (2016). [CrossRef]

**19. **Y. London, Y. Antman, E. Preter, N. Levanon, and A. Zadok, “Brillouin optical correlation domain analysis addressing 440 000 resolution points,” J. Lightwave Technol. **34**(19), 4421–4429 (2016). [CrossRef]

**20. **O. Shlomi, E. Preter, D. Ba, Y. London, Y. Antman, and A. Zadok, “Double-pulse pair Brillouin optical correlation-domain analysis,” Opt. Express **24**(23), 26867–26876 (2016). [CrossRef] [PubMed]

**21. **R. Cohen, Y. London, Y. Antman, and A. Zadok, “Brillouin optical correlation domain analysis with 4 millimeter resolution based on amplified spontaneous emission,” Opt. Express **22**(10), 12070–12078 (2014). [CrossRef] [PubMed]

**22. **Z. Ma, M. J. Zhang, Y. Liu, X. Y. Bao, H. Liu, Y. N. Zhang, and Y. C. Wang, “Incoherent Brillouin optical time-domain reflectometry with random state correlated Brillouin spectrum,” IEEE Photonics J. **7**(4), 6100407 (2015). [CrossRef]

**23. **J. Z. Zhang, M. T. Zhang, M. J. Zhang, Y. Liu, C. K. Feng, Y. H. Wang, and Y. C. Wang, “Chaotic Brillouin optical correlation domain analysis,” Opt. Lett.under review.

**24. **M. Santagiustina and L. Ursini, “Dynamic Brillouin gratings permanently sustained by chaotic lasers,” Opt. Lett. **37**(5), 893–895 (2012). [CrossRef] [PubMed]

**25. **J. Z. Zhang, Z. P. Li, M. Zhang, Y. Liu, and Y. Li, “Characterization of Brillouin dynamic grating based on chaotic laser,” Opt. Commun. **396**, 210–215 (2017). [CrossRef]

**26. **D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. **45**(7), 879–890 (2009). [CrossRef]

**27. **J. Z. Zhang, A. B. Wang, J. F. Wang, and Y. C. Wang, “Wavelength division multiplexing of chaotic secure and fiber-optic communications,” Opt. Express **17**(8), 6357–6367 (2009). [CrossRef] [PubMed]

**28. **Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. **281**(9), 2656–2662 (2008). [CrossRef]

**29. **H. D. I. Abarbanel, R. Brown, and M. B. Kennel, “Lyapunov exponents in chaotic systems: their importance and their evaluation using observed data,” Int. J. Mod. Phys. **5**(9), 1347–1375 (1991). [CrossRef]

**30. **J. H. Jeong, K. Lee, K. Y. Song, J. M. Jeong, and S. B. Lee, “Differential measurement scheme for Brillouin optical correlation domain analysis,” Opt. Express **20**(24), 27094–27101 (2012). [CrossRef] [PubMed]

**31. **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]

**32. **Y. Wang, L. Kong, A. Wang, and L. Fan, “Coherence length tunable semiconductor laser with optical feedback,” Appl. Opt. **48**(5), 969–973 (2009). [CrossRef] [PubMed]

**33. **A. López-Gil, S. Martin-Lopez, and M. Gonzalez-Herraez, “Phase-measuring time-gated BOCDA,” Opt. Lett. **42**(19), 3924–3927 (2017). [CrossRef] [PubMed]