Detecting cm-scale hot spot over 24km-long single-mode fiber by using differential pulse pair BOTDA based on double-peak spectrum

In distributed Brillouin optical fiber sensor when the length of the perturbation to be detected is much smaller than the spatial resolution that is defined by the pulse width, the measured Brillouin gain spectrum (BGS) experiences two or multiple peaks. In this work, we propose and demonstrate a technique using differential pulse pair Brillouin optical timedomain analysis (DPP-BOTDA) based on double-peak BGS to enhance small-scale events detection capability, where two types of single mode fiber (main fiber and secondary fiber) with 116 MHz Brillouin frequency shift (BFS) difference have been used. We have realized detection of a 5-cm hot spot at the far end of 24-km single mode fiber by employing a 50-cm spatial resolution DPP-BOTDA with only 1GS/s sampling rate (corresponding to 10 cm/point). The BFS at the far end of 24-km sensing fiber has been measured with 0.54 MHz standard deviation which corresponds to a 0.5°C temperature accuracy. This technique is simple and cost effective because it is implemented using the similar experimental setup of the standard BOTDA, however, it should be noted that the consecutive small-scale events have to be separated by a minimum length corresponding to the spatial resolution defined by the pulse width difference. ©2017 Optical Society of America OCIS codes: (060.2370) Fiber optics sensors; (190.4370) Nonlinear optics, fibers; (290.5900) Scattering, stimulated


Introduction
Optical fiber sensors have attracted much interest lately, due to their use in hazardous and hard to access environments [1][2][3].The distributed feature and long distance sensing capability of Brillouin optical time-domain analysis (BOTDA) has placed it in the center of a lot of scientific research works [4,5].Nowadays, BOTDA sensor constitutes the most advanced and reliable sensing system especially in application fields such as structural health monitoring, leakage detection in the oil and gas industry, temperature monitoring over high power cables [6,7] amongst others.For standard BOTDA sensor, the spatial resolution is determined by the pulse width which is limited by the acoustic phonons lifetime (~10 ns) [8] corresponding to 1 m, while the Brillouin gain spectrum (BGS) experiences broadening and amplitude reduction when the pulse width is smaller than 10ns [9].
A major technique that achieves long-range sensing with sub-meter spatial resolution is differential pulse width pair (DPP)-BOTDA [10,11].In DPP-BOTDA, two traces of Brillouin signals are generated by using two long differential pulses.The differential signal is obtained by taking subtraction between the two generated Brillouin signals.Then the spatial resolution is given by the pulse width difference of original long pulses [10].In 2012, Dong et al demonstrated 2-cm resolution over 2-km using differential pulse width pair (DPP) in transient domain [12].Another method to achieve cm-scale resolution is pre-excitation pulse technique [13].This technique takes advantage in the pre-existence of acoustic wave in optical fiber due to the direct current (DC) leakage provided by a low extinction ratio electrooptic modulator (EOM) used to reshape the pump pulse.The acoustic wave created by electrostriction has a lower response to amplitude and phase changes (~10 ns) than optical waves.In other words, any fast variation of amplitude and phase of the pump within the duration of acoustic wave affects the steady-state amplification of probe wave.The acoustic wave pre-excitation can also be obtained by applying a very short π-phase shifted or dark pulse [14][15][16][17].Stella M. Foaleng et al investigated 5-cm resolution over 5-km-long fiber using pre-excitation pulses technique [18].Although, these works focus on high resolution, extending the sensing range while keeping a high spatial resolution remains a challenge.A. Dominguez-Lopez et al recently achieved 5 cm spatial resolution over 25-km single mode fiber by using a scanning method in which a fixed frequency separation was maintained between probe sidebands while the Brillouin signal was scanned by sweeping the pump frequency [19].Despite the merit offered by the combination of this novel scanning technique and DPP-BOTDA, in performance enhancement of long-range BOTDA sensor [20], its implementation is complex compared to standard BOTDA.However, some field applications only need high spatial resolution at critical locations (for example, the junctions of power cables), while m-scale is enough for other parts.
In this paper, a technique which is based on the use of double-peak BGS to detect 5-cm perturbation length at the far end of 24-km single mode fiber (SMF) by employing a 50-cm spatial resolution DPP-BOTDA with only 1GS/s sampling rate (corresponding to 10 cm/point) was numerically and experimentally demonstrated.In achieving this, the main and secondary fibers with Brillouin frequency shift (BFS) difference larger than the BGS bandwidth were used.The cm-scale perturbation (5 cm) was detected by using a small section of secondary fiber, while the spatial resolution was 50 cm for the rest of the sensing length.This technique enables the detection of perturbations which correspond to one-tenth (1/10) of intrinsic spatial resolution given by the pulse width with a relatively low sampling rate.Our technique is simple and cost effective because it is implemented using the similar experimental setup of the standard BOTDA.

Limitation of spatial resolution
In standard BOTDA sensing when the spatial resolution is high enough to resolve a given perturbation, the resulting BGS has a single peak.Conversely, when the length of the perturbation to be detected is smaller than the spatial resolution defined by the pulse width, the BGS measured in that section tends to have two or multiple peaks.The signal in such situation contains two components.One component is contributed by the targeted perturbed segment, while the other is provided by the nearby sections.This concept is illustrated in Fig. 1, where a 5-cm perturbation section (shown in blue color) is to be detected by using a BOTDA sensor which has 50-cm (red color) intrinsic spatial resolution.In fact, by using 50cm spatial resolution, each sample signal is supposed to contain local spatial information on at least 50 cm all along the sensing length.So, when aiming to detect the 5-cm perturbation section with a 50-cm resolution BOTDA sensor, it is logically impossible to find a signal sample containing only spatial information related to that short (5 cm) segment.As it is shown in Fig. 1, every sample of that sub-spatial resolution perturbed segment (5-cm) also, contains local spatial information of the neighborhood sections as depicted by the sampling positions (a), (b) and (c).
The statement "main BGS" will subsequently refer to the spectrum that is centered on the BFS of the main fiber, while "secondary BGS" will indicate the spectrum that is centered on the BFS of the perturbed section.The main BGS contains the information related to the nearby sections, while all information related to the short perturbed section is ascribed to the secondary BGS.
The principle of the proposed technique is based on separating the original double-peak spectrum into two distinct spectra.In achieving this, three major conditions were considered when dealing with double-peak BGS scheme.First, when the peak frequency difference between the main and the secondary BGSs is within the linewidth of the main BGS, the secondary spectrum is totally covered by the main one.The system works like a typical standard BOTDA sensor and it is not able to detect perturbations that are smaller than the spatial resolution defined by the pump pulse width.Second, if the peak frequency separation is larger than, but very close to the linewidth of the main BGS, the peak of the secondary spectrum appears more like a bump thereby distorting the main BGS.Therefore, it becomes difficult to fully reconstruct the secondary BGS.Lastly, when the peak frequency difference is large enough, the secondary spectrum appears far away from the main BGS.The influence of the main BGS on the secondary BGS is alleviated and the secondary BGS can be fully reconstructed, and then DPP-BOTDA based on double-peak BGS works properly.Consequently, the analysis of the secondary BGS provides temperature and/or strain information over segments much shorter (few cm) than the pulse width dependent spatial resolution of the sensor.When the BFS difference is quite larger than the bandwidth of the main BGS, cm-scale perturbation can be detected in critical sections, while the spatial resolution remains defined by the pulse width for the rest of sensing length.

Numerical simulation
The numerical simulation was realized based on the coupled three-wave equations governing the stimulated Brillouin scattering (SBS) process under the assumption of plane-wave interaction in a lossless SMF fiber.We assume a situation in which the acoustic wave amplitude growth is slower than the acoustic frequency.Equations ( 1), (2), and (3) describe respectively the pump pulse traveling in ( + z) direction, the continuous probe in (-z) direction and the acoustic phonons created by electrostriction and propagating in ( + z) direction as illustrated in Fig. 2.
where p E , s E and ρ are the field amplitudes of the pump pulse, continuous probe and acoustic wave, respectively; n is the index of refraction of the fiber; c is the light velocity in the vacuum; / 2 Equation ( 4) is then substituted into Eq.( 1) and ( 2) to obtain Eq. ( 5) and ( 6).
( ) Γis the Brillouin gain coefficient.Equations ( 5) and ( 6) have been used to simulate the interaction of pump and probe wave in the optical fiber.The sensing fiber is composed of two types of SMF (main and inserted) fiber.The main fiber (15.95 m) has a BFS of 10.850 GHz.The inserted fiber (5 cm) with a BFS of 11.025 GHz is located in the middle of the sensing length.First, we perform the simulation using standard BOTDA scheme with a 5-ns pump pulse which corresponds to 50 cm spatial resolution.As depicted in Fig. 3(a), the 3D spectrum experiences broadening and the inserted section is difficult to clearly discriminate.Second, we used DPP-BOTDA technique with 5 ns differential pulse width for 50 cm spatial resolution.Two long pulses of 60 and 55 ns have been launched separately in the fiber.Figure 3(b) shows a narrowed gain spectrum obtained from the differential process.In the middle of the sensing length, one can clearly identify an upshift around 11.025 GHz, corresponding to the spectral components of the inserted section.The BGS depicted in Fig. 4(a) is for the inserted section of Fig. 3(a).Its peak frequency is equal to 10.860 GHz.This value corresponds neither to the BFS of the main fiber (10.850GHz) nor to that of inserted fiber (11.025GHz).This situation confirms the disability of standard BOTDA in detecting 5 cm perturbation using a 50-cm spatial resolution.In contrast, the spectrum measured in the inserted section using DPP-BOTDA experiences two peaks as shown in the red curve of Fig. 4(b).The main BGS has a peak frequency of 10.850 GHz, which corresponds to the BFS of the main fiber.The secondary BGS located on the righthand side of the main BGS is centered on 11.025 GHz, which is the BFS of the inserted fiber.Moreover, the secondary BGS can be reconstructed independently of the main BGS, thus accurate information related to the inserted fiber segment can be obtained.
Based on previous analysis, it is believed that DPP-BOTDA is the suitable scheme to implement the double-peak BGS technique due to its narrowband BGS feature.The black spectrum in Fig. 4(b) was measured when the BFS of the inserted fiber was set to 10.895 GHz.In this case, the secondary BGS is too close to the main BGS, thus, the secondary BGS is hampered by the influence of the main BGS, which increases the frequency errors.So in double-peak BGS technique, utmost care is needed when considering the frequency difference between the BFS of the main fiber and that of the perturbed section.In order to analyze the influence of the peak frequency difference between the main and secondary BGS on the sensor's accuracy, several measurements were performed by varying the BFS of the inserted fiber.As reported in Fig. 5, when the peak frequency separation is equal to 35 MHz, the frequency error is 7 MHz.The measurement error drops to 1.3 MHz for 55 MHz peak frequency difference and frequency error smaller than 0.1 MHz is obtained when the BFS separation is larger than 125 MHz.It should be noted that as the BFS difference increases, the measurement error decreases.
For the double-peak BGS technique, when the sensing fiber has a uniform BFS, to be detected, any perturbation must induce a frequency shift larger than the bandwidth of the main BGS.However, in practice, the need for large frequency shift in the perturbed sections can be alleviated by inserting short segments of another type of fiber having a large BFS separation with respect to the main fiber in these critical sensing locations where high spatial resolution is required.Therefore, any event inducing a frequency shift even smaller than the bandwidth of the main BGS in those critical locations could be detected.Although this method enables the detection of cm-scale events, it cannot discriminate perturbation sections located very close to each other within the spatial resolution.In other words, consecutive short perturbations have to be separated by a minimum length corresponding to the spatial resolution defined by the pulse width difference.

Experimental setup
As shown in Fig. 6, a distributed-feedback (DFB) laser with a narrow linewidth operating at 1550 nm has been used as light source.The output is split into two arms using a 50/50 optical coupler.An electro-optic modulator (EOM1) is driven by an arbitrary function generator (AFG) to generate pump pulse.A polarization scrambler (PS) is used to reduce the polarization-dependent fluctuation.An Erbium-doped fiber amplifier (EDFA) is used to amplify the pump pulse which is coupled into the fiber through a three-port optical circulator.In the other branch, a frequency-shifted probe is generated by modulating the intensity of the continuous wave (CW) light thanks to EOM2 controlled by a microwave and a DC bias voltage supplier.The CW probe is then launched into the far end of the sensing fiber through an isolator.Although dual-sideband has been sent into the sensing fiber, a narrow-band filter before the detector is used to select only the Stokes component.A photodetector (PD) is connected to an oscilloscope, which is controlled by a computer to record the Brillouin time traces.

Detecting 5-cm over 6-km-long SMF fiber
The sensing fiber used in this experiment was composed of two types of SMF fiber with different BFSs, which had a total length of about 6 km.At the far end, three sections (20, 10, and 5 cm) separated by 2 m loose fiber, were inserted; as shown in Fig. 7 depicting the fiber arrangement.The BFSs of main and inserted fibers were 10.83 and 10.68 GHz respectively, at room temperature.A pump peak power (222 mW) was sent in the near end of the fiber, while 0.75 mW probe wave was injected into the far end.Measurements were performed in DPP-BOTDA scheme by employing 55/60 ns pulse pair for 50 cm spatial resolution.The signal was acquired through 2.5 GS/s sample rate and 3k averaging times.The Brillouin signal has been swept over 300 MHz frequency range (from 10.6 to 10.9 GHz) with a frequency step of 4-MHz.The 3D mapping of the BGS distribution depicted in Fig. 8(a) reveals a strong signal-to-noise ratio (SNR).The far end of the fiber can be clearly seen, thus indicating the possibility of performing accurate measurements over the whole sensing length.The shift of a spectral component situated at the far end of the BGS shows the presence of the inserted fiber segments.By zooming into that section one can clearly identify all these segments.As shown in Fig. 8(b), the corresponding spectral components are centered on 10.68 GHz. Figure 8(c) reports the BFS as a function of position in the last 5 m.
The inserted and the respective loose fiber sections are fully identified.The inserted 5-cm fiber segment is detected exactly at 5947.72 to 5947.77m with a standard deviation of 0.52 MHz.

Detecting a 5-cm-long hot spot at a range of 24-km
In a second experiment, we checked the temperature measurement capability of our system by using 24-km-long SMF fiber which has a mean BFS of 10.87 GHz.The previous three inserted segments have been replaced by four new sections (50, 20, 10 and 5 cm) of SMF fiber having a mean BFS of 10.76 GHz.The sections were respectively separated by 1-m loose fiber as shown in Fig. 9; depicting the fiber arrangement at the far end.The optical powers were set to 240 and 0.712 mW for pump pulse and CW probe, respectively.The signal has been acquired with 1 GS/s sample rate (corresponding to 10cm/point) and 2k averaging times.The same 50-cm spatial resolution DPP-BOTDA scheme employed in the previous experiment has been used.In order to detect 5-cm hot spot, two groups of measurements have been conducted.First, a reference measurement was done by keeping the entire sensing fiber at room temperature (28°C).The 3D BGS in Fig. 10(a) shows a distortion-free spectrum over the whole sensing length.A top view of the spectral component that is downshifted at the end of the main BGS is shown in Fig. 10(b).The spectral components of each inserted segment are centered on 10.76 GHz corresponding to the BFS of the secondary fiber.Figure 10(c) presents the BGSs measured respectively in the 20 (blue triangle dot), 10 (red circle dot), and 5 cm (black square dot) inserted fiber sections.The peaks located on 10.876 GHz are the center frequencies of the main BGSs, while those situated on 10.76 GHz are the center frequencies of the secondary BGSs.The spectrum of the first inserted section (50 cm) is not shown in Fig. 10(c) because this section can be resolved by our sensor while functioning in standard DPP-BOTDA scheme.Hence the corresponding spectrum experiences a single peak.Such feature is not taken into account in the framework of the present study.Second, the 5cm segment was bonded to the surface of a semiconductor Peltier heater and its temperature was increased to 48°C using a DC power supply.Figure 10(d) reports the spectra measured in the center of the 5-cm segment at both room (black square dot) and high (red circle dot) temperatures, respectively.The peak frequency of the spectrum measured at room temperature was determined by using Lorentz fit (magenta solid line) and corresponds to the BFS (10.76 GHz) of the inserted fiber.On the other hand, the BGS measured when the same fiber section was under high temperature, has two peaks (peak 1 and peak 2).The values of these peaks have been determined by using Lorentz multiple peaks fit function.Therefore, the blue spectrum represents the cumulative fit, also known as dual Lorentz fit.The red (peak1) and green (peak2) spectra represent Lorentz fitting result when each peak is considered as the center frequency of an entire spectrum (see Fig. 10(d)).It should be noted that these two spectra inherent in dual Lorentz fitting allow determining the values of peak 1 and peak 2. Peak 1(10.783GHz) corresponds to the BFS of the hot spot and peak 2 (10.76 GHz) is the BFS of an unheated part of the inserted 5-cm fiber section.This result can be explained by the fact that, to facilitate the splicing process, the length of the inserted fiber section was slightly longer than 5 cm; however, only 5-cm-long segment was strictly pasted to the surface of the heater.Figure 11 depicts the BFS (left axis) and corresponding temperature (right axis) as a function of the position for the far end of the sensing fiber.The black triangle dotted curve is the measurement result at room temperature.It is apparent that all the inserted sections have the same BFS (10.76 GHz).The red circle dotted curve shows the measurement result when the 5-cm section was heated to 48°C.In that section, the BFS corresponding to the hot spot is shifted while the BFS of the other three sections matches well with the curve measured at room temperature.The blue curve reports the measured temperature distribution over the sensing fiber.It has been obtained by subtracting the data measured at room temperature from that measured at high temperature.Obviously, the measured temperature over the hot spot, located at 24016.16 to 24016.21m matches perfectly with the real temperature (48°C).The BFS at the far end of 24-km-long sensing fiber was measured with 0.54 MHz standard deviation which corresponds to a 0.5°C temperature accuracy.The abrupt variation in temperature distribution around 24013 and 24014 m cannot be considered as temperature fluctuations, but rather due to the differential between the data recorded at room temperature and those recorded at high temperature; since the signal amplitude fluctuates with the dithering of DC power supply used to lead the EOM1 in the pump path.

Conclusion
The concept of DPP-BOTDA based on double-peak BGS technique has been investigated both theoretically and experimentally.Its ability to detect 5-cm perturbation length which corresponds to one-tenth (1/10) of the spatial resolution (50 cm) defined by the pulse width has been proved.A 5-cm hot spot has been detected at the far end of 24-km-long single-mode fiber with 0.5°C temperature accuracy.The method discussed in this paper has the advantage of mitigating the trade-off between the spatial resolution and pulse width.Some features of this technique make it more suitable for the detection of events inducing large frequency shift.However, by employing another type of fiber having a large BFS separation with respect to the main fiber in critical sensing locations, the system becomes sensitive to events inducing smaller frequency shift in those locations.We believe that double-peak BGS technique is suitable for those applications such as temperature monitoring in the joint junctions of power cables, which only requires high spatial resolution at critical locations, while m-scale is enough for other parts.

Fig. 8 .
Fig. 8. 3D gain spectra; (a) over the whole sensing fiber length; (b) Top view on the far end; and (c) measured Brillouin frequency shift as function of position.

Fig. 11 .
Fig. 11.BFS and corresponding temperature as function of position; (black triangle dot) 5 cm section at room temperature; (red circle dot), 5 cm section at high temperature, (blue line) temperature distribution over the end of the fiber.