1. Introduction

Distributed temperature or strain sensors based on Brillouin optical time domain analysis (BOTDA) have attracted great attention for the past decade due to their widely employment in large structures such as pipelines and electrical power cables [1–3]. The basic configuration of this technique consists of a pump pulse and counter-propagating continuous probe wave, which are spectrally separated by the Brillouin frequency shift (BFS), producing an acoustic field through electrostriction that initiates a power transfer between the two optical waves during the interaction [1]. Thus, the distributed information can be obtained by measuring the spectral shift of the peak Brillouin gain/loss spectrum at each position along the fiber. However, in such single-tone probe based techniques [1], the non-local effect induced by the pump depletion phenomenon [4,5] would impose large error on the estimated BFS at the end of sensing fiber in case of long-range measurement. Therefore, the allowable power of the probe wave that can be injected into the sensing fiber is limited below −13 dBm to secure the BFS error less than 2 MHz [5], which further constrains the sensor performance in terms of the signal-to-noise ratio (SNR) [3]. As a robust solution to overcome the non-local effect, the BOTDA sensor with dual-tone probe wave based on dual-sideband (DSB) modulation is then proposed [4–7], which has been widely used in different BOTDA systems [2], since ideally the pump power can be always balanced by the zero net gain on the pump pulse generated from the two probe tones. However, according to the recent model [8], due to the asymmetric feature of the Brillouin gain/loss process, the net gain is actually non-zero when scanning the frequency offset between the pump and probe wave, which would highly distorts the pulse spectrum, further resulting in the distortion of the BGS/BLS. The severeness of this effect is directly related to the probe power and the sensing range, constraining the allowable probe power below −6 dBm when more than 25 km sensing range is used [8]. Two solutions are proposed recently to solve this problem [9,10]. The one is to keep fixed frequency separation between the two frequency tones [9], in which the frequency separation is selected as twice of the dominant BFS over the last ~20 km of sensing fiber, ensuring that the accumulated net gain on the pump pulse generated by the two probe tones is zero. The method can be realized by scanning either the frequency of the pump pulse or the frequency of the probe tones together, so that the BGS/BLS distortion problem can be mitigated regardless of the BFS distribution along the sensing fiber. This way, the allowable probe power can be safely enhanced from −6 dBm to the threshold of amplified spontaneous Brillouin scattering (ASpBS) (around 5 dBm) [9], thus leading to considerably SNR improvement. Moreover, this technique can be directly combined with optical pulse coding techniques [11,12] to further boost the SNR performance. The other solution is to dither the frequency of the probe wave [10], which could also create a flat net gain over the pump pulse. This method could not only perfectly avoid the non-local effect, but also allow the probe power increased beyond the threshold of ASpBS (8 dBm demonstrated in [10]), which is expected to be capable of providing larger SNR improvement in case of long sensing range in comparison with method in [9] when single pump pulse is used. Nevertheless, it cannot support coding techniques so far, since the dithering of the probe frequency breaks the linearity of the system required by the coding/decoding process.

In this paper, after deeply study of the method based on dual-tone probe with fixed frequency separation [9], we discover that when using this method, if the BFS of the sensing fiber is not entirely uniform, especially in the case that the fiber consists of two long segments with large BFS difference (> 100 MHz), there will be always only one probe tone interacting with pump pulse in the front fiber segment. It means that such a process is equivalent to that using conventional BOTDA technique with single-tone probe, there will be non-local effect occurring in the front fiber segment [4,5], which would impose systematic errors on the BFS of the hotspot located at the end of the front fiber section. This phenomenon would constrain the injected probe power far below the threshold of ASpBS, thus degrading the SNR performance of the system. In order to solve this problem that doesn’t exist in [10], we propose an alternative solution in this paper, which could eliminate the traditional non-local effect and the pump distortion problem simultaneously. In the proposal, instead of using two probe tones with fixed frequency separation, two pairs of orthogonally-polarized dual-tone probe waves with opposite frequency scanning direction are employed. In this case, the spectrum of pump pulse will be downshifted after interacting with one probe-tone pair at one polarization state, and be upshifted after interacting with the other probe-tone pair at orthogonal polarization state. This way, the accumulated net gain on the pump pulse generated by the four probe tones is zero as well, thus ensuring that the pump distortion problem can be overcome. Moreover, in the case of the above mentioned fiber configuration, there will be always one probe pair (two probe tones) interacting with the pump pulse in the front fiber segment, the process of which is equivalent to conventional dual-tone probe BOTDA method based on DSB modulation, so that the impact of non-local effect can be avoided. The experimental results validate the theoretical analysis, and demonstrate the feasibility of the proposal.

2. Principle

The distortion of pump pulse in conventional DSB-based BOTDA sensor has been deeply investigated in [8,9] as described in Fig. 1(a). It can be seen that when the scanned pump-probe frequency offset is higher or lower than the dominant BFS over the last several kilometers of sensing fiber (${\nu }_{{\rm B}}$), the pump pulse spectrum (black curves) will downshift or upshift from its original spectrum resulting from the asymmetric of Brillouin loss (red curves) and gain (blue curves) spectrum generated by the upper and lower probe tones, respectively. It has been observed that in case of long sensing range (> 50 km), the effect of pulse distortion, which would further lead to BGS/BLS distortion and estimated BFS error, is non-negligible when the probe power is higher than −6 dBm/tone [9], which is far below the threshold of ASpBS (about + 5 dBm).

 

Fig. 1 Schematic descriptions of the pump-probe Brillouin interactions in spectral domain: (a) the standard DSB-based scanning method; (b) the fixed frequency separation method proposed in [9]; where v_B is the dominant BFS over the last ~20 kilometers of sensing fiber.

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Therefore, the method that keeps fixed frequency separation ($2{\nu }_{{\rm B}}$) between the two frequency tones has been proposed to solve this problem [9], thus the allowable probe power that imposes significant constraints to the SNR and performance of BOTDA sensors can be raised to the threshold of ASpBS without pump distortion. In this method, the gain and loss spectra generated by the two probe tones exactly cover the same spectral region and mutually cancel out, regardless of the scanning frequency, as shown in Fig. 1(b). In the case of a very long sensing range (longer than ${\alpha }^{-1}$ ≈20 km), the frequency separation between the two probe tones has to be tuned to match twice of the dominant BFS over the last $L_{eff}={\alpha }^{-1}$≈20 km of fiber, since most of the pump pulse distortion cumulates along the last fiber segment (equivalent to the non-linear effective length $L_{eff}$), where the probe power propagating along the fiber is the highest. This means that the BFS distribution over the segment far away from the last $L_{eff}$ fiber segment is not critical for selecting the frequency separation between the two probe tones. For example, as shown in Fig. 2, assuming a 50 km-long sensing fiber consists of two long segments with same length (the length of each section is 25 km) but large BFS difference (more than 100 MHz), as the $S_1$ and $S_2$ segments shown in Fig. 2, the selected fixed frequency separation should be very close to $2{\nu }_{{\rm B}2}$, where ${\nu }_{{\rm B}2}$ is the BFS of $S_2$ fiber segment.

 

Fig. 2 Configuration of sensing fiber. Black curve: the dominant BFS of sensing fiber versus the distance; Green curve: the probe power versus distance. The hotspot is located at the end of the front segment of sensing fiber.

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However, it should be pointed out that when scanning the pump frequency with this fiber configuration, although the gain and loss spectra generated by the two probe tones can always mutually cancel out inside the $S_2$ fiber segment as shown in Fig. 3(a), the two spectra would move away from each other inside the $S_1$ fiber segment having the BFS of ${\nu }_{{\rm B}1}$, as depicted in Fig. 3(b), which means that the net gain generated by the two probe tones is no longer zero. Under this situation, there is always only one probe tone interacting with pump pulse inside the $S_1$fiber segment, indicating that this process is equivalent to that in the traditional BOTDA sensor using single probe tone, which may heavily suffer from the non-local effect [4,5], depending on the level of the probe power along the $S_1$fiber segment. If the injected probe power is ${\text{P}}_0=+5$ dBm/tone, which is the same power level used in [9], the probe power at the end of $S_1$ fiber segment (at point A shown in Fig. 2) should be ${\text{P}}_{\text{A}}=0$dBm/tone after experiencing fiber attenuation. Note that such high power level would not only induce pulse distortion, but also give rise to strong non-local effect in the $S_1$ fiber segment [5]. The injected probe power level of ${\text{P}}_0=+1$ dBm/tone would not lead to obvious pulse distortion, since in this case the probe power at point A is ${\text{P}}_{\text{A}}=-4$dBm/tone, but which is still far above the safe probe power level (−13 dBm) that starts to induce obvious non-local effect [5]. Therefore, a large systematic error would be imposed on the estimated BFS of the hotspot located before point A, as the red section shown in Fig. 2.

 

Fig. 3 Schematic descriptions of the pump-probe Brillouin interactions based on the method that keep fixed frequency separation 2v_B2. (a) the Brillouin interaction process in S₂ segment; (b) the Brillouin interaction process in S₁ segment (v_B1 < v_B2).

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Aiming at alleviating the pump distortion problem and overcoming the above mentioned non-local effect simultaneously when the high injected probe power is used, a novel BOTDA method based on orthogonally-polarized four-tone probe is proposed in this paper. Being different from the conventional BOTDA scheme, in the proposal there are two pairs of dual-tone probe waves with orthogonal polarization states, as the red lines and the blue lines shown in Fig. 4, respectively, the configuration of each pair is the same as that in conventional DSB-based BOTDA method. The frequency sweeping direction of one probe-tone pair (the red one) is from ${\nu }_{{\rm B}}+{\text{f}}_{\text{s}}$ to ${\nu }_{{\rm B}}-{\text{f}}_{\text{s}}$, while that of the other probe-tone pair (the blue one) is from ${\nu }_{{\rm B}}-{\text{f}}_{\text{s}}$ to ${\nu }_{{\rm B}}+{\text{f}}_{\text{s}}$ with the same sweeping step, where ${\nu }_{{\rm B}}$ also denotes the dominant BFS over the last ~20 km kilometers of sensing fiber and ${\text{f}}_{\text{s}}$ denotes half of the frequency sweeping range, which is set to be a few hundred MHz in the proposal.

 

Fig. 4 Schematic descriptions of the frequency sweeping direction in the proposal. The dashed arrows represent the sweeping direction of its corresponding probe tone.

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In this proposed method, the net gain on the pump pulse generated by each probe pair is the same as that in conventional DSB-based scheme, respectively, as shown in Fig. 5, where ${\nu }_{\mathrm{mod}}$ stands for the modulation frequency of one probe-tone pair (the red one). For instance, in the case of ${\nu }_{\mathrm{mod}}>{\nu }_{{\rm B}}$, as illustrated in Fig. 5(a), the net gain generated by one probe-tone pair (red) would upshift the pulse spectrum, while that generated by the other orthogonally-polarized probe-tone pair (blue) would downshift the pulse spectrum. Note that at each given fiber position, the total contribution of the above mentioned two net gain cannot be mutually cancelled out, since the efficiency of Brillouin interaction highly depends on the polarization relationship between pump and probe wave [13,14]. However, because the polarization state of the light propagating along the fiber is random [15], the accumulated contribution of the gain generated by all the four probe tones could be considered as zero when using long sensing range.

 

Fig. 5 Schematic descriptions of the pump-probe Brillouin interactions of the orthogonally-polarized four-tone probe scheme in spectral domain.

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Returning to the configuration shown in Fig. 2, the process of Brillouin interaction in the front segment ($S_1$ fiber segment) using the proposed method is depicted as Fig. 6. It can be observed that there are always two probe tones (one probe-tone pair) interacting with the pump pulse, which means that the process is exactly equivalent to that in conventional DSB-based BOTDA method, providing much better tolerance for non-local effect with respect to the process in the previous method [9]. In this case, considering the pulse distortion problem, the highest allowable injected probe power is still + 1 dBm/tone. Thus, the probe power at the end of $S_1$ fiber segment is about −4 dBm/tone, such power level in conventional DSB-based method would just induce minor pump distortion problem [8,9]. Actually, the total injected power of the probe wave at lower/higher frequency is equivalent to 4 dBm, since there are two frequency tones injected into the receiver simultaneously. Therefore, by using the proposed method, the BFS of the hotspot located at the end of $S_1$ fiber segment can be correctly estimated without the impact of non-local effect.

 

Fig. 6 Schematic description of the pump-probe Brillouin interaction inside S1 segment using the proposed BOTDA scheme based on the orthogonally-polarized four-tone probe scheme in spectral domain when the BFS of S1 section v_B1 is largely different from v_B2.

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It has to be mentioned that since the maximum frequency difference between the two probe-tone pairs is in MHz scale, it is difficult to extract just one probe tone from the four-tone probe wave at the receiver part. Therefore, the probe tones at higher or lower frequency from both probe-tone pairs have to be detected together. Just because of such a small frequency difference, the polarization relationship between the two detected probe tones can be kept orthogonal after propagating through relative long distance [15], which means that there will be no frequency beating problem between the two detected probe tones in the receiver. The following experimental results could demonstrate this point, where no beating phenomenon is observed. In spectral domain, the BGS obtained by this proposed method can be expressed as the sum of two equal-amplitude Lorentz spectra attributed to the two detected probe tones, respectively:

A solution to solve this problem is to use the fiber with high-order acoustic mode, in which the high-order BGS is helpful to distinguish the moving direction of the BFS with respect to ${\Omega }_B\text{/2}\pi$ at each fiber position. Still taking the case shown in Fig. 2 as an example, the BGS corresponding to different situations in S₁ fiber segment and S₂ fiber segment are shown in Figs. 7(a) and 7(b), respectively, where ${\Omega }_B\text{/2}\pi$ is set to be the BFS of S₂ fiber segment (${\Omega }_B\text{/2}\pi ={\nu }_{B2}$). It can be seen that when there is no hotspot, the BGS at the S₁ fiber segment consists of two Lorentz spectra with large frequency separation, which are located at ${\nu }_{B1}$ and $2{\nu }_{B2}-{\nu }_{B1}$, respectively, as the black curve shown in the case (ii) of Fig. 7(a). According to the position of the second-order BGS in the two Lorentz spectra, we can distinguish that the BFS ${\nu }_{B1}$ in this case is lower than ${\nu }_{B2}$, which means that the Lorentz spectrum at lower frequency denotes the real signal. Being differently, the BGS at the S₂ fiber segment manifests as one single Lorentz spectrum when there is no hotspot, as the black shown in the case (ii) of Fig. 7(b), since the two Lorentz spectra exactly overlap. When the hotspot is introduced, these two spectra start to move away or towards the set center frequency ${\nu }_{B2}$, depending on the BFS of the hotspot gets higher or lower, as the case (i) and case (iii) shown in Fig. 7(b), respectively. The BGS of these two cases, which manifest as the synthetic spectrum with two peaks, have to be fitted by using the fitting function based on Eq. (1) for obtaining the amount of BFS change. After that, by observing the moving direction of second-order BGS in these two cases, the moving direction of BFS change can be distinguished.

 

Fig. 7 Illustration of the BGS of hotspot at different temperature changes in (a) S1 fiber segment and in (b) S2 fiber segment. Blue dashed curve: the BGS component attributed to the blue probe tone shown in Fig. 4; Red dashed curve: the BGS component attributed to the red probe tone shown in Fig. 4; Black curve: the synthetic BGS used for fitting.

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3. Experimental results and discussion

To demonstrate the proposed technique, the experiment setup is shown in Fig. 8(a). The continuous wave from a narrow linewidth tunable laser with output power of 16 dBm operating at 1550 nm is split into two branches by a 50/50 coupler. On the probe branch, the light is split into two branches again through another 50/50 coupler, each of which is modulated by an electro-optic modulator (EOM) to generate the carrier-suppressed double-sideband (CS-DSB) signal. After that, the two pairs of orthogonally-polarized dual-tone probe waves are obtained by coupling the two signals through a high extinction ratio (ER) polarization beam combiner (PBC). Subsequently, the 4-tone probe wave is injected into the far end of the sensing fiber after being amplified by an erbium doped-fiber amplifier (EDFA) and going through a polarization switch (PS, type: PSW-002 from General Photonics) to avoid polarization fading. On the pump branch, the optical beam is pulsed by two cascaded EOMs to generate a 20 ns pump pulse with high ER (> 60 dB), which is then amplified by an EDFA to reach the power of 100 mW before being injected into the fiber. At the receiver part, by filtering the lower frequency tones together in the two orthogonally-polarized probe pairs, the Brillouin response, which is the sum of the two orthogonally-polarized probe tones, is finally detected by a photodiode (PD) connected to an oscilloscope with 500 MSamples/s. The sensing fiber consists of two fiber segments (S₁ and S₂ fiber segments) with different BFS, the length of which are 24.454 km and 24.425 km, respectively. At room temperature of 28°C, for the pump wavelength of 1550 nm, the BFSs of these two segments are deliberately selected as ${\nu }_{B1}=10.652GHz$ and ${\nu }_{B2}=10.882GHz$, respectively, to obtain a large BFS difference (230 MHz), which matches the configuration shown in Fig. 2.

 

Fig. 8 (a) Experimental setup of the proposal; (b) implementation of the method in [9] based on the experimental setup of our proposal. PC: polarization controller; EOM: electro-optic modulator; PG: pulse generator; Cir.: circulator; PS: polarization switch; PD: photodiode; PBC: polarization beam combiner; DWDM: dense wave length division multiplexing; Pol.: polarizer.

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The proposed method and the previous method based on dual-tone probe with fixed frequency separation [9] are both experimentally carried out under the same experimental condition for comparison. Based on the experimental setup shown in Fig. 1(a), the method in [9] is implemented by adding two filters with different center frequencies right after the EOM1 and EOM2, respectively, and replacing the PBC by a coupler and a polarizer, as shown in Fig. 8(b). The filtering frequency of filter1 matches the frequency of the upper sideband of one probe wave, while that of filter2 matches the frequency of the lower sideband of the other probe wave. In the experiment, the center of the scanning frequency${\nu }_B$in both methods is fixed to match the dominant BFS over the last segment of the sensing fiber (${\nu }_{B2}$~10.882 GHz). The sweeping range of the pump pulse frequency for the previous method is from 10.35 GHz to 11.414 GHz with the frequency step of 2 MHz, to cover the BGS of both fiber segments. For the proposed method, the frequency sweeping range of the probe wave at one polarization (i.e. RF1 in Fig. 8) is from 11.414 GHz to 10.35 GHz with frequency step of 2 MHz, and that of the probe wave at the other polarization (i.e. RF2 in Fig. 8) is from 10.35 GHz to 10.414 GHz. The injected probe power at the far end of the sensing fiber is set as + 1 dBm/tone. As previously analyzed, this is the highest power level can be allowed to prevent the pump pulse from getting distorted for both methods.

A set of temporal envelopes of the output pump pulses measured at the end of the sensing fiber for different pump-probe frequency offsets using the proposed scanning method are depicted in Fig. 9(a). It can be seen that the pulses remain essentially undistorted at the fiber output regardless of the probe frequency detuning, demonstrating that the proposed method has the same performance in terms of the mitigation of pulse distortion as the previous method. However, the peak power of the pump pulse at the fiber output as a function of scanning frequency difference between pump and probe reveals different performance by using both methods, as illustrated in Fig. 9(b). The substantial power drop at the BFS of the front fiber segment (${\nu }_{B1}=10.652GHz$) clearly observed when using the previous method, indicating that there should be large pump depletion when the pump pulse propagates along the front fiber segment. As previously explained in this paper, the reason comes from the fact that the fixed frequency separation (${\nu }_B={\nu }_{B2}=10.882GHz$) between the two probe tones in the previous method is largely different from the BFS of the front fiber segment (10.652 GHz), resulting in the situation that only one probe tone interacts with pump pulse inside the front fiber segment. This process is equivalent to that in the traditional BOTDA sensor using single probe tone, which would heavily suffer from the non-local effect. However, by using the proposed method, the peak power of the pump pulse is almost constant as the frequency difference between pump and probe varies, as the red curve shown in Fig. 9(b), meaning that there is no obvious non-local effect.

 

Fig. 9 (a) A set of temporal envelopes of the output pump pulses measured at the end of the sensing fiber for different pump-probe frequency offsets using the proposed scanning method; (b) peak power of the pump pulse at the fiber output as a function of scanning frequency difference between pump and probe.

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In order to investigate the non-local effect more intuitively, a 4-m-long hotspot is loosely introduced at the end of the front segment of sensing fiber (i.e. the red region illustrated in Fig. 2). The temperature of the hotspot varies from 42°C to 72°C in 5°C steps. Figure 10(a) illustrates the measured BGS profiles at the hotspot with each temperature step when the previous method is used, the skewing effect [5] imposed by the non-local effect is clearly observed. Nevertheless, when using the proposed method, the BGS remains unaltered as the temperature varies, as shown in Fig. 10(b), a good tolerance for the non-local effect is revealed. Note that actually the BGS obtained from the proposed method consists of two Lorentz spectra as illustrated in Fig. 7(a), we just show the spectrum at lower frequency in Fig. 10(b) for the sake of visualization.

 

Fig. 10 The BGS profiles at the hotspot located at the end of the front section of sensing fiber using (a) the previous method; (b) the proposed scanning method.

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For further demonstration, the BFS at the hotspot with each temperature step using both methods are obtained by fitting the corresponding BGS, as depicted in Fig. 11, where the linear regression performed to the BFS data obtained from the proposed method shows a good agreement with temperature. However, the BFS obtained from the previous method, which presents a parabolic tendency, proves that the method highly suffers from the non-local effect inside the front fiber segment.

 

Fig. 11 The BFS at the hotspot with each temperature step for both methods

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In order to validate the performance of the fitting method described previously, we replace the 4-m-long hotspot at the end of the front segment of sensing fiber by a 2-m-long hotspot, the BFS of which has 35 MHz difference with respect to that of the uniform fiber segment. For convenience the center of the scanning frequency is tuned to match the dominant BFS over the front fiber segment (${\nu }_B={\nu }_{B1}=10.652GHz$), so that a two-peak BGS at the same hotspot can be quickly obtained. Note that in this case we just focus on the BGS at the end of the front fiber segment, the problems existing in the last fiber segment are ignored. The measured and fitted BGS inside and outside the hotspot at the end of front fiber segment are shown in Fig. 12(a), respectively, in which a nice agreement between the measured data and fitted curve demonstrates the validation of our fitting algorithm. Additionally, it can be observed from Fig. 12(a) that the two peaks of high-order BGS move away from each other at the hotspot location, which matches the situation (i) of Fig. 7(b), meaning that the BFS of the hotspot is higher than that of the uniform part of the fiber. Moreover, the fitted BFS profile around the hotspot obtained by the proposal is also shown in Fig. 12(b), by observing the rising edge of the hotspot, the 2 m spatial resolution can be verified.

 

Fig. 12 (a) The measured and fitted BGS profiles inside and outside the hot-spot location; (b) fitted BFS profile around the hot-spot location.

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At last, a 104-km-long sensing fiber that consists of three fiber segments is used for demonstrating the performance of the proposed sensor in terms of long sensing range. The lengths of the three fiber segments are about 55 km, 24 km and 25 km, with BFSs of 10.652 GHz, 10.882 GHz and 10.652 GHz at room temperature, respectively. In this experiment, the method in [9] and the proposed method are both carried out for comparison. The experimental conditions are set as 2 m spatial resolution, and 16000 averages per trace, which are exactly the same as the conditions reported in [9]. The probe power is set as the + 1 dBm/tone for both method, which is the highest allowable probe power limited by the pulse distortion problem that may occur in the second fiber segment (from 55 km to 79 km) as previously analyzed. The retrieved BFS profiles over the whole sensing fiber obtained by both methods are plotted in Fig. 13(a). It can be seen that the BFS profile obtained by using our proposal has better SNR performance, this is simply because the two orthogonally-polarized probe tones are injected into the detector simultaneously, thus providing twice of the signal power with respect to that using method in [9], in which only one probe tone is acquired by the detector. This statement can be further confirmed by observing the frequency uncertainties of the BFS profiles for both methods, as depicted in Fig. 13(b), which are obtained by calculating the standard deviation (STD) of the BFS values around each fiber position, by using a moving computational window with 20 acquired points. It can be seen that the STD at the end of the sensing fiber by using the method in [9] is 9 MHz, which is exactly twice of the STD using our proposal (4.5 MHz).

 

Fig. 13 (a) The estimated BFS along the 104-km-long sensing fiber by using the proposal and the method in [9]; (b) the standard deviation of BFS versus distance using the proposal and the method in [9].

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In order to verify that the proposed method is not affected by non-local effects, a 2 m hotspot placed at the end of the second fiber segment (point A in Fig. 13(a)) and an another 2 m hotspot placed at the end of the third fiber segment (point B in Fig. 13(a)) are measured. For this purpose, the two hotspots are heated up to 65°C, while the rest of the sensing fiber is maintained at ambient temperature (28°C), presenting 40 MHz BFS difference with respect to that of the two hotspots. The fitted BFS profile around hotspot A and hotspot B by using both methods are shown in Figs. 14(a) and 14(b), respectively. As expected, both methods can detect the hotspot with correct spatial resolution, while the estimated BFS at the hotspot A obtained by the method in [9] shows ~5 MHz BFS error, which is imposed by the non-local effect existing in the second fiber segment. This result demonstrates the capability of our system to provide a 2 m spatial resolution over more than 100 km distance with no impact of non-local effect.

 

Fig. 14 The fitted BFS profiles for both methods around (a) 2 m hotspot placed at the end of the second fiber segment; (b) 2 m hotspot placed at the end of the third fiber segment.

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4. Conclusion

In this paper, the tolerance of the non-local effect using the BOTDA method based on dual-tone probe wave with fixed frequency separation has been studied. We have discovered that the non-local effect would occur in some situations, for instance, when the sensing fiber consists of two long segments with large BFS difference (> 100 MHz). In such a special case there will be always only one probe tone interacting with pump pulse in the front fiber segment, the process of which is exactly equivalent to that of conventional BOTDA method based on sing-tone probe wave. Therefore, the system would suffer from the non-local effect, which imposes systematic errors on the estimated BFS of the hotspot located at the end of the front fiber segment. In order to solve this problem while maintaining the original shape of pump pulse at the output of the fiber, a novel method based on four-tone probe wave has been proposed, in which the probe light consists of two pairs of orthogonally-polarized dual-sideband probe waves with opposite frequency scanning direction. The net gain on the pump pulse generated by the four probe tones is zero, so that the pulse distortion problem can be eliminated. Moreover, when using the proposed method, the Brillouin process inside the front fiber segment is equivalent to that of conventional DSB-based BOTDA method, thus avoiding the impact of non-local effect. The highest probe power allowed to be injected into the fiber is + 1 dBm/tone, which is limited by the pump pulse distortion problem that may occur in the fiber segment with large BFS difference. The performance of the proposed method in terms of the tolerance of non-local effect has been experimentally demonstrated by using a 48.879-km-long standard single mode fiber consisting of two long fiber segments. The capability of long-range sensing of the proposal has been also validated by using a 104-km-long sensing fiber. It has to be mentioned that compared with conventional BOTDA method, two more steps have to be performed to realize the proposal. The one is that the two probe tones have to be detected together, so that more complex fitting method has to be developed. The other step is that the fiber with high-order acoustic mode has to be used to distinguish the moving direction of BFS change with respect to the center scanning frequency. These two aspects are expected to be improved in our future work.