1. Introduction

In recent years, distributed optical fiber sensors based on stimulated Brillouin scattering (SBS) have received great attention for the purpose of health-monitoring in the civil and geotechnical fields, due to the ability of a large area of coverage. In the common configuration, named Brillouin Optical-fiber Time Domain Analysis (BOTDA), a pulsed pump lightwave interacts with a counter-propagating cw Stokes lightwave, so that, at each fiber section, the Stokes beam is amplified by a factor depending on the local SBS gain and local pulse intensity. When performing measurements over long fibers (tens of km) the fiber attenuation reduces the pump power, and therefore the signal-to-noise ratio (SNR) [1]. Moreover, the pump beam transfers energy to the Stokes beam as it propagates down the fiber, therefore its energy is depleted in a measure depending on the whole gain distribution along the fiber. This nonlocal effect is known to induce a distortion in the Brillouin gain spectra (BGS), especially in the common case of fibers with nearly uniform Brillouin shift distribution. This distortion affects the accuracy of Brillouin frequency shift estimation [2,3].

Different techniques have been proposed to extend the range of BOTDA sensors. One technique is based on the recovery of pump energy by distributed Raman amplification. The method is aimed to counteract the effect of fiber attenuation on SNR degradation over long fibers. Although an astonishing sensing range of 120 km has been reported by this method [1], it has the drawback of requiring high Raman powers and a more complex interrogation system with respect to standard BOTDA systems. Another approach makes use of coded pump pulses with the purpose of increasing the SNR. Distributed sensing over 120 km sensing length has been also reported by this technique [4]. Finally, a time-division multiplexing [5,6] method has been proposed and demonstrated.

Recently, we proposed a technique capable of alleviating nonlocal effects due to pump depletion in long-range BOTDA measurements [7]. The method is based on the use of a double sideband (DSB) probe beam composed by the Stokes and the anti-Stokes component. The two beams have equal intensities at their launching section and are frequency-shifted with respect to the pump beam by the same amount. By using a DSB probe, pump depletion due to interaction with the Stokes beam can be compensated by the pump gain arising from interaction with the anti-Stokes beam. On the receiver side, the depleted anti-Stokes line emerging from the fiber is filtered out and the Stokes gain is measured. The technique, whose effectiveness has been experimentally demonstrated for both time-domain and frequency-domain configurations [7,8], has the advantage that only a slight modification of the conventional BOTDA configuration is required. Moreover, as the pump gain obtained by the anti-Stokes line matches the pump depletion induced by the Stokes line, nonlocal effects are, at a first order, canceled out and the BGS shape is preserved. In contrast with Raman-assisted configurations, the DSB technique focuses on the compensation of nonlocal effects due to pump depletion, rather than compensation of fiber attenuation. On the other hand, a reduced pump depletion also improves the SNR as a result of the higher pump energy available.

While the gain-loss technique has been proved to be effective in reducing nonlocal effects, its range of validity is limited when higher powers and/or longer fibers are involved [9]. Actually, two mechanisms come into play, causing a limited compensation of nonlocal effects. First, the Stokes line is amplified along the pulse length while the anti-Stokes line is depleted. Therefore, even though the two probe lines may have equal intensities before interacting with the pump, the Stokes energy integrated along the pulse width is higher than the corresponding anti-Stokes energy, thus leading to a residual pump depletion. Furthermore, real pump pulses have some leakage, depending on the characteristics of the modulator employed to form the pulses. Pump leakage interacts with the Stokes and anti-Stokes cw components along the fiber length before pulse arrival. As a consequence, a power unbalance between Stokes and anti-Stokes power is generated along the fiber. Still, this mechanism leads to a reduced compensation of pump depletion.

In this work, we show that the gain-loss technique can be enhanced by use of a DSB probe, in which the injected anti-Stokes power is higher than the injected Stokes power. In this way, the two mechanisms described above can be counteracted, leading to a more efficient compensation of pump depletion. In particular, we show that for each measuring condition an optimal value of the Stokes/anti-Stokes power ratio exists, by which nonlocal effects are best compensated.

The paper is organized as follow: in section 2 we report the results of a numerical analysis showing the influence of Stokes/anti-Stokes power ratio on pump depletion. In Section 3 we describe the experimental set-up used to validate the technique and report the results over 8km- and 50km- single-mode fibers with 5 meter spatial resolution. Conclusions will follow.

2. Numerical analysis

The interaction between a pulsed pump beam and a counter-propagating double sideband probe beam was analyzed by carrying out a number of simulations, based on the following system of coupled equations [10]:

In Eqs. (1-3), I_P, I_S and I_AS denote the pump, Stokes and anti-Stokes intensity, respectively, n is the fiber refractive index, c is the light velocity in the vacuum, g_B is the Brillouin gain, and α is the fiber linear loss. The frequency offset between the pump and the Stokes line, indicated as ν, is assumed to be equal to the frequency offset between the pump and the anti-Stokes beam, so the pump-Stokes and pump-anti-Stokes interactions are described by the same gain coefficient. Moreover, we assume that the pump pulse width is sufficiently longer than the phonon lifetime (≈10 ns), so that a quasi-stationary model can be employed. The effect of the finite extinction ratio of the modulator used to generate the pump pulses is taken into account in our simulations, by superimposing to the pulse a dc level representing the leakage from the modulator.

Simulations have been carried out by considering a fiber length of 10 km, a pulse width of 500 ns, a pulse peak power of 100 mW, a Brillouin peak gain of 1.4⋅10⁻¹¹ m/W, an intrinsic SBS linewidth of 35 MHz and a linear loss of 0.2 dB/km. Note that a pulse width of 500 ns, corresponding to a spatial resolution of 50 m, is well above the typical resolution of long-range BOTDA measurements (a few meters or less). This choice has been done to simplify the theoretical simulation process. Actually, the method employed to solve the equations requires a computation time increasing quadratically with the number of fiber sections used for discretization, which in turns depends on the ratio between fiber length and pulse length [11].

A first set of simulations has been performed by considering a uniform fiber (constant Brillouin frequency shift). The pulse leakage is set to 30 dB. Equations [1–3] were solved numerically for a range of pump-probe frequency shifts, so as to retrieve the BGS at each fiber section. After solving the equations, a curve-fitting procedure with a single Lorentzian fitting function was applied to the retrieved BGS. The results obtained for a Stokes input power of 500 µW and various anti-Stokes input powers are reported in Fig. 1 . In particular, Fig. 1(a) reports the SBS peak gain, while Fig. 1(b) reports the full-width-at-half-maximum (FWHM) bandwidth of the fitted spectra. From Fig. 1(a) it is seen that, for a single sideband probe the peak gain decreases of about 8.5 dB along the fiber. Note that fiber attenuation is responsible for a BGS peak reduction of a mere 2 dB (0.2 dB/km × 10 km), while the rest is due to SBS-induced pump depletion. In case of a DSB probe the gain distribution along the fiber is modified, depending on the injected anti-Stokes power. In particular, increasing the anti-Stokes input power the peak gain is increasingly higher at the fiber input section, while reducing at a lower rate along the fiber. The lower depletion rate is obviously due to the presence of the anti-Stokes signal, which transfers energy to the pump pulse. On the other hand, the higher BGS peak gain at the fiber input section can be explained by considering that, increasing the anti-Stokes input power the intensity of the cw Stokes beam is also higher, due to the energy transfer with the anti-Stokes beam intermediated by the pump leakage. Therefore, the interaction at the input section involves a higher Stokes power, giving rise to a higher BGS gain. Note that for higher anti-Stokes powers (> 5000 μW in our simulation) the gain distribution is no longer monotone, rather the gain first reduces and then increases in the last portion of the fiber, revealing a condition of overcompensation of pump depletion.

 

Fig. 1 BGS peak gain (a) and bandwidth (b) distribution along a uniform 10-km fiber, calculated for a Stokes input power of 500 µW and an anti-Stokes input power ranging from 0 μW (single sideband probe) to 10000 μW.

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From Fig. 1(b) we note that in case of single sideband probe beam the BGS bandwidth increases up to about 62 MHz. This is due to the different gain experienced by the spectral components of the BGS in presence of pump depletion [10]. On the other hand, the same figure shows that increasing the anti-Stokes input power up to 1500 μW a narrower BGS is achieved at each fiber section, thanks to the spectral compensation operated by the anti-Stokes component of the probe beam. However, it is also seen that this trend is reversed for higher anti-Stokes powers. For anti-Stokes input powers higher than 1500 μW, the rate at which the BGS bandwidth increases along the fiber becomes larger, finally leading to BGS bandwidths even larger than in the case of a single sideband probe. To better illustrate this point, we report in Fig. 2 the normalized BGS at the fiber rear section (z = 10000 m), as extracted by the calculated signals. The figure shows that for an input anti-Stokes power of 3000 μW or larger, the BGS exhibits a spectral dip around the resonance. This effect can be explained by considering that, at each fiber section the spectral components of the BGS are amplified by a factor proportional to the intensity of the anti-Stokes component, the latter being maximum at the fiber rear section.

 

Fig. 2 Normalized Brillouin gain spectrum calculated at the rear section of a uniform 10-km fiber, for a Stokes input power of 500 µW and an anti-Stokes input power ranging from 0 μW (single sideband probe) to 10000 μW.

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For too large anti-Stokes input powers, this amplification cannot be sustained for all the spectral components of the BGS: more precisely, the gain factor is lower around the resonance due to the larger energy transfer from the pump beam to the Stokes beam. It is interesting to note that the BGS broadening rate starts to increase for such an anti-Stokes input power, that the overall BGS peak gain reduction is lower than 2 dB, which represents the loss due to fiber attenuation. That means that an overcompensation of the SBS gain drop associated to pump depletion leads to a less uniform BGS bandwidth profile.

The numerical analysis suggests that an optimal value of the anti-Stokes input power exists, for which pump depletion is best compensated. For lower or higher anti-Stokes input powers the BGS bandwidth profile along the fiber is less uniform than in the optimal case. In order to establish the optimal anti-Stokes input power to be set for a given set of parameters, we adopt, as figure of merit, the standard deviation of the BGS bandwidth distribution along the fiber. In other words, the optimal power is found as the one giving rise to the most uniform BGS bandwidth distribution.

The results of this analysis are reported in Fig. 3 . The Stokes input power was set to 500 µW, 1000 µW and 2000 µW, respectively, while the other parameters are the same as in the previous simulation. We observe that for each fixed Stokes input power, there exists an anti-Stokes input power for which the standard deviation of the BGS bandwidth distribution is the lowest. It is important to note that, in any considered case the optimal anti-Stokes input power is larger than the Stokes input power. In particular, the minimum found for a Stokes input power of 500 µW, 1000 µW and 2000 µW, is P_ASL=1700 µW, 2500 µW and 3900 µW, respectively. An optimal anti-Stokes input power higher than the Stokes input power was expected, following the considerations reported in the previous section. Therefore, the use of an unbalanced DSB probe appears to be more effective than a balanced DSB probe. Note also that the calculated curves have quite large minima, indicating that the choice of the optimal anti-Stokes input power is not critical. From Fig. 3 we observe that, even in the optimal case the standard deviation is not zero, i.e. the BGS bandwidth profile is not flat. Also, when increasing the Stokes input power the minimum standard deviation also increases. This indicates that the technique is more effective when operating at low Stokes input powers. On the other hand, it must be considered that a lower Stokes input power also results in a lower SBS gain, and therefore a lower SNR.

 

Fig. 3 Standard deviation of the calculated BGS bandwidth distribution along a uniform 10 km fiber, as a function of the anti-Stokes input power and for three different Stokes input powers.

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We carried out other simulations by setting the pulse leakage to 20 dB or 40 dB. The results indicate that the minimum BGS bandwidth standard deviation increases with pump leakage, therefore the latter should be kept as low as possible. As regards the effect of the pump leakage on the optimal anti-Stokes input power, the latter will increase or decrease with pump leakage, depending on which is the dominant contribution to residual pump depletion. In particular, in case of relatively intense and/or long pulses (such as the case of Fig. 3), the Stokes/anti-Stokes unbalance is mainly produced by the interaction of the probe with the pump pulsed component. In this case, the optimal input anti-Stokes power is higher when the pulse leakage is reduced (see the rightmost column in Table 1 ). Actually, in case of a large pulse leakage the injected anti-Stokes signal must be kept low enough to avoid a rapid depletion of the anti-Stokes energy along the fiber and therefore a less efficient compensation. On the other hand, in case of a small leakage level the depletion rate of the anti-Stokes energy is smaller, so the anti-Stokes input signal can be increased to better compensate the unbalance induced by the pump pulsed component.

Table 1. Optimal anti-Stokes input power as calculated for different values of the pulse extinction ratio (ER) and pulse peak power (P_p).

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The situation changes for narrower and/or weaker pulses. In this case, the main contribution to the Stokes/anti-Stokes power unbalance is the interaction of the probe with the pump dc component. In this case, the optimal anti-Stokes input power reduces when the pulse leakage is lower, finally converging to the Stokes input power at very low leakage levels [10]. To give quantitative results, we report in the leftmost column of Table 1 the optimal anti-Stokes input power as calculated in the same conditions as before, except for the pulse peak power set to 10 mW.

A new set of simulations has been done, by considering this time a non uniform fiber. In fact, it is known that nonlocal effects, beside leading to a broadening of the BGS bandwidth, give rise to systematic errors in the Brillouin frequency shift determination when the latter is not uniform [3].

Numerical tests were performed by assuming a 20-MHz perturbation located along the last 500 m of an elsewhere uniform 10 km fiber. Still, a Stokes input power of 500 µW was considered. Figure 4 reports the Brillouin shift profile along the fiber obtained by applying the curve-fitting procedure to the calculated signals. It is seen that when a single sideband probe beam is considered, the Brillouin frequency shift at the perturbation is overestimated by about 5 MHz. This is because the leftmost components of the spectral gain profile centered at 20 MHz, are more attenuated than the rightmost components, due to pump depletion along the preceding fiber length. Therefore, the BGS along the perturbation is distorted, and its center of gravity is blue-shifted. Of course, in case of negative perturbation an underestimation of the Brillouin frequency shift at the perturbed region is expected, based on similar considerations. On the other hand, Fig. 4 illustrates that this error is reduced using a DSB probe beam with a proper value of the Stokes/anti-Stokes input power ratio. Note that for too large input anti-Stokes powers, the overcompensation of pump depletion leads to increasing systematic errors along the fiber.

 

Fig. 4 Brillouin frequency shift profile reconstruction along the last 5 km of a non uniform 10 km fiber, obtained by Lorentzian fitting the numerically computed BGS. The Stokes input power was 500 µW while the anti-Stokes input power was ranging from 0 μW (single sideband probe) to 10000 μW.

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In conclusion, the numerical analysis suggests that, by adequately tuning the Stokes/ anti-Stokes power ratio in a DSB-BOTDA configuration, the BGS bandwidth variation and the systematic errors in Brillouin frequency shift reconstruction are minimized. From an experimental point of view, the choice of this power ratio may be done by trying to minimize the BGS bandwidth variation along the sensing fiber.

3. Experimental results

The experimental scheme depicted in Fig. 5 has been used to validate the technique. The configuration has only slight modifications with respect to a conventional BOTDA system. Light from a 1550 nm distributed feedback (DFB) diode laser is first split by a 3-dB optical coupler. In the upper branch, the two probe sidebands are generated by driving the electro-optic modulator IM1, operating in the suppressed-carrier regime, with an opportune rf signal. The fiber Bragg grating FBG1 reflects the anti-Stokes line while transmitting the Stokes line. By an optical circulator the two sidebands are sent to two separate erbium-doped fiber amplifiers (EDFA).

 

Fig. 5 Experimental set-up for DSP-BOTDA measurements. DFB-LD: distributed feedback diode laser; IM: electro-optic intensity modulator; EDFA: erbium-doped fiber amplifier; PS: polarization scrambler; FBG; fiber Bragg grating; PD: photodetector; DAQ: acquisition card.

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After amplification, the probe lines are recombined and finally launched in the fiber. In the lower branch, pump pulses are generated through another electro-optic modulator (IM2) (extinction ratio ≈30 dB), amplified and polarization-scrambled before being launched in the opposite side of the fiber. The probe beam emerging from the fiber is sent to a second fiber Bragg grating (FBG2) with a reflection spectrum perfectly matched to FBG1, so as to reject the anti-Stokes component. Finally, the intensity of the filtered probe is acquired by use of an ac-coupled photodetector (125 MHz bandwidth). The set-up permits to arbitrarily control the power of the Stokes and anti-Stokes components launched into the sensing fiber, by properly setting the optical gain of EDFA1 and EDFA2.

The first tests were carried out along an 8 km single-mode fiber. Measurements were performed by sweeping the frequency difference between the Brillouin pump and probe signal over a 200 MHz range centered on the expected Brillouin frequency shift of the fiber. The pump pulse width was set to 50 ns (5 meters spatial resolution), the input peak pump power was ≈400 mW, while the input Stokes power was 200 µW. We report in Fig. 6 the Brillouin gain peak and bandwidth distributions measured along the fiber, for different anti-Stokes input powers. The results agree qualitatively with the numerical analysis shown in the previous Section. In particular, increasing the anti-Stokes input power the Brillouin gain increases at the front section, while the overall gain drop is reduced.

 

Fig. 6 Brillouin gain spectrum peak gain (a) and bandwidth (b) distribution along the 8 km fiber, measured for an input Stokes power of 200 µW and an anti-Stokes input power ranging from 0 μW (single sideband probe) to 4000 μW.

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In particular, note that for an anti-Stokes input power of 4000 µW the overall gain loss is reduced below fiber attenuation (≈1.6 dB), therefore a condition of overcompensation occurs. As predicted by the numerical analysis, in this condition the BGS bandwidth tends to be higher in the final portion of the fiber, with respect to the case of optimal compensation (compare the magenta and the black curves in Fig. 6(b)).

We show now the Brillouin frequency shift profile reconstruction obtained in the various cases (see Fig. 7 ). Due to the winding tension, the strain was not uniform along the fiber, in particular a change in Brillouin frequency occurred along the last 400 meters of the spool. It is seen that the mean Brillouin frequency along the last 200 m increases from ≈10849 MHz in case of single sideband probe, to ≈10852 MHz in case of input anti-Stokes power equal to 2000 µW or 4000 µW. A mean Brillouin frequency shift of 10852 MHz was verified to be the most accurate value, by performing a measurement with the pump and probe launching sections inverted. Noticeably, the condition of best estimation of the Brillouin frequency shift also corresponds to that leading to a more uniform BGS bandwidth, whose measured standard deviation decreases from ≈2.2 MHz in case of single sideband probe to ≈1.6 MHz in case of DSB probe with P_ASL = 2000 μW. This results agrees with the numerical predictions shown in the previous section.

 

Fig. 7 Brillouin frequency shift profile reconstruction along the last km of the 8 km-long fiber. The Stokes input power was set to 200 µW, while the anti-Stoke input power was ranging from 0 μW (single sideband probe) to 4000 μW.

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Another set of measurements was carried out along a uniform single-mode 50km-long fiber spool. The first measurements were performed by adopting a pulse width of 200 ns (20 m spatial resolution), while setting the Stokes input power to 500 µW. In order to show the effect of overcompensation, we performed measurements with an anti-Stokes input power up to 5500 μW. Figure 8 clearly reveals that for moderate input anti-Stokes power the gain profile slope is reduced, while for higher anti-Stokes powers (> 1000 μW in our experiment) the gain distribution is not monotone, increasing in the last portion of the fiber. This result agrees with the theoretical predictions reported in Fig. 1(a).

 

Fig. 8 BGS peak gain distribution along the 50-km fiber, measured for a pulse width of 200 ns, a Stokes input power of 500 µW, and different anti-Stokes input powers.

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In Fig. 9 we report the Brillouin shift profile reconstructions. For clarity purposes, we only report the results for P_ASL = 0 μW (single sideband probe), P_ASL = 500 μW and P_ASL = 1000 μW. It is seen how the accuracy of the reconstruction improves by moving from a single sideband probe configuration (blue curve), to a dual sideband configuration (red and green curves), with the best result achieved for the unbalanced DSB probe case. The standard deviation of the retrieved Brillouin frequency shift profile is ≈3.4 MHz in the case of single sideband probe, ≈2.7 MHz in the balanced DSB case and ≈1.6 MHz for P_ASL = 1000 μW. The corresponding values of the BGS bandwidth standard deviation are ≈3.61 MHz, ≈2.40 MHz and ≈2.08 MHz, respectively, with input anti-Stokes powers larger than 1000 μW giving rise to less uniform BGS bandwidth distributions.

 

Fig. 9 Brillouin frequency shift distribution along a uniform 50-km fiber, measured for a pulse width of 200 ns, a Stokes input power of 500 µW, and an anti-Stokes input power ranging from 0 µW (single sideband probe) to 1000 µW.

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Last measurements were carried out by using a pulse width of 50 ns (5 meters spatial resolution). The retrieved Brillouin frequency shift profiles are reported in Fig. 10 . Although in this case the measurements are less accurate due to the lower SNR associated to the shorter pulse, the results confirm that adopting an unbalanced double sideband probe beam one obtains an improvement in the accuracy in the Brillouin frequency shift reconstruction. In particular, the standard deviation of the Brillouin frequency shift reconstruction in the last km of the fiber is ≈20 MHz for the single sideband case, ≈10 MHz in the balanced DSB case and ≈4 MHz for P_ASL = 1000 μW. The corresponding values of the BGS bandwidth standard deviation are ≈11.3 MHz, ≈11.2 MHz and ≈4.5 MHz.

 

Fig. 10 Brillouin frequency shift distribution along a uniform 50-km fiber, measured for a pulse width of 50 ns, a Stokes input power of 500 µW, and an anti-Stokes input power ranging from 0 µW (single sideband probe) to 1000 µW.

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4. Conclusions

A long-range BOTDA configuration has been proposed and experimentally demonstrated. The technique takes advantage of the use of an unbalanced DSB probe beam, so as to compensate pump depletion more efficiently with respect to a previously proposed configuration making use of a balanced DSB probe beam.

A limitation of the proposed method is that, only SBS gain loss due to pump depletion can be compensated. In fact, if one uses a higher anti-Stokes input power aimed to compensate the gain loss due to fiber attenuation, this results in a distortion of the BGS leading to systematic errors in the Brillouin frequency shift estimation. A possible solution is to combine the proposed technique with methods aimed to increase the SNR, such as those based on coding schemes applied to the pump pulse [4].

As a final remark, we note that in our experimental scheme the two probe sidebands are first spatially separated and then combined, therefore they generally will have a different state-of-polarization (SOP) along the sensing fiber. Even though the pump field is polarization-scrambled, the different SOP of the two probe sidebands increases the polarization-induced noise, especially in the rightmost fiber region where the intensity of the anti-Stokes component is higher. A possible solution may be scrambling both pump and probe fields, or using a dual parallel Mach-Zehnder (DP-MZ) modulator to generate the DSB probe beam. By driving the DP-MZ modulator with opportunely phase-shifted rf signals, an unbalanced DSB probe beam with arbitrary Stokes/anti-Stokes power ratio can be generated, with the two sidebands having the same SOP.