A new technology for chaotic Brillouin optical correlation domain analysis (BOCDA) has been proposed and experimentally demonstrated with high spatial resolution. However, the off-peak amplification induced by the chaotic autocorrelation sidelobes limits the measurement range of chaotic BOCDA system. The time-gated scheme is introduced to suppress the off-peak amplification. With the pump pulse of 120 ns duration, the time-gated chaotic BOCDA has been experimentally achieved with a 9 cm spatial resolution over a 10.2 km measurement range. The standard deviation in the local Brillouin frequency shift is ± 1.8 MHz.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Nowadays, the construction of artificial intelligence infrastructure has been developed rapidly. Distributed fiber sensors based on stimulated Brillouin scattering (SBS) have been intensively regarded as a quite competitive technology for structural health monitoring of large civil structures because they can carry out long-range distributed temperature or strain measurement .
The most extensive application based on SBS is Brillouin optical time domain analysis (BOTDA) [2, 3], in which the measurement range can reach 72 km whereas the spatial resolution is restricted to 1 m because of the inherent limitation of the phonon lifetime . To increase the spatial resolution of the BOTDA system, numerous complicated and time-consuming schemes such as differential pulse-width pair [5–7], dark pulse , and Brillouin echoes , have been proposed. Besides, the ultra-long measurement range of the BOTDA system has been extended to above 120 km based on optical pulse coding  or pre-pumped Golay coding  and distributed Raman [12, 13] or Brillouin amplification [14, 15]. The ultra-fast measurement for distributed dynamic strain has been demonstrated in BOTDA system based on an optical chirp chain probe wave .
Another significant SBS-based configuration is Brillouin optical correlation domain analysis (BOCDA) , which features high spatial resolution and randomly accessible sensing position. An ordinary BOCDA system based on the continuous lightwave with the sinusoidal frequency modulation suffers from a trade-off between the measurement range and the spatial resolution . To overcome the trade-off problem, many techniques such as double lock-in amplifiers , differential measurement  or combination of differential measurement and double modulation  have been demonstrated. However, these methods considerably increase the complexity of the BOCDA systems.
In fact, for the BOCDA system, the Brillouin interaction is spatially confined to the correlation peak, which is theoretically related to the coherence length of the source. Therefore, high spatial resolution mandates the use of sources with comparatively low coherence. Recent advances for controlling the coherence of sources in BOCDA include phase-modulation by a binary pseudo random bit sequence (PRBS) [22, 23] or perfect Golomb codes [24, 25], and direct modulation by PRBSs . However, these schemes allow only one correlation peak in the fiber under test (FUT) to avoid ambiguity which practically limits the dynamic range of the measurement . To extend the measurement range, the time-gated scheme by overlaying an amplitude pulse modulation on top of the PRBS-based BOCDA is utilized . For one thing, the amplitude pulse modulation guarantees that a large number of correlation peaks can be simultaneously addressed along the fiber. For another, the residual off-peak amplification is restricted to the spatial length of the modulation pulse instead of existing in the entire sensing fiber. But, 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.
Recently, the BOCDA systems based on new low-coherence sources, such as four-wave-mixing  and amplified spontaneous emission (ASE) , have been demonstrated with the improved spatial resolution. Very recently, the chaotic laser, another type of low coherence light with an extensive application [30, 31], has been successfully applied to BOCDA systems [32, 33]. Nevertheless, the off-peak SBS interaction induced by the chaotic autocorrelation sidelobes , which are the same as the “coding noise” of PRBS, contributes an additional noise mechanism, leading to the limited 3.2 km measurement range of the present chaotic BOCDA system.
In this paper, the time-gated chaotic BOCDA is firstly proposed and experimentally verified, where an amplitude pulse is modulated on the chaotic light signal in the pump branch. Consequently, the residual SBS interactions existing outside the central correlation peak could be largely inhibited. The experimental results are finally demonstrated with a 9 cm spatial resolution over a 10.2 km measurement range.
2. Principle of operation
Stimulated Brillouin scattering is a nonlinear interaction, which can couple counter-propagating pump and probe waves detuned in frequency, mediated by a stimulated acoustic field through electrostriction effect. Effective coupling requires that the difference between the two optical frequencies matches the Brillouin frequency offset νB of the fiber.
The complex envelopes of the acoustic density variations in position z along a fiber of length L and at time t are given by :
where vg is the group velocity of light in fiber, τ is the acoustic phonon lifetime, AP (t) denotes the instantaneous complex envelope of the pump wave entering the fiber at z = 0 and propagating in the positive z direction, whereas the probe wave propagates from z = L in the negative z direction. The position-dependent temporal offset θ (z) is defined as θ (z) = (2z - L)/ vg. In the proposed scheme, the pump, modulated by a square pulse simultaneously, and probe waves are generated from a same chaotic source, which are expressed by the following equations:
here u (t) is a common, normalized envelope function with an average magnitude of unity with regard to chaotic signals, and AP0 and AS0 are constant magnitudes of the pump and probe, respectively. In Eq. (2), rect (ξ) equals 1 for \ξ \ ≤ 0.5 or zero elsewhere and τP is the duration of the pump amplitude pulse that is adjustable and greater than acoustic phonon lifetime τ.
As in Eq. (4), the , the expectation value of the acoustic field magnitude at position z (for t »τ), is relevant to the C< θ(z) >. Where C < θ(z) > is the cross correlation between chaotic pump and probe waves due to the fact that the output of chaotic source can be assumed in terms of an ergodic random process. The acoustic field would be confined to a single correlation peak width, within which only does the SBS amplification interaction. Thus, the spatial resolution is theoretically determined by the sole narrow segment , whose extent Δz is given by the width of the dominant correlation peak, located at the center of the fiber where θ (L / 2) = 0. Note that the chaotic pump wave is modulated by an amplitude pulse. Suppose that the is subject to the function of rect (ξ), which causes only the magnitude of the acoustic field within the peak exists. The acoustic field in each correlation peak is stimulated once the pump pulse reaches the position z and grows up to the steady state condition. Then the SBS amplification quickly decays to zero at the terminal of each pulse. The configuration is analogous to a time-gated PRBS-based BOCDA scheme .
The schematic diagram of the previous chaotic BOCDA [32, 33] is illustrated in Fig. 1(a). The chaotic signal is split in two paths, pump branch maintaining the center frequency ν0 and probe branch detuned in frequency which matches the Brillouin frequency offset. And then it is launched into two opposite-ends of the FUT. At the center (z = L / 2) of the sensing fiber, the acoustic field is steadily and permanently generated in the correlation peak (CP). Besides, there are also residual side peaks near the main peak, which are the result of a weak amplitude autocorrelation of the chaotic signal occurring at the delay time τd of the external cavity, and a non-zero average value of the correlation function outside the peaks . Such residual off-peak SBS amplification contributes an additional noise mechanism, and the detrimental interactions persistently accumulate along the fiber.
For the suppression of the background noise structure, we propose a new time-gated chaotic BOCDA scheme, as depicted in Fig. 1(b). The pump wave is amplitude-modulated by a square pulse with a pulse width of greater than acoustic phonon lifetime. And the cross correlation between chaotic pump and probe waves operates at specific positions where rect (ξ) equals 1. A bit of modulated pump waves is extracted to integrate with the whole probe waves. Consequently, in the vicinity of the fiber center the pump and probe are correlated within integration time, i.e., the modulated pulse width τP. The driving force for the acoustic field generation keeps a steady non-zero value. In all other locations, the SBS interaction is largely inhibited. Since the time-gated chaotic BOCDA scheme provides a strong suppression of the Brillouin background noise structure at the positions except the CP, a large enhancement of the measurement range will be obtained.
Figure 2(a) shows the waveforms of the experimentally measured pump light signals with and without the amplitude pulse modulation, as are denoted by the red and blue lines, respectively. Compared with the chaotic BOCDA system without the pulse modulation, a short section of the red curve around 280 ~400 ns is obviously amplitude-modulated by a 120 ns square pulse in the time-gated scheme. Figure 2(b) displays the autocorrelation characteristics of the chaotic pump signals with and without the amplitude pulse, respectively. It can be seen that the accumulated background noise structure can be largely suppressed by the amplitude pulse modulation. In particular, a magnified view of the side-lobe at the external cavity of τd = 123.8 ns is illustrated in the inset of Fig. 2(b). The autocorrelation coefficient at τd = 123.8 ns is decreased from C1 = 0.205 to C2 = 0.053 by the amplitude pulse modulation.
We further compare the Brillouin gain spectra (BGS) in the chaotic BOCDA systems with and without the pump pulse modulation. Figure 3(a)-3(c) show the BGS at different positions of 5.0, 8.5, and 10.0 km along a 10.2-km long sensing fiber in both systems, respectively. The red and blue lines represent the BGS with and without the utilization of the time-gated scheme, respectively. Obviously, in the chaotic BOCDA system without the pulse modulation, the background structure of the Brillouin gain spectrum increases with the sensing fiber length and conversely keep relatively small changes in the time-gated chaotic BOCDA system. Moreover, the linewidth of the BGS in the time-gated chaotic BOCDA system is stabilized at 49.6 MHz. The signal-to-background ratio (SBR) defined as the amplitude ratio of the signal peak to the background peak  is experimentally measured to quantitatively evaluate the equality of the extracted BGS. Figure 3(d) shows the SBR as a function of the fiber position. The obvious increments of SBR, δ1 = 2.43 dB at the front and δ2 = 1.48 dB at the end, could be obtained along the entire fiber with the time-gated scheme. When the sensing fiber is longer than 8.0 km, the SBRs of the chaotic BOCDA system without the pulse modulation are almost constant at 1.00 dB, which means the signals of Brillouin frequency shift (BFS) are submerged in the background structure induced by the off-peak amplification. However, by utilizing the time-gated scheme to suppress the off-peak interaction, the signal of the BFS can be extracted when the sensing fiber reaches 10 km.
The parameters of the pump pulse, the pulse duration and extinction ratio, are further optimized to achieve the best performance of the time-gated chaotic BOCDA system. Figure 4(a) illustrates the SBR versus the pulse duration from 10 up to 200 ns when the correlation peak is located at a specific fiber position z = 7.5 km. It can be seen that the optimal pulse duration is 120 ns. This is because for pulses shorter than 50 ns, the acoustic field does not have enough time to reach the steady-state condition. In contrast, longer pulses introduce more noise accumulated from the side-lobes outside the correlation peaks. Besides, the extinction ratio approaches the maximum 24.3 dB driven by the modulation voltage of 3.5 V for the used electro-optic amplitude modulator (EOM).
3. Experimental setup and results
The experimental setup of the time-gated chaotic BOCDA is depicted in Fig. 5. The chaotic source consisting of a semiconductor laser with an external-cavity optical feedback generates the chaotic signal by selecting appropriate injection current and feedback length. The chaotic output is split into probe and pump branches by a 90/10 fiber coupler. The upper as the probe wave (90%) is modulated in a suppress-carrier, double-sideband format by an EOM, driven by a sine-wave whose frequency matches the BFS of the sensing fiber. Then the modulated probe light through a programmable optical delay generator (PODG), is amplified by an erbium-doped fiber amplifier to 8 dBm. A PODG is employed to realize the localization of correlation peak in the sensing fiber. A polarization scrambler (PS) is used to prevent polarization-dependent fading of the SBS interaction. Light in the pump branch is modulated by another EOM, driven by an optimized square pulse, and then is amplified to 25 dBm. As mentioned before, the pulse duration is 120 ns, and the repeating period is 110 μs exceeding the time-of-flight through the FUT. The pump and probe waves are launched into two opposite-ends of the FUT, respectively. When the chaotic pump and probe waves meet at some location of the FUT, the chaotic probe wave is subject to SBS amplification. The amplified probe signal is transmitted through an optical fiber circulator (OC) and a band-pass filter (BPF), which ensures that only the Stokes wave is retained. The optical power of the filtered wave is recorded by a digital optical power meter (OPM) with an integrating sphere sensor. In the inset ‘A’ of Fig. 5, the autocorrelation trace of the output chaotic signal is given. According to the correlation peak width Δτ = 0.27 ns, the theoretical spatial resolution of the sensing system is approximately 2.70 cm . The structure of the FUT is made up of a 10.2 km single-mode fiber (G.655), in which a hot zone about 150 m is placed near 10 km as depicted in the inset ‘B’ of Fig. 5.
The relationship of the BGS with temperature is illustrated in Fig. 6. Figure 6(a) shows the temperature-dependence of BGS in the FUT. The single correlation peak is located into the hot-zone by adjusting PODG. The temperature is changed from 21 °C to 55 °C in succession. A phenomenon that the center frequency of the BGS moves from 10.616 GHz to 10.658 GHz can be obviously observed. From these BGS, we may plot the temperature-dependence of BFS and the uncertainty of the estimated BFS as shown in Fig. 6(b). According to the fitting curve, the temperature coefficient is 1.22 MHz/°C. Figure 6(b) further shows that the maximum standard deviation in the reconstruction of the local BFS is ± 1.8 MHz with 25 times of the repeating measurements. This measurement uncertainty of the BFS is a little higher than that in the previous chaotic BOCDA system . The slight increase of the measurement uncertainty of the BFS is probably related to the modulation of the pump pulse on the chaotic light. As described in , the measurement uncertainty is achieved by calculating the maximum standard deviation of the BFSs. Thus, the measurement uncertainty of the BFS is determined by the BGS, and the broader the BGS, the higher the measurement uncertainty. As we know, the measured BGS is a convolution of the pump spectrum and the actual Brillouin spectrum of the FUT. In the time-gated chaotic BOCDA system, the pulse modulation on the chaotic pump light broadens its optical spectrum to some extent, which ultimately leads to the linewidth increasing of the BGS from 45 MHz to 49.6 MHz. The linewidth widening of the BGS gives rise to the increase in the measurement uncertainty of the BFS.
Figure 7 shows the BFS distribution along the FUT in the chaotic BOCDA systems without (a) and with (b) the time-gated scheme. For the chaotic BOCDA without the time-gated scheme, it’s practically impossible to distinguish between the room temperature and heated zone when the sensing distance exceeds 8.0 km, as is illustrated in Fig. 3(d). However, the time-gated chaotic BOCDA can measure the temperature variation in the heated zone near 10 km due to the suppression of off-peak interaction along the entire sensing fiber.
Figure 8(a) shows a three-dimensional plot of the BGS measured along the FUT. Obviously, the BFS at the hot spot section is clearly distinguished. In the experiment, the temperature of the hot-zone is set to 55 °C and the room temperature is maintained at 21 °C. And there is about 42 MHz BFS at the hot spot section. This value of the BFS matches well with the real temperature variation of 34 °C. Figure 8(b) plots the measured distribution of the BFS along the FUT. And the spatial resolution of the time-gated chaotic BOCDA system can be measured by the value of 10% ~90% of the rise and fall time equivalent length in meter for the hot spot section, where the rise and fall time equivalent length are 8.86 cm and 9.24 cm, respectively. Therefore, the spatial resolution can approximately approach 9 cm along the 10.2 km FUT, which is nearly consistent with the above theoretically expected one.
Besides, we further analyze the effect of pump depletion in the time-gated chaotic BOCDA system. The chosen fiber length of 1 km is comparatively short. This is because that a short fiber has a good uniformity to ignore the effect of the BFS fluctuation, and on the other hand, it can avoid the decrease of signal-to-noise ratio induced by fiber attenuation. The duration of the pump pulse is 120 ns. The chaotic probe signal is generated in the double-sideband suppress-carrier mode. Here, a depletion factor d is introduced to characterize the amount of depletion and its definition comes from . Figure 9(a) shows the depletion factor d as a function of the probe power for the lower frequency sideband, where a fixed input pump peak power is 6 W. Figure 9(b) represents the depletion factor d versus the pump peak power while keeping the probe power constant (3.6 mW). We can see that the pump depletion is checked to be below 0.2%, having a negligible effect on the measurements. One probable reason is that the chaotic pump wave provides the SBS amplification on the chaotic probe waves only within the correlation peak at the meeting location of the FUT, and is not involved in the energy transfer during the whole process of transmission. Another possible reason is that the double-sideband modulation using a symmetric probe waves is much more tolerant to pump depletion . Therefore, the pump pulse plays an important role in the suppression of the off-peak amplification, which is not accompanied by the pump depletion.
In conclusion, a high-resolution long-reach distributed fiber sensor based on time-gated chaotic Brillouin optical correlation domain analysis has been achieved. The destructive stimulated acoustic field induced by the residual off-peak Brillouin interactions has been largely inhibited. The extracted Brillouin gain spectrum is distinctly improved to increase the performance of the chaotic BOCDA system. Under the optimized condition of the modulated pump pulse, the distributed temperature sensing with a 10.2 km-long test fiber and a spatial resolution of 9 cm is experimentally demonstrated. The improved chaotic BOCDA technology will have a great potential in structural health monitoring of large civil structures.
National Natural Science Foundation of China (NSFC) (61527819); 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.
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