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Abstract
Guided acoustic wave Brillouin scattering has gained considerable interest in recent years because of its capacity to detect mechanical features of materials surrounding the optical fiber. Nevertheless, distributed measurements using this mechanism are rarely taken because of the impracticality of the method’s forward scattering mechanism. Recently, remarkable work using ingenious schemes has managed to address the difficulty, which opens a brand new way to achieve position-resolved substance identification. However, due to the long acoustic wave lifetime and insufficient signal-to-noise ratio (SNR), current spatial resolution is restricted to 15–50 m, which is far from practical requirements. Here we propose a novel opto-mechanical time-domain analysis based on coherent forward stimulated Brillouin scattering probing to greatly improve the achievable spatial resolution. The coherent transverse acoustic wave is first created by a long activation pulse and then probed by a short two-tone probe pulse. The two-tone probing process involves a coherent stimulated interaction between the probe pulse and the excited transverse acoustic wave. The interaction, which we first propose here, shows a distinct phase-sensitive characteristic. This new coherent stimulated probing process, if it is well controlled, will enhance the forward stimulated Brillouin scattering intensity and thus improve the SNR of the sensing. Moreover, higher SNR backward stimulated Brillouin scattering is used to detect the intensity evolution of the probe pulse. Owing to this new sensing scheme combined with a more robust demodulation algorithm, we demonstrated a 2 m spatial resolution opto-mechanical measurement over a 225 m long fiber in which we were able to distinguish air from alcohol. These advances greatly facilitate the practicability of forward stimulated Brillouin scattering.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Brillouin scattering is an intriguing nonlinear effect involving the interaction between light and acoustic fields [1,2]. It has been exploited for decades in the distributed fiber sensing domain to measure position-resolved temperature and strain [3–5]. Recently, its capability has been extended to chemical sensing [6,7] through the employment of transverse acoustic waves, which are a set of acoustic fields existing in acoustic waveguides [8,9]. This novel kind of acousto-optic interaction, known as guided acoustic wave Brillouin scattering (GAWBS) [10–15], specifically forward stimulated Brillouin scattering (FSBS) [14,15] in the highly coherent case, has been used in a wide variety of photonic applications, such as high-performance lasers [16,17], optical isolators and circulators [18], frequency comb generation [19], and metrology [20–22].
FSBS can be categorized into two types: radial mode and torsional-radial mode induced scattering [10], both of which have demonstrated the ability to sense mechanical impedance outside the guiding fiber [6,23]. However, the forward scattering characteristic renders the FSBS sensor incapable of spatially resolved distributed measurements. More recently, two remarkable works based on opto-mechanical time-domain reflectometry (OMTDR) [24] or local light phase recovery (LPR) [25] have been independently proposed to realize distributed FSBS resonance measurement for the first time, with a spatial resolution of 15–50 m [24,25]. Both schemes can be divided into three main stages. First, some kind of FSBS interaction is used to sense the transverse acoustic information. Either OMTDR uses the energy transfer between two tones to read the acoustic wave, or else LPR utilizes the pre-excited acoustic vibration-induced phase modulation of a single tone pulse. Second, one employs some technique to record the accumulated FSBS information. The backscattered light from the injected pulse is used to record the optical power at each position in either scheme, with the difference being that OMTDR uses the Rayleigh scattering while LPR uses stimulated Brillouin scattering. Finally, a demodulation algorithm based on differentiation is used to retrieve the local response of the transverse acoustic oscillation. The demodulation methods used in each scheme are determined by the nature of the FSBS interaction.
The spatial resolution of distributed FSBS sensor comes from two sources. One is using pulses’ backscattered light to record the evolution of optical power, so that each measurement point contains information about the state of the adjacent fiber. The other spatial resolution-determining factor is the data-processing. Due to the sensitivity to noise of the operation of differentiation, data smoothing is essential for the demodulation of a distributed FSBS spectrum, which inevitably degrades the spatial resolution. The SNR of the original data determines the smoothing window length, which is then closely associated with the spatial resolution.
In the OMTDR method, the use of a long pulse required by a steady FSBS interaction, as well as the low-SNR detection method using weak Rayleigh scattering, restricts the further improvement of spatial resolution. In the LPR method, although the separation of the activating and probing process permits the employment of a short reading pulse, the single tone probing only applies phase modulation to the probe light, which has a relative weak energy transfer efficiency between the carrier and sideband frequencies. Therefore, it has relatively low SNR and thus restricts high spatial resolution sensing. The current spatial resolution, fundamentally limited by the noise level of the scattered light, poses a restriction on the practical applicability.
In this paper, we theoretically and experimentally propose a novel method named opto-mechanical time-domain analysis (OM-TDA) based on coherent stimulated probing to remarkably improve the performance of a distributed FSBS sensor. The new protocol employs a coherent interaction between a pre-stimulated transverse acoustic wave and a two-tone optical probe pulse. A long optical multi-tone activation pulse is used to pre-excite a transverse acoustic wave which dynamically modulates the refractive index. The dynamically modulated refractive index resembles a moving grating [26–28] and we call this a transverse Brillouin dynamic grating (TBDG). The TBDG permits stable energy transfer between the pump and the Stokes components of the following probe pulse. As for the probing process to sense the excited acoustic wave, unlike the previous work [25] where the probing process is a phase modulation process, our scheme uses a two-tone forward stimulated Brillouin scattering probing process, which has stronger interaction intensity and contributes greatly to the SNR improvement. However, the stimulated probing process concerns coherent interplay with the TBDG, which, if not harnessed carefully, would be detrimental to the sensing result. To record accumulated FSBS interaction with distance, we employ a detection scheme resembling the common Brillouin optical time domain analysis (BOTDA) [29] system to detect the intensity of the two frequency components involved in probe pulse. BOTDA needs injection of light from both ends of the fiber; therefore, the proposed protocol is conventionally named OM-TDA [30]. We use a robust demodulation method based on division followed by differentiation to map the distributed FSBS spectrum. Thanks to the proposed OM-TDA scheme and our efforts to improve the SNR, we experimentally demonstrate a distributed measurement with 2 m spatial resolution for identification of air and alcohol, thereby confirming the technique’s utility in practical applications.
2. PRINCIPLE OF OPERATION
The fiber not only acts as a waveguide for light, but also guides the acoustic wave propagation. Cylindrical single-mode fiber can only support the fundamental light mode, while it can support abundant acoustic modes such as longitudinal, radial, torsional, and flexural elastic waves [9]. While the optical mode is largely confined in the core of the fiber, having no chance to sense the fiber’s surroundings directly, the existence of acoustic modes relies on the guidance of the acoustic waves by the cladding-exterior boundary, making it possible to perceive changes in the external mechanical properties of the surrounding medium. It should be noted that not all the acoustic modes, including longitudinal acoustic modes that resemble bulk acoustic waves, are sensitive to changes at the cladding-external medium boundary. However, transverse acoustic modes, which depend on the resonance across the fiber, are distinctly affected by any alteration of boundary.
Acoustic waves can influence the propagation of light through the photo-elastic effect, which provides opportunities to identify components of surrounding materials by detecting light waves in standard fibers by the process of FSBS. Radial acoustic modes denoted ${R_{0,m}}$ are used here, to represent a set of simplest transverse acoustic fields. The change of external acoustic impedance influences the reflectivity of acoustic waves at the boundary, that is, the changed acoustic impedance affects the acoustic wave lifetime, which is reflected in the spectral linewidth of the FSBS. The quantitative relationship between the mechanical impedance of the external medium and the FSBS spectrum is given by [6,24,25]
where $\Delta v$ denotes the total FSBS linewidth, $\Delta {v_i}$ is the intrinsic FSBS linewidth mainly determined by viscous damping of the acoustic wave, $\Delta {v_b}$ is the linewidth induced by the partial acoustic reflection at the boundary, which is determined by acoustic propagation time across the fiber diameter, ${t_r}$, the acoustic impedance of the exterior material, $Z$, and of silica, ${Z_f}$.
Fig. 1. Schematic of the OM-TDA. (a) A dual-tone long activation pulse and short probe pulse are launched sequentially into the fiber. The beat frequencies between two tones within each of the two pulses are equal. The transverse acoustic wave is excited by the activation pulse to create a stable state, which enhances the energy transfer between the two tones of the probe pulse and is subsequently detected. The blue part of the fiber indicates a different external material compared with rest of the fiber. (b) The low-power CW probe is injected into the fiber from the far end to map the intensity evolution of the two corresponding tones of the probe pulse (orange and violet lines in a) via BSBS. The frequency of the CW probe is swept to get BOTDA signals of the two tones. The BSBS frequency ${\Omega _B}$ is the frequency difference between the CW probe and probe pulse. (c) The BOTDA signals are integrated over frequency to get smoother intensity traces ${P_1}(z)$ and ${P_2}(z)$. (d), (e) The two traces measured are processed mainly by division and differentiation corresponding to Eq. (3) to get the FSBS strength at each frequency. (f) The FSBS frequency, $\Omega $, is swept and the measurement procedure is repeated to obtain the FSBS spectrum as a function of distance along the fiber.
Figure 1 illustrates the operating principle of the distributed OM-TDA measurement scheme. The long activation pulse with two optical frequency components (${\omega _3}$ and ${\omega _4}$), whose beat frequency approximates the acoustic wave resonance frequency, is launched into the fiber, so as to stimulate quasi-steady state transverse acoustic standing wave in the form of a TBDG. Shortly after, another dual-tone (${\omega _1}$ and ${\omega _2}$) short pulse with frequency difference equaling the frequency of the TBDG immediately follows the activation pulse, acting as the probe pulse to detect the lifetime of the existing TBDG in a coherent stimulated scheme. Distinct energy transfer, which is enhanced by the TBDG, occurs between the two frequency components of the probe pulse. We introduced a frequency shift ${\Omega _s}$ between the activation and probe pulse frequencies to separate them, because what we need is the intensity information of the probe pulse, as explained below. This energy transfer from the activation pulse to the probe pulse can be treated as the interaction among two light fields and a steady acoustic field, and quantified by the steady-state coupled nonlinear differential equations [15,24]:
where ${P_{1,2}}(z)$ denote the power of higher and lower frequency components of the probe pulse respectively, $\alpha (z)$ is the optical loss along the fiber, and $g(\Omega ,z)$ is the nonlinear opto-mechanical coefficient, also referred to as the FSBS spectrum. Note that Eq. (2) holds true only if ${P_1}(z){P_2}(z) = {P_3}(z){P_4}(z)$ and ${\varphi _1} - {\varphi _2} = {\varphi _3} - {\varphi _4}$, where ${P_{3,4}}(z)$ are the power of higher and lower frequency components of the activation pulse, respectively, and ${\varphi _j}$ ($j = 1$, 2, 3, 4) are the initial phases of the corresponding tones in the probe and activation pulses. The analysis can be found in Supplement 1.Analyzing Eq. (2), we find that the distributed FSBS spectrum can be extracted by
Apparently, only if both ${P_1}(z)$ and ${P_2}(z)$ are available via measurement, can the distributed FSBS spectrum be demodulated by Eq. (3). To attain ${P_1}(z)$ and ${P_2}(z)$, it is necessary to conduct a probing process. We introduce backward stimulated Brillouin scattering (BSBS), using the BOTDA technique described above for this purpose, enabling us to measure ${P_1}(z)$ and ${P_2}(z)$ indirectly. BOTDA has been used previously to measure nonlinear parameters of fibers [31]. BOTDA is much simpler and has higher SNR compared with the Rayleigh scattering used in the OM-TDR scheme [24]. A low-power continuous wave (CW) is launched into the fiber from the end opposite to that from which ${P_1}(z)$ to ${P_4}(z)$ are launched, enabling us to detect the intensity evolution of the two components of the probe pulse, ${P_1}(z)$ and ${P_2}(z)$, as shown in Fig. 1. Note that the conventionally named probe light in BOTDA is simply called the “CW probe” here, and the traditional pump pulse in BOTDA is referred to as the probe pulse in OM-TDA. The power of the CW probe is low enough to have negligible influence on the local power of the probe pulse. The frequency of the CW probe is swept, enabling us to obtain the distributed BSBS spectrum (BOTDA signal) for each tone of probe pulse as shown in Fig. 1(b). The BOTDA signals are then integrated over frequency to merge the BOTDA signal into intensity traces shown in Fig. 1(c). This integration has better performance than spectrum fitting used in Ref. [25] on mitigating the strong intensity fluctuations in the raw measured traces which are caused by the temperature or strain-induced inhomogeneity of the Brillouin frequency shift along the fiber. Under the small BSBS gain approximation, the synthesized traces in Fig. 1(b) can be expressed as [25]
where $\kappa $ is the optical power-voltage conversion coefficient, ${g_B}$ is the averaged BSBS gain coefficient, $\Delta z$ is the spatial resolution of the BOTDA system, and $L$ is the length of the sensing fiber. All these parameters are independent of $z$, so the obtained traces ${P_1}^\prime (z)$ and ${P_2}^\prime (z)$ are directly proportional to ${P_1}(z)$ and ${P_2}(z)$, respectively, meaning that replacing ${P_{1,2}}(z)$ with ${P_{1,2}}^\prime (z)$ has no effect on the results of demodulated FSBS spectral linewidth according to Eq. (3). This enables us to determine the most important data, namely ${P_1}(z)$ and ${P_2}(z)$. From ${P_1}(z)$ and ${P_2}(z)$ we then retrieve the FSBS spectrum at one desired frequency using Eq. (3). The first step in demodulating the probe signals is to take the ratio $ {P_2}(z)/{P_1}(z) $. This step improves the SNR by employing common mode rejection to eliminate similar intensity fluctuations between the two probe frequencies, which are caused by fiber loss and inhomogeneity of BSBS gain along the fiber. In fact, the ratio $ {P_2}(z)/{P_1}(z) $ represents the accumulated energy transfer from the higher-frequency probe tone (${\omega _1}$) to the lower-frequency tone (${\omega _2}$). This transfer is sensitive to the acoustic properties of the materials surrounding the fiber, as shown in Fig. 1(d). The next data processing step is the differentiation of $ {P_2}(z)/{P_1}(z) $, whose result gives the energy-transfer rate, as shown in Fig. 1(e). The final measurement step is to sweep FSBS frequency, $\Omega $, and repeat the previous data processing steps to obtain the three-dimensional map of the FSBS spectrum versus distance, as illustrated in Fig. 1(f).Fig. 2. Experimental apparatus for distributed measurement based on OM-TDA. (a) Experimental setup where the blue path shows the FSBS process and the green path is used to generate the CW probe for BOTDA detection. The sensing fiber is a standard single-mode fiber with or without coating. The abbreviations here denote: PC, polarization controller; EOM, electro-optic modulator; AWG, arbitrary waveform generator; EDFA, erbium-doped fiber amplifier; MG, microwave generator; PS, polarization scrambler; ISO, isolator; PD, photodetector; ACQ, acquisition equipment. (b) Optical spectral components of the activation and probe pulses in the blue path of Fig. 2(a) as well as the spectrum of the CW probe in the green path. Here, ${\omega _c}$ is the frequency of the suppressed carrier, ${\Omega _s}$ is the frequency separation between the adjacent activation pulse and probe pulse tones, $\Omega $ is the frequency of the excited transverse acoustic wave, ${\Omega _B}$ is near the BSBS resonant frequency of the fiber and is swept to obtain the BOTDA signal of the two probe pulse tones. All symbols of the frequency components here are in line with those in Fig. 1.
3. EXPERIMENTAL SETUP
The experimental setup is very compact compared with previous work [24,25], as shown in Fig. 2(a). Light from a 1550 nm distributed feedback (DFB) laser is split into two paths. The upper path, shown in blue in Fig. 2(a), prepares the activation and probe pulses. Two sequential radio-frequency (RF) pulses drive a double-sideband electro-optic modulator (EOM) working in the carrier-suppressed mode, generating the sequential activation and probe pulses. The first, longer pulse width RF pulse, lasts longer than the acoustic wave lifetime ($\sim{1}\;\unicode{x00B5} {\rm s}$), generates the activation pulse. It is synthesized from two frequency components with frequency separation of $\Omega $, and thus generates four light tones (two groups of two) as shown in Fig. 2(b). Fortunately, the beat signals of each pair of tones are in phase, so that they cooperate to stimulate the TBDG and there is no need to filter out one sideband. Other beat frequencies between pairs of frequencies that are not relevant to the formation of the TBDG can be safely ignored. The second, shorter RF pulse, pulse width of tens of nanoseconds, generates the probe pulse. It has a single frequency of $\Omega /{2}$ which generates two light tones with the same beat frequency, $\Omega $, as the TBDG. The frequency separation ${\Omega _s}$ between the activation and probe pulses is set large enough (2 GHz in our experiment) to weaken the BSBS interaction between the activation pulse and the CW probe, which would otherwise adversely influence the measurement of ${P_1}(z)$ and ${P_2}(z)$. Then each of the frequency components is amplified via an erbium-doped fiber amplifier and coupled into the sensing fiber through a circulator.
The lower green path is used to detect the intensity evolution of the probe pulse using BSBS. An EOM and an optical filter are used to create a CW single sideband, which is redshifted by frequency ${\Omega _B}$. ${\Omega}_B$ is swept over a frequency range that is near the BSBS resonant frequency of the two tones in the probe pulse to get the BOTDA signal of each tone. A polarization scrambler is used to mitigate the fluctuation of BSBS gain along the fiber due to polarization mismatching. The backward scattered Rayleigh noise is filtered out before the receiver. The frequency sweeping of $\Omega $ for FSBS and ${\Omega _B}$ for BSBS are realized by changing the output of the arbitrary waveform generator and the microwave generator, respectively. Due to the low bandwidth requirement, a high-performance arbitrary waveform generator is not necessary and can be replaced by a low-cost commercial electric circuit.
To get high SNR, we choose the strongest resonance at about 322 MHz, corresponding to acoustic mode ${R_{0,7}}$ for the work reported in this paper. See Supplement 1 for justification of the choice of this acoustic mode. The measured relative FSBS gain for each mode is shown in Fig. S1, which is consistent with that shown in other work [6,24,25]. We choose high-power and long ($\sim{1}\;\unicode{x00B5} {\rm s}$) activation pulses in our experiment because they can excite stronger TBDG for higher SNR sensing. However, these relatively long, intense activation pulses cause strong amplified spontaneous Brillouin scattering which will have a detrimental effect on the measured BOTDA signal in our scheme. We solve this problem by modulating the activation pulse with pseudo-random phase coding. For details, see Supplement 1 and Fig. S3.
4. RESULTS AND ANALYSIS
A. Coherent Stimulated Forward Brillouin Scattering Probing
The interaction between the two tones of the probe pulse and the TBDG is very different from conventional stimulated Brillouin scattering. With the approximation that the TBDG is unchanged during its interaction with the probe pulse, the evolution of each tone of the probe pulse is as follows:
If $\Delta=k\pi $ ($k = {\rm integer}$), the gain spectrum shows a Lorentzian profile:
If $\Delta = (2k + 1)\pi /2$, the gain spectrum shown in Eq. (5c) can be simplified to
A more obvious phase-sensitive feature can be extracted in the resonant scenario where $\Omega = {\Omega _m}$:
which means the energy transfer is sinusoidal with the phase difference. If $ - \pi /2 + 2k\pi \lt \Delta \lt \pi /2 + 2k\pi $, $S({\Omega _m},\Delta ) \gt 0$, which implies the forward energy transfer from the upper tone to the lower tone, namely Stokes scattering. If $\Delta = (2k + 1)\pi /2$, then $S({\Omega _m},\Delta ) = 0$, meaning the TBDG has no effect on FSBS interaction in the probe pulse. When $\pi /2 + 2k\pi \lt \Delta \lt 3\pi /2 + 2k\pi $, we have $S({\Omega _m},\Delta ) \lt 0$, which is the case where the energy transfer is reversed, flowing from the lower tone to the upper one, namely anti-Stokes scattering.Fig. 3. Energy transfer as a function of distance along the fiber for several phase differences between the beat note of the activation pulse and that of probe pulse. (a) Accumulated energy transfer at phase differences 0, $\pi /{2}$, and $\pi $. These traces are smoothed through a 1 m moving average to reduce the high-frequency noise. (b) Energy transfer versus phase difference at the output of fiber.
To verify the aforementioned phase-sensitive process, we conduct the experiment where we used a 1.5 µs long activation pulse followed by a 10 ns probe pulse and $\Omega $ is fixed at a resonant transverse acoustic frequency. In this experiment the phase difference is tuned by adjusting the RF signal applied to the EOM. For details, see Supplement 1. Figure 3(a) shows the accumulated energy transfer intensity at phase differences of 0, $\pi /{2}$, and $\pi $. Forward, near-zero, and reverse energy transfers are observed, respectively, a result which is consistent with the analysis above. When the phase difference is swept from 0 to ${6}\pi $, the energy transfer at the far end of the fiber varies sinusoidally as a function of phase difference, as shown in Fig. 3(b).
Fig. 4. FSBS spectra and spectral widths for different activation and probe pulse lengths. (a) Demodulated FSBS spectra at a fixed fiber location for 1.5 µs activation pulse length and different probe pulse lengths. (b) Spectral width as a function of probe pulse length. The spectral width shows only a weak dependence on the probe pulse length. (c) Demodulated FSBS spectra with different activation pulse lengths. The frequency span is reduced to 320–324 MHz when the activation pulse is longer than 0.8 µs. (d) Spectral width as a function of activation pulse length. Longer activation pulses help to determine the acoustic linewidth with improved accuracy.
This part of work shows the coherent nature of the stimulated probing process in our OM-TDA scheme and provides a physical explanation. This new phenomenon may have potential applications and should be further studied. In the following experiments described in this paper, the phase difference is fixed at 0 to exploit the enhanced Stokes scattering for a strong and stable FSBS interaction.
Fig. 5. Experimental results for high spatial resolution opto-mechanical time-domain analysis. The sensing fiber is 225 m of the standard single-mode fiber. The coating of the last 25 m segment is removed to enable sensing of the surrounding medium. A 5 m length in the middle of the stripped fiber is immersed in alcohol while the rest of the stripped segment is exposed to the air. (a), (b) Measured ${P_1}(z)$ and ${P_2}(z)$ versus distance along the fiber at each scanning frequency, $\Omega $. (c) Accumulated energy transfer as a function of distance at each scanning frequency. (d) Three-dimensional map of distributed FSBS spectrum. Signals in the black box belong to the uncoated fiber segment. (e) Distributed FWHM of the FSBS (black line) and Brillouin frequency shift (BFS) of the BOTDA signal (blue line) at the uncoated end of the fiber. The experimental uncertainty of the linewidth for five different measurements is indicated by red error bars. (f) Spectra of the FSBS for fiber surrounded by alcohol (red dots) and air (black squares). The data have been fitted by Lorentzian line shapes.
B. Effect of Pulse Length
The pulse lengths of the activation and probe pulses are two primary adjustable parameters in the coherent-stimulated-probing-based OM-TDA scheme. If not chosen properly, the pulse lengths can have considerably adverse effects on the final FSBS results. In this section, we focus on the influence of these two pulse lengths (the activation and probe pulse lengths) on the FSBS resonant spectrum exposed to air by varying each of the two pulse lengths in turn while keeping the other fixed.
First, to determine the effect of the probe pulse length, the activation pulse length is kept fixed at 1.5 µs and the probe pulse length is varied 10 ns to 60 ns in 10 ns steps. The resulting demodulated FSBS spectra at a fixed fiber position are presented in Fig. 4(a) and the corresponding full width at half-maximum (FWHM) as a function of probe pulse length is shown in Fig. 4(b). Theoretically, the FSBS spectral width is independent of the probe pulse width. However, experimentally, the FSBS spectral width increases slightly with increasing probe pulse length, as shown in Fig. 4(b). This weak dependence can be explained by the inhomogeneity of the FSBS spectrum along the fiber, because a longer pulse corresponds to larger spatial resolution and thus the averaged spectrum is broadened. This is verified by our experiment results presented in Fig. S2, where longer pulses correspond to a more blurry three-dimensional FSBS map.
Second, the probe pulse length is fixed at 20 ns while activation pulse lengths were varied from 0.1 µs to 1.9 µs. Figure 4(c) shows the resulting FSBS spectra measured at a fixed fiber position and Fig. 4(d) presents the corresponding FWHM as a function of activation pulse length. As expected, for short activation pulses, the FWHM decreases as the activation pulse length increases. However, when the activation pulse length is greater than 0.8 µs, the linewidth of the FSBS spectrum becomes independent of the activation pulse length, which is consistent with the steady-state approximation inherent in Eq. (2). We note that the optimal duration of the activation pulse is determined by the transverse acoustic wave lifetime, so that a shorter activation pulse is able to excite a stable acoustic wave when the fiber is immersed in liquids. However, to make the sensor more general, the activation pulse width is chosen to match the air-surrounded scenario which has the longest acoustic lifetime.
C. High Spatial Resolution Experimental Demonstration
We conducted an OM-TDA experiment in order to demonstrate a 2 m spatial resolution distributed measurement of mechanical impedance. The activation pulse is set to 1.5 µs with around 1.2 W peak power for each tone. The subsequent probe is a short, 10 ns long pulse of 1.7 W peak power for each of the two frequency components. Considering that the activation pulse has four tones while the probe pulse has two tones, the power chosen here enables the beats of the two pulses to have almost the same amplitude (see details in Eqs. S12 and S13), so that the progression of the probe pulse follows steady-state Eq. (2). The sensing fiber is a 225 m long standard single-mode fiber, while the coating layer of the last 25 m is removed. Then a 5 m segment in the middle of the uncoated fiber is immersed in alcohol, while the rest of the uncoated fiber is exposed to air. The FSBS frequency, $\Omega $, is tuned from 318 MHz to 326 MHz, with an increment of 0.1 MHz. ${P_1}(z)$ and ${P_2}(z)$ measured by the BOTDA technique at different values of $\Omega $ are shown in Fig. 5(a) and 5(b), respectively. The fluctuation of intensity along the fiber is due to the inhomogeneity of the BSBS gain along the fiber, while fluctuations along the frequency axis mainly result from uneven output power of arbitrary waveform generator at different frequencies. Figure 5(c) gives the accumulated energy-transfer intensity at different FSBS frequencies, as expressed by ${P_2}(z)/{P_1}(z)$. The intensity fluctuations evident in Figs. 5(a) and 5(b) are suppressed in Fig. 5(c). The energy coupling is faster in the parts of the stripped fiber in air due to the existence of stronger acoustic wave in such a case as shown in Fig. 5(c). Figure 5(d) shows the distributed FSBS spectrum of the 225 m fiber demodulated via Eq. (3). The segment in the black box is the three-dimensional map of the 25 m uncoated fiber, while the other part corresponds to the coated fiber. The air-surrounded parts show narrower and taller spectra than in the alcohol-surrounded and coated fiber owing to lower acoustic energy dissipation at the fiber’s outer boundary. The FSBS spectra of coated fiber are much wider and weaker but still recognizable as shown in Fig. S4. The slight frequency fluctuations of the FSBS spectral peak in air, as shown in the black box in Fig. 5(d), are not the measurement errors, which is verified by the stable patterns from several repeated measurements. This central frequency fluctuation might be due to the inhomogeneity of the fiber and needs further study. To reduce the sensitivity of differential process to noise, segmental differentiation is employed. The differentiation is performed between two averages obtained from two adjacent data segments [25], which means the data shown in Fig. 5(c) is convolved with a window function $[ \begin{array}{l} {1_{N \times 1}}\\{( - 1)_{N \times 1}}\end{array} ]$, where $N$ is the segmental length. $N$ corresponding to 1 m is used in our process, indicating the spatial resolution is about 2 m. The spatial resolution induced by data processing here dominates the effect on the spatial resolution that is due to the probe pulse length.
The spectrum at each position is fitted with a Lorentzian line shape, the spectral width of which is shown in Fig. 5(e) (black line). The FWHM uncertainty determined from five repetitions of the measurements is less than 0.3 MHz for the fiber section immersed in alcohol and 0.03 MHz for fiber segments in air. Meanwhile, the identification of the fiber immersed in the alcohol is also possible once the alcohol is allowed to evaporate, cooling the fiber locally. When the cover used to prevent evaporation of the alcohol is removed, the BOTDA signal of the probe pulse exhibits different Brillouin frequency shift at this segment, as shown in Fig. 5(e) (blue line). However, BOTDA cannot distinguish liquids outside the cladding when there is no evaporation while the FSBS-based sensing still works. In fact, distributed acoustic impedance results obtained via OM-TDA will not be affected by the sensitivity of the BOTDA signal to temperature or strain, because the integration over frequency in Fig. 1(c) has eliminated this sensitivity. The alcohol segment identified from the FSBS linewidth is about 1 m shorter than that identified by the BOTDA signal with 1 m spatial resolution, which indicates that the spatial resolution of the FSBS sensor is 1 m worse than the BOTDA system used here. This demonstrates a 2 m high spatial resolution distributed acoustic impedance measurement. The spectra shown in Fig. 5(f) are the averaged results of FSBS resonance in alcohol and in air, with spectral widths of 2.21 MHz and 0.45 MHz, respectively, in excellent agreement with previous work [25].
5. DISCUSSION
The spatial resolution is eventually limited by the signal-to-noise ratio. One of the main noise sources in the measurement is the polarization fluctuation of the BOTDA signal in a standard single-mode fiber [32–34]. Although a random polarization scrambler and 5000 times averaging are used to alleviate intensity fluctuations in each recorded signal, the signal nevertheless still fluctuates slightly from measurement to measurement, which prevents further improvement of spatial resolution. Perhaps, OM-TDA implemented in polarization-maintaining fiber [35] could achieve sub-meter spatial resolution. On the other hand, better spatial resolution requires shorter probing pulse to be used. However, the BOTDA signal becomes much weaker when the probe pulse width is shorter than $\sim{10}\;{\rm ns}$ (longitudinal acoustic lifetime). The deteriorated signal-to-noise ratio with the shortening of the probe pulse width poses a limit to the improvement of spatial resolution. Other alternative methods rather than the simple BOTDA-based probing process are expected to improve the spatial resolution further. Meanwhile, fibers with specially designed very thin protective coating have been developed [36,37]. Such fiber could be used without the need to strip the protective coating, thereby preventing the fragility of bare fiber, but also possibly enhance the sensitivity of FSBS spectra to changes in the outer boundary acoustic impedance.
In our scheme, the limitation on measurement range is the same as for OMTDR [24]. FSBS is a cascaded light scattering process, which means the injected two tones of the probe pulse can generate higher-order Stokes and anti-Stokes components at frequencies ${\omega _2} - n\Omega $ and ${\omega _1} + n\Omega $. These components are becoming significant as the propagation distance increases. Meanwhile, the newly generated frequency components will also influence the two primary tones at ${\omega _1}$ and ${\omega _2}$ through Kerr nonlinearity-induced four-wave mixing [38]. These factors are not included in our current model of the OM-TDA and can thus lead to unacceptable demodulation errors if the FSBS interaction becomes too strong. In our experiment, the $\sim{1}\;{\rm W}$ peak power of the probe pulse limits the sensing range to several hundred meters.
Measuring time is another performance that can be further improved. In the earlier two works [24,25] and our scheme, many times of frequency scanning is time consuming. Scanning free excitation or probing schemes are desired. Recent work proved the feasibility of using spontaneous Brillouin scattering to avoid the scanning of BOTDA frequency with the spatial resolution of 8 m [39]. The large number of averaging used to alleviate the polarization noise is also time-consuming. Using an alternative orthogonal polarization scrambler to reduce the averaging time or using polarization-maintaining fibers as the sensor has the potential to greatly reduce the measurement time.
It is worth mentioning that although the pre-excitation of transverse acoustic wave [25] and the two-tone energy transfer probing [24] have been proposed in earlier schemes, our OM-TDA scheme is not a simple combination of them. This is manifested in the controllable energy transfer behavior in our scheme. In previous schemes, the energy transfer is fixed, either from the upper tone to the lower tone [24] or from a single tone to the sidebands [25]. However, in our proposed coherent forward stimulated Brillouin scattering, the energy transfer which happens between the upper tone and lower tone of the optical probing pulse is phase-sensitive and can be finely controlled to obtain positive, negative, or zero energy transfer behavior. The coherent forward stimulated Brillouin scattering is a brand new physical process, which may have potential applications in other fields, such as microwave photonics, spectroscopy, etc.
FSBS sensors not only have application prospects in distributed chemical sensing, but also the potential for monitoring the fabrication of nano-structure waveguides. Highly confined optical and acoustic fields in such waveguides enhance the FSBS process, which may improve the spatial resolution to extremely high level, using our OM-TDA scheme.
6. CONCLUSION
We demonstrate an opto-mechanical time-domain analysis scheme based on coherent forward stimulated scattering probing to achieve high spatial resolution distributed FSBS spectrum measurement in standard single-mode optical fiber. The dominant limitations for spatial resolution improvement currently are the low SNR on account of the sensitivity of the process of mathematical differentiation to noise. In this work, we have proposed for the first time the coherent forward stimulated Brillouin scattering probing process involving coherent interaction among the two tones of a probe pulse and the pre-excited TBDG. The technique demonstrates a unique phase-sensitivity, which greatly improves the SNR of the sensing. BOTDA is used to detect the local intensity of each of two tones within the probe pulse. Thanks to this new kind of opto-mechanical time-domain analysis scheme, spatial resolution of 2 m in a 225 m long fiber is achieved experimentally.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (2017YFF0108700); National Natural Science Foundation of China (61575052).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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