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Abstract
In this manuscript, we demonstrate that an array of tapers, consecutively formed along a single-mode optical fiber, can be used to realize a localized, dynamic strain sensing position with a Brillouin Optical Frequency-Domain Analysis (BOFDA) sensor. The multi-taper realizes a periodic modulation of the Brillouin frequency shift, which appears as a spectral resonance in the baseband transfer function acquired by the BOFDA sensor. Any strain acting along the multi-taper affects the magnitude of this resonance, offering a means to perform dynamic strain measurements in that position. Fabricating multi-taper arrays with a different period, more dynamic sensing positions can be realized along the same fiber. Measurements on two vibrating cantilevers were performed at a sampling rate of 46 Hz, using two multi-taper arrays with a length of 72 mm and 75 mm, respectively.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Distributed optical fiber sensors based on Brillouin scattering realize spatially resolved strain and temperature measurements in single-mode optical fibers [1]. These sensors usually retrieve the measurand by extracting the Brillouin frequency shift (BFS), which is the frequency shift between two counter-propagating beams (the “pump” and the “probe”) ensuring the maximum power transfer. Different configurations exist, capable of retrieving the spatially resolved BFS distribution. Usually, these configurations are only intended for static measurements, due to the relatively long acquisition times. However, several techniques have been demonstrated, capable of performing dynamic measurements [2]. For example, a fast Brillouin sensing technique based on the use of an optical chirp chain (OCC) probe has been recently proposed, featuring a 3.2 s measuring time over a 150-km single-mode fiber with a 6 m spatial resolution [3]. Another accelerating method is based on a digital optical frequency comb (DOFC) probe signal, by which dynamic measurements of up to 1 kHz vibration frequency have been reported over a 10 km long fiber and with a spatial resolution of 51.2 m [4]. A much better spatial resolution can be achieved by adopting a scheme relying on the pre-activation of a stationary acoustic wave, such as the Brillouin optical frequency-domain analysis (BOFDA) [5,6] and the Brillouin optical correlation-domain analysis (BOCDA) [7]. Compared to other sensing technologies, BOCDA sensors permit to randomly address an arbitrary position of the sensing fiber, through a proper localization of the correlation peak. This feature can be exploited to acquire dynamically the changes in the Brillouin backscattered power occurring at the correlation peak, which therefore acts as a localized dynamic sensing position. As an example, in Ref. [8] a sampling rate of 200 kS/s and a spatial resolution of 8 cm were demonstrated at a single sensing position. Furthermore, by fast moving the correlation peak, distributed sensing at more positions can be obtained at progressively lower sampling rates [8].
Compared to the BOCDA technology, the BOFDA measurement technique does not provide random accessibility, as each frequency of the acquired transfer function contains information about the Brillouin interaction between the pump and probe lights over the entire fiber. To obtain spatial information, the modulation frequency of a vector network analyzer (VNA) must be swept over a proper range, which is a time-consuming process. Another factor limiting the acquisition rate in BOFDA sensors is that such sweep must be repeated for several pump-probe frequency shifts, in order to reconstruct the BFS spatial distribution. These factors lead to an acquisition time in the minutes range, typically.
Owing to its high spatial resolution and long-range capabilities [9], it would be desirable to use the BOFDA method also to perform dynamic strain measurements, at least in some fiber positions. One method to accelerate the measurement process consists in restricting the pump-probe frequencies to a single value, typically chosen along the positive or negative slope of the Brillouin gain spectrum (BGS) [10–12]. In BOFDA measurements, however, the acquisition time is still limited by the necessity to perform a whole VNA frequency scan. In these conditions, the maximum acquisition rate can be estimated by dividing the intermediate frequency (IF) bandwidth chosen for the VNA measurements, by the number of sensing points. For example, for a fiber length of 100 m, a spatial resolution of 1 cm, and an IF bandwidth of 10 kHz, the maximum acquisition rate will be 10 kHz/10,000 = 1 Hz.
In order to further accelerate the measurement, we propose here a method relying on the realization of a proper BFS periodical distribution along a short piece of fiber, in such a way that that piece of fiber can be uniquely associated to a specific frequency of the fiber response. In this way, any perturbation acting on that fiber segment can be dynamically tracked by monitoring only that frequency, thus much faster than in conventional BOFDA sensing. In the following, the proposed approach is demonstrated, first numerically and then experimentally, using an array of tapers to realize the BFS modulation.
2. Principle of operation
The operation principle is illustrated in Fig. 1 (from (a) to (d)). A periodical array of tapers, with a period ${L_{period}}$, is realized along a piece of the fiber. Each taper produces a change in the local BFS of the fiber, in a measure dependent on the taper diameter [13]. For example, tapering a standard SMF-28 fiber down to a waist diameter ϕ = 50 µm induces a shift in the BFS of about 30 MHz. The latter roughly corresponds to the bandwidth of the BGS; therefore, each taper fully modulates the Brillouin gain when probing the fiber with a probe light downshifted from the pump by a frequency equal to the BFS of the unperturbed fiber. In the frequency-domain, the Brillouin gain modulation appears as a resonance centered at:
where n is the fiber refractive index and c is the light velocity in the vacuum.
Fig. 1. (a) Multi-taper array. (b) BFS profile. (c) Brillouin gain profile in the time-domain. (d) Brillouin gain profile in the frequency-domain.
When some strain is applied along the multi-taper, the entire BFS profile will shift by some quantity Δν. If we denote with ν0 and ν1 the BFS of the untapered and tapered fiber, respectively, the BFS along the strained multi-taper will vary periodically from ν0 + Δν to ν1 + Δν. This new BFS profile will result in a reduced Brillouin gain modulation, as schematically illustrated in Fig. 2. This reduced Brillouin gain modulation will be detected as a reduced magnitude of the fiber response at the resonance frequency expressed by Eq. (1). In the following section, we will analyze the influence of the various parameters of the BFS modulation on the resulting dynamic sensing capabilities.
Fig. 2. Effect of the strain on the Brillouin gain modulation amplitude. The frequencies ν0 and ν1 are the BFS of the untapered and tapered fibers, respectively.
3. Numerical modeling
Stimulated Brillouin scattering (SBS) interaction between a cw probe wave and a counterpropagating, intensity-modulated pump wave can be described in the frequency domain through a baseband transfer function (TF) equal to [14]:
In Eq. (3), ${g_{B0}}$ is the SBS peak gain coefficient, $\Delta ^{\prime}(z )$ is the normalized detuning between the pump-probe frequency shift $\Delta {f_{pp}}$ and the local BFS, i.e., $\Delta ^{\prime}(z )= 2\pi ({\Delta {f_{pp}} - BFS(z )} )/\mathrm{\Gamma }$ ($\mathrm{\Gamma }$ is the acoustic damping rate). and $\omega ^{\prime} = \omega /\mathrm{\Gamma }$. In BOFDA sensors, the transfer functions are acquired for several pump-probe frequency shifts, and inverse-Fourier-transformed to obtain the positional information.
The model expressed by Eqs. (2) and (3) can be used to simulate the baseband transfer function for any given BFS distribution. In the following, we consider a 1-m optical fiber in uniform conditions, except for a central region where the BFS is modulated with a period of 8 mm. The simulated TF is shown in Fig. 3, where we have assumed an input pump (probe) power of 300 mW (1 mW), a Brillouin gain coefficient of 0.2 (m·W)-1, a BFS modulation amplitude of 30 MHz, and a number of periods set to 4, 8, or 16. As discussed in Ref. [13], a BFS modulation of 30 MHz can be realized by tapering the fiber down to ϕ = 50 µm. Fiber tapering also affects the SBS gain peak: for the chosen waist size, the gain peak in the waist was ∼4.3 times smaller than outside the taper [13]. In our simulations, the gain peak modulation was included through a z-dependent ${g_{B0}}$ in Eq. (3). Figure 3 confirms the presence, in the simulated data, of a resonance at a frequency ${f_{res}} \approx 12.9{\; }{GHz}$, which satisfies Eq. (1) with ${L_{period}} = 8{\; }{mm}$ and $n = 1.45$. As the width of such resonance is twice the inverse of the roundtrip time of the light over the whole array, it narrows down when increasing the number of tapers. The TF also exhibits fast oscillations over the whole frequency span. The period of these oscillations is $c/2nL$; however, the envelope of the TF keeps unchanged with the fiber length.
Fig. 3. TF amplitude calculated for a 1-m long fiber, comprising an array of 4, 8 or 16 tapers. The pump-probe frequency shift is tuned to the BFS of the untapered fiber.
Other simulations were performed to analyze the influence of the BFS modulation amplitude, on the magnitude of the resonant peak. The simulation results, obtained by varying the BFS modulation amplitude from 5 MHz to 30 MHz, are reported in Fig. 4. First, we note that the various curves are vertically shifted by 3 dB each other. Therefore, doubling the number of tapers also doubles the magnitude of the TF at the resonance frequency. Second, we observe that, increasing the BFS modulation amplitude results in a higher resonant peak magnitude. However, this magnitude tends to saturate when the BFS modulation amplitude approaches the BGS bandwidth, as expected. We must also consider that, while smaller tapers produce an increased BFS modulation, this also result in a more fragile structure [13]. Based on these arguments, all subsequent simulations have been conducted for a BFS modulation amplitude of 30 MHz.
Fig. 4. TF at the resonance frequency of the multi-taper array with 4, 8 or 16 tapers, as a function of the BFS modulation amplitude along the multi-taper.
When the multi-taper is glued to some structure, it is generally subjected to both tensile and compressive strains. In Fig. 5 we report the TF magnitude at the resonant peak, as a function of the strain-induced BFS shift, for a few pump-probe frequency shifts. The results are reported only for the 4-tapers array, as those related to 8 or 16 tapers can be obtained by vertically shifting the curves by 3 dB or 6 dB, respectively. In other words, the number of tapers has no influence on the sensitivity of the resonant peak magnitude on the applied strain. Figure 5 reveals that, by properly tuning the pump-probe frequency shift, a monotonic range can be obtained for accommodating both positive and negative strains.
Fig. 5. TF at the resonance frequency of the multi-taper array with 4 tapers, as a function of the tensile/compressive strain induced BFS shift.
As our method relies on the acquisition of the TF amplitude at the sole multi-taper resonance frequency, it is important to verify that any strain acting in other portions of the fiber has a negligible influence on this value.
To this aim, we have calculated the ratio between the sensitivity of the resonant peak magnitude to strain changes occurring outside the multi-taper, and the sensitivity to strain changes occurring on the multi-taper. For these simulations, we have assumed a pump-probe frequency shift detuned by -10 MHz from the BFS of the untapered fiber. The crosstalk values, expressed in dB, are shown in Fig. 6, as a function of the length of fiber subjected to strain. We see that the crosstalk level is highly dependent on the strained length, being maximum (minimum) when the latter is an odd (even) multiple of half the multi-taper period. We also observe that the crosstalk depends on the number of tapers. In fact, the curves in Fig. 6 are vertically separated from each other by 3 dB. Therefore, on one hand the number of tapers influences the sensitivity of the resonant peak to the strain acting on the multi-taper, on the other hand realizing an adequate number of tapers is essential to guarantee a low level of crosstalk. For example, for a multi-taper composed by 8 tapers, the crosstalk in the worst condition is ≈ -8.5 dB. In other words, any strain applied outside the array will lead to a spurious change of the multi-taper resonance peak, being at least ≈ 7 times smaller than the change produced by the same amount of strain when applied on the multi-taper.
Fig. 6. Crosstalk of the multi-taper array, as a function of the length of the strained fiber, normalized to half the taper length (4 mm in our simulations).
While the simulations shown in this section have been performed for a fixed multi-taper period of 8 mm, the results are valid for any other choice of this period. However, one should consider that, while choosing a shorter period has the advantage of reducing the overall length of the array (for a fixed number of tapers), it also results in a higher resonance frequency (see Eq. (1)). Therefore, in practical cases the minimum period is limited by the maximum frequency of the TF that can be measured, i.e., by the VNA frequency range.
4. Experimental results
For our experiments, a multi-taper array has been realized along a piece of SMF-28 single-mode fiber, using a Vytran GPX3800 glass processor. The glass processor tapers the fiber by heating the glass up to its softening point, while simultaneously applying a tensile force to reduce its cross section [13]. The glass processor ensures a high level of control and repeatability of the tapering process.
The fabricated array was formed by 8 consecutive tapers, each one built using a period ${L_{period}} = 8{\; }{mm}$, a waist size ϕ = 50 µm, and a downtaper and uptaper region with length $DT = UT = 3{\; }{mm}.$ The chosen parameters ensure an adiabatic transition across each taper [13], and, therefore, minimal loss. The measured transmission loss across the whole array was about 0.5 dB, which may be attributed to the scattering loss originating from the core and from surface roughness of the taper [15].
The BOFDA measurements were carried out using the scheme shown in Fig. 7. In brief, the light from a 20-mW external cavity laser, operating at 1551 nm, is divided into two branches. The upper branch is used to generate the probe light through suppressed-carried, double-sideband (DSB) modulation. The light exiting from the modulator is first amplified by an erbium-doped fiber amplifier (EDFA), then filtered out by means of a fiber Bragg grating (FBG) selecting the longer-wavelength sideband, and finally injected into one end of the sensing fiber. In the lower (pump) branch, the laser beam is modulated by means of another amplitude modulator, biased at its quadrature point and driven by the output port of a VNA. The latter has a frequency range spanning from 300 kHz to 20 GHz, allowing a minimum resolution of 5 mm and a maximum sensing length of 333 m [5]. The modulated pump passes through a polarization switch, used to mitigate the polarization dependance of the Brillouin interaction. Finally, the pump beam is amplified by another EDFA and launched into the opposite end of the sensing fiber. The Brillouin backscattered light is fed into a photo-detector, whose output is sent to the VNA which extracts the amplitude and phase of the modulating frequency over the scanned range.
Fig. 7. Experimental setup for BOFDA measurement (EDFA, erbium-doped fiber amplifier; FBG, fiber Bragg grating).
In Fig. 8 we report the TF magnitude acquired for a pump-probe frequency of 10,866 MHz (corresponding to the BFS of the multi-taper in the non-tapered regions), acquired for a modulation frequency range spanning from 1.5 MHz to 20 GHz in frequency steps of 1.5 MHz. The figure reveals the presence of a resonance around 11.4 GHz. According to Eq. (1), this resonance frequency corresponds to a multi-taper period of ≈ 9.1 mm, thus slightly longer than the nominal value. This should be attributed to the fabrication tolerance of our glass processor. The resonance width is 2.6 GHz, approximately equal to twice the roundtrip time over the whole array. The inset shows a segment of the inverse-Fourier-transformed signal, corresponding to a 15-cm portion covering the multi-taper region. The modulation of the Brillouin gain induced by the tapers is clearly visible.
Fig. 8. Transfer function magnitude measured at the pump-probe frequency shift of 10,866 MHz. The inset shows a portion of the inverse-Fourier-transformed data.
As a next step, we have analyzed the strain dependence of the TF amplitude at the resonance frequency. To this aim, the multi-taper was stretched using the positioner stages of the Vytran glass processor. The TF amplitude around ${f_m} = 11.4\; {\rm{GHz}}$, averaged over a span of 2 GHz, is shown in Fig. 9 as a function of the strain induced BFS shift. The measurements are reported for three different pump-probe frequency shifts. Based on the achieved results, the optimal pump-probe frequency shift is 10,858 MHz, i.e., 8 MHz below the BFS of the non-tapered fiber. For this frequency shift, the TF decreases by 3.3 dB when the BFS is shifted by 28 MHz, with a sensitivity of -0.12 dB/MHz.
Fig. 9. TF amplitude around ${f_m} = 11.\; 4{{GHz}}$, as a function of the strain induced BFS shift, with the strain applied along the multi-taper (solid lines) or outside the multi-taper (dashed and dotted lines).
The same figure reports the variation of the TF amplitude when the same amount of strain is applied along a fiber segment external to the multi-taper. Two different strained lengths were selected: one approximately equal to an even number of half taper lengths ($\Delta L = 153\; {mm})$, and another one approximately equal to an odd number of half taper lengths ($\Delta L = 176\; {mm})$. The total variation of the TF over the chosen range was ≈ 0.6 dB in the former case, or ≈ 0.07 dB in the latter case.
In order to demonstrate the dynamic sensing capabilities of the proposed approach, the 72-mm long multi-taper was glued onto the surface of a 70-cm cantilevered beam, in a position close to its fixed end. The cantilever was then put in free vibration, while using the BOFDA sensor to acquire the TF magnitude at a pump-probe frequency shift of 10,858 MHz. The modulation frequency was swept from 11,300 MHz to 11,500 MHz in steps of 2 MHz (for a total of 101 scanned frequencies), while the IF bandwidth was set to 10 kHz. During this measurement, the polarization switch PS was kept to a fixed state. For this measurement, the sampling frequency was verified to be 46 Hz. This value is about half the theoretical sampling rate, roughly estimated as 10 kHz/101 = 99 Hz, where the discrepancy can be attributed to the extra-time required for data transfer. The damped oscillation of the vibrating cantilever is clearly visible in Fig. 10, where the TF modulation has been converted in strain units, using the previously obtained sensitivity of -0.12 dB/MHz and a BFS/strain conversion factor of 500 kHz/µε. Figure 10 also shows, as an inset, the static BFS distribution measured by the same BOFDA apparatus conventionally operated. The BFS profile reveals the composition of the fiber under test, featuring a 4-m piece of bend-insensitive fiber with a BFS of 10,682 MHz, a 4.5m of SMF-28 (along which we have realized the multi-taper), followed by another 3.5-m piece of bend-insensitive fiber.
Fig. 10. Dynamic strain measurement of the cantilever beam put in free vibration. The inset shows the static BFS profile.
As a final experiment, we have realized, along the same fiber, a second multi-taper array. This second multi-taper was formed by 9 tapers with a period of 8.3 mm, resulting in a total length of 75 mm and a resonance frequency of 12.1 GHz. The second multi-taper was attached to another cantilever. Figure 11 shows the fast Fourier transform of the strain waveforms acquired along the two arrays, using two different VNA frequency intervals, and putting both cantilevers in free vibration. The oscillation frequencies of the two cantilevers (3.6 Hz and 3.2 Hz, respectively) are clearly visible in the figure.
Fig. 11. Magnitude of the FFT of the strain waveform acquired along the first cantilever (${f_m} = 11.4\; {GHz}$), and the second cantilever (${f_m} = 12.1\; {GHz}$).
5. Conclusions
A novel approach for localized and dynamic strain sensing has been demonstrated, based on the use of a multi-taper array. The method is fully compatible with high-spatial resolution BOFDA sensing. Therefore, it can be exploited to realize a dynamic sensing position, in addition to static sensing over the whole fiber. Owing to the low loss of the fabricated tapers, the method can be extended to multiple sensing positions. Furthermore, it can be also realized using other means for modulating the BFS along the fiber, e.g., by thermal core expansion (TCE). The use of TCE would avoid the reduction of structural strength resulting from fiber tapering.
Funding
Università degli Studi della Campania Luigi Vanvitelli (Programma "Valere").
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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