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Abstract
We demonstrate distributed optical fiber-based pressure measurements with sub-bar pressure resolution and 1 m spatial resolution over a ∼100 m distance using a phase-sensitive optical time-domain reflectometry technique. To do so, we have designed a novel highly birefringent microstructured optical fiber that features a high pressure to temperature sensitivity ratio, a high birefringence and a mode field diameter that is comparable to that of conventional step-index single mode fibers. Our experiments with two fibers fabricated according to the design confirm the high polarimetric pressure sensitivities (−62.4 rad×MPa−1×m−1 and −40.1 rad×MPa−1×m−1) and simultaneously low polarimetric temperature sensitivities (0.09 rad×K−1×m−1 and 0.2 rad×K−1×m−1), at a wavelength of 1550 nm. The fiber features a sufficiently uniform birefringence over its entire length (2.17×10−4 ± 7.65×10−6) and low propagation loss (∼3 dB/km), which allows envisaging pressure measurements along distances up to several kilometers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Pressure sensing is of a great importance in oil and gas industry and in geotechnics [1–3]. These applications require the ability to measure pressure in multiple points with a high spatial resolution over long distances [4]. However, traditional electrical sensors such as piezometers or load cells cannot offer that capability. Optical fiber-based sensor technology could provide a solution. In this context several optical fiber point pressure sensors have been developed, e.g. sensors based on fiber Bragg gratings [5], rocking filters [6] or interferometric methods [7]. On the other hand, only a very few demonstrations of fully distributed fiber-based pressure sensors have been reported [8–13]. A most likely reason for that is the negligible to small pressure sensitivity of conventional optical fibers, combined with their high cross-sensitivity to mechanical load and temperature.
It is known though that specialty optical fibers, such as side-hole fibers [14] and microstructured optical fibers (MOFs) [15], fibers with special coatings [13] and engineered fiber cables [12] can feature enhanced pressure sensitivities. One possibility relies, for example, on exploiting the sensitivity of the birefringence of dedicated optical fibers to pressure and in this respect highly birefringent MOFs have already been proposed for distributed hydrostatic pressure sensing [16,17]. Such fibers can be designed to feature a birefringence that is very sensitive to pressure whilst being negligibly sensitive to temperature changes. Enabling a pressure measurement then requires the ability to accurately measure the birefringence, either polarimetrically or based on wavelength encoding by ways of a fiber Bragg grating (FBG) inscribed in the core region of the MOF. Distributed pressure measurements were demonstrated based on interrogation methods exploiting Brillouin (Brillouin dynamic gratings (BDG)) [9] and Rayleigh scattering (phase-sensitive optical time-domain reflectometry (φOTDR) [11] and optical frequency-domain reflectometry (OFDR) [8]), either with commercially available or custom highly birefringent MOFs. However, either the pressure sensitivity was insufficient to achieve sub-bar pressure measurement resolution [9], or the fibers had a non-uniform pressure response along their length and featured relatively high propagation loss [11].
In this paper, we address these drawbacks, and we propose a new MOF design that is optimized for distributed hydrostatic pressure sensing, that allows for pressure measurements with sub-bar resolution, and that is almost insensitive to temperature changes. Our manuscript is structured as follows. Section 2 introduces the method for modelling our highly birefringent MOF design and we simulate the sensing properties of the proposed MOF. Note that results described in section 2 were already partially reported in [18]. Section 3 describes the manufacturing of these novel specialty fibers. Section 4 deals with the characterization of the phase birefringence distribution in the fabricated fibers and of their pressure and temperature sensitivities. Section 5 closes the manuscript with a conclusion on the sensing capabilities of our specialty MOFs.
2. Microstructured optical fiber modelling
The starting point for our design is a so-called highly birefringent Butterfly MOF [15]. The birefringence of this MOF has been reported to be very sensitive to hydrostatic pressure whilst remaining only very weakly sensitive to temperature changes. This fiber was initially developed to be used in conjunction with an FBG that essentially converts the birefringence of the fiber into the spectral spacing between the two Bragg resonances corresponding to the two orthogonally polarized modes propagating in the MOF. We have already demonstrated that it is feasible to carry out distributed pressure measurements using this fiber [11]. However, those initial measurements have shown that small variations (∼100 nm) of the dimensions of the microstructure along the fiber lead to a non-uniform birefringence along the fiber and hence to a non-uniform pressure response along the fiber. This non-uniformity of the birefringence compromises the detection of small pressure changes [11], and hence we looked into designing a new MOF that can be fabricated such that these non-uniformities are less pronounced. In comparison with the initial MOF design described in [15], we enlarged the air hole pitch, the airhole diameter and the size of the core area, such that small variations occurring during the drawing process have a lower relative importance. Also, we omitted the GeO2-doped region in the core, as the microstructure provides for sufficient mode confinement. This eliminates the difference between the thermal expansion coefficients of the core and cladding in the MOF and allows further reducing the polarimetric temperature sensitivity. In addition, sensing over long distances (in excess of 1 km) requires lowering the propagation loss in the fiber. The loss in the initial Butterfly MOF (∼24 dB/km) mainly stems from the roughness of the surface of the airholes that surround the core area. Increasing both the pitch and the core region size should therefore reduce the propagation loss, whilst providing a mode field diameter close to that of conventional telecommunication-grade SMF-28 fiber.
The cross-section of the final fiber design is depicted in Fig. 1. The external cladding diameter is 125 µm. The pitch Λ = 6.5 µm, the small airhole diameter d1 = 0.23Λ = 1.5 µm, the large airhole diameter d2 = 0.9Λ = 5.85 µm. The core region is formed by introducing a defect in a central vertical row of airholes and has an area of ∼6×11 µm2. Two rows of large airholes and a row of small airholes provide for the confinement of light in the core region and for the waveguide birefringence [19]. The slow polarization axis of the fiber is parallel to the vertical axis of the reference coordinate system in Fig. 1. The phase modal birefringence of the optical fiber is given as:
where n1 and n2 are the effective refractive indices along the slow and fast orthogonal polarization axes, respectively.When hydrostatic pressure is applied to the uncoated birefringent MOF, it induces a specific asymmetric stress distribution in the fiber cross-section. This stress induces material birefringence in the core area, which in its turn modifies the phase modal birefringence. The distribution of the refractive index ni(x,y) in the stressed fiber is then given as [16]:
with i = 1 and 2 for the slow and fast polarization axis, respectively, n0 is the refractive index of the MOF silica, described by the Sellmeier equation [20], and the terms Δni(x, y) represent the pressure-induced modifications of the refractive index distributions. These сan be calculated as follows:To find the distribution of Δn1(x, y) and Δn2(x, y) in the fiber cross-section, we first calculate the principal stresses in the loaded fiber. Once the stress-induced corrections to the refractive indices are known, this data is used as an input to the optical simulations, which allow calculating the propagation constants β1 and β2, and the effective refractive indices n1 and n2. Subsequently, the phase (B) and group (G = B – λdB/dλ) modal birefringence can be calculated.
To quantify how applied hydrostatic pressure affects the birefringence, we carried out extensive computer simulations using the commercially available finite element method (FEM) software COMSOL Multiphysics. The simulations were performed on 2D cross-sections of the fibers, and their sensing properties were studied in terms of their polarimetric sensitivity. In these simulations we considered a fiber without any coating material. Pressure and temperature sensitivities are respectively given by:
Using the method described above, we studied the properties of the proposed fiber design. The distributions of the electric field E of the two orthogonally polarized fundamental optical modes at a wavelength λ = 1550 nm are shown in Fig. 2. The mode field size of the new MOF is ∼5.3×8.6 µm2, which leads to a mode field diameter (MFD) that is close to that of conventional birefringent fibers (∼10 µm) and to a loss of about 1 dB when coupled to a standard optical fiber due to the MFD mismatch, as obtained from simulations of the overlap integral. The mode is well-confined within the core area. The confinement loss LC, calculated at λ = 1550 nm using Eq. (5), is about 0.1 dB/km:
Fig. 2. Distribution of the magnitude of the electric field in the cross-section of the MOF shown in Fig. 1: (a) y-polarization and (b) x-polarization.
The phase modal birefringence B of the MOF is 3.2×10−4 at λ = 1550 nm, which is comparable to that of a Panda fiber [21]. Figure 3 shows how the phase (B) and group (G) modal birefringence depend on wavelength. The absolute values of both B and G increase with wavelength, which is typical for birefringent MOFs.
Figure 4 shows the linear decrease of B with applied pressure and temperature. The polarimetric pressure sensitivity KP equals −32.1 rad×MPa−1×m−1 and the polarimetric temperature sensitivity KT equals −0.0057 rad×K−1×m−1 at λ = 1550 nm. This magnitude of KP is smaller than that of side-hole fiber (∼60 rad×MPa−1×m−1) [14], but it is still about 4 times larger than that of the commercially available MOF (NKT PM-1550-01) used in previously reported distributed pressure measurements (∼7.5 rad×MPa−1×m−1) [9]. The negligible value for KT provides for a cross-sensitivity to temperature that is much lower than that of side-hole fibers [22].
Fig. 4. Evolution of the birefringence B as a function of (a) applied hydrostatic pressure and (b) temperature.
Both the pressure and temperature sensitivities depend on wavelength as shown in Fig. 5. KP follows a 1/λ law, similar to the behavior of the Butterfly MOF [15]. The absolute value of KP decreases with wavelength, whilst the absolute value of KT increases with the operating wavelength. Although the pressure sensitivity is higher at shorter wavelengths, the absolute value of the birefringence is lower at shorter wavelengths, which limits the range of measurable pressures.
Fig. 5. (a) Spectral dependence of polarimetric pressure sensitivity; (b) spectral dependence of polarimetric temperature sensitivity.
The polarimetric temperature sensitivity KT is of the order of 10−3 rad×K−1×m−1. This is two orders of magnitude less compared to side-hole fiber and stems from the absence of GeO2 doping in the core region [22]. The high pressure and very low temperature sensitivities result in a very high KP/KT ratio (Fig. 6). For our MOF design, and to the best of our knowledge, this ratio reaches a record high value of ∼5600 K/MPa at a wavelength of 1550 nm. This value can be compared to that of a side-hole fiber, which is about 150 K/MPa at 1550 nm, and to that of the commercial NKT PM-1550-01 MOF, which is about 610 K/MPa at the same wavelength. A KP/KT ratio of about 5600 K/MPa means that a temperature change of 560 K would appear as a pressure change of only 1 bar, and hence we can safely state that our MOF appears well-suited for pressure sensing in applications exposed to large temperature variations.
3. Fiber fabrication
Following the design described in the previous section and in view of fabricating our MOF with the well-known stack-and-draw technique [23], we have first assembled the preform with cross-section shown in Fig. 7(a). The preform holds an arrangement of silica capillaries and solid rods that is essentially a macro-scale reproduction of the targeted airhole pattern in the final fiber design.
Prior to producing the preform, we fabricated 6 silica capillaries with an outer/inner diameter ratio of 2.125, 54 capillaries with a diameter ratio of 1.081 and 157 solid silica rods. We assembled the 50 cm-long preform stack with these rods and capillaries and we then inserted it in an outer jacketing tube with a diameter ratio of 1.077. A pressurizing system was connected to the jacketed stack to provide control over the gas pressure regimes inside the preform during the cane drawing process. The preform was then drawn under different pressures applied between the stack and the jacketing tube into several intermediate 1 m-long canes. Finally, we used one of the canes (Fig. 7(b)) for the fiber drawing. The two-stage drawing process allows sintering the capillaries and rods and limiting the deformations of the airhole microstructure during the fiber manufacturing.
The obtained MOFs have an outer diameter of 125 µm and are coated with a ∼70 µm-thick acrylate coating. Figure 8 shows micrographs of the cross-sections of the as-built fibers, labelled as MOF A and MOF B. Both fibers were drawn from the same cane, but under different pressurizing conditions. The length of MOF A is 98 m, and the length of MOF B is 100 m. The propagation loss in both manufactured MOFs measured with a classical optical time-domain reflectometer (OTDR) is approximately 3 dB/km. This value shows significant improvement in comparison with the value of ∼24 dB/km mentioned earlier [11]. In addition, the fibers appear to splice well with Panda fiber: we achieved a splice loss <1.5 dB when spliced with a Fujikura LZM-100 CO2-laser system.
Fig. 8. Scanning electron micrographs of the cross-sections of the manufactured MOFs (a) A and (b) B.
We used the as-built microstructure geometry obtained from processing the reflection electron micrographs to study the optical properties of the fabricated MOFs with COMSOL Multiphysics. Table 1 summarizes the simulation results. MOF A has a more elliptical core region than MOF B, larger airholes (∼8 µm, against ∼7.3 µm in MOF B) and features a larger B and KP. We also simulated the influence of the 70 µm thick acrylate coating (DeSolite 3471-3-14) on the pressure and temperature polarimetric sensitivities. The applied coating has little impact on KP, but significantly affects KT – it changes sign from negative to positive and its absolute value increases by about an order of magnitude for both fibers. The acrylate coating features a higher thermal expansion coefficient than silica, which in its turn creates additional stress in the fiber when temperature changes.
Table 1. Overview of the simulated properties of the fabricated MOFs.
4. Fiber characterization
4.1 Experimental setup
To characterize the actual specifications of our MOFs, we exploited wavelength-scanning phase-sensitive optical time-domain reflectometry (φOTDR) and the interrogation method described in [11,24]. Figure 9 shows the scheme of the experimental φOTDR setup. We used a tunable semiconductor laser emitting at a wavelength around 1550 nm with a linewidth of 100 kHz. The scanning range and the scanning step in the Rayleigh spectra measurements were defined by the internal laser controller. By changing the scanning range and step, the pressure measurement range and resolution can be tuned. We placed a polarization controller (PC) before the electro-optical modulator (EOM) to control the optical power. To form a scanning pulse with a duration of 10 ns (resulting in a 1 m spatial resolution), we used a high extinction ratio (40 dB) EOM driven by a pulse generator. A polarizer (P), placed after the EOM, allowed aligning the interrogating pulses along the slow polarization axis of the lead-in Panda fiber. An erbium-doped fiber amplifier (EDFA) amplified the optical pulses before injecting them into the MOF. We also used a second PC for aligning the pulse polarization along one of the polarization axes of the MOF. An optical circulator was used to launch the interrogation pulse into the MOF and collect the backscattered signal. The backscattered light was collected from port 3 of the circulator and amplified by the second EDFA. We used a tunable optical filter to reduce the amplified spontaneous emission added by the EDFA. Finally, we detected the backscattered signal with a 3 GHz bandwidth photodetector (PD) and recorded it with a 10 GS/s oscilloscope (Osc). All backscatter traces were averaged over 1000 measurements to reduce the measurement noise.
Fig. 9. Experimental setup including the φOTDR system and the MOF under test in the temperature-controlled pressure chamber.
Note that for the characterization of the pressure sensitivity, the entire fiber length was pressurized in an air pressure chamber equipped with optical fiber feedthroughs. Should only a short section of the fiber be subjected to pressure changes, the spatial resolution of the pressure measurements would be defined by the length of the interrogating pules. Given that the minimal pulse length was limited to 10 ns by the pulse generator, this would result in a 1 m spatial resolution.
4.2 Phase birefringence measurement
First, we attempted to characterize the distribution of the phase modal birefringence B along the MOFs.
Based on the results of the simulations, the approximate value of B for MOF B is 2.1×10−4, corresponding to a frequency shift Δν ≈ 29.6 GHz as calculated using Eq. (6). We first measured the Rayleigh spectra from the slow axis by scanning the interrogating pulses around the frequency ν0slow in a 31.25 GHz range in steps of 125 MHz and recording the backscatter traces at each frequency. After aligning the polarization of the pulses along the fast axis, we tuned their frequency to ν0fast = ν0slow + Δν (where Δν = 30 GHz), and we recorded the Rayleigh spectra from the fast axis. One set of measurements was completed within approximately 8 minutes, during which the temperature variations (less than 0.1 K) can be ignored.
We then calculated a cross-correlation of the Rayleigh spectra from the orthogonal axes, and we obtained the frequency shifts from quadratic fitting of the correlation peaks at each point along the fiber with 1 m spatial resolution (Fig. 10). The birefringence B is then given as:
where νfast and nfastg are the interrogating pulse frequency and the group refractive index along the fast axis.Fig. 10. Phase birefringence distribution in MOF B. The left vertical axis indicates the measured frequency shift, whilst the right vertical axis is scaled in terms of the phase birefringence B.
The measured mean birefringence B = 2.17×10−4 is in good agreement with the simulation results (2.1×10−4) and a standard deviation σB = 7.65×10−6 is comparable to that of commercially available MOF, whilst featuring a two-fold improvement over the Butterfly MOF [10,11].
MOF A featured strong polarization-dependent losses: the amplitude of the backscatter signal recorder from the slow axis was several times lower than that of the signal from the fast axis, reducing the amplitude of the correlation peaks. Also, small variations of the polarization state of the scanning pulses affected the recorded Rayleigh spectra. Due to these issues, we were not able to record the birefringence distribution in MOF A.
4.3 Pressure and temperature sensitivities characterization
To measure the actual sensitivities of the fabricated MOFs, we placed the fibers in a pressurized air chamber that allows working in a range from 0 to 5 bar above atmospheric pressure. The temperature variations in the chamber during each set of the Rayleigh spectra measurements from both polarization axes (taking about 10 min) were less than 0.1 K. In this case the Rayleigh spectra were measured in a 3 GHz range in steps of 12.5 MHz.
The distributions of the pressure induced differential frequency shifts (DiffFS) for MOFs A and B are shown in Fig. 11(a) and Fig. 12(a), respectively. The negative sign of the DiffFS corresponds to a decrease of the birefringence with increasing applied pressure, and thus to a negative polarimetric pressure sensitivity. The DiffFSs exhibit a larger non-uniformity at higher applied pressures. This can be attributed to small variations of the state of polarization of the interrogating pulses throughout the total duration of the experiment, which took about 6 hours. The pressure changes were accompanied by temperature variations in the pressure chamber that result from air compression and decompression, and those in their turn affected the state of polarization in the non-polarization maintaining optical fiber feedthroughs in the pressure chamber. These variations ultimately affect the position of the cross-correlation peaks of the backscatter spectra.
Fig. 11. (a) DiffFS distributions along MOF A under various applied pressures; (b) mean frequency shift in MOF A as a function of pressure change; (c) mean frequency shift in MOF A as a function of temperature change (slow axis); (d) mean frequency shift in MOF A as a function of temperature change (fast axis).
Fig. 12. (a) DiffFS distributions along MOF B under various applied pressures; (b) mean frequency shift in MOF B as a function of pressure change; (c) mean frequency shift in MOF B as a function of temperature change (slow axis); (d) mean frequency shift in MOF B as a function of temperature change (fast axis).
Figure 11(b) and Fig. 12(b) show the mean values of the differential frequency shift in the pressurized MOFs as a function of the applied pressure. We derived the mean DiffFS using an 88 m-long MOF section ΔzA between 52 m and 140 m for MOF A (Fig. 11(a)), whilst for MOF B we used a 92 m-long section ΔzB between 48 m and 140 m (Fig. 12(a)). We calculated the pressure sensitivities dν/dP from linear fits of the experimental data and we found −207.2 MHz/bar for MOF A (corresponding to a polarimetric pressure sensitivity KP = −62.4 rad×MPa−1×m−1) and −133.2 MHz/bar for MOF B (corresponding to a polarimetric pressure sensitivity KP = −40.1 rad×MPa−1×m−1). These values are in a good agreement with the results of our simulations (−57.8 rad×MPa−1×m−1 and −41.5 rad×MPa−1×m−1 for MOFs A and B, respectively).
Finally, we studied the sensitivity of the MOFs to temperature. The fibers were placed in an oven, in which the temperature was increased about 20°C above room temperature (∼22°C). Note that the temperature increase had to be limited given the presence of the acrylate coating. However, this 20°C temperature range is sufficient to characterize the temperature sensitivities of the MOFs. The temperature inside the oven was monitored with a thermistor with a resolution of 0.05°C. The temperature variations in the oven during each set of measurements were below 0.1 K. We scanned the frequency of the interrogating pulses in 37.5 GHz range with 125 MHz step.
The mean values of the frequency shifts as a function of the temperature change along the slow axis for MOFs A and B are shown in Fig. 11(c) and Fig. 12(c), respectively, whilst the mean frequency shifts along the fast axis are shown in Fig. 11(d) and Fig. 12(d). For calculating the mean frequency shifts we also used the MOF sections ΔzA and ΔzB mentioned above. The temperature sensitivities along the orthogonal polarization axes of the studied fibers are dν/dTslow = −1.268 GHz/K and dν/dTfast = −1.271 GHz/K for MOF A and dν/dTslow = −1.191 GHz/K and dν/dTfast = −1.184 GHz/K for MOF B. We obtained the mean temperature-induced DiffFS of 3 MHz/K and 7 MHz/K for MOFs A and B, respectively. These values correspond to polarimetric sensitivities KT 0.09 rad×K−1×m−1 (MOF A) and 0.2 rad×K−1×m−1 (MOF B) and are in a fair agreement with the simulations results for coated fibers. This results in KP/KT ratios of −693 K/MPa for MOF A and −200 K/MPa for MOF B, and that means that a temperature change of 1 K results in an apparent pressure change of 0.015 bar and 0.05 bar for MOFs A and B, respectively.
5. Conclusion
We presented a novel highly birefringent MOF for distributed hydrostatic pressure sensing. Several fibers were manufactured according to a specialty design using a two-stage stack-and-draw technique, and we characterized the sensing properties of two of them. We carried out both simulations and experiments to demonstrate the high polarimetric pressure sensitivity KP (−62.4 rad·MPa−1×m−1 and −40.1 rad×MPa−1×m−1) and low polarimetric sensitivity KT (0.09 rad×K−1×m−1 and 0.2 rad×K−1×m−1) at a wavelength of 1550 nm. The polarimetric pressure sensitivity in each MOF is comparable to that of side-hole fibers and Butterfly MOF, and up to 8.3 times larger than in commercially available highly birefringent MOFs, and high enough to enable distributed pressure sensing with sub-bar resolution. The MOFs also feature a uniformity of the birefringence along their length that is comparable to that of commercially available highly birefringent MOFs. The polarimetric temperature sensitivity of the coated MOF is an order of magnitude lower than that of Panda fiber and features a two-fold improvement over recently demonstrated elliptical-core side-hole fiber. With our fibers, we have demonstrated distributed pressure measurements with sub-bar pressure resolution and 1 m spatial resolution over a ∼100 m distance. Given the low propagation loss of about 3 dB/km, which corresponds to 21 dB/km improvement compared to the Butterfly MOF, and given the uniform high phase birefringence of the order of 10−4, which is comparable to that of commercially available MOFs, our fibers appear to be excellent candidates for distributed pressure sensing over distances up to several kilometers, for example, in downhole applications.
Funding
European Union’s Horizon 2020 Research and Innovation program under the Marie Sklodowska-Curie Action (ITN FINESSE, grant 722509); Interreg (Fotonica pilootlijnen, NWE758); Industrial Research Fund (IOF); Methusalem; OZR of Vrije Universiteit Brussel.
Acknowledgments
This work was performed as part of the Innovative Training Network FINESSE, funded by the European Union’s Horizon 2020 Research and Innovation program under the Marie Sklodowska-Curie Action through grant 722509; Vrije Universiteit Brussel also acknowledges support Interreg (NWE758, Fotonica pilootlijnen); Industrial Research Fund (IOF); Methusalem; OZR of Vrije Universiteit Brussel.
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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