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Abstract
A self-temperature-calibrated gas pressure sensor with a sandwich structure made of single-mode fiber (SMF)-hollow core fiber (HCF)-SMF is proposed and experimentally demonstrated. A Fabry–Perot interferometer (FPI) is formed by the SMF-HCF-SMF structure along the axial direction, and an antiresonant reflecting optical waveguide (ARROW) is formed by the ring-cladding of the HCF along the radial direction. A micro-channel is drilled on the ring-cladding of the HCF using a femtosecond laser to facilitate air entering/exiting the HCF. The FPI functions as the pressure sensor, and the ARROW functions as the temperature sensor. The initial wavelength and pressure sensitivity of the FPI can be calibrated from the temperature obtained by measuring the optical thickness of the ARROW. The experimental results show that the ARROW exhibits a temperature sensitivity of ~0.584 nm/°C, and the pressure sensitivity of the FPI ranges from 3.884 to 0.919 nm/MPa, within the temperature range of 37–1007 °C. The simplicity and durability of the sensor make it suitable for reliable gas pressure measurement in high-temperature environments.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The fiber optic gas pressure sensor is one of the most important devices in industrial and environmental monitoring fields [1]. In the past decades, fiber-tip Fabry–Perot interferometers (FPIs) based on various diaphragms have shown good potential for pressure sensing applications [2–4]. However, their stability and durability are limited by the creep behavior of the thin diaphragms [2]. Recently, various fiber optic diaphragm-free gas pressure sensors with open cavities, including the FP-based sensor [5–8] and antiresonant (AR)-based sensor [9,10], have been developed for gas pressure sensing applications. The FP-based sensor is a type of interferometer that spectral characteristics are governed by the optical path difference between two beams reflected from two mirrors, whereas the AR-based sensor is a type of optical waveguide that spectral characteristics are governed by the thickness of the first high-index layer [11]. Various types of AR-based fibers have been reported, including photonic crystal fibers [11], Kagome fibers [12], negative curvature fibers [13], and hollow-core fibers (HCFs) [14–16].
The diaphragm-free gas pressure sensors utilize the relationship between the gas pressure and the refractive index (RI) of the open cavity to measure the gas pressure. However, gas pressure sensitivities of either FP-based sensors or AR-based sensors decrease rapidly with the increasing temperature. Therefore, it is necessary to obtain the temperature in advance for measuring the gas pressure. Various hybrid sensors employing Fiber Bragg Gratings (FBGs) or Fabry–Perot interferometers (FPIs) have been extensively investigated for the measurement of multi-parameters [17–19]. However, it is noteworthy that the spectra of both the FP and AR mechanisms are included in the reflected spectrum of the sandwich structure made of single mode fiber (SMF)-HCF-SMF [20]. Therefore, the combined FP and AR mechanisms are expected to be used for measuring temperature and gas pressure. Compared with dual-cavity FPIs [18,19], the sensor based on FP and AR mechanisms can achieve dual-parameter measurement with only a single cavity.
In this paper, we present an AR-based self-temperature-calibrated Fabry–Perot gas pressure sensor, realized via a SMF-HCF-SMF structure with an open micro-channel fabricated on the ring-cladding of the HCF using the femtosecond (fs) laser micromachining. A FPI is formed by the SMF-HCF-SMF structure along the axial direction, and an antiresonant reflecting optical waveguide (ARROW) is formed by the ring-cladding of the HCF along the radial direction. The FPI functions as the pressure sensor, and the ARROW functions as the temperature sensor. The initial wavelength and pressure sensitivity of the FPI can be calibrated from the temperature obtained by measuring the optical thickness of the ARROW. The proposed sensor is novel and simple, with a wide working temperature range.
2. Principle
Figure 1(a) shows the schematic of the proposed sensor, which comprises an HCF sandwiched between two segments of SMFs. The fabrication of the gas pressure sensor consists of the following steps. Firstly, the cleaved lead-in SMF was spliced to the HCF. In the fusion splicing process, appropriate splicing parameters were employed to avoid the collapse of the air-core of the HCF. The discharge intensity and time of the commercial fusion splicer (KL-300T, JILONG) were 50 bit and 500 ms, respectively. Secondly, the HCF was cleaved at a distance l from the splice point, with the help of a microscope. Thirdly, a micro-channel with dimensions of ~40 μm × 20 μm × 10 μm was fabricated on the ring-cladding of the cleaved HCF using an fs laser (Spitfire Ace, Spectra-Physics), to facilitate air entering/exiting the HCF. Figure 1(b) shows the top view of the HCF with a micro-channel. Finally, the fabricated HCF was spliced to another segment of the SMF, which was further cut obliquely. Figure 1(c) shows the side view of the interface of HCF/SMF with a micro-channel. The center wavelength, repetition rate, pulse duration, and pulse energy of the fs laser were 800 nm, 1 kHz, 35 fs, and 0.3 μJ. respectively. The fs laser was focused by an objective lens (MPlan FL N, Olympus) with an amplification factor of 20X and an NA of 0.45. Due to the large thickness of the ring-cladding of the HCF (44/128μm), drilling a micro-channel on the flat end surface of the HCF is easier than drilling through the ring-cladding of the HCF.
Fig. 1 (a) Schematic of the gas pressure sensor, (b) top view of the HCF with a micro-channel fabricated using the fs laser, and (c) side view of the interface of HCF/SMF.
In addition to the FPI along the axial direction, an ARROW is formed by the ring-cladding of the HCF along the radial direction. The ARROW mechanism can be explained as follows: An air-core with low refractive index of n1 is sandwiched between the ring-cladding with high refractive index of n2 and the air-cladding with low refractive index of n1, forming an optical waveguide. The ring-cladding of the HCF can be regarded as an FP resonator along the radial direction. When the wavelength of the incident light satisfies the resonant condition of the FP resonator, the light will be confined to the ring-cladding. Otherwise, lights will return to the air-core and propagate forward.
When l is greater than the critical length Lc, which is defined as the length of the HCF when the AR spectrum appears, the reflected spectrum of the sensor becomes similar to the spectrum of two cascaded FPIs. The critical length can be obtained from Eq. (1) [20].
where n1, n2, and n3 are RIs of air, the ring-cladding of the HCF, and the core of the SMF, respectively. n1 = 1, n2 = 1.443, n3 = 1.449. 2r and d are the inner diameter and the thickness of the ring-cladding of the HCF, respectively. For an HCF with an inner/outer diameter of 44/128 μm, the critical length Lc was computed to be ~245 μm. Therefore, when l is greater than 245 μm, the combination of the FP and AR mechanisms makes the sensor promising for measuring the temperature and pressure.To experimentally investigate the FP and AR mechanisms of the gas pressure sensor, HCFs with different lengths were employed to conduct the experiment. Figures 2(a)-2(d) shows the reflected spectra of the sensors. The black lines correspond to the FP mechanism, and the red envelopes, which were obtained using the cubic spline interpolation method from the valleys of the black lines, correspond to the AR mechanism. The red envelopes show a maintaining free spectral range (FSR), which is consistent with the theory that the antiresonant wavelength of the ARROW is independent of the length of the HCF. With the increase of the length of HCFs, the antiresonant wavelength of the ARROW becomes more obvious. The wavelength resolutions of the FPI and ARROW of Fig. 2(d) are 2pm and 10pm, respectively.
Fig. 2 Reflected spectra and their envelopes for sensors with different HCF lengths: (a) 337 μm, (b) 556 μm, (c) 1260 μm, and (d) 1468 μm.
The peak wavelength of the FPI, λFP, is expressed as [20]
where mFP is an integer. The RI of air is a function of the temperature (T) and pressure (P), as shown in Eq. (3) [21].where a = 2.8793 × 10−9 and b = 0.003671. For a gas pressure sensor with an open cavity, the length of the HCF is a function of the temperature, as shown in Eq. (4) [22].where l0 and αl are the length of the HCF at 0 °C and the thermal expansion coefficient of the silica fiber, respectively. Typically, αl = 0.55 × 10−6/°C [22]. The applied pressure has no effect on the length of the HCF [9]. From Eqs. (2)–(4), we can see that the peak wavelength of the FPI depends on both the temperature and pressure, as shown in Eq. (5).where f (T, P) = [1 + aP/(1 + bT)](1 + αlT). Figure 3(a) shows the temperature dependence of f (T, P) under the standard atmospheric pressure (Ps = 101.325 kPa). It can be seen that the peak wavelength first decreases with the temperature and then increases, reaching its minimum value at approximately 105 °C. The pressure sensitivity of λFP, SFP(T), can be expressed aswhere g (T) = (1 + αlT)/(1 + bT). Figure 3(b) shows the temperature dependence of g (T). It can be seen that, when the temperature increases from 25 °C to 1000 °C, the pressure sensitivity decreases by about 77%, indicating that the temperature plays an important role for the pressure sensitivity. Thus, it is necessary to obtain the temperature in advance for gas pressure measurement.The antiresonant wavelength of the ARROW, λAR, can be expressed as [14]
where mAR is an integer. For an AR-based gas pressure sensor with an open cavity, the RI and thickness changes of the ring-cladding of the HCF are extremely low, and the pressure sensitivities induced by them will almost largely counteract each other [9]. Thus, the RI and thickness of the ring-cladding of the HCF are simplified as functions of the temperature, as shown in Eqs. (8) and (9) [22]. where n20, d0, and αn are the RI and thickness of the ring-cladding of the HCF at 0 °C, and the thermo-optic coefficient of the silica fiber, respectively. Typically, αn = 1.333 × 10−5/°C [22]. From Eqs. (3), (7), (8), and (9), we can see that the antiresonant wavelength of the ARROW depends on both the temperature and pressure. However, it is worth noting that the optical thickness of the ARROW, LAR, depends solely on the temperature, as shown in Eq. (10).The temperature sensitivity of the optical thickness of the ARROW, SAR, can be expressed as follows.Typically, n20 = 1.443 [18]. As αn >> n20αl + 2αnαlT, the optical thickness of the ARROW almost has a linear relationship with the temperature. Once LAR(T) can be recovered from the reflected spectrum, the temperature can be obtained as shown in Eq. (12).where TR is the room temperature.As the reflected spectrum of the sensor is similar to the spectrum of two cascaded FPIs, the peak wavelengths of the FPI and antiresonant wavelengths of the ARROW can be measured directly from the reflected spectrum. Then, mFP and mAR can be obtained by the peak to peak method [23]. From Fig. 2(d), it can be measured that the peak wavelength of the FPI with the mFP of 1915 is 1533.179nm, and the antiresonant wavelength of the ARROW with the mAR of 57 is 1548.500nm. From Eqs. (2) and (7), the optical thickness of the ARROW can be derived as
From Eqs. (4) and (9), it can be seen that the ratio of the length of the HCF and the thickness of the ring-cladding, l(T)/d(T), is a constant (34.953), which can be calculated from the length of the HCF (1468.019μm) and the thickness of the ring-cladding (42μm). Thus, the optical thickness of the ARROW can be derived asThe gas pressure sensitivity can then be recovered by substituting the obtained temperature into Eq. (6). In addition to the influence of the temperature on the pressure sensitivity of the FPI, the temperature influence on the wavelength, λFP (T, PS), should also be considered. Finally, the gas pressure can be obtained as follows.
3. Experiments and discussions
The experimental setup, as shown in Fig. 4, was used to investigate the pressure and temperature properties of the gas pressure sensor. The sensor was sealed in the pressure chamber. The pressure chamber is made of an alundum tube and a stainless-steel tube. The connecting part between them was sealed with glue. The pressure in the range of 0–5 MPa was supplied using a compressed Nitrogen gas cylinder. A pressure meter with a precision of 0.01 MPa was used to calibrate the pressure in the chamber. The sealed sensor was placed at the center of the muffle furnace (GHA 12/300, Carbolite∙Gero) with a temperature range of 20–1200 °C and a precision of 0.5%. A homemade demodulator was used to interrogate the peak wavelength of the FPI and the antiresonant wavelength of the ARROW. A tunable wavelength-scanning laser with a wavelength range of 1520–1580 nm, a linewidth of 0.05 nm, and an output power of 2 mW was used as the light source of the demodulator.
The temperature and pressure properties of the sensor were then evaluated. Under the standard atmospheric pressure (Ps = 101.325 kPa), the temperature was increased from 37 °C to 1007 °C. At each temperature step, the pressure was increased from Ps to 5 MPa and then decreased to Ps, with a step of ~0.5 MPa. Figures 5 (a) and 5(b) shows the temperature properties of the peak wavelength of the FPI and the optical thickness of the ARROW, respectively. It can be seen that the peak wavelength of the FPI first decreases with the temperature and then increases, reaching its minimum value at around 100 °C. The temperature sensitivity of the optical thickness of the ARROW is about 0.584 nm/°C. In order to measure the temperature more accurately, it is necessary to establish a quadratic model of the relationship between the optical thickness of the ARROW and the temperature.
Fig. 5 Temperature properties of (a) the peak wavelength of the FPI and (b) the optical thickness of the ARROW.
Figure 6 shows the variations in the peak wavelength of the FPI, antiresonant wavelength of the ARROW, and the optical thickness of the ARROW with respect to the gas pressure at 37 °C. With the increase in the gas pressure, the peak wavelength of the FPI increases, whereas the antiresonant wavelength of the ARROW decreases. The pressure has a slight disturbance on the optical thickness of the ARROW, which is caused by measurement errors of λFP, λAR, and l(T)/d(T).
Fig. 6 Peak wavelength of the FPI, antiresonant wavelength and optical thickness of the ARROW with respect to the gas pressure.
Figure 7(a) shows the experimental relationships between the peak wavelength shift of the FPI and the gas pressure at different temperatures. The peak wavelength shifts exhibit a good linearity with the gas pressure. The pressure sensitivities at different temperatures are obtained using linear fittings, as shown in Fig. 7(b). The red circles represent the experimental results, whereas the black line represents the theoretical value. The pressure sensitivity decreases from 3.884 nm/MPa at 37 °C to 0.919 nm/MPa at 1007 °C. As the wavelength resolution of the FPI is 2pm, the resolution for the gas pressure measurement ranges from 0.51 kPa to 2.2 kPa. The experimental results of the pressure sensitivity are in good agreement with the theoretical values, thus confirming the theoretical analysis prediction that the pressure sensitivity is sensitive to the temperature.
Fig. 7 (a) Peak wavelength shift and (b) the pressure sensitivity of the FPI under different temperatures.
From the above experimental results, we can conclude that the combination of the FP and AR mechanisms provides the self-temperature calibration capability of the gas pressure sensor. The feasibility of the proposed gas pressure sensor was verified by the theoretical analysis and experimental results.
4. Conclusions
A self-temperature-calibrated gas pressure sensor based on the FP and AR mechanisms was demonstrated. The sensor was constructed with a sandwich structure made of SMF-HCF-SMF, and an open micro-channel was drilled using an fs laser. The peak wavelength sensitivity of the FPI ranges from 3.884 nm/MPa at 37 °C to 0.919 nm/MPa at 1007 °C, and the ARROW exhibits a temperature sensitivity of ~0.584 nm/°C. The optical thickness of the ARROW obtained from the FP and AR mechanisms can be used for temperature calibration. The proposed sensor is novel and simple, with a wide working temperature range, and would find extensive applications for gas pressure sensing in high-temperature environments. We believe that other types of hybrid sensors can be realized using the similar method.
Funding
National Natural Science Foundation of China (NSFC) (61575021, 61775020).
References
1. G. Liu and M. Han, “Fiber-optic gas pressure sensing with a laser-heated silicon-based Fabry-Perot interferometer,” Opt. Lett. 40(11), 2461–2464 (2015). [CrossRef] [PubMed]
2. Y. Z. Zhu, K. L. Cooper, G. R. Pickrell, and A. B. Wang, “High-temperature fiber-tip pressure sensor,” J. Lightwave Technol. 24(2), 861–869 (2006). [CrossRef]
3. S. Watson, M. J. Gander, W. N. MacPherson, J. S. Barton, J. D. C. Jones, T. Klotzbuecher, T. Braune, J. Ott, and F. Schmitz, “Laser-machined fibers as Fabry-Perot pressure sensors,” Appl. Opt. 45(22), 5590–5596 (2006). [CrossRef] [PubMed]
4. Y. Zhang, L. Yuan, X. Lan, A. Kaur, J. Huang, and H. Xiao, “High-temperature fiber-optic Fabry-Perot interferometric pressure sensor fabricated by femtosecond laser,” Opt. Lett. 38(22), 4609–4612 (2013). [CrossRef] [PubMed]
5. S. Silva, L. Coelho, and O. Frazao, “An all-fiber Fabry-Perot interferometer for pressure sensing in different gaseous environments,” Measurement 47, 418–421 (2014). [CrossRef]
6. B. Xu, C. Wang, D. N. Wang, Y. Liu, and Y. Li, “Fiber-tip gas pressure sensor based on dual capillaries,” Opt. Express 23(18), 23484–23492 (2015). [CrossRef] [PubMed]
7. B. Xu, Y. M. Liu, D. N. Wang, D. G. Jia, and C. Jiang, “Optical fiber Fabry–Perot interferometer based on an air cavity for gas pressure sensing,” IEEE Photonics J. 9(2), 7102309 (2017). [CrossRef]
8. Z. Zhang, J. He, Q. Dong, Z. Bai, C. Liao, Y. Wang, S. Liu, K. Guo, and Y. Wang, “Diaphragm-free gas-pressure sensor probe based on hollow-core photonic bandgap fiber,” Opt. Lett. 43(13), 3017–3020 (2018). [CrossRef] [PubMed]
9. M. Hou, F. Zhu, Y. Wang, Y. Wang, C. Liao, S. Liu, and P. Lu, “Antiresonant reflecting guidance mechanism in hollow-core fiber for gas pressure sensing,” Opt. Express 24(24), 27890–27898 (2016). [CrossRef] [PubMed]
10. Y. B. Yang, D. N. Wang, B. Xu, and Z. K. Wang, “Optical fiber tip interferometer gas pressure sensor based on anti-resonant reflecting guidance mechanism,” Opt. Fiber Technol. 42, 11–17 (2018). [CrossRef]
11. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27(18), 1592–1594 (2002). [CrossRef] [PubMed]
12. G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St J Russell, “Models for guidance in kagome-structured hollow-core photonic crystal fibres,” Opt. Express 15(20), 12680–12685 (2007). [CrossRef] [PubMed]
13. W. Belardi and J. C. Knight, “Effect of core boundary curvature on the confinement losses of hollow antiresonant fibers,” Opt. Express 21(19), 21912–21917 (2013). [CrossRef] [PubMed]
14. A. M. Zheltikov, “Ray-optic analysis of the (bio)sensing ability of ring-cladding hollow waveguides,” Appl. Opt. 47(3), 474–479 (2008). [CrossRef] [PubMed]
15. R. Gao, Y. Jiang, and Y. Zhao, “Magnetic field sensor based on anti-resonant reflecting guidance in the magnetic gel-coated hollow core fiber,” Opt. Lett. 39(21), 6293–6296 (2014). [CrossRef] [PubMed]
16. R. Gao, D. Lu, J. Cheng, Y. Jiang, L. Jiang, and Z. Qi, “Humidity sensor based on power leakage at resonance wavelengths of a hollow core fiber coated with reduced graphene oxide,” Sens. Actuators B Chem. 222, 618–624 (2016). [CrossRef]
17. N. N. Dong, S. M. Wang, L. Jiang, Y. Jiang, P. Wang, and L. C. Zhang, “Pressure and Temperature Sensor Based on Graphene Diaphragm and Fiber Bragg Gratings,” IEEE Photonics Technol. Lett. 30(5), 431–434 (2018). [CrossRef]
18. H. C. Gao, Y. Jiang, Y. Cui, L. C. Zhang, J. S. Jia, and J. Hu, “Dual-cavity Fabry-Perot interferometric sensors for the simultaneous measurement of high temperature and high pressure,” IEEE Sens. J. 18(24), 10028–10033 (2018). [CrossRef]
19. Z. Zhang, J. He, B. Du, F. Zhang, K. Guo, and Y. Wang, “Measurement of high pressure and high temperature using a dual-cavity Fabry-Perot interferometer created in cascade hollow-core fibers,” Opt. Lett. 43(24), 6009–6012 (2018). [CrossRef] [PubMed]
20. X. Zhang, H. Pan, H. Bai, M. Yan, J. Wang, C. Deng, and T. Wang, “Transition of Fabry-Perot and antiresonant mechanisms via a SMF-capillary-SMF structure,” Opt. Lett. 43(10), 2268–2271 (2018). [CrossRef] [PubMed]
21. K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993). [CrossRef]
22. Y. Guo, Z. Y. Wang, Q. Qiu, J. Su, Y. X. Wang, S. J. Shi, and Z. F. Yu, “Theoretical and experimental investigations on the temperature dependence of the refractive index of amorphous silica,” J. Non-Cryst. Solids 429, 198–201 (2015). [CrossRef]
23. Y. Jiang, “High-resolution interrogation technique for fiber optic extrinsic Fabry-Perot interferometric sensors by the peak-to-peak method,” Appl. Opt. 47(7), 925–932 (2008). [CrossRef] [PubMed]
