A simple fiber-optic sensor for simultaneous measurement of high pressure and high temperature was proposed. The sensor was simply fabricated by splicing two sections of silica capillary tubes (SCTs) with different inner diameters to the single-mode fiber. The thick core SCT functions as a Fabry-Perot (FP) micro-cavity and an anti-resonant reflecting waveguide at the same time. The two different sensing mechanisms lead to the high contrast sensitivity values of pressure and temperature (‒3.76 nm/MPa, 27.7 pm/°C and 4.24 nm/MPa, 0.82 pm/°C). We also proposed a simple and effective method to evaluate the actual sensitivities of two-parameter sensors by using linear programming, which shows that our sensor is more sensitive than others in high pressure and high temperature simultaneous detection. Besides, low cost, good mechanical property and convenient reflective probe make the sensor more competitive in actual application.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The simultaneous measurement of high pressure and high temperature is essential in many industrial production processes, especially in those under dangerous and harsh working environment. Kinds of optical fiber sensors based on the combination of fiber Fabry-Perot (FP) micro-cavity and fiber Bragg grating (FBG) have been reported for simultaneous measurement of pressure and temperature [1–3]. On the one hand, diaphragms made of different materials can be fabricated onto the fiber tips to form the FP micro-cavities for pressure sensing [4,5]. But these diaphragms cannot survive in the high-pressure environment due to their poor mechanical strength. Meanwhile, some diaphragms cannot either survive in high-temperature environment due to the limitation of the materials . To improve the mechanical strength, the FP micro-cavity based on a silica bubble at the end of the single mode fiber (SMF) that can survive 40 MPa was achieved by using the arc discharge fabrication method . But its pressure sensitivity was only 0.315 nm/MPa. The sensitivity of this kind of fiber pressure sensor can be improved to more than 1nm/MPa by decreasing the thickness of bubble sidewall to sub-micron. However, it influences the superior limit of the pressure detection . Besides, a series of complex steps were needed to fabricate these FP micro-cavities mentioned before. On the other hand, most of the FBGs applied for temperature sensing will be unstable if the temperature is higher than 200 °C . Although the reported FBGs fabricated by using femtosecond laser or ion beam etching can work well under higher temperature, they are with high fabrication cost and low fabrication efficiency [8–10]. Furthermore, the temperature sensitivities of these FBGs are only less than 15 pm/°C [1–3]. Recently, a compact sensor based on a dual-cavity FP interferometer was proposed for simultaneous measurement of high pressure and high temperature . Pressure can be detected based on gas refractive index (RI) variation in the first FP cavity. The second FP cavity based on the hollow-core fiber (HCF) can not only be used for temperature sensing but also function as a micro gas inlet into the first FP cavity. The sensor is simple and cost-effective, but its pressure and temperature sensitivities are still limited by the principle of the FP cavity. Anti-resonant reflecting guidance mechanism in HCF was also applied for pressure sensing . The femtosecond laser-drilled microchannel was created on the ring cladding of the HCF that was spliced between SMFs. The high sensitivity of 3.592 nm/MPa was achieved based on the pressure-induced RI variation of the air in the hollow-core. The proposed device with a simple and robust structure can survive under the temperature higher than 500 °C with a temperature cross-sensitivity of 0.0075 MPa/°C. However, it cannot be used to detect pressure and temperature simultaneously, and the transmission structure influences the flexibility of its application. In addition, it is worth to mention that, due to the existence of the cross-sensitivity for most of the two-parameter sensors based on the sensing matrix [1–3,13–17], the individual sensitivity value cannot be directly used for evaluating the sensor performance. There needs to be a simple and uniform method for the sensitivity evaluation of these sensors.
In this paper, we proposed a simple reflective fiber-optic sensor for simultaneous and sensitive measurement of high pressure and high temperature. The sensor was simply fabricated by splicing two sections of capillary silica tubes (SCTs) with different inner diameters to the single mode fiber (SMF). The thick core SCT functions as a FP micro-cavity and an anti-resonant reflecting waveguide at the same time. The anti-resonant phenomenon can be observed from the envelope of the FP interference fringe shown in the reflection spectrum. The two different sensing mechanisms lead to the high contrast sensitivity values of pressure and temperature (‒3.76 nm/MPa, 27.7 pm/°C and 4.24 nm/MPa, 0.82 pm/°C). Besides, we proposed a simple and effective sensitivity evaluation method to compare the fabricated sensor with other two-parameter (pressure and temperature) sensors by using linear programming. The results show that our sensor is more sensitive in pressure and temperature simultaneous measurement. It can have great actual application potential together with the advantages of low cost, easy fabrication, robust structure and convenient reflective probe.
2. Fabrication and principle
The configuration of the proposed sensor is shown in Fig. 1(a). A section of thick core silica capillary tube (SCT) with an external diameter of 125 µm was spliced to the lead-in SMF, and then it was spliced to another section of thin core SCT with an internal diameter of 5 µm and an external diameter of 125 µm. During the splicing process, appropriate parameters were adopted to avoid the collapse of the air core of the SCT. The whole simple fabrication process includes only cutting and splicing, and the sensor is with perfect mechanical property.
The principle of the proposed structure can be described in Fig. 1(b). Along the axial direction of the structure, the light beams reflected by the two splicing interfaces M1 and M2 form FP interference, and the thick core SCT works as a FP gas-cavity. The central wavelength of the mth order interference valley is given by 
Meanwhile, along the radial direction, when the light reaches the side wall of the thick core SCT, the light beams reflected by the inner and outer walls M3 and M4 can also form FP interference, and the side wall of the thick core SCT can be briefly regarded as a FP silica-cavity. At the central resonant wavelength, most part of the light passes out of the side wall, which results in the sharp periodic loss dips in the transmission spectrum. When the wavelength of light gradually deviates from the central resonant wavelength, more part of the light is confined in the hollow core of SCT, and the loss of the light reduces gradually. This finally results in a loss dip bandwidth of less than 10 nm [12,20,21]. When the propagating wavelength is far away from a resonant wavelength, the light is internally reflected and confined in the hollow core of the fiber as the guided core mode. As a result, the thick core SCT also works as an anti-resonant reflecting optical waveguide. The m'th anti-resonant wavelength λm’ can be expressed as follows 12]. When the pressure is increased to 2 MPa, the maximum variation of n1 occurs in the inner surface of the cladding with a value of about 2.4 × 10−5, which means that the value of ∂n1/∂p is about 1.2×10−5/MPa. Based on Eq. (4), the value of ∂nair/∂P at 25 °C can be calculated to be approximately 2.68×10−3/MPa. Therefore, the influence of the pressure on the value of n1 can be ignored, and the pressure sensitivity based on the anti-resonant wavelength shift can be derived as
Compared Eq. (6) with Eq. (2), as the increasing of the pressure, the FP fringe and the anti-resonant dip shift to opposite wavelength directions, which can be used for differential demodulation to further increase the pressure sensitivity of the sensor. Besides, along with the variation of the temperature, the shift of anti-resonant dip is more sensitive than that of the FP fringe by comparing Eq. (7) with Eq. (3), for the TOC of the silica material is much larger than its TEC value. From Eq. (7) it can also be seen that, for the existence of the item n1/(n12‒ nair2), the temperature sensitivity of the anti-resonant reflecting optical waveguide is about twice as much as that of the traditional fiber inline FP silica-cavity which can be calculated by (λm/n1)·(∂n1/∂T) . Therefore, the temperature sensitivity of the sensor is improved by applying the anti-resonant reflecting guidance mechanism. Here, setting nair=1.0, n1=1.458, ∂nair/∂p = 2.68×10−3/MPa, and λm = λm’ = 1550 nm, the pressure and temperature sensitivities based on the wavelength shift of the FP interference valley are calculated to be 4.16 nm/MPa and 0.85 pm/°C, and the pressure and temperature sensitivities based on the anti-resonant wavelength shift are calculated to be ‒3.69 nm/MPa and 22.1 pm/°C respectively.
3. Experimental results and discussions
We fabricated three sensor samples named A, B and C by changing the side wall thickness of the thick core SCT. The inner diameters of the SCTs are 20 µm, 50 µm, and 80 µm, and the thicknesses of the side walls are 52.5 µm, 37.5 µm, and 27.5 µm, respectively. Their microscopy images are shown in Figs. 2(a)–2(c). For each sample, the thick core SCT was cut under a microscope to achieve a length of about 750 µm by using a common optical fiber cutter. Due to the errors of the cutting setup, the actual lengths of the thick core SCTs for samples A, B and C are measured to be 717 µm, 823 µm and 760 µm respectively. A broadband light source ranging from 1450 nm to 1650 nm and an optical spectrum analyzer (OSA, AQ6370B) were used to measure the reflection spectra of the samples through a circulator. The reflection spectrum results are shown in Fig. 2(d). All three sensor samples show FP interference fringes in their reflection spectra. Meanwhile, for each sample, the envelope of the interference fringe is a periodic function of wavelength λ, which is induced by the anti-resonant reflecting guidance mechanism. According to Eq. (5), the free spectral range (FSR) of the envelope can be calculated by
The FSR theoretical values of three samples are 21.4 nm, 30.4 nm and 40.5 nm respectively based on Eq. (5) and Eq. (8), which are basically in accordance with the measured values shown in Fig. 2(d). Both theoretical and experimental results show that the value of FSR is inversely proportional to the thickness d of the side wall of the SCT. This also proves that the reflective thick core SCT can also works as an anti-resonant reflecting optical waveguide. For the common anti-resonant reflecting waveguide based on the SCT, the resonant effect accumulates along the length of the SCT at resonant wavelengths . Therefore, the length of the thick core SCT in the proposed fiber structure can influence the visibility of the envelope. If the thick core SCT is not long enough, the envelope is not obvious. But on the other hand, the thick core SCT cannot be too long. The visibility of the FP interference fringe decreases as the increasing of the length of the thick core SCT, which also influences the sensor performance.
Then the sample A was fixed into the pressure chamber which was connected with a pressure pump. A digital pressure meter with a resolution of 0.001 MPa was employed to show the numerical value of pressure in the chamber. The whole experimental setup is shown in Fig. 3. The pressure chamber was firstly evacuated by the pressure pump. The smallest pressure value we could achieve in the pressure chamber was measured to be 0.012MPa. Then the gas pressure in the chamber was increased from 0.012 MPa to 2.7 MPa in an interval of 0.3 MPa at room temperature. At each step, the reflection spectrum was recorded after the value of the pressure meter was stable. The spectrum results at 0.3 MPa, 0.9 MPa, 1.5 MPa, 2.1 MPa and 2.7 MPa are shown in Fig. 4(a). The interference fringe and its envelope both shift along with the increasing of the pressure. Detailly, the variations of the upper envelope and the interference valley around 1550 nm are individually shown in Figs. 4(b) and 4(c). It is clear that the envelope exhibits a blue-shift when pressure increases, which is opposite to the interference valley.
In order to test the reliability of the sample A, the gas pressure in the chamber was decreased from 2.7 MPa to 0.012 MPa, and the reflection spectra of the sample A were also recorded. We extracted the precise central wavelength values of the chosen envelope and the interference valley in both pressure increasing and decreasing processes. The results are plotted and linearly fitted in Fig. 4(d). It can be seen that all the fitting curves exhibit excellent linear relationships. For the envelope, the pressure sensitivities are ‒3.76 nm/MPa and ‒3.76 nm/MPa when pressure increases and decreases, respectively. The pressure sensitivities of the interference valley are 4.24 nm/MPa and 4.23 nm/MPa when pressure increases and decreases, respectively. Therefore, the sample A shows good repeatability and reliability in pressure sensing. Besides, all the experimental results are accord to the theoretical expectations and calculations.
The pressure responses of samples B and C were also investigated by using the same method, and the results are shown in Fig. 5. The envelope sensitivities of sample B are ‒3.70 nm/MPa and ‒3.67 nm/MPa respectively when gas pressure increases and decreases, while the interference valley sensitivities of sample B are both 4.16 nm/MPa. For sample C, the envelope sensitivities in the pressure increasing and decreasing processes are ‒3.55 nm/MPa and ‒3.61 nm/MPa, respectively, while the interference valley sensitivities are both 4.28 nm/MPa. It is clear that samples B and C also show good repeatability and reliability in pressure sensing. What’s more, these three samples have quite similar envelope sensitivities and the interference valley sensitivities, which can be explained by Eq. (2) and Eq. (6). The pressure sensitivities based on the shift of the envelope and interference valley are both independent of the thickness of side wall and the length of the thick core SCT. This characteristic can be very helpful to increase the sensor consistency in the mass production process, for the influence of the structural dimension errors on the sensitivities can be ignored.
The temperature responses of three sensor samples were also investigated by placing them into an electrical oven with an upper limit of 320 °C. For each sensor sample, the temperature was increased from 30°C to 300°C with an interval of 30°C under atmospheric pressure. At each temperature point, the reflection spectrum of the sample was recorded. The measured reflection spectra of sample A at 30°C, 120°C, 210°C and 300°C are shown in Fig. 6(a). It is obvious that envelope shifts to longer wavelength direction as the increasing of the temperature, while the interference fringe exhibits almost no wavelength shifting.
The detail results for the shifting of the upper envelope and the interference valley around 1550 nm are shown in Figs. 6(b) and 6(c) respectively. The linear fitting sensitivities of the envelope and the interference valley are 27.7 pm/°C and 0.82 pm/°C, which can be shown in Fig. 6(d) and are in accordance to the calculation results. The temperature sensitivity of the sensor based on the wavelength shift of the envelope is much higher than that of the FPI based sensor [13,14] owing to the anti-resonant reflecting guidance mechanism, which is also proved in other transmission sensors based on the same resonant reflecting guidance mechanism [12,24]. What’s more, for the temperature sensitivity based on the wavelength shift of the interference fringe is quite small, the sensitive pressure measurement can be achieved by only monitoring the central wavelength of the interference valley with a low temperature cross-sensitivity of 1.92×10−4 MPa/°C. The temperature responses of samples B and C are shown in Fig. 7. Their envelope sensitivities are 29.3 pm/°C and 26.2 pm/°C respectively, and their interference fringes shown in the reflection spectra are also with very low temperature sensitivities. The temperature responses of three samples also exhibit good consistency.
For the proposed sensor is based on all-silica, it can survive under the temperature even higher than 800 °C, which has been proved by other reported all-silica sensors [11,24,25]. Here, we fabricated another sample with the SCT inner diameter of 20 µm. It was placed in another tube furnace with the temperature upper limit of 950 °C. The tube furnace was heated from 300 °C to 900 °C with an interval of 100 °C. After being kept at 900 °C for one hour, it was then cooled from 900 °C to 300 °C. In the whole process, the refection spectrum of the sample was measured at each temperature point. The measured spectra at 300 °C, 500 °C, 700 °C, and 900 °C in both temperature increasing and decreasing processes are shown in Fig. 8(a). The experimental results show that the proposed sensor can survive under the temperature as high as 900 °C. The mean central wavelength shift values of the upper envelope and the interference valley around 1550nm at the same temperature in both temperature increasing and decreasing processes as well as their error bars are calculated. The linear fitting results are shown in Fig. 8(b). The sensitivities of the new fabricated sample during the range of 300 °C and 900 °C are basically in accordance with the temperature sensitivities of the samples A, B and C during the range of 30 °C and 300 °C.
The comparison of the proposed sensor with other reported sensors for the simultaneous measurement of pressure and temperature is shown in Table 1. From the comparison results we can see, although many optical fiber sensors can be applied for the simultaneous measurement of pressure and temperature, only the all-silica based sensors can survive under high pressure and high temperature environment [11,13–15]. Among them, the sensor proposed in this paper and the others based on the three-beam FPI are with the advantages of easy fabrication and compact size, but the use of the photonic crystal fiber  increases the cost of the sensor.
Apart from the sensor parameters shown in Table 1, the sensitivity is also an essential key to evaluate the sensor. To demodulate the pressure and temperature from the spectrum, the central wavelengths of the two different dips are needed to be monitored simultaneously. Ideally, it’s best that one dip is only sensitive to pressure and the other dip is only sensitive to temperature. In this case, higher sensitivity value means better sensor performance. But actually, due to the existence of the cross-sensitivity for the two dips, there are two pressure sensitivity values and two temperature sensitivity values for the same sensor, and the pressure and temperature are needed to be demodulated from the matrix
When the sensor proposed in this paper is used for individual pressure detection, the pressure sensitivity can double by using the differential demodulation method because the envelope and the interference valley shift to opposite wavelength directions as the variation of the pressure. When the sensor is used for individual temperature detection, the temperature sensitivity is about twice as much as that in  owing to the anti-resonant reflecting guidance mechanism. Meanwhile, the sensor consists of only SMF and SCT, which decreases the cost greatly. Besides, the length of the thick core SCT doesn’t need to be controlled very precisely. The reflection spectrum of the proposed sensor can exhibit obvious FP interference fringe and anti-resonant envelope even when the length of the thick core SCT ranges from about 700 µm to more than 800 µm, and this length value has nearly no influence on the pressure and temperature sensitivities. Therefore, the thick core SCT can be cut by using a common optical fiber cutter, which simplifies the fabrication process. What’s more, the reflective probe makes the proposed sensor easier to use.
In summary, we proposed a simple fiber-optic sensor for simultaneous and sensitive measurement of high pressure and high temperature by splicing two sections of SCTs to SMF. By using two different sensing mechanisms including FP micro-cavity and anti-resonant reflecting waveguide, the two pressure sensitivities are with different signs, and one temperature sensitivity is improved while the other one is quite small, which makes the sensor more sensitive in both individual-parameter detection and two-parameter simultaneous detection. Besides, it is with the competitive advantages of low cost, easy fabrication, robust structure, convenient reflective probe and good sensing consistency.
National Natural Science Foundation of China (11574063, 11874010, 11874133); Natural Science Foundation of Shandong Province (ZR2018MF031); Weihai Science and Technology Development Program (2015DXGJUS002).
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