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Abstract
A Fabry-Pérot interferometer (FPI) with an asymmetric tapered structure and air microbubble with an ultrathin wall is designed for high-sensitivity strain measurement. The sensor contains an air microbubble formed by two single-mode fibers (SMF) prepared by fusion splicer arc discharge, and a taper is applied to one side of the air microbubble with a wall thickness of 3.6 µm. In this unique asymmetric structure, the microbubble is more easily deformed under stress, and the strain sensitivity of the sensor is up to 15.89 pm/µɛ as evidenced by experiments.The temperature sensitivity and cross-sensitivity of the sensor are 1.09 pm/°C and 0.069 µɛ/°C in the temperature range of 25-200°C, respectively, thus reducing the measurement error arising from temperature variations. The sensor has notable virtues such as high strain sensitivity, low-temperature sensitivity, low-temperature cross-sensitivity, simple and safe process preparation, and low cost. Experiments confirm that the sensor has good stability and repeatability, and it has high commercial potential, especially strain measurements in complex environments.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fibers which possess the merits of corrosion resistance, anti-electromagnetic interference, as well as economical and abundant raw materials [1], are used in many areas such as biomedicine, aviation, machinery, and information technology [2,3]. Optical fiber sensors are becoming increasingly popular due to their advantages including high sensitivity and small structural dimensions, rendering them especially suitable for the monitoring and collection of physical, chemical, and biological data [4–8]. For example, they deliver excellent performance in the measurement of refractive index, temperature, stress, pressure, and other entities [9–14]. There are several types of optical fiber sensors, for example, Fiber Bragg Gratings (FBGs) [15–17], Mach Zende Interferometers (MZIs) [18–20], and Fabry-Pérot interferometers (FPIs) [21,22]. The FBG and MZI-based sensors have low sensitivity despite the simple preparation process. Moreover, the thermo-optical effect or the temperature effect due to thermal expansion produces additional spectral drifts leading to a large temperature cross-sensitivity for FBG and MZI fiber optic sensors [23].
In strain measurements, FPI-based optical fiber sensors offer many benefits over conventional sensors, such as high sensitivity, linear response, low-temperature cross-sensitivity, and miniatured size compared to other sensing structures [24]. Several techniques have been proposed to produce FPI sensors with good strain sensitivity. For example, Tian et al. have used a fusion splicer (Fujikura, FSM-100P+) to embed microspheres into a tapered hollow-core fiber (HCF), consequently enabling them to have the flexibility to change the cavity length of the FPI by controlling the diameter of the tapered HCF and size of the embedded microspheres. The sensor has a strain sensitivity of 16.2 pm/µɛ and temperature cross-sensitivity of 0.086 pm/°C [25]. Cai et al. have prepared an asymmetric microbubble FPI sensor using the chemically-etched erbium-doped fiber (EDF) with a strain sensitivity of 10.15 pm/µɛ and temperature cross-sensitivity of 0.42 pm/°C [26]. However, the fabrication requires expensive equipment, complex pre-processing, special optical fibers, and hazardous chemicals, thereby increasing the cost and production complexity. Although optimized fabrication processes can improve the temperature cross-sensitivity to 0.115 pm/°C, further enhancement of strain sensitivity and reduction of the temperature cross-sensitivity is still required.
In this study, an asymmetric tapered Fabry-Pérot interferometer (ATFPI) with an ultra-thin-walled air microbubble is designed and demonstrated to have high sensitivity. The ATFPI is made by splicing two segments of SMF with a fusion splicer and repeatedly discharged on one side of the air bubble to form a tapered structure. The silica layer around the air bubble decreases steadily during the fibe- pulling and cone-thinning process, resulting in a wall thickness of only 3.6 µm. The wall thickness and radius of the air bubble can be controlled by means of the axial tensile stress. The ATFPI shows a strain sensitivity of 15.89 pm/µɛ near the 1,550 nm resonance wavelength with a measurement range of 0-1200 µɛ. The temperature range is 25-200 °C and the temperature sensitivity is 1.09 pm/°C. The temperature cross-sensitivity is only 0.069 µɛ/°C. The experimental results indicate that the asymmetric tapered structure gives rise to greater stress concentration and enhanced strain sensitivity. Our study reveals that the ATFPI has high sensitivity, low temperature cross-sensitivity, small size and better measurement stability and repeatability, and therefore, it has excellent prospects in aerospace applications, oil extraction, and energy engineering.
2. Sensor fabrication and working principles
Figure 1 illustrates the preparation of the asymmetric tapered fiber with on a micro-bubble FPI. As shown in Fig. 1(a), two SMF segments on the coating are and wiped clean with alcohol before cutting by an optical fiber cutter and placing into a fusion splicer (Fujikura 80s). The left and right motors of the fusion splicer are controlled to set the optical fibers in the proper position. The discharge time and power parameters are tuned, “-5” power is selected, and the discharge time is selected to be 800 ms, and the flat end is rounded through the initial discharge, as shown in Fig. 1(b). The two SMF sliding surfaces are dipped into a small amount of refractive index matching liquid (Nd: 1.47), so that the tips of both fiber segments are covered by the fluid, as shown in Fig. 1(c). The refractive index matching solution is an oil-based material that offers improved stability, fluidity, and lowered surface tension, making it more suitable for experimental operations. The optical fibers are then put back into the fusion splicer, and the left and right motors are moved to align the cores of the two fibers, so that the two sections of the optical fibers are slightly squeezed and fusion-spliced, as shown in Fig. 1(d). The fusion mode is adjusted to “SMF-SMF”, and the discharge power and discharge time are increased to “+20” and 1200 ms, respectively, and the initial formation of micro-bubble is shown in Fig. 1(e). The left and right motors of the fusion splicer are moved simultaneously to the left, causing the formed microbubble to deviate from the center of the discharge area as shown in Fig. 1(f). The discharge time and discharge power are appropriately reduced and the fiber at the centre is discharged to form a structure as shown in Fig. 1(g). The size of the microbubble is further monitored during the discharge period and the changes in the interference spectra are observed under the combination of slight tensile stress, low discharge time, and small discharge power to successfully fabricate the ATFPI, as shown in Fig. 1(h). In addition, only a common fusion splicer is used throughout the fabrication and no additional equipment is required.
The optical microscopy image of the asymmetric taper fiber composed of quartz is shown in Fig. 2. The wall thickness of the sensor can be reduced to about 3.6 µm by adjusting the discharge time and discharge power. The length of the bubble is 34.47 µm, average radius of the taper waist is 18.46 µm, and the distance of the bubble off-center is 21.28 µm. The small bubble structure results in a thinner fiber wall thickness, which allows the strain to act more effectively on the bubble, making it more sensitive to changes in the external environment.The small bubble improves the strain sensitivity of the sensor, while the radius of the tapered structure and the off-center distance of the bubble further enhance the strain response.
Fig. 2. Microscopic pictures of the ATFPI: (a) the bubble length is 34.47 µm and the wall of 3.6 µm and (b) the average diameter of the taper waist is 18.46 µm and the distance of the bubble off-center is 21.28 µm.
Changes in the external environment can produce slight deformation of the fiber optic sensor and impact the air bubble. The variation of the bubble give rise to a drift of the interference spectrum of the fiber, which can be exploited in sensing. As shown in Fig. 3, the color gradient indicates the stress distribution in different parts of the strain sensor. The fiber has a thin wall thickness and an off-center structure, thus enabling the strain to work more effectively on the bubble. Therefore, the air bubble is more sensitive to external changes and has a higher strain sensitivity.
Figure 4 demonstrates the sensing and working principles of the ATFPI, where M1 and M2 are the two reflective surfaces of the bubble inside the fiber. Light emitted from the super-continuum light source with an intensity of I0 enters the optical fiber and reaches the M1 reflecting surface for the first reflection with a reflection intensity of I1. Some of the light passes through the M1 reflecting surface and reaches the M2 reflecting surface for a second reflection with a reflection intensity of I2. The two beams of reflected light are coupled in the core of the SMF producing the interference phenomenon.
Since the reflected energy of quartz/air is about 4%, it can be deduced that the third reflected light intensity inside the bubble is only 0.006% of the original light intensity. The higher-order reflected light energy is extremely weak and almost negligible and therefore, it can be considered as two-beam interference, i.e., Fabry-Perot interference. As for the two-beam interference, the expression for the interference spectrum is given by:
where θ is the phase difference shift caused by the transmission of light in the air cavity. With regard to two-beam interference, the reflection spectrum has the cosine characteristic. The free spectral range (FSR) of the reflectance spectrum are expressed by Eq. (2) and Eq. (3): where m is the number of fiber interference levels, λm is the FPI resonant wavelength position corresponding to the interference level, neff is the refractive index of air, and L is the length of the air bubble.Strain is an essential entity in continuum mechanics to quantitatively describe the deformation of an object. Measuring strain by FPI is the most direct and efficient method. Without considering the fusion loss, the strain acting on the sensor is the same as the strain applied to the whole fiber by moving the platform and hence, the strain of the FPI sensor can be expressed by:
Based on the interference spectrum FSR, the variation of the lumen length L can be readily calculated or monitored. Therefore, the strain sensitivity of the optical fiber strain sensor with the FP cavity can be obtained:
The asymmetric tapered structure can be used to increase the bubble diameter by reducing the thickness of the microcavity walls. According to Eq. (7), the strain sensitivity of the sensor increases when the diameter of the bubble increases. For FPI sensors, the phase should be an integer multiple:
The wavelength corresponding to the interference peak of FPI can be expressed as:
The temperature sensitivity is finally obtained:
3. Results and discussion
The experimental setup used to monitor the strain response of the ATFPI is described in Fig. 5. A one-part-two 3 dB ring coupler is used to feed the light signal from an amplified spontaneous emission (ASE, 450-2500 nm) to the sensor, and then reflected light is coupled to the optical spectrum analyzer (OSA, resolution 0.02 nm) to monitor and record the interference spectra. The axial stress changes are controlled by the two three-dimensional (3D) moving platforms. As for the linear change, the strain is defined as the ratio of the change to the initial amount, as shown in Eq. (4). To prevent destruction of the sensor when stress is applied, the distance between the two moving platforms is set to 20 cm, and the axial stress applied to the sensor is 200 µɛ each time.
Fast Fourier transform (FFT) is performed on the reflectance spectra of the ATFPI structure to obtain the main components of the synthesized spectrum. In the FFT theory, the spatial frequency response is the inverse of the FSR [27]. According to the inset plot in Fig. 6, λm = 1,534.16 nm and λm + 1 = 1,569.04 nm at 1,550 nm. The FSR of 34.88 nm is calculated from Eq. (2) and a spatial frequency response of 0.0309 is obtained from the graph. For validation, the spatial frequency response is multiplied by the FSR and the product is rounded to 1. There is only one strong peak in the plot, proving that the ATFPI is two-beam interference. Furthermore, the structure has a single-component Fabry-Pérot cavity. In other words, the reflection spectrum exhibits the cosine characteristics required for two-beam interference.
The micro bubble inside the optical fiber sensor experiences small deformation when the external stress changes, resulting in a drift in the reflectance spectrum. Drift is utilized to determine the FSR, bubble length, and strain sensitivity of the sensor. Axial pull-off experiment was performed on the sensor, resulting in its destruction at an applied strain of 2400 µɛ. The interference spectra overlap with previously measured stress range spectra when stresses higher than 1800 µɛ. (see Fig. S1 in the Supplement 1 for the exact stressing process, and S2 showing picture of the destroyed sensor). The wavelength variation is proportional to strain in accordance with Eq. (6). The strain applied to the fiber causes the reflection spectrum to shift towards longer wavelengths, resulting in a redshift of the interference spectrum. The total reflection spectrum drift is approximately 19 nm. When strain increases, the interference spectrum moves in the direction of increasing wavelength. Figure 7(a) shows that at 1,550 nm, the FSR of 34.88 nm can be obtained from Eq. (2), leading to the bubble length of 34.51 µm by Eq. (3). The microscopic image reveals that the actual length of the bubble is 34.47 µm with an error of only 0.04%. Figure 7(b) demonstrates the linear relationship between the two parameters at different stress levels and wavelengths with R2 = 0.99836, indicating a good linear correlation between the two variables. Based on the fit of the wavelength drift to stress, the slope shows a strain sensitivity of 15.89 pm/µɛ.
Fig. 7. Strain response of the ATFPI: (a) Reflection spectra of the ATFPI for different strain levels and (b) Relationship between the strain and wavelength drift of the ATFPI.
Numerical simulation is performed to explore the intrinsic mechanism of the high strain sensitivity. Figure 8 shows the deformation of the bubble inside the sensor (20x magnification). As expressed by Eq. (4), an increase in the horizontal length of the bubble by 0.2 µm decreases the vertical length of the bubble by 0.05 µm. The stress effects are mainly concentrated in the weakest regions of the wall thickness and are accompanied by significant deformations in the form of slight depressions and bubbles. The length of the bubble is subsequently amplified to enhance the scalability and monitoring capability.
Figure 9 shows the linearly fitted curves for forward applied stress and reverse released stress. The strain sensitivity of the ATFPI is determined by two sets of experiments: forward applied stress and reverse released stress. The reproducibility is verified by comparing the sensitivity of the two sets of experiments. In the forward strain phase, the axial stress increases from 0 to 1200 µɛ, and the strain sensitivity of the ATFPI is 15.89 pm/µɛ. In the opposite stress-release phase, the axial stress decreases from 1,200 to 0 µɛ. At this point, the strain sensitivity of the ATFPI is measured to be 15.90 pm/µɛ, and a spectral change is recorded every 200 µɛ. While the forward tension period is time-consuming, the sensor structure will be deformation, and the bubble inside the ATFPI will not be completely recovered to its original shape after the tension is released. According to Eq. (11), the wavelength corresponding to the FPI interference peak is related to the cavity length, causing subtle discrepancies between the experimental measurements of the forward applied tension and the directional released tension. We reduce the experimental time and optimise the repetitive experiments shown in Fig. 9, which reduces the mismatch error between the increasing and decreasing strain.
Stability experiments are performed on ATFPI at room temperature. The changes in the interference spectra are recorded after holding for 5 min for each increase of 200 µɛ during the forward application of 0-1,200 µɛ. As shown in Fig. 10, the stability of the sensor is verified by the consistency of the reflection spectrum valleys near 1,550 nm for different axial stresses. To assess the comprehensive stability of the ATFPI, the axial strain is kept at 200 µɛ to detect the wavelength drift of the interferometric spectra during a 60-min period. The complex environment on the experimental platform inevitably produces slight vibration. This fluctuation may be originated from the 3D moving platform or from the starting machine of the light source, and the data may be skewed by post-processing of the experimental data, which will lead to small errors in the stability experiments. Figure 10 shows that the interference fringe variation is below 40 pm, thereby providing good stability of the ATFPI.
Temperature changes, in conjunction with stress, have the potential to change the shape of the bubbles inside the fiber, thereby impacting the phase of the sensor. This change creates an optical range difference, which subsequently leads to a drift in the interference peaks in the FPI's interference spectrum. To prevent the ATFPI from moving during the temperature experiments, the sensing portion of the optical fiber is secured on the metal base of the thermostat platform with a high-temperature tape. As shown in Fig. 11(a), the temperature is raised from 25 °C to 200 °C in steps of 25 °C and the interference spectra are collected at each temperature. The fiber optic material for ATFPI is mainly SiO2, which has a crystal structure with covalent bonds between atoms that are resistant to deformation due to temperature changes, resulting in a lower coefficient of thermal expansion. According to Eq. (12), the temperature sensitivity of the fiber optic FPI sensor is related to the thermal expansion coefficient of the material, the thermo-optic coefficient and the wavelength corresponding to the interference peak. The ATFPI contains an air bubble that is unaffected by the thermo-optical coefficient. The temperature sensitivity is only affected by the coefficient of thermal expansion and the wavelength corresponding to the interference peak. Its cavity length does not affect the temperature sensitivity. As shown in Fig. 11(a), the reflectance spectrum remains stable as temperature increases, indicating that the sensor is not affected by thermal expansion. As shown in Fig. 11(b), after several repeated experiments, the temperature response of the sensor is obtained by calculating the mean value of the wavelength drift of the wave valley near 1534 nm and then fitting it linearly to the temperature. ATFPI has a temperature sensitivity of 1.09 pm/°C and a temperature cross-sensitivity of 0.069 µɛ/°C.
Fig. 11. Temperature response of the sensor: (a) Reflection spectra of the sensor at different temperature and (b) Relationship between the mean value of dip wavelength shift and temperature.
Table 1 compares the characteristics of our sensors with those of previously reported FPI-based strain sensors [21,22,25,26,28,29]. It can be seen that our sensor has higher strain sensitivity and lower temperature cross-sensitivity over a wide strain measurement range. The unique asymmetric structure has a thinner wall, thereby making the fiber insensitive to temperature changes. Furthermore, the sensor can be easily manufactured without costly equipment or hazardous chemicals, thus increasing the safety and cost effectiveness in manufacturing.
Table 1. Comparison between our sensor and previously reported FPI-based sensors.
4. Conclusion
A high-sensitivity strain sensor based on an asymmetric tapered Fabry-Perot interferometer with an ultra-thin wall is designed and analyzed. The utilization of melt splicing in the manufacturing of ATFPI offers the benefits of simplicity, cost effectiveness and safety. The sensitivity parameters are optimized by data analysis of the interferometric spectra. The experimental results show that the strain sensitivity is as high as 15.89 pm/µɛ in the range of 0-1200 µɛ, and the temperature sensitivity is 1.09 pm/°C in the temperature range of 25-200 °C. In this unique asymmetric tapered structure, the small wall thickness and wide measuring range contribute to the excellent performance without compromising the strain sensitivity. As a result, the temperature cross-sensitivity of the ATFPI is 0.069 µɛ/°C, rendering it less sensitive to temperature variations. This strain sensor has notable merits such as high strain sensitivity, low-temperature cross-sensitivity, good repeatability and stability. Furthermore, it boasts a small size, low cost, and simple preparation process and has immense potential in applications such as microstrain monitoring.
Funding
National Natural Science Foundation of China (12304480); Natural Science Foundation of Heilongjiang Province (JQ2023F001); Local Universities Reformation and Development Personnel Training Supporting Project from Central Authorities; Natural Science Foundation of Heilongjiang Province (LH2021F007); China Postdoctoral Science Foundation (2020M670881); Study Abroad returnees merit based Aid Foundation in Heilongjiang Province (070-719900103); City University of Hong Kong Strategic Research Grant (SRG) (7005505); City University of Hong Kong Donation Research Grants (DON-RMG 9229021, 9220061).
Acknowledgments
This work was jointly supported by National Natural Science Foundation of China [12304480], Heilongjiang Provincial Natural Science Foundation of China [JQ2023F001], Local Universities Reformation and Development Personnel Training Supporting Project from Central Authorities, Natural Science Foundation of Heilongjiang Province [LH2021F007], China Postdoctoral Science Foundation funded project [2020M670881], Study Abroad returnees merit based Aid Foundation in Heilongjiang Province (070-719900103); City University of Hong Kong Strategic Research Grant (SRG) [7005505], as well as City University of Hong Kong Donation Research Grants [DON-RMG 9229021 and 9220061].
Disclosures
The authors declare no conflicts of interest.
Data availability
The data generated or analyzed as part of the research are not available to the public as they may be restricted for privacy reasons. To access the data, please send an e-mail to 1369151353@qq.com.
Supplemental document
See Supplement 1 for supporting content.
References
1. G. Zhang, Q. Ge, H. S. Wang, et al., “Simultaneous temperature and strain measurement using TCF based Mach-Zehnder interferometer,” Opt. Fiber Technol. 67, 102687 (2021). [CrossRef]
2. B. Piątek, T. Howiacki, M. Kulpa, et al., “Strain, crack, stress and shape diagnostics of new and existing post-tensioned structures through distributed fibre optic sensors,” Measurement 221, 113480 (2023). [CrossRef]
3. T. H. Kim, “Analysis of optical communications, fiber optics, sensors and laser applications,” J. Mach. Comput. 3(2), 115–125 (2023). [CrossRef]
4. L. H. Xu, C. Liu, Y. Shi, et al., “High-sensitivity photonic crystal fiber methane sensor with a ring core based on surface plasmon resonance and orbital angular momentum theory,” Optik 286, 170941 (2023). [CrossRef]
5. W. Liu, Y. Shi, Z. Yi, et al., “Surface plasmon resonance chemical sensor composed of a microstructured optical fiber for the detection of an ultra-wide refractive index range and gas-liquid pollutants,” Opt. Express 29(25), 40734–40747 (2021). [CrossRef]
6. W. Liu, C. Liu, J. X. Wang, et al., “Surface plasmon resonance sensor composed of microstructured optical fibers for monitoring of external and internal environments in biological and environmental sensing,” Results Phys. 47, 106365 (2023). [CrossRef]
7. C. R. Liao, C. Xiong, J. L. Zhao, et al., “Design and realization of 3D printed fiber-tip microcantilever probes applied to hydrogen sensing,” Light: Adv. Manuf. 3(1), 1–13 (2022). [CrossRef]
8. M. Q. Zou, C. R. Liao, Y. P. Chen, et al., “3D printed fiber-optic nanomechanical bioprobe,” Int. J. Extreme Manuf. 5(1), 015005 (2023). [CrossRef]
9. P. Roriz, S. Silva, O. Frazão, et al., “Optical fiber temperature sensors and their biomedical applications,” Sensors 20(7), 2113 (2020). [CrossRef]
10. J. Deng and D. N. Wang, “Ultra-sensitive strain sensor based on femtosecond laser inscribed in-fiber reflection mirrors and Vernier effect,” J. Lightwave Technol. 37(19), 4935–4939 (2019). [CrossRef]
11. L. H. Xu, C. Peng, T. Y. Meng, et al., “High-sensitivity ring-core photonic crystal fiber sensor based on surface plasmon resonance for ultra-low refractive index detection,” Mod. Phys. Lett. B 38(02), 2350216 (2024). [CrossRef]
12. L. H. Xu, C. Liu, H. H. Fu, et al., “Orbital angular momentum-excited surface plasmon resonance for liquid refractive index sensing by photonic crystal fiber with high sensitivity and wide detection range,” Opt. Eng. 61(09), 096101 (2022). [CrossRef]
13. W. Liu, C. J. Hu, L. Zhou, et al., “A square-lattice D-shaped photonic crystal fiber sensor based on SPR to detect analytes with large refractive indexes,” Physica E Low Dimens. Syst. Nanostruct. 138, 115106 (2022). [CrossRef]
14. C. Liu, J. W. Lü, W. Liu, et al., “Overview of refractive index sensors comprising photonic crystal fibers based on the surface plasmon resonance effect,” Chin. Opt. Lett. 19(10), 102202 (2021). [CrossRef]
15. J. K. Sahota, N. Gupta, and D. Dhawan, “Fiber Bragg grating sensors for monitoring of physical parameters: A comprehensive review,” Opt. Eng. 59(06), 1 (2020). [CrossRef]
16. J. J. Chen, B. Liu, and H. Zhang, “Review of fiber Bragg grating sensor technology,” Front.Optoelectron.China 4(2), 204–212 (2011). [CrossRef]
17. Z. H. Cai, B. Z. Li, Z. Y. Bai, et al., “Encrypted optical fiber tag based on encoded fiber Bragg grating array,” Int. J. Extreme Manuf. 5(3), 035502 (2023). [CrossRef]
18. N. Zhang, W. Xu, S. H. You, et al., “Simultaneous measurement of refractive index, strain and temperature using a tapered structure based on SMF,” Opt. Commun. 410, 70–74 (2018). [CrossRef]
19. P. Lu, L. Q. Men, K. Sooley, et al., “Tapered fiber Mach–Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009). [CrossRef]
20. L. C. Li, L. Xia, Z. H. Xie, et al., “All-fiber Mach-Zehnder interferometers for sensing applications,” Opt. Express 20(10), 11109–11120 (2012). [CrossRef]
21. S. Liu, Y. P. Wang, C. R. Liao, et al., “High-sensitivity strain sensor based on in-fiber improved Fabry–Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014). [CrossRef]
22. Y. F. Wu, Y. D. Zhang, J. Wu, et al., “Temperature-insensitive fiber optic Fabry-Perot interferometer based on special air cavity for transverse load and strain measurements,” Opt. Express 25(8), 9443–9448 (2017). [CrossRef]
23. B. Xu, M. Chen, K. Yang, et al., “Ultra-high sensitivity strain sensor based on biconical fiber with a bulge air-bubble,” Opt. Lett. 46(8), 1983–1986 (2021). [CrossRef]
24. A. Miliou, “In-fiber interferometric-based sensors: Overview and recent advances,” Photonics 8(7), 265 (2021). [CrossRef]
25. K. Tian, M. Zhang, J. B. Yu, et al., “High sensitivity, low temperature-crosstalk strain sensor based on a microsphere embedded Fabry–Perot interferometer,” Sens. Actuators, A 310, 112048 (2020). [CrossRef]
26. L. Cai, J. Wang, M. Q. Chen, et al., “A high-sensitivity strain sensor based on an unsymmetrical air-microbubble Fabry-Pérot interferometer with an ultrathin wall,” Measurement 181, 109651 (2021). [CrossRef]
27. W. Zhang, H. Y. Li, L. Q. Zhu, et al., “Dual-parameter optical fiber probe based on a three-beam fabry-perot interferometer,” IEEE Sens. J. 21(4), 4635–4643 (2021). [CrossRef]
28. Q. Li, J. X. Wang, H. W. Mu, et al., “A Fabry–Pérot interferometer strain sensor composed of a rounded rectangular air cavity with a thin wall for high sensitivity and interference contrast,” Opt. Commun. 527, 128920 (2023). [CrossRef]
29. P. H. Zhang, L. Zhang, Z. Y. Wang, et al., “Sapphire derived fiber based Fabry-Perot interferometer with an etched micro air cavity for strain measurement at high temperatures,” Opt. Express 27(19), 27112–27123 (2019). [CrossRef]
