Open Access
Add to BibSonomy
Abstract
We proposed a novel torsion sensor based on the Lyot filter with the twisted polarization-maintaining fiber (PMF) acting as the birefringence medium. Lyot filter is formed by two linear polarizers and a piece of PMF. Based on the high birefringence of the PMF, the output polarization rotates with a rate equal to the twisting rate applied on the PMF, and the sensor realizes a high sensitivity of 90.072 dB/rad. The proposed sensor also demonstrated a low strain sensitivity of $\textrm{2}\mathrm{.32\ \times 1}{\textrm{0}^{\textrm{ - 6}}}$ rad/μɛ. On the other hand, based on the phase hits of the polarization interference, the wavelength sensitivity reaches 15.477 nm/rad. The monitoring range of the wavelength demodulation is complementary with the intensity demodulation in one cycle, making the valid sensing range of the proposed sensor expand. The proposed highly sensitive compact torsion sensor, with large sensing range and low crosstalk, has potential applications in many fields such as manufacturing industry, civil engineering, aerospace industry and modern smart structure monitoring.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Torsion is one of the most important mechanical parameters in the field of civil engineering, manufacturing industry, mechanical production and so on. Based on the torsion measurement in the structure, the stress state and internal injury can be monitored in real time to make sure the structure of buildings in a healthy state [1]. The torsion is also measured to monitor the quality of products and the movement of intelligent machines. Therefore, it has attracted great interest for researchers to design various torsion sensors. The conventional torsion sensors are based on electrical methods or electromagnetic phenomena and have realized high sensitivity as well as precision [2,3]. However, for those sensors, electromagnetic interference is inevitable and the bulky structure is difficult to be embedded into the small machine, limiting the application of torsion sensors under actual circumstances.
In comparison, optical fiber sensor has been regarded as a possible effective way for the torsion measuring because of their inherent advantages such as low electromagnetic interference, compact size, light weight and the ability of long-distance transmission. So far, various novel torsion fiber sensors have been designed in recent years [4–22]. In general, optical fiber torsion sensors can be divided into two classes: grating-based sensors and interferometer-based sensors. For the grating-based sensors, Lin et al. proposed a torsion sensor based on the configuration of a corrugated long-period grating (LPG) by etching a fiber [4]. Shi et al. realized a torsion sensor based on a fiber ring, with a pair of rotary LPGs written by a CO2 laser [5].In addition, the fiber optic torsion sensor based on fiber Bragg gratings (FBGs) [6–8], titled FBGs (TFBGs) [9,10] and the phase-shifted FBG (PSFBG) [11] has been proposed to obtain higher sensitivity and reduce the cross interference. Ahmad et al. have reported the distributed measurements of fiber contortions via a Bragg-grating-inscribed twisted multicore optical fiber [12].
Instead, the torsion sensors based on the interference have been realized by utilizing the difference between the reference path and the sensing path. The difference is caused by the asymmetry of the fiber structure or the light path of fiber sensors. Zhao et al. have proposed and demonstrated a Mach-Zehnder interferometer (MZI) formed by a twin-core fiber cascaded with a side-hole fiber [13]. Jiang et al. have reported a highly sensitive torsion sensor based on MZI constructed by a dual side-hole fiber with a helical structure [14]. Ren et al. have reported an in-fiber directional torsion sensor based on MZI, in which a section of two-mode fiber is sandwiched between two single mode fibers by core-offset splicing [15]. Among the torsion sensor based on interference, one of the most classical structures is the Sagnac interferometer, whose principle is the index difference between polarized light in the both clockwise direction and counterclockwise direction. Htein et al. have introduced a two-semicircular-hole fiber (TSHF) with a germanium(Ge)-doped elliptical core and two large semicircular-holes in a Sagnac loop as twist sensor [16]. The other types of Sagnac structure have been studied, such as highly birefringent photonic crystal fiber [17], low birefringence photonic crystal fibers [18], side leakage photonic crystal fiber [19], suspended twin-core fibers [20] and PM-elliptical core fibers [21].
The Lyot filter is a unique type of polarization interferometer. The Lyot filter is formed by two linear polarizers and a birefringent cavity sandwiched in the middle. Due to high contrast, low cost, and high stability, the Lyot filter has been widely researched. Currently, different kinds of Lyot filters were reported, such as bulk Lyot filters and all-fiber Lyot filters [22], but there is little research on its application in torsion sensing. Recently, Huang et al. proposed a reflection-type and transmission-type twist sensor based on a Lyot filter, which used polarization-maintaining fiber (PMF) as birefringent medium and measured torsion by twisting single mode fiber (SMF) in the light path. [23,24]. Huang et al. also proposed the Lyot filter based on the birefringent SMF written by using the femtosecond laser [25].
In this work, a highly sensitive torsion sensor based on the all-fiber Lyot filter is fabricated by inserting a section of twisted PMF between two fiber linear polarizers. The structure places the PMF in the sensing area of twisting, the high birefringence of the PMF makes the polarization rotate with the twist rate applied on the PMF, so the sensor exhibits a high sensitivity of up to 90.072 dB/rad. Moreover, based on the phase hits of the polarization interference at the special twist angle, the sensitivity reaches 15.477 nm/rad and the range of highest sensitivity is complementary with the range of highest intensity sensitivity in the same period, making the valid angle range of the proposed sensor expand. The strain cross-sensitivity is only $2.32 \times {10^{ - 6}}$ rad/$\mu \varepsilon$ and the sensor has the strain sensitivity of the wavelength when the sensitivity about twist is lowest, thus realizing the dual-parameters measurement.
2. Principle
The schematic configuration of the proposed sensor based on the Lyot filter is illustrated in Fig. 1. The structure of the sensor is formed by two linear polarizers and a piece of PMF inserted in the middle of polarizers. $\theta$ is the twist angle of the PMF in the sensing area, $\alpha$ and $\beta$ are the polarized direction of the first polarizer and the second polarizer compared with the fast axis of the PMF.
Fig. 1. (a) Schematic diagram of Lyot filter based on twisted PMF. (b) Schematic diagram of PMF with the influence of torsion.
The input light changed into linearly polarized light after transmitting through the first polarizer, and the polarized light is divided into two beams propagating along the fast-axis and slow-axis based on the angle between the direction of the polarized light and the axis of the PMF. Two parts of polarized light have relative phase difference $\varDelta \varphi $ because of the birefringence of the PMF. The two beams are projected into the direction of the second polarizer and couple together, which creates the interference spectrum based on polarized interference.
Based on the transfer matrix method, the Jones matrix of the Lyot filter without twist is as follow:
Compared with the SMF, The output polarization rotates with a rate equal to the twist rate applied on the PMF [26], which makes the twist on the PMF influence the intensity of the inference dip maximumly. The Jones matrix of the PMF with twist is that:
Here:
where ${\delta _L}\textrm{ = }\frac{{2\pi }}{\lambda }BL$ is the relative phase difference of the PMF, ${\delta _C}\textrm{ = 2(1 - g/2)}\theta$ relates to the optical rotation effect of the twisted PMF, $R( - \theta )$ is the rotation matrix about the twist angle $\theta $ due to the twist of the axis of the PMF. Since the birefringence of the PMF is high, the ${\delta _L}$ is dominant during twisting. After propagating through the proposed sensor, the output state of polarization can be calculated as follows:According to the theory, the initial contrast of the spectrum depends on the relation between the $\alpha$ and $\beta$. As the twist angle changing, the optical rotation effect and the change of the coordinate system of PMF make the output direction of the polarization from PMF change, and lead the projection of two beams on the last direction of polarizer change. The effect makes the contrast of interference spectrum change and the twist angle can be demodulated by tracking the dip intensity change.
The interference spectrum with different twist angles has been simulated in Fig. 2. The original value of $\alpha$ and $\beta$ is ${45^ \circ }$ and ${41^ \circ }$, respectively. It is clearly seen that the initial angle determines the original contrast of interference spectrum and the minimum transmittance changes while the twist angle increasing. The minimum transmittance is highly sensitive to the twist at the range of low twit angel, which means that the proposed have high potential on the sensing of small twist angle. Due to the high birefringence of the PMF, $\alpha \approx {\alpha _0}\textrm{ + }\theta $. If the $\alpha$ is unequal to the $\beta$ in the original state, the original state $\theta = 0$ will be located in the middle of the process of intensity increasing. It makes the variation trend of intensity different when twist in the opposite direction, and makes it possible to realize a directional torsion sensor.
Fig. 2. (a) Simulation results of the interference spectrum versus with different twist angle θ. (b) Simulation results of the phase hits.
Specially, at a specific twist angle, the projection of the beam on the last direction of polarizer changes from the forward direction to the negative direction, corresponding to the jumping phase of ${e^{i\pi }}$.
Therefore, the left limit and the right limit of the phase difference are $\Delta {\varphi _1}\textrm{ = }\frac{{2\pi }}{\lambda }\Delta n{L_{PMF}}$ and $\Delta {\varphi _2}\textrm{ = }\frac{{2\pi }}{\lambda }(\Delta n + \frac{\lambda }{{2{L_{PMF}}}}){L_{PMF}}$, respectively. Consequently, the torsion sensitivity of resonant dip can be deduced as [27]:
The change of the wavelength of resonant dip is in inverse proportion to the phase difference $\Delta n_{eff}^{PMF}$ and the length ${L_{PM}}$ of the PMF. It has the potential to enhance the sensitivity by using the all-fiber structure without tapering, and expands the application of the sensor in the area of the wavelength demodulation.
3. Experimental details
The schematic diagram of the experimental setup for the torsion measurement of the proposed sensor is illustrated in Fig. 3(a). A Broadband source (BBS) is used in the experiment, with the wavelength ranging from 1200 nm to 1700nm. The spectrum of the proposed sensor is measured by an optical spectrum analyzer (OSA, AQ6370 Yokogawa). The input end of the first polarizer was connected to the light source and the output end of the second polarizer was connected with the OSA. Both of the Polarizers are In-line Polarizers (ILP-1550-900-1FA). The PMF is used as the birefringent medium, with the birefringence of $3.87 \times {10^{\textrm{ - }4}}$ and the length of 30 cm. As mentioned above, the contrast of spectrum depends on the angle between the direction of input polarization state and the fast-axis of PMF. In order to get the highest contrast, A polarization controller (PC) was inserted between the first polarizer and the PMF. Additionally, it is worth to be noted that: because the PMF is placed in the twist area, the initial direction of the polarization can be controlled by twisting the PMF instead of the PC. It significantly reduces the difficulty of adjusting the original state of polarization and the cost of the whole structure.
Fig. 3. (a) Experiment setup of the torsion sensor based on a Lyot filter. (b) Original spectrum of the proposed sensor
Fig. 4. (a)Transmission spectrum evolution of the proposed sensor under the torsion rate from 0° to 92°. (b)Dependence of transmission on the applied torsion.
In the experiment, the input end of the PMF was fixed on a fiber holder, and a fiber rotator was placed on the other side. A support platform was set up at the same height to make sure that the twisted fiber is horizontal. Before the twist measurement, with the OSA monitoring the interference spectrum, the PC is adjusted to obtain the highest interference modulation depth. The original spectrum without twist is shown in Fig. 3(b). The highest interference depth is about 28 dB and the free spectral range (FSR) between two dips is about 19 nm.
To investigate the relation between the interference modulation depth and the twist angle, we adjusted the fiber in the sensing area to make the fiber straight at first, and then the rotator was twisted with the increment of ${4^ \circ }$ in the clockwise (CW) direction or the counterclockwise (CCW) direction. The interference spectrum with different twist angles is shown in Fig. 4. It is clearly seen that with the angle of twist increasing, the output direction of the polarization from PMF changes, causing the change of interference depth evidently. The slope in the linear fitting region from 0°to -16°and 16°is 0.9835 and 1,2124, respectively. The period is asymmetrical because the angle between the axis of the PMF and the direction of the first Polarizers is not 45°in practice. Especially, when the twist angle is close to the angle with the highest interference depth, the sensitivity of the sensor is evidently higher than the other, which means the proposed sensor has the huge potential on the measurement of small angel changing.
Fig. 5. (a)Transmission spectrum evolution of the proposed sensor under the torsion rate from 0° to 16°. (b) the relationships between the transmission and the angle of the twist with the direction of CW and CCW.
In order to make further more research on the preferment of the sensor in the range of small twist angle, we twisted the PMF from $\textrm{ - }{16^ \circ }$ to ${16^ \circ }$, with the increment of ${2^ \circ }$ in CW or CCW directions. As shown in Fig. 5. The slopes in the linear fitting region from ${0^ \circ }$ to $\textrm{ - }{6^ \circ }$ and region from ${0^ \circ }$ to ${6^ \circ }$ are 1.572 and 1.564, respectively, corresponding to the twist sensitivity of 90.072 dB/rad and 89.656 dB/rad. Assuming the intensity resolution of 0.1 dB for the typical OSA, the torsion sensor achieved a torsion resolution of about ${10^{\textrm{ - 3}}}$ rad. And the slope in the linear fitting region from $\textrm{ - }{\textrm{6}^ \circ }$ to $\textrm{ - }{16^ \circ }$ and region from ${6^ \circ }$ to ${16^ \circ }$ reduces to 0.498 and 0.752, corresponding to the twist sensitivity of 28.547 dB/rad and 43.108 dB/rad. A comparison between our twist experimental results and other works is summarized in Table 1 . It is obvious that our proposed twist structure has a higher sensitivity than the others and is even one order of magnitude higher within the small twist angle
Fig. 6. (a) Transmission spectra after the twist with the PMF of 30 cm. (b) the relationships between the dip wavelength and the angle closed to the angle of the phase hits with the PMF of 30 cm. (c) Transmission spectra after the twist with the PMF of 15 cm. (d) the relationships between the dip wavelength and the angle closed to the angle of the phase hits with the PMF of 15 cm.
Table 1. Torsion sensitivity of several different sensors
The wavelength shift of the interference dips was investigated with the twist angle changing. As shown in Fig. 6(a) and Fig. 6(b), it can be seen that the wavelength shift changes periodically in the range from $\textrm{ - }{164^ \circ }$ to ${164^ \circ }$, and the sensitivity is highest at the twist angle in the range from 30° to 60°. It is reasonable since the jumping phase by π occurs at the special twist angle, causing the interference dips to exchange the place with the crest. The slope is 0.1529, corresponding to the twist sensitivity of 8.76 nm/rad. Compared with the structure only based on the PMF [1] with the sensitivity of 0.789 nm/rad, the point of the phase hits can increase the sensitivity obviously, and avoid processing damage to the mechanical strength of the optical fiber.
Fig. 7. The relationships between the wavelength, the intensity and the twist angle in a whole period with the PMF of 15 cm.
As mentioned above, the jumping phase occurring at the position of a special twist angel leads to the wavelength shift. In a period, the wavelength of the interference dip shifts half of the FSR, which is in inverse proportion to the optical path difference. The sensitivity of the wavelength demodulation can be increased by reducing the optical path difference. With the birefringence of PMF being constant, the sensitivity is inversely proportional to the length of PMF. As shown in Fig. 6(c) and Fig. 6(d), the wavelength of the interference dip shifts periodically with the PMF of 15 cm, and the slope at the angle of the phase hits reaches 0.2703, corresponding to the twist sensitivity of 15.477 nm/rad. With the wavelength resolution of 0.02 nm for the OSA, the torsion sensor achieved a torsion resolution of about $1.3 \times {10^{\textrm{ - 3}}}$ rad. The sensitivity is approximately equal to double times of the sensor with the PMF of 30 cm. The result fits well with the theory mentioned above. The sensitivity of the sensor is higher than most of the sensors with the same birefringence and can increase in multiples by reducing the length and the birefringence of the fiber. Moreover, pre-torsion can be introduced in this structure to make sure the special angle of the phase hits located at the initial position. It can make the sensitivity highest and linear at the initial position and confirm whether the direction of the twist is CW or CCW, which allows for twist direction distinguishability.
Furthermore, as shown in Fig. 7, it can be clearly seen that: the dip of wavelength changes acutely in the region of A, D and E. But the proposed sensor gets the best performance of intensity demodulation in the region of B and C. The range of wavelength demodulation is complementary with the range of intensity demodulation, and the valid angle range of the proposed sensor can be expanded by utilizing both the intensity demodulation and the wavelength demodulation.
In the experiments, the torsion measurements were repeated to estimate the accuracy by twisting the same angle in both the CW and the CCW direction. The experiment was repeated three times and the results were given in Fig. 8. The Fig. 8(a) for the intensity demodulation movement and (b) for the wavelength demodulation. The standard deviations in terms of the intensity and wavelength shift are 0.2658 dB and 0.1774nm, respectively. It means that the torsion sensor has a measurement accuracy of ± 0.1734° for the intensity demodulation and ±0.6570° for the wavelength demodulation.
Fig. 8. Torsion measurement results achieved by repeating the torsion measurement in both the CW and the CCW direction for (a) the intensity demodulation (b) the wavelength demodulation.
The additional axial strain is introduced in our fiber because the twisted PMF is clamped, the influence of the axial strain should be investigated in this research. By moving the fiber bolder through the displacement platform, the axial strain in the range of 0 to 2000$\mu \varepsilon $ was applied on the twisted PMF. As shown in Fig. 9, the intensity of the interference dip is nearly unrelated to the axial strain on the twisted PMF, which ensures the reliability of the proposed sensor using the model of intensity demodulation. In addition, the wavelength of the interference dip moves following the increase of the axial strain, Linear fit on experimental data shows that the twist sensor has the strain sensitivity of 4.15 pm/$\mu \varepsilon $ with the twist angle of ${0^ \circ }$. The low sensitivity caused by the twist at the angle of ${0^ \circ }$ is 0.217 nm/rad, which is two orders of magnitude lower than the highest sensitivity. The proposed sensor has the potential in the measurement of double parameters or the elimination of the cross interference by the sensing matrix.
Fig. 9. (a)The relationships between the transmission and the strain applied in the sensor with the angle of 0°, 10°and 20°, respectively. (b) The relationships between the dip wavelength and the strain applied in the sensor with the angle of 0°
It is worth noting that, the proposed length of PMF in the experiments is set to adapt the experimental device. In fact, the structure of the Lyot filter is possible to be more compact. As shown in Fig. 10(a), the sensor with the PMF length of 4 cm can realize the similar performance as mentioned above. Moreover, the Mach-Zehnder interferometer can be introduced in the Lyot filter. As shown in Fig. 10(b), the multimode fiber with the length of 2 mm and the core diameter of 105$\mu m$ is fused on both ends of the PMF, and the multimode fiber plays the role of splitting and combining light for the Mach-Zehnder interference. Because of the phase matching between the polarization interference and the Mach-Zehnder interference, the interference peak is sharper and has much more higher quality factor than the pure PMF-based Lyot filter.
4. Conclusion
In conclusion, we propose a highly sensitive torsion sensor based on Lyot filter by inserting the twisted PMF between two fiber linear polarizers. The experimental results are consistent with the theoretical simulation, which confirms the great performance of the Lyot filter based on the twisted PMF. The proposed sensor exhibits a high sensitivity of 90.072 dB/rad. Based on the phase hits occurring at the special twist angle, the sensitivity reaches 15.477 nm/rad. The sensor also demonstrated a strain sensitivity of $2.32 \times {10^{ - 6}}$ rad/$\mu \varepsilon$. Based on the complementary monitoring range between the wavelength demodulation and the intensity demodulation, the valid sensing range of the proposed sensor expands. Therefore, the proposed torsion sensor with various desirable merits including high sensitivity, large sensing range and immunity to strain cross-sensitivity, is anticipated to have potential applications in various fields such as civil engineering, manufacturing industry and mechanical production.
Fig. 10. Transmission spectrum evolution of the proposed sensor under the torsion rate from 0° to 24° from (a) the sensor with the PMF length of 4 cm (b) the sensor with the PMF length of 4 cm and multimode fiber, with the length of 2 mm and the core diameter of 105$\mu m$
Funding
National Natural Science Foundation of China (11874010).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. Q. Zhou, W. G. Zhang, L. Chen, T. Y. Yan, L. Y. Zhang, L. Wang, and B. Wang, “Fiber torsion sensor based on a twist taper in polarization-maintaining fiber,” Opt. Express 23(18), 23877–23886 (2015). [CrossRef]
2. D. Vischer and O. Khatib, “DESIGN AND DEVELOPMENT OF HIGH-PERFORMANCE TORQUE-CONTROLLED JOINTS,” IEEE Trans. Robot. Automat. 11(4), 537–544 (1995). [CrossRef]
3. P. L. Fulmek, F. Wandling, W. Zdiarsky, G. Brasseur, and S. P. Cermak, “Capacitive sensor for relative angle measurement,” IEEE Trans. Instrum. Meas. 51(6), 1145–1149 (2002). [CrossRef]
4. C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol. 19(8), 1159–1168 (2001). [CrossRef]
5. Y. P. Wang and Y. J. Rao, “Long period fibre grating torsion sensor measuring twist rate and determining twist direction simultaneously,” Electron. Lett. 40(3), 164–166 (2004). [CrossRef]
6. D. E. Ceballos-Herrera, I. Torres-Gomez, A. Martinez-Rios, L. Garcia, and J. J. Sanchez-Mondragon, “Torsion Sensing Characteristics of Mechanically Induced Long-Period Holey Fiber Gratings,” IEEE Sens. J. 10(7), 1200–1205 (2010). [CrossRef]
7. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014). [CrossRef]
8. L. L. Xian, P. Wang, and H. P. Li, “Power-interrogated and simultaneous measurement of temperature and torsion using paired helical long-period fiber gratings with opposite helicities,” Opt. Express 22(17), 20260–20267 (2014). [CrossRef]
9. J. Wo, M. Jiang, M. Malnou, Q. Sun, J. Zhang, P. P. Shum, and D. Liu, “Twist sensor based on axial strain insensitive distributed Bragg reflector fiber laser,” Opt. Express 20(3), 2844–2850 (2012). [CrossRef]
10. Y. P. Wang, M. Wang, and X. Q. Huang, “In fiber Bragg grating twist sensor based on analysis of polarization dependent loss,” Opt. Express 21(10), 11913–11920 (2013). [CrossRef]
11. X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fiber twist sensor based on a fiber Bragg grating with 81 degrees tilted structure,” IEEE Photonics Technol. Lett. 18(24), 2596–2598 (2006). [CrossRef]
12. R. Ahmad, P. S. Westbrook, W. Ko, and K. S. Feder, “Probing micron-scale distributed contortions via a twisted multicore optical fiber,” APL Photonics 4(6), 066101 (2019). [CrossRef]
13. Y. J. Zhao, A. Zhou, H. Y. Guo, Z. Zheng, Y. M. Xu, C. M. Zhou, and L. B. Yuan, “An Integrated Fiber Michelson Interferometer Based on Twin-Core and Side-Hole Fibers for Multiparameter Sensing,” J. Lightwave Technol. 36(4), 993–997 (2018). [CrossRef]
14. P. Jiang, Y. Ouyang, H. Guo, and A. Zhou, “Highly sensitive torsion senor based on dual-side-hole fiber Mach-Zehnder interferometer,” Opt. Express 27(23), 33880 (2019). [CrossRef]
15. Y. Ren, X. Liu, X. Zhang, and J. Yang, “Two-mode fiber based directional torsion sensor with intensity modulation and 0 degrees turning point,” Opt. Express 27(20), 29340–29348 (2019). [CrossRef]
16. L. Htein, D. S. Gunawardena, Z. Y. Liu, and H. Y. Tam, “Two semicircular-hole fiber in a Sagnac loop for simultaneous discrimination of torsion, strain and temperature,” Opt. Express 28(23), 33841–33853 (2020). [CrossRef]
17. H. M. Kim, T. H. Kim, B. Kim, and Y. Chung, “Temperature-Insensitive Torsion Sensor With Enhanced Sensitivity by Use of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photonics Technol. Lett. 22(20), 1539–1541 (2010). [CrossRef]
18. P. Zu, C. Chan, Y. Jin, T. Gong, Y. Zhang, L. H. Chen, and X. Dong, “A Temperature-Insensitive Twist Sensor by Using Low-Birefringence Photonic-Crystal-Fiber-Based Sagnac Interferometer,” IEEE Photonics Technol. Lett. 23(13), 920–922 (2011). [CrossRef]
19. W. G. Chen, S. Q. Lou, L. W. Wang, H. Zou, W. L. Lu, and S. S. Jian, “Highly Sensitive Torsion Sensor Based on Sagnac Interferometer Using Side-Leakage Photonic Crystal Fiber,” IEEE Photonics Technol. Lett. 23(21), 1639–1641 (2011). [CrossRef]
20. R. M. S. Orlando Frazão, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777 (2010). [CrossRef]
21. B. Song, H. Zhang, Y. Miao, W. Lin, J. Wu, H. Liu, D. Yan, and B. Liu, “Highly sensitive twist sensor employing Sagnac interferometer based on PM-elliptical core fibers,” Opt. Express 23(12), 15372–15379 (2015). [CrossRef]
22. J. S. Pan, T. S. Huang, Y. C. Ge, W. F. Lin, and L. P. Sun, “Highly Birefringent Microfiber Hybrid Interferometer Sensor,” IEEE Photonics Technol. Lett. 33(17), 959–962 (2021). [CrossRef]
23. B. Huang and X. W. Shu, “Highly Sensitive Twist Sensor Based on Temperature-and Strain-Independent Fiber Lyot Filter,” J. Lightwave Technol. 35(10), 2026–2031 (2017). [CrossRef]
24. H. Bo, X. Shu, and Y. Du, “Intensity modulated torsion sensor based on optical fiber reflective Lyot filter,” Opt. Express 25(5), 5081 (2017). [CrossRef]
25. B. Huang, Y. Wang, and C. Mao, “Lyot Filter With Femtosecond Laser-Induced High Birefringence Single-Mode Fiber for Torsion, Transverse Load and Temperature Sensing,” IEEE Access 8, 25764–25769 (2020). [CrossRef]
26. Z. J. Fang, F. Yang, H. W. Cai, and R. H. Qu, “Coupled-mode equation of polarization modes of twisted birefringent fibers in a unified coordinate,” Appl. Opt. 52(3), 530–537 (2013). [CrossRef]
27. S. Y. Xu, W. J. Chang, Y. Y. Luo, W. J. Ni, Y. Zheng, L. Wei, Z. L. Xu, Z. G. Lian, Y. A. Zhang, Y. Q. Huang, and P. P. Shum, “Ultrasensitive Broadband Refractometer Based on Single Stress-Applying Fiber at Dispersion Turning Point,” J. Lightwave Technol. 39(8), 2528–2535 (2021). [CrossRef]
28. B. Yin, H. S. Li, S. C. Feng, Y. L. Bai, Z. B. Liu, W. J. Peng, S. Liu, and S. S. Jian, “Temperature-Independent and Strain-Independent Twist Sensor Based on Structured PM-CFBG,” IEEE Photonics Technol. Lett. 26(15), 1565–1568 (2014). [CrossRef]
29. Y. Wang, X. Huang, and M. Wang, “Temperature insensitive birefringent LPG twist sensing based on the polarization properties,” IEEE Photonics Technol. Lett. 27(22), 2367–2370 (2015). [CrossRef]
30. C. Jiang, Y. Q. Liu, Y. H. Zhao, C. B. Mou, and T. Y. Wang, “Helical Long-Period Gratings Inscribed in Polarization-Maintaining Fibers by CO2 Laser,” J. Lightwave Technol. 37(3), 889–896 (2019). [CrossRef]
