Qiang Zhang
Jie Zhang1
Shiwei Yang- 1Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan, China
- 2Collaborative Innovation Centre of Extreme Optics, Shanxi University, Taiyuan, China
In this paper, we propose and demonstrate experimentally an optomechanical torsion sensor using a microfiber mechanical resonator. The torsion angle could be obtained by monitoring the resonant frequency shifts of the microfiber resonator. Theoretical and experimental results show that the shift of resonant frequency is non-linear to the torsion angle, and the fundamental mode is more sensitive than other higher modes. The highest sensitivity of the sensor tested in our experiments is 1,687 Hz/degree, and the corresponding resolution of torsion angle is up to 0.0006°, which is 2 orders of magnitude higher than that of the reported fiber-optic torsion sensors. The proposed sensor is a promising candidate for the practical engineering applications.
1 Introduction
Torsion detection is essential in the security monitoring of large-scale mechanical equipment and anthropomorphic robotics applications [1–3]. Fiber-optic sensor is one of the most common torsion sensors owe to their advantages such as small size, light weight, robustness, telemetry, and immunity to electromagnetic interference [4, 5]. A number of fiber-optic torsion sensing mechanisms have been reported over the past few years, such as long-period fiber gratings [6, 7], fiber Bragg gratings [8, 9], Mach-Zehnder interferometers [10, 11], Sagnac interferometers [12, 13], and multimode interferometers [14, 15]. However, the angle resolutions of the reported fiber-optic torsion sensors based on those sensing mechanisms are more than 0.1°, so how to further reduce the detectable minimum torsion angle is a challenge for the fiber-optic torsion sensors.
Optomechanical systems studying the interaction between light and mechanical resonator provide a promising platform for ultrasensitive sensing technologies [16–27]. Various ultrasensitive optomechanical sensors have been demonstrated and used to measure multiple physical quantities, such as magnetic fields [28–31], displacements [32], accelerations [33–35], masses [36–39], ultrasounds [40–43], current [44], and temperature [45]. Therefore, it is significant to extend optomechanical ultrasensitive sensing mechanisms to fiber-optic sensing technologies. In this letter, we propose and experimentally demonstrate a microfiber optomechanical torsion sensor, where the torsion angle could be obtained by monitoring the resonant frequency shifts of the microfiber resonator. The torsion sensor is fabricated by splicing a microfiber between two single mode fibers (SMFs). The high acoustic impedance mismatching at the splicing spots resulted from the huge difference of the diameters between the microfiber and SMFs could confine vibrating modes to the microfiber section to make the microfiber work as a mechanical resonator. The resonant frequency of the microfiber mechanical resonator changes when a torsion angle is applied to the proposed device. The theoretical and experimental results show that the shift of resonant frequency is non-linear to the torsion angle, and the fundamental mode is more sensitive than other higher modes. The highest sensitivity of the sensor tested in our experiments is 1,687 Hz/degree, and the corresponding detectable minimal torsion angle is low to 0.0006°, which is 2 orders of magnitude higher than that of the reported fiber-optic torsion sensors. Therefore, the proposed device is a promising candidate for the practical applications.
2 Fabrication of microfiber optomechanical torsion sensor
A schematic diagram of the fabrication process of the sensor is shown in Figure 1A. The process for the fabrication of this device is simple and repeatable. Using an oxyhydrogen flame to scan a SMF with axial stress, a microfiber could be fabricated easily, and the length and diameter of the microfiber could be tailored accurately by changing the parameters of the oxyhydrogen flame. In our experiments, the microfiber is fabricated by a commercial optical fiber tapering machine (AFBT-8000, Shandong Coupler Technology), where the diameter error of the microfiber is less than 0.2 μm. Then, the microfiber is cleaved at the red dashed line, and the part with uniform waist is spliced with a SMF by a fusion splicer (S183ver.2, FITEL), where the splicing parameters are the arc power 70, fusion time 0.8 s and the offset is 300. The same fabrication process is applied to the other end of the microfiber, where the length of the microfiber is designed according to the practical need. As a result, the microfiber with uniform diameter is spliced between two SMFs, and it could work as a mechanical resonator because of the high acoustic impedance mismatching at the splicing spots. It should be noted that an offset is useful for protect the microfiber from deformation when it is spliced with the SMFs. Meanwhile, the flatness of the end faces in the microfiber dominates the quality factor Qm of the mechanical resonator. The optical micrograph of the microfiber torsion sensor is shown in Figure 1B, where the diameter and length of the microfiber are 13 μm and 950 μm, respectively. The white scale bar at the lower right corner in Figure 1B is 50 μm.
FIGURE 1. (A) Schematic of the fabrication process of the sensor. (B) Optical micrograph of the sensor. The white scale bar at the lower right corner is 50 μm.
3 Principle of microfiber optomechanical torsion sensor
Micromechanical resonators have extraordinary sensitivity, and have been applied to measure tiny force and mass changes by monitoring the resonant frequency shifts [46, 47]. As shown in Figure 1, the abrupt junctions between the microfiber and SMFs could confine resonant mechanical modes to the microfiber section, thereby enabling high mechanical quality factors Qm at low gas pressures. A large difference between the diameters of SMF and microfiber is beneficial to reduce the clamping loss and improve the Qm of the resonator. The resolution of sensor benefits from the Qm of the resonator. The resonant frequency fn of the nth mode of the microfiber resonator can be expressed as [48]:
where L and A are the length and cross-sectional area of the microfiber, E and I is the Young’s modulus and the moment of inertia, d is the diameter of the beam, ρ is the density, and σ is the axial tensile stress in the microfiber.
According to Eq. 1, the resonant frequency of the microfiber resonator could shift by adjusting the axial tensile stress. Figure 2 shows the theory model of the microfiber resonator with a torsion angle θ. The line AB changes to AC when a torsion angle θ is applied to the microfiber resonator, where the corresponding axial tensile stress σ from the torsion angle θ is [49]:
FIGURE 2. Schematic diagram of the sensor at a torsion angle θ.
Combining Eqs 1, 2, the torsion angle θ could be demodulated by analyzing the resonant frequency shift of the microfiber resonator. Figure 3 shows that the theoretic frequency shifts ∆fn of different mechanical resonant modes as a function of torsion angle θ for a microfiber with a length of 950 μm and a diameter of 13 μm. The frequency shift of the fundamental mode is more than other higher modes, and the frequency shifts will decrease as the mode n increases. Therefore, it is more sensitive to choose the fundamental mode as a sensing quantity than other modes.
FIGURE 3. Calculated shifts of mechanical resonant frequencies as a function of torsion angle θ.
4 Experiment and discussion
The scheme of the experimental setup for characterizing the sensor is shown in Figure 4. The light from a continuous-wave laser with a wavelength of 1,550 nm (LSM-DFB-1550, OPEAK) is injected into the variable optical attenuator and the sensor by standard SMFs, where the lead-in SMF connects with the sensor by a fiber-optic adapter. The transmission light from the sensor is converted to the corresponding electrical signal by a fast photodetector (PDB440, Thorlabs). By demodulating the electrical signal from the photodetector with an electronic spectrum analyzer (ESA, RBW is 1 Hz), we can get the resonant frequency of the microfiber mechanical resonator and the torsion angle. The sensor is mounted onto a mechanical holder with a rotary stepper positioner (Attocube, ANR51/RES) and a piezoelectric stack (Green, PI, PD050.3x1). The piezoelectric stack is used to excite the microfiber mechanical resonator to monitoring the shift of the resonant frequency, because the thermal noise of the microfiber resonator is difficult to be identified directly in our experiments. It should be noted that it is possible to abandon the piezoelectric stack for the proposed sensing mechanism when the thermal noise of the microfiber resonator could be detected successfully. The sensor and holder are fixed in a vacuum chamber with a gas pressure of 5 × 10−7 mbar in our experiments.
FIGURE 4. Schematic of the experimental setup, including a vacuum chamber (VC), variable optical attenuator (VOA), photodetector (PD), and electronic spectrum analyzer (ESA).
The measured normalized mechanical power spectrum of fundamental mode for the sensor with 950-μm length and 13-μm diameter is shown in Figure 5. The circular points and red solid line are the experimental data and fitted curve according to the response function of the mechanical resonator, respectively. Figure 5 shows that the resonant frequency of the fundamental mode is 64.102 kHz and the linewidth is 12 Hz. Therefore, the corresponding Qm of the mechanical resonator is 5,300. The inset is the mode shape of the resonant mode in Figure 5.
FIGURE 5. Normalized mechanical power spectrum of the fundamental mode for the sensor. Inset mode shape of the fundamental mode.
To demonstrate the torsion sensor, we tested the response of the sensor to the torsion by using the rotary stepper positioner at room temperature. Figure 6 shows the measured and calculated mechanical resonant frequency shifts of the sensor as a function of torsion angle from 0° to 50°. The black solid line represents the calculated curve according to the Eqs 1, 2. The red solid line and square symbols are the fitting curve and measured frequency shifts. As shown in Figure 6, when the torsion angle increases, the resonant frequency shifts to the large frequency. The change of the resonant frequency is 44.562 kHz over 50° change in the torsion angle. The resonant frequency shift is non-linearly proportional to the torsion angle, and becomes larger as the torsion angle increases. The difference between the calculated and measured curves is mainly due to the splicing spots between the SMF and the microfiber, where the properties of the splicing spots are different from the microfiber. When the power of arc discharge is lower than the optimal value, air bubbles appear in the splicing spots, which results in the decrement of the connection area A between the microfiber and the SMF. The corresponding shift of resonant frequency reduces according to Eqs 1, 2. In our experiments, the splicing spots of the sensors are easy to break when the torsion angle is larger than 50°. Therefore, the splicing technique between the SMF and microfiber needs to be further optimized to improve the measure range and sensitivity of the proposed sensor. According to the fitting curve of the measured data, the highest sensitivity of the sensor tested in our experiments is 1,687 Hz/degree, and the corresponding resolution of torsion angle is up to 0.0006°. To the best of our knowledge, the maximum of the resonant wavelength shifts for the reported fiber-optic torsion sensors is 320 pm/degree in Ref. [13], and the corresponding the resolution of torsion angle is 0.064° using an optical spectrum analyzer with a representative resolution of 20 pm. The resolution of torsion angle is improved about 2 orders of magnitude for the proposed sensor. Therefore, the proposed device can provide a real-time high-sensitive measurement of the torsion angle.
FIGURE 6. Measured and calculated mechanical resonant frequency shifts of the sensor as a function of torsion angle.
5 Conclusion
In conclusion, we have demonstrated a novel optomechanical torsion sensor based on a microfiber mechanical resonator. The torsion angle can be determined directly from a measure of the resonant frequency shift of the microfiber mechanical resonator. Experimental results show that the achieved highest sensitivity of the sensor with a 950-μm length and 13-μm diameter reaches 1,687 Hz/degree. The proposed torsion sensor has advantages of small size, light weight, multiplexing, remote measurement, and immunity to electromagnetic interference, and therefore could be used in some precision machinery equipment fields. For example, the torsion sensors for intelligent robots should be compact and light to avoid a major modification in kinematics and dynamics of robots. In addition, low torsional stiffness is beneficial to reduce the influence on the natural frequency of the robot arm. The proposed torsion sensor could also be embedded into mechanical shafts to monitor the torque loads and health condition of the shafts, and particularly suitable for applications in harsh environments.
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.
Author contributions
Conceptualization, QZ and YL; methodology, JZ and SY; experiments, RZ and YX; writing—original draft preparation, QZ and YL All authors have read and agreed to the published version of the manuscript.
Funding
This work was supported by the funding from the National Natural Science Foundation of China (NSFC) (12174232, U21A6006, 11804208, and 11774209) and Shanxi 1331KS.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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Keywords: optomechanics, torsion sensor, optical fiber, mechanical resonator, microfiber
Citation: Zhang Q, Zhang J, Yang S, Zhai R, Xie Y and Li Y (2023) Microfiber optomechanical torsion sensor. Front. Phys. 11:1147644. doi: 10.3389/fphy.2023.1147644
Received: 19 January 2023; Accepted: 13 April 2023;
Published: 21 April 2023.
Edited by:
Zhangqi Yin, Beijing Institute of Technology, ChinaReviewed by:
Hailang Dai, Shanghai Jiao Tong University, ChinaJin-hui Chen, Xiamen University, China
Copyright © 2023 Zhang, Zhang, Yang, Zhai, Xie and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Qiang Zhang, qzhang@sxu.edu.cn; Yongmin Li, yongmin@sxu.edu.cn