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Abstract
A high sensitivity optical fiber twist sensor based on Suspend Core Fiber Sagnac Interference (SCFSI) is proposed and experimentally demonstrated. By filling the air hole of the Suspend Core Fiber (SCF) with alcohol, the twist sensitivity of the twist sensor is greatly improved to 8.37 nm/°. Moreover, the valid angle measurement range of the sensor can be expanded by utilizing the combination of intensity demodulation and wavelength demodulation. The sensor not only has high twist angle sensitivity but also exhibits a capability of temperature calibration. Since the wavelength shifts of the interference fringes of Mach-Zehnder Interferometer (MZI) formed in the suspend core of SCF appears insensitive to twist angle, the parasitic interference formed by MZI can be used for temperature calibration. Due to compact structure, easy fabrication and low temperature cross sensitivity, the proposed sensor has a great potential for structural health monitoring, such as buildings, towers, bridges, and many other infrastructures.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Twist information is important for rotating systems, motion tracking in robotic tools and structural health monitoring of large civil structures [1–3]. The electronic twist sensors are unstable in strong electromagnetic environments, limiting their applications. Optical fiber sensors are immune to electromagnetic interference, and their small size and light weight make them an ideal candidate for embedding into a variety of structures [4]. In recent years, there is mainly two kinds of optical fiber-based twist sensors, that is, the fiber grating-based twist sensors and the fiber interferometer-based twist sensors [5]. For the fiber grating-based twist sensors, Long Period Gratings (LPGs) or Fiber Bragg Gratings (FBGs) are used as the sensor heads because of their large dynamic range and high sensitivities [6–8]. However, a shortcoming of these sensors is that the fabrication of fiber gratings requires the expensive laser, such as the earliest proposed UV exposure method [9], the extremely popular femtosecond laser direct writing method [10] and CO2 laser beam exposure [11] method in recent years. On the other hand, the fiber interferometer-based twist sensor with the advantages of compactness, simplicity and high sensitivity, have also been widely used as twist sensors. So far there are many kinds of fiber twist sensors based on different interferometric principles [12–17]. Among various optical fiber twist sensing schemes, the Sagnac Interferometer (SI) based sensors are quite promising because the free spectral range (FSR, represents the interval wavelength between two adjacent dip) of the interference spectral is easily controlled. In principle, the fiber SI is constituted by inserting a section of birefringence fiber into the single mode fiber (SMF) loop. And the twist sensitivity of the sensor is related to birefringence [18]. Therefore, a better sensing performance can be achieved by using an appropriate birefringence value of the birefringence fiber. Recently, a variety of special fibers has been commercially available and widely applied in the SI to construct high-performance twist sensors [19–21].
In recent years, a number of optical fiber-based twist sensors have been reported with the improvement of the sensitivity in succession. For example, a Side Hole Fiber (SHF) sensor was demonstrated in 2019 [19]. The birefringence of SHF in the SI loop would vary with the twist rate, giving rise to wavelength shift and power variation responses to twist applied on the SHF. With a dip tracking method, a twist sensitivity of 0.085 nm/° (corresponding to 2.2 nm/(rad/m)) is achieved. A cascaded polarization maintaining fiber twist sensor was proposed in 2022 with a sensitivity of 0.73 nm/° [20]. Even more impressive, the sensor proposed in [21] exhibited an extremely high sensitivity of 5 nm/°. Despite these progress in sensitivity, the problem of temperature crosstalk during sensing is rarely considered. Up to now, there are mainly two schemes used for solving temperature crosstalk. One is the sensitivity matrix method and the other is the reference FBG method. However, these methods still have some limitations. For instance, in [21,22], the researchers utilized the sensitivity matrix method to discriminate the twist and temperature. This method usually requires capturing two kinds of dip wavelengths with different sensitivity responses. However, when the FSR of the transmission spectrum exceeds the monitoring window of a spectrometer, it is hardly to capture two dip wavelengths in a narrow spectrum window. Also, when the two dip wavelengths have similar responses, it is difficult to distinguish the temperature crosstalk and results in measurement errors. In addition, the two dips must exhibit a high-linearity, otherwise the sensitivity matrix method is not valid. All these limitations constrain the promotion of sensitivity matrix method. In the other hand, some researchers inscribed a reference FBG into the sensor to demodulate the temperature [14]. However, this method would result in structural redundancy. Therefore, it is of great significance to develop a high sensitivity twist sensor with a new temperature compensation method.
Recently, Microstructure Optical Fibers (MOFs) have attracted tremendous research interests. The flexibility in MOF structural design allows researchers to create suitable fiber structures that are easily modified to achieve high performance sensing according to their needs. As a branch of MOF, Suspended Core Fiber (SCF) features four large air holes, providing a convenient way to fill with alcohol, in which way the birefringence of the fiber could be manipulated to achieve a high-performance twist sensing.
In this paper, a high sensitivity optical fiber twist sensor based on a Suspended Core Fiber Sagnac Interferometer (SCFSI) is proposed and experimentally demonstrated. By filling the air hole of the SCF with alcohol, the sensitivity of the twist sensor is greatly improved to 8.37 nm/°, which is the highest sensitivity reported in SI-based twist sensors as far as we know. Meanwhile, temperature calibration can be achieved by a naturally occurring parasitic interference in the suspended core of the SCF. This calibration method is more practical than traditional sensitivity matrix method, and more adaptable to harsh environments than the reference FBG method. Experimental results show that the proposed sensor has the advantages of simple structure, easy fabrication, high sensitivity and low temperature crosstalk, making it a potential candidate for developing high performance sensors with low temperature crosstalk.
2. Fabrication procedure and sensing principle
Figure 1 (a) shows a schematic diagram of the proposed twist sensor based on SI with the SCF. The sensor is fabricated by simply splicing a SCF sandwiched between two single mode fibers and embedded in a 3 dB coupler. The optical signal from a Broadband Light Source (BLS, SC-5-FC, YSL) is split into clockwise and counterclockwise beams via a 3 dB coupler as it enters the loop. As the two polarization states propagate through the 10 cm length SCF, a phase difference is accumulated, leading to interference when the two beams are recombined at the coupler. The inference spectrum can be measured with an Optical Spectrum Analyzer (OSA, Anritsu, MS9740A). The SCF is mounted on a fiber holder (represented by the yellow line) on one side and a fiber rotator on the other side, keeping it straight at the initial state. Figure 1(b) shows a cross-sectional image of the SCF. The SCF is composed of a nearly rectangular core surrounded by four fan-shaped air holes, which are symmetrically located around the fiber core (the effective refractive index is 1.444 at 1550 nm). The lengths of short and long axes of the rectangular core are 6.06 and 7.47 µm, respectively. Due to its asymmetric fiber core structure, the SCF appears a birefringence. Additionally, high numerical aperture also makes it multimode operation, allowing higher-order modes to be excited at the fusion point between the SCF and SMF. Then the generated multimode interference can be regarded as a Mach-Zehnder Interferometer (MZI) in the core of the SCF. This system thus enables the simultaneous acquisition of SCFSI and MZI.
Fig. 1. Schematic diagram of the proposed sensing system (a) and microscope image of the SCF micro-structured optical fiber (b).
Ignoring any insertion losses of the Signac loop, the transmission ratio of optical intensity injected into the SI in terms of phase difference can be described as
where K is the split ratio coefficient of the 3 dB coupler, here is 0.5; Δθ is the angle of the fast axis of the SCF on the incident and output end faces. For the case of no twist of the fiber, Δθ is 0; ${\varphi _{SI}} = 2\pi BL/\lambda$ is the phase difference introduced by the two orthogonal guided modes propagating through the SCF. $B = {n_x} - {n_y}$ is the birefringence between the fast and slow axis of polarization modes, which is a function of twist and wavelength; and λ is the operation wavelength.When the fiber is twisted, the linear defect can introduce different mechanical stress to the rectangular core, causing the torsion-induced circular birefringence. The birefringence caused by the twist can be described as [23]
where L is the fiber length, τ is twist rate defined by the torsion change rate per unit length, α=gτ and g is a constant determined by the photo-elastic coefficients of the material. In the case of the silica, the value of the g is 0.08 [18,24]. As illustrated in the microscope image of SCF, the asymmetric fiber core creates a birefringence. Additionally, if the four air holes are filled with alcohol, the birefringence characteristics of SCF can be modulated.The finite-element method (FEM) is employed to investigate the mode properties of the SCF. The geometry of the fiber used for the simulation is shown in Fig. 2(a), in which pink regions represent the air and grey represents the silica glass core. The simulated electric field intensity distributions for the x-polarized and y-polarized fundamental modes are shown in Figs. 2(b) and (c), respectively. Additionally, Fig. 2(e) illustrates the geometry of the SCF filled with alcohol, in which blue region represents the alcohol and grey represents the silica glass core. The simulated electric field intensity distributions for the x-polarized and y-polarized fundamental modes are depicted in Figs. 2(f) and (g). Two examples of higher order modes exist within the SCF core before and after filling with alcohol are presented in Figs. 2 (d) and (h).
Fig. 2. Fiber geometry of the theoretical model simulation without (a) and with (e) alcohol filled, the simulated electric field intensity distributions of the x-polarized (b) and y-polarized (c) fundamental modes and an example higher order mode (d) without alcohol filled, the simulated electric field intensity distributions of the x-polarized (f) and y-polarized (g) fundamental modes and an example higher order mode (h) with alcohol filled at 1510 nm, respectively.
As illustrated in Figs. 2 (b), (c), and (d), the effective index difference between the modes in Figs. 2 (b) and (d) is Δneff1 = 1.194 × 10−3 and between the modes in Figs. 2(c) and (d) is Δneff2 = 1.174 × 10−3. The values of Δneff1 and Δneff2 are much higher than B, making the FSR of the MZI much smaller than that of the SCFSI. It can be seen from Fig. 2 (b) and (c) that there is a phase birefringence of B = |nx−ny|= 2.0 × 10−4 at 1510 nm in the SCF. And B is decreased to 6.0 × 10−5 when the four air holes are filled with alcohol, as shown in Fig. 2 (f) and (g). We simulate the birefringence B on dependence of wavelength and the transmission spectrums of SCF without and with alcohol filled as shown in Fig. 3 (a) and (b). It can be seen from Fig. 3 (a) that the air holes with the alcohol filled leads to a decrease in fiber birefringence. This can be understood as follow. After filling with alcohol into the air holes, the effective refractive index of cladding can be increased. So the effective refractive index difference between the solid core and the cladding decreases after the alcohol is filled into the air holes, causing the birefringence reduced. And Fig. 3 (b) illustrates that the FSR increases with the decrease of B. When the SCF is twisted, the twist sensitivity can be calculated by taking derivation of phase matching conditions on both sides, and then the twist sensitivity can be expressed as
Fig. 3. The simulated birefringence B versus wavelength λ of SCF with and without alcohol filled (a) and the simulated transmission spectrums of SCFSI with and without alcohol filled (b).
The twist in SCF leads to a variation in birefringence, causing the wavelength shift of transmission spectrum of SCFSI. As illustrated in Fig. 4 (a) and (b), the selected wavelength shifts from 1500 nm to 1503 nm and from 1600 nm to 1640 nm, respectively, when the SCF with and without alcohol filling is twisted. The simulation results show that the wavelength shift of the transmission spectrum in Fig. 4(b) is significantly greater than that in Fig. 4(a). This result is consistent with the analysis from Eq. (3), indicating that a low birefringence may lead to a high sensitivity of SCFSI.
Fig. 4. The simulated transmission spectrum shifts with the twist angle without (a) and with (b) alcohol filled.
3. Experimental results and discussion
Figure 5(a) shows the measured interference spectrum with the wavelength range of 1350-1750nm at room temperature in the experiment. It can be observed that there are three dips at 1545 nm, 1550 nm and 1565 nm in the SCFSI spectrum. The inset of Fig. 5(a) is an enlarged spectrum of the yellow-shaded rectangle region, which reveals a clear MZI spectrum. It is evident that MZI and SCFSI occur simultaneously in the experiment. To facilitate the analysis of the results, an enlarge spectrum range from 1440 nm to 1560 nm is selected for further experiment, as shown in Fig. 5(b). To analyze the components of the superimposed spectrum, Fast Fourier Transform (FFT) is used to demodulate the transmission spectrum, as described in Fig. 5(c). As expected, two peaks at 0.0075 nm-1 and 0.4265 nm-1 can be found. The peak at 0.0075 m-1 represents the interference from SI, which is selected as the SCFSI sensing peak. The peak at 0.4265 m-1 represents the interference between the x-fundamental mode and higher order mode, which is selected as the MZI sensing peak. Therefore, SCFSI and MZI spectrums are obtained by filtering frequency 0.0075 nm-1 and 0.4265 nm-1, respectively, as shown in Fig. 5 (d). Taking equation $FS{R_{SI}} = {{{\lambda ^2}} / {BL}}$ and $FS{R_{MZI}}\textrm{ = }{{{\lambda ^2}} / {\Delta {n_{eff}}L}}$ into account, we determine that B is 1.955 × 10−4 and Δneff is 9.823 × 10−2, which are close to the FEM results of 2.0 × 10−4 and 1.174 × 10−3. This proves that these two components are due to the SCFSI and MZI, respectively.
Fig. 5. Combination interference spectrum (inset: MZI spectrum in the yellow shaded area) (a), an enlarge spectrum range from 1440 nm to 1560 nm (b), FFT analysis (c) and the SCFSI and MZI spectrums after FFT filtering demodulation (d).
The SCFSI is used for sensing the twist angle. In order to investigate the twist response of the sensor, we rotate the rotator to twist the fiber from 0° to 360° with an increment of 5°. At the same time, we record the transmission spectrums for each applied twist angle. To clearly observe the spectrum evolution, only part of the transmission spectrums of SCFSI is illustrated in Fig. 6 (a) with different twist angles ranging from 0° to 45°. Each transmission spectrum in Fig. 6(a) is the SCFSI spectrum, which is obtained by FFT demodulation. We can obviously observe a variation of intensity and wavelength for each resonance dip associated to a variable twist angle applied on the fiber.
Fig. 6. Transmission spectrums evolution of SCFSI under twist from 0° to 45° in step of 5°(a) and the relationships between the wavelength, the intensity and the twist angle (b).
Figure 6 (b) illustrates the relationships between the wavelength, the intensity and the twist angle. It can be clearly seen that the wavelength dip changes sharply in the region of A and C. The twist sensitivity of SCFSI is 1.22 nm/° in the range of 0° to 80° and -1.01 nm/° in the range of 190° to 250°. And the SCFSI exhibits an intensity demodulation in the region of B and D. The range of intensity demodulation is complementary with the range of wavelength demodulation, and the valid angle range of the proposed sensor can be expanded by utilizing the combination of intensity demodulation and the wavelength demodulation.
Repeatability and stability of the sensing elements are essential performances in practical monitoring of the environment. The repeatability test is conducted by alternating the twist angle of 30° and 60° three cycles at room temperature. Besides, the transmission spectrums under the same twist angle are recorded twice at a 5-min interval to investigate the stability of characteristic spectrum on continuous working time. The experimental results are shown in Fig. 7. It can be found that the dip position of the transmission spectrum shows a reciprocating shift with twist angle-increase and decrease processes, and they remain unchanged at the same twist angle with the maximum deviation of σ=0.027 nm. Therefore, the sensor has good twist measurement repeatability and stability.
Fig. 7. Repeatability and stability measurement. Transmission spectrums of twist angle of 30° and 60° (a) and dip position fitting during the cycle test (b).
To further improve the twist sensitivity of the sensor, a 10 cm long SCF is vertically immersed into the alcohol solution for 2 hours to uptake the alcohol solution into the holes via capillary action [25]. After that, the measured transmission spectrum of the SCF sensor without alcohol filled is shown in Fig. 8 (blue line), while the red line in Fig. 8 represents the transmission spectrum of the SCF sensor with alcohol filled. It can be observed that the intensity of transmission spectrum exhibits a significant decline after the injection of alcohol as illustrated in Fig. 8. And the FSR becomes larger than before. This phenomenon is mainly due to the decrease of birefringence after alcohol filling, which is consistent with above analysis. It is noteworthy that the FSR of the dense fringes almost unchanged as illustrated in the inset of Fig. 8. This is because the dense fringes are generated by MZI within the SCF solid core, which can be regarded as another interference channel. Therefore, the alcohol in the four big air holes has limited effect on the inside-core MZI.
To further demonstrate the improvement in twist sensing after filling with alcohol, a twist sensing experiment based on the alcohol filling SCF sensor is performed for comparison. And the transmission spectrums of SCFSI are illustrated in Fig. 9 (a). The relationship between the wavelength, the intensity and the twist angle are depicted in Fig. 9 (b). The dip wavelength shifts rapidly in the region of B, which exhibits a high sensitivity. The achieved maximum of the twist sensitivity for the alcohol filling SCF sensor is 8.57 nm/° in a twist range of 125° to 150°, which is 7 times higher than that of 1.22 nm/° of the SCFSI sensor without alcohol. In practical application, a high twist sensitivity of 8.57 nm/° can be achieved by pre-twisting the sensor by 125°. The proposed sensor gets the best performance of intensity demodulation in the region A. The range of intensity demodulation is complementary with the range of wavelength demodulation. And the valid angle range of the proposed sensor can be expanded by utilizing both the intensity demodulation and the wavelength demodulation.
Fig. 9. Transmission spectrums evolution of the proposed sensor under the torsion rate from 0° to 250° (a) and the relationships between the wavelength, the intensity and the twist angle (b).
According to the experimental results, it is found that air hole filled with alcohol can effectively improve the performance of the sensor. However, sometimes the auxiliary method may introduce some undesired effect in the measurement, resulting in a temperature crosstalk. To diminish the effect of temperature crosstalk, the characteristic of the parasitic MZI in SCFSI sensor is investigated after air hole is filled with alcohol.
The temperature response characteristic of the parasitic MZI is explored by placing the sensor in a temperature controller while the temperature is increased from 30°C to 36°C with step of 2°C. In order to clearly show the trend of the wavelength shift, only the dip region of the MZI spectrum at each temperature is displayed in the inset of Fig. 10(a). As illustrated in Fig. 10 (a), the temperature sensitivity of the parasitic MZI in SCFSI is -0.56 pm/°C, which is far less than the twist sensitivity of 8.57 nm/° in the twist range of 125° to 150°. This means that the influence of temperature crosstalk on twist angle measurement can be ignored in this range. Moreover, Fig. 10 (b) exhibits the relationships between the wavelength, the intensity and the twist angle of MZI. It can be seen from the inset in the lower left corner of Fig. 10 (b) that the intensity of MZI varies significantly with increasing twist, yet the interference fringes dip is relativity stable. It can be seen that the maximum wavelength fluctuation of MZI over the entire twist range is only 0.2 nm, as shown in the inset of Fig. 10 (b) in the upper right corner. This is because the MZI occurs inside the core of SCF and the twist does not change the interference length of the two interference modes in fiber core. Therefore, there is no significant wavelength fluctuation in the dip position of the interference fringes. Hence, in practical twist measurement, the wavelength shift of the MZI spectrum can be attributed to temperature. This characteristic can be used as a temperature-calibrated caliper to achieve temperature compensation in twist measurements. According to the above analysis, the alcohol filled SCFSI sensor can greatly improves the twist sensitivity without causing great temperature crosstalk.
Fig. 10. Temperature response of MZI (a) and the relationships between the wavelength, the intensity and the twist angle of MZI (b).
Table 1 lists various fiber optic twist sensors with different interference structures based on SI. It is evident that the twist sensitivity of the proposed sensor is comparable to the best result of the twist sensor reported so far. And the temperature calibration method is distinct from the previous research. We believe that this method can provide some help for the development of temperature-calibrated sensors in the future.
Table 1. Comparison of the current study with previously reported SI-based twist sensors
4. Conclusion
In summary, a high sensitivity twist sensor with temperature compensation mechanism has been proposed and experimentally demonstrated based on a SCFSI in this paper. The sensor is fabricated by simply splicing a SCF sandwiched between two single mode fibers and embedded in a 3 dB coupler. The influence of alcohol on birefringence characteristic of the SCF is investigated and discussed in detail using FEM, demonstrating the decreases of the birefringence after the air holes of the SCF are filled with alcohol, resulting in the increase of the sensitivity performance. Experiment results demonstrate that the maximum sensitivity of SCFSI sensor before and after filling alcohol in the air holes is 1.22 nm/° and 8.57 nm/° in twist range of 0° to 80° and 125° to 150°, respectively, exhibiting a great improvement in the twist sensitivity. As far as we know, the sensitivity of 8.57 nm/° is the best performance of the SI-based twist sensor. In addition, the repeatability and stability characteristic of the SCFSI is investigated at 5 min intervals for three circles, the maximum wavelength deviation is 0.027 nm. Moreover, unlike most of the previous reported SI based twist sensors, the SCF used in the experiment is a multimode fiber, which allows a natural parasitic MZI in fiber core. This characteristic is experimentally investigated and utilized as a caliper to achieve temperature calibration in our scheme. The temperature sensitivity of the parasitic MZI is -0.56 nm/°C. And the wavelength shifts of the interference fringes of MZI is less dependent on twist angle, but more correlation with temperature, making the MZI a temperature calibration ruler. Therefore, the proposed twist sensor with this distinctive temperature demodulation mechanism is highly desirable for practical applications due to its various advantages such as ease of fabrication, high sensitivity, and temperature independence.
Funding
National Natural Science Foundation of China (12174022); Beijing Municipal Natural Science Foundation (1232028).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request
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