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Abstract
A highly sensitive optical fiber Mach–Zehnder interference curvature sensor based on MMF-GIMMF-MMF, which was made by sandwiching the graded-index multimode fiber (GIMMF) between two pieces of very short stepped-index multimode fibers (SIMMFs) spliced with input-single-mode fiber (SMF) and output–SMF, respectively, was proposed. The core diameter of the SIMMFs and GIMMF was 105 µm and 50 µm, respectively, and cladding diameter of them were both 125 µm. The sensing principle of the MMF-GIMMF- MMF sensors and the influences of structure parameters on the interference spectrum characteristics were theoretically analyzed in detail. Experimental results showed that when the length of the GIMMF was short enough (usually ≤ 10 mm), interference spectrum was induced by the interaction between the core modes and the low-order cladding modes due to the special structure of the designed Mach–Zehnder interferometer. Intensity of the interference valleys was highly sensitive to the applied bending but nearly independent of the surrounding temperature, on the contrary, the dip wavelength showed negligible sensitivity to the applied bending but relatively high temperature sensitivity. Thus, a temperature- independent curvature sensor could be realized by tracing the intensity variation of interference valley. In addition, different interference valley exhibited different intensity-based curvature sensitivity, providing more options for curvature sensing applications. Especially, total length of the sensor could be as short as 3 mm with length of GIMMF and SIMMFs only 1mm, the maximum curvature sensitivity could reach up to -78.75 dB/m-1 in the small curvature range of 0-2.36 m-1. Owing to its compact size, easy fabrication, good reproducibility and low cost, the proposed sensor is promising for bending-related high-precision engineering applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fiber sensors have the advantages of immunity to corrosion, electromagnetic interference resistance, minor size, and capability of remote sensing. Various temperature, curvature, strain, biomedicine, and physiological optical fiber sensors have been developed in the last decades. Among these parameters, the curvature is an important one because precise curvature detection is critical for a wide range of industrial fields such as health monitoring of bridge and road [1,2], mechanical bending angle measurement [3] and medical treatment [4–7]. To date, different types of fiber-optic curvature sensors have been reported. In 2019, Sun proposed a large–measurement range bending sensor based on a microfiber probe with a taper waist diameter of about 5 µm, achieving a maximum curvature sensitivity of –700 pm/m-1 in the range of 8.73 − 11.82 m−1[8]. Yuan reported a ring-core fiber-based Mach–Zehnder interferometer with curvature sensitivity up to –3.68 nm/m-1 in the measurement range of 1.3856–3.6661 m-1[9]. Susana reported a singlemode-multimode-singlemode (SMS) fiber structure using a section of 40-mm multimode mode fiber (MMF), achieving a curvature sensitivity of 8.7 nm/m-1 in the range of 1.1 − 1.42 m-1 [10]. However, the above curvature sensors based on wavelength-based demodulation scheme required expensive spectral equipment and the response time was limited. In addition, the wavelength might be easily affected by temperature, which would lead to the measurement error in the curvature sensing. To resolve these issues, Liu proposed a curvature sensor fabricated by inscribing fiber Bragg gratings into multicore fibers, achieving a maximum sensitivity of 15.9 dB/m-1 in the curvature range from 0 to 0.7 m-1 [11]. Y. Zhang et al proposed a curvature sensor based on seven-core fiber (7CF) inscribed with Bragg grating by UV light exposure with a curvature sensitivity of -7.27 dB/m-1 in the curvature range of 0 − 1 m-1 [12]. W. Cui et al reported a bending sensor using an abrupt biconical taper inscribed with FBG, achieving a maximum sensitivity of 0.1196 dB/m-1 in the curvature range from 0 to 1.4 m-1 when the waist diameter of FBG is 57 µm [13]. However, these structures still have some shortcomings such as a relatively low curvature sensitivity, narrow curvature range or complex fabrication. Therefore, how to design a fiber optic curvature sensor with lower temperature cross sensitivity, higher curvature sensitivity, and more compact size is of great significance to the practical sensing of curvature.
Indeed, various SMS fiber structures based on multimode interference have attracted widespread attention [10,14,15,16]. In the MMF, specific MMF eigenmodes can be excited when the light field enters the MMF. Different modes transmit along different paths and interfere with each other at the same time. One of the notable superiorities of the SMS fiber structure based on multimode interference was that they had a superior performance with a simple manufacturing process. Nevertheless, the research for the SMS fiber structure to date mainly focused on a stepped-index multimode fiber (SIMMF) rather than a graded-index multimode fiber (GIMMF). GIMMF was commonly used in mode field adapters [17], and telecommunications to suppress dispersion between modes. Some studies on the application of GIMMF-based SMS structure in the sensing fields such as refractive index and temperature have also been reported [18–20], however, in these studies, the sensing principle was based on the interference between the core modes of GIMMF. Due to the small dispersion between GIMMF modes, only when the length of GIMMF was long enough (usually longer than 40cm) could the interference dips between the core modes be observed within a limited wavelength range, which limits its sensing in a small space. As far as we know, there are no research on the interference between core and cladding modes of GIMMF to date, and there are still many unknown characteristics of GIMMF in fiber sensing to be explored.
In this work, we sandwiched a section of GIMMF between two short SIMMFs to form a new type of Mach-Zehnder interferometer, namely MMF-GIMMF-MMF structure sensor, using the same cladding diameter but different core diameter for SIMMF and GIMMF, thus enabling an easy fabrication for the sensor. The sensing principle of this sensor and the influences of structure parameters on the interference spectrum characteristics were theoretically analyzed in detail, providing theoretical guidance to the major parameter designs of the curvature sensor. The interference spectrum characteristics and curvature sensing properties of the sensor with different GIMMF length were experimentally investigated, the results of which basically agreed well with those of simulated results and theoretical expectation. Especially, when the length of GIMMF was short enough (≤ 10 mm), intensity of the interference valleys was highly sensitive to the applied bending but nearly independent of the surrounding temperature. Therefore, a temperature-independent curvature sensor could be realized by tracing the intensity variation of interference valley. The length of the used GIMMF could be as short as 1mm, to the best of our knowledge, this is the first time to combine such short length GIMMF and SIMMFs to construct the optical fiber Mach–Zehnder interferometer for curvature sensing, which has the advantages of high curvature sensitivity, low temperature cross-talk, low cost, compact structure, small size, and good reproducibility.
2. Principle and simulations
In this study, SIMMF and GIMMF used to design the sandwich multimode fiber Mach– Zehnder interferometer were purchased from the Yangtze Optical Fiber Company. The RI distribution of multimode fibers was expressed as
The structure diagram of the sandwich multimode fiber Mach–Zehnder interferometer is shown in Fig. 1(a). The sensor was made by sandwiching the GIMMF between two pieces of 1-mm SIMMFs spliced with input − SMF and output–SMF, respectively. The core diameter of SMF, GIMMF, and SIMMF is 8.3 µm, 50 µm, and 105 µm, respectively, and their cladding diameter are the same value (125 µm). The RI distribution of the SIMMF (q = ∞) and the GIMMF used in this study (q = 2) is shown in Fig. 1(b).
Fig. 1. (a) Schematic diagram of MMF-GIMMF-MMF fiber structure; (b) RI distribution of GIMMF and SIMMF.
The basic principle for this sensor could be explained as follows. As shown in Fig. 1(a), when the light was launched into SIMMF1 through the input − SMF, a portion of the optical power was coupled to the core mode of GIMMF and the rest to the cladding mode because of the mode field mismatch. Light in the core of GIMMF traveled along a trajectory similar to a sine curve [20], as shown by the yellow dashed line in Fig. 1(a), and then transmitted to SIMMF2, where part of the cladding modes of GIMMF were coupled to the guided mode of SIMMF2, interfering with the core modes of GIMMF, and finally coupled into the fundamental mode of the SMF. The GIMMF with a core diameter of 50 µm could support LP01∼05 mode transmission [17], whose mode field distribution are shown in Fig. 2. The interference pattern of this structure could be simply understood as the interaction between core modes and the dominant cladding modes of GIMMF. The interference effects might also exist between different core modes or between different cladding modes of GIMMF, but their FSR were so large that they might only play the role of modulating the main interference pattern in the limited spectral range. As a result, the transmission power of the MMF-GIMMF-MMF structure could be given by
According to Eq. (2), the resonant wavelength (${\lambda _{{\rm{dip}}}}$) and the Free spectral range(FSR) could be expressed as
where $\varDelta {n_{eff}}$ represents the effective refractive index difference between the GIMMF core modes and cladding modes.For a straight MMF, the refractive index (RI) distribution of the cross section is symmetric along the fiber axis. As for the curvature sensing, the equivalent refractive index of the outer convex portion of curved fiber is higher than that of the inner convex portion and the mode field of the transmission modes shift to the outer convex portion. The RI distribution of the cross section of the curved GIMMF can be equivalent straight GIMMF after the conformal mapping [21]:
where n0 is the RI distribution of GIMMF before bending, C represents the value of curvature, and x is a coordinate. The positive x-axis is vertical to the core axis of curved GIMMF, with the center of the core as the origin and pointing the convex direction of GIMMF.According to Ref. [22], the normalized extinction ratio (ER) could be expressed as
where Ico and Icl represent the intensity in the fiber core and intensity of certain cladding modes, respectively. Its value is equal to the square of the double integral of the electromagnetic field distribution of the core or cladding mode and that of the input field [23]. According to Eq. (5), bending will change the refractive index distribution of the cross section of the multimode fiber, which will change the electromagnetic field distribution of the transmission modes, at the same time, Ico and Icl will also change, transmission energy is converted between different modes. Obviously, the change of Ico and Icl would be manifested by the increase or decrease in ER of the interference spectrum, providing the possibility of intensity demodulation for curvature measurement.As for the temperature sensing, the resonant wavelength could be expressed as [9]:
To demonstrate the aforementioned analyses, as shown in Fig. 3, the transmission of light in the straight MMF-GIMMF-MMF was simulated using Rsoft with the Beam PROP function. The free-space wavelength was set as 1550 nm. The other important simulation parameters are given in Table 1. After the reconvergence study, the grid size of X, Y, and Z, the Pade order, and boundary condition were set as 0.025 µm, (4,4), Simple Transparent Boundary Condition, respectively. It can be seen from Fig. 3 that there is energy transmission in both the core and cladding of GIMMF. When reaching SIMMF2, the core modes and cladding modes are jointly coupled to the fundamental mode of the output SMF. Therefore, in the transmission spectrum of this structure, the interference dips generated by the interference of the GIMMF core modes and the cladding modes can be observed.
Table 1. Parameters of simulation
The influences of length of SIMMF and GIMMF on the spectrum of the sensor were also researched by the Rsoft beam propagation method, respectively. As shown in Fig. 4(a), the length of GIMMF was fixed at LGIMMF = 1 mm, the length of SIMMF was set to be 0, 1, 2, 3, and 4mm, respectively, indicating that length of SIMMF imposed a great influence on the FSR of the spectrum, with the increase of the SIMMF length, the FSR tended to decrease, but little influence on the fringe visibility. Nevertheless, there was no interference spectrum when LSIMMF =0 mm, this was because there were no GIMMF cladding modes being excited with absence of SIMMF. Considering the visibility of the fringe pattern and the total length of the MMF-GIMMF-MMF fiber sensor, SIMMF with 1 mm length was selected to construct the proposed sensor in the following simulation. Figure 4(b) is the influences of the GIMMFs length on the interference spectrum, showing that when the length of SIMMF (LSIMMF) = 1 mm, the FSR decreased with the increase of GIMMF length from 0 to 5 mm. Especially, the fringe visibility of the Mach-Zehnder interferometer without GIMMF (LGIMMF =0 mm), i.e., becoming a normal SMS fiber structure, was very weak, which could be attributed to the small overlap of mode field between the core modes of the SIMMF in the core region of SMF. Based on the above simulated results and theoretical analysis, it can be concluded that the proposed MMF-GIMMF-MMF fiber structure with appropriate structured parameters has the advantages of higher spectral contrast and much compact size as compared with those of the traditional SMS fiber structures. These characteristics would enable the proposed structure much suitable for sensing applications such as bending, vibration, acceleration, or strain, etc., in a small space.
Fig. 4. (a) Simulated results of the influence of SIMMF length on the spectrum of the sensor with LGIMMF = 1 mm; (b) simulated results of the influence of GIMMF length on the spectrum of the sensor with LSIMMF = 1 mm.
By comprehensively considering the fringe visibility and the total length of the sensor, SIMMFs and GIMMF with both 1 mm length was selected to construct the proposed MMF- GIMMF-MMF structure in the following simulation, fabrication and experiments. In order to investigate the curvature sensing characteristics of the sensor with LSIMMF = LGIMMF = 1 mm, the variation of the transmitted light intensity of the sensor with curvature was simulated in Rsoft by changing the RI distribution of GIMMF cross section according to Eq. (5) when the central wavelength of incident light is 1292.05nm and 1422 nm, corresponding to the wavelengths of Dip 1 and Dip2 in Fig. 4(a) (blue line), respectively. The results are shown in Fig. 5, the transmitted light intensity of the sensor monotonously increased by 10.4 dB when the central wavelength of incident light is 1292.05 nm and monotonously decreased by 18 dB when the central wavelength of incident light is 1422 nm in the curvature range from 0 to 2.4 m-1, indicating that the micro-bending of the sensor will lead to drastic changes in light intensity and the curvature can be demodulated by monitoring the changes of intensity.
Fig. 5. The simulated results of the transmitted light intensity changes with curvatures varying from 0 to 2.4 m-1 when the central wavelength of incident light set as (a) 1292.05 nm; (b) 1422 nm.
3. Experiment and discussion
3.1 Sensor fabrication and the spectral properties
The fabrication process of the MMF-GIMMF-MMF sensor is shown in Figs. 6(a)–(c). First, we peeled off the coating of the optical fiber to be used, and used precision optical fiber cutting knife to carefully cut its end to achieve flatting end face, and then the SMF and SIMMF were spliced by an optical fiber splicer (KL-300T). Second, the spliced point of the SMF-SIMMF was vertically aligned with the cutting knife and fixed on the optical fiber precision cutting platform. Then, we turned the rotation controller of the translation station to move the SMF-SIMMF outward 1mm and cut the optical fiber. The process was repeated twice to produce two SMF-SIMMF (1-mm). Subsequently, the GIMMF and SMF-SIMMF (1-mm) were fused together and the length of GIMMF was precisely controlled in the same way. Finally, the fabricated SMF-SIMMF-GIMMF was fused with another SMF-SIMMF (1-mm) to form the MMF-GIMMF-MMF structure. In the experiments, several MMF-GIMMF-MMF structures with GIMMF lengths from 1 mm–7 cm had been fabricated. And then, the impact of GIMMF length (1mm–7 cm) on the interference spectrum could be investigated, as shown in Figs. 7(a) and (b). As expected, the FSR decreased with the increase of GIMMF length, which was in accordance with the simulation. However, the fringe visibility suffered obvious decay when the length of the GIMMF was longer than 10 mm, which might be attributed to the decrease in cladding mode energy with the increase of transmission distance. Furthermore, the transmission spectra of GIMMF with length of 3, 5 and 7 cm in Fig. 7(b) revealed that the envelopes (dashed line) could be observed when the length of GIMMF was relatively long (>2 cm), which were extracted from the dense interference spectrum (solid line) by a low-pass filter.
Fig. 7. Interference spectrum of the MMF-GIMMF-MMF fiber structure with different lengths of GIMMF of (a) 1, 3, 6, 8, 10, and 20 mm; (b) 3, 5, 7 cm; spatial frequency spectra of the sensor with different lengths of GIMMF of (c) 1, 3, 8, 10 mm; (d) 3, 5, 7 cm.
In order to analyze detailed characteristics of these interference fringe in Figs. 7(a) and (b), whose spatial frequency spectra were calculated by the FFT method, as shown in Figs. 7(c) and (d), respectively. It can be seen from Fig. 7(c) that there was only one dominant frequency when the length of GIMMF was smaller than 10 mm, and it would increase with the increase of GIMMF length. While for the sensor with GIMMF length of 3, 5 and 7 cm, Fig. 7(d) manifested that apart from one dominant frequency at high frequency area, new frequency components appeared in low frequency area. For the purpose of studying the interference pattens corresponding to these new frequency components, we immersed the sandwich multimode fiber MZI with LGIMMF =1 mm and 3 cm into glycerol (RI = 1.4746) and recorded their spectra for comparison, the results are shown by the orange-yellow line in Fig. 7(a) and Fig. 7(b), respectively. Due to the RI of glycerol was larger than that of cladding, the high-order cladding modes of GIMMF might turned into radiation modes and disappear, but this has little effect on the transmission of low-order cladding modes. It can be seen from Fig. 7(a) that, the spectrum of the sensor with LGIMMF = 1 mm in glycerol only decayed as a whole as compared with that in air, indicating that its interference was between the core modes and the low-order cladding modes. However, the spectrum envelope of the sensor with LGIMMF = 3 cm in Fig. 7(b) disappeared, while the dense interference spectrum still remaining. Therefore, it can be concluded that the frequency component located at high frequency area in Fig. 7(d) were induced by the interference between the core modes and low-order cladding modes of GIMMF, which was corresponding to dense interference spectrum in Fig. 7(b). While the dominant frequency at low frequency area in Fig. 7(d) was induced by the interference between the low-order and high-order cladding modes of GIMMF, which functioned as a modulation for the dense interference spectrum in Fig. 7(b). These is reasonable due to that the accumulated phase difference between the low-order and high-order cladding modes of the GIMMF increase with the increase of LGIMMF, only when it is longer than a certain value (usually>2 cm), the interference spectrum between them would appear within the limited spectral range (e.g., 1250–1650 nm). Nevertheless, in the practical applications, too small FSR and fringe visibility will reduce the dynamic range of the sensor. Therefore, taking into account these two main factors, the following experiments were mainly focused on the MMF-GIMMF-MMF sensors with structure parameters of LSIMMF =LGIMMF = 1 mm, and the total length of the sensor was only 3 mm. Finally, we studied the polarization dependence of the sensor according to the method of Ref. [24], and the results manifested that the interference spectrum of the proposed sensor is polarization-independent.
3.2 Curvature and temperature sensing experiments
The curvature experimental device is shown in Fig. 8. Light emitted from a broadband light source (BBS, CONQUER ASE, 1250-1650 nm) passed through the MMF-GIMMF-MMF structure, which was held at the middle of precision translation stages by two magnets. And then, the interference spectrum was recorded by using an optical spectral analyzer (OSA, AQ6370D, 600-1700 nm) with resolution of 0.02 nm. Different curvature values of the MMF-GIMMF- MMF structure were realized by that one of the translation stages was fixed, and the distance between the two translation stages could be adjusted through the rotary controller of the other one. The curvature with different displacement of the translation stage was calculated by [9]
where c is the curvature value, R is the bending radius, L is the length between two magnets when the fiber is straight, and x is the displacement of the moveable stage. In the experiment, L and x were set as 60 mm and 1 µm, respectively. Two MMF-GIMMF-MMF sensors with LSIMMF =LGIMMF = 1 mm were used for the tests, the interference spectra of them are shown in Fig. 9(a).Fig. 9. (a) Transmission spectrum of the sensor with LGIMMF = 1 mm; (b)∼(f) curvature responses of Dip 1∼Dip 3.
It can be seen from Fig. 9(a) that after considering the optical path loss, the interference spectra of two same sensors made by the above method basically agreed with the simulated results. The differences between them may be resulted from not considering material dispersion in simulation and the measurement error for the length of the sensor. Figures 9(b)–(f) show the curvature responses of three different interference dips at 1271.28 nm, 1401.28 nm and 1591.92nm, which were signed as Dip 1, Dip 2 and Dip 3 in Fig. 9(a), respectively. As for Dip 1, with the increase of the curvature, the intensity of interference valley obviously increased while the redshift of the wavelength was very small in the curvature range of 0–2.36 m-1. The relationship between the intensity of Dip 1 and curvature is drawn by the blue line in Fig. 9(d), indicating that it responded nonlinearly with curvature and the fitting curve can be expressed as
where y is intensity with the units of decibel (dB). The intensity of Dip 1 was much more sensitive in the high curvature range, especially the maximum sensitivity reached 17.6 dB/m-1 in the linear range of 1.599 − 2.36 m-1, which was approximately 150 times and ∼2.5 times larger than that of the taper-FBG fiber structure with waist diameter of 57 µm [13] and the seven-core fiber (7CF) inscribed with Bragg grating [12], respectively. The wavelength-based curvature sensitivity of Dip 1 was only ∼0.8 nm/m-1 (red line in Fig. 9(d)).Similarly, with the increase of curvature, Dip 2 and Dip 3 also mainly show the change of the intensity of the interference valley, and the shift of wavelength is relatively small, so the sensor is more suitable for intensity demodulation during curvature sensing. As shown in Figs. 9 (e) and (f), the intensity of Dip 2 and Dip 3 decreased monotonically in the curvature range from 0 to 2.36 m-1, and the corresponding curvature sensitivity could reach up to -78.75 dB/m-1 and -74.03 dB/m-1 in the linear range of 2.16-2.36 m-1, respectively. The overall intensity trends of Dip 1 and Dip 2 with curvature are consistent with the simulation results in Figs. 5(a) and (b), respectively. These results mean that different interference dips have different intensity-based curvature sensitivity. This provides more options for curvature sensing applications; we can choose one of the interference valleys that has the best performance according to the requirement in practical application. Compared to Dip 2 and Dip 3, Dip 1 is more suitable for applications where curvature sensing resolution is not critical, such as curvature sensing based optical fiber wearable breathing belts [4,5,6]. In contrast, for Dip 2 and Dip3, a properly designed package structure can stabilize the sensor to a specific radius of curvature, an intensity modulated ultra-sensitive curvature sensing (e. g. -78.75 dB/m-1) can be achieved, which has more potential in monitoring small external fluctuations. Such as monitoring small vibration signals [25], pulse signals [7] or tactile perception [26], etc.
In practical applications, temperature property of a sensor is also very important. Therefore, the temperature response of the sandwich multimode fiber MZI with LSIMMF =LGIMMF = 1 mm was also studied. The sensor was fixed on the temperature controller with a resolution of ±1 °C, and the data were recorded after the temperature controller reached the preset temperature for 10 min. As shown in Fig. 10(a), as expected, Dip 1 redshifted with the increase of temperature, and the relationships between its wavelength, intensity, and temperature are shown by the red and blue lines in Fig. 10(b), respectively, indicating that in the range of 40–130 °C, the temperature sensitivity of Dip 1 reached 102 pm/°C while the intensity fluctuation only being ±0.2457 dB. Such small variation in intensity was usually caused by fluctuations of the light source, which could be eliminated by means of a differential compensation method [27]. Apparently, the responses of Dip 2 and Dip3 to temperature were the same as to that of Dip1. Indeed, the temperature sensitivity of Dip 1 was relatively high, which was approximately 3.4 times and ∼2 times larger than that of the single MM-HCF-MM fiber structure [28] and the MM-SMF-MM fiber structure [29], respectively. However, since the interference valley intensity of the MMF-GIMMF-MMF sensors were independent of temperature, a temperature-independent micro-bending sensor could be realized by only tracing the variation of the interference valley intensity in the curvature range of 0–2.36 m-1.
Fig. 10. Temperature properties of MMF-GIMMF-MMF fiber structure with LGIMMF = 1 mm, (a) spectrum evolution; (b) wavelength shift and transmission variation.
For the purpose of verifying the general regularity of the spectrum evolution with bending for the MMF-GIMMF-MMF sensors of LGIMMF ≤ 10 mm, we further inspected the sensors with LGIMMF = 1.8, 3, 4, 6 and 8 mm under the condition of LSIMMF = 1 mm, respectively. As a result, the total length of the constructed MMF-GIMMF-MMF sensors was only 3.8, 5, 6, 8, and 10 mm, respectively. Herein, we randomly selected some of the interference valleys for investigation. The experimental results are shown in Figs. 11(a)–(d), indicating that the intensity of interference valleys change significantly with increase of the bending in such a small curvature range, while the shift of interference wavelength is unconspicuous. These results were in accordance with that of MMF-GIMMF-MMF sensor with LGIMMF = 1 mm shown in Fig. 9(c), indicating that the spectrum evolution with bending for the MMF-GIMMF-MMF sensors of LGIMMF ≤ 10 mm have the same regularity. Furthermore, in order to evaluate the stability of the proposed sensor, the MMF-GIMMF-MMF sensor with LGIMMF =1.8 mm was placed for 30 days and repeated experiments for bending sensing were carried out. The results are shown in Fig. 11(e), it could be seen that the reproducibility for the bending response of the sensor was good, and the intensity-based curvature sensitivity was 21.34 dB/m-1 and 20.98 dB/m-1 within the linear range of 1.2-1.696 m-1 for the first and the second testing, respectively. Therefore, the proposed sensor has good stability.
Fig. 11. Curvature responses of the sandwich multimode fiber MZI with different GIMMF lengths of (a) 1.8 mm; (b) 3 mm; (c) 6 mm; (d) 8 mm; (e) the intensity of Dip A as a function of curvature for the first day and the thirty days.
Finally, Figs. 12(a) and (b) are the spectral evolution of the MMF-GIMMF-MMF sensor with LGIMMF = 4 and 8 mm for the bending range from 0 to 1.9 m-1, respectively, energy transformation among different interference valleys induced by the bending could also be observed as well, which was similar to that of the sensor with LGIMMF = 1 mm (Fig. 9(b)). These were reasonable because when the LGIMMF was relatively short (≤ 10 mm), the interference was mainly induced between the core modes and the low-order cladding modes. According to Eq. (6) and the Law of conservation of energy, when the bending was in a small range (e. g. 0 to 2.4 m-1), the leaking of the low-order cladding modes could be neglected, thus leading to the ER of some interference pattens decreased while others increased as a consequence of the re-distribution of the intensity among difference low-order cladding modes. In addition, the same as to the results in Figs. 9(d)–(f), different interference valleys in Figs. 12(a) and (b) showed different intensity-based curvature sensitivity and linear measurement range. As a result, we can choose one of the interference valleys that has the best performance according to our requirement in practical application.
Fig. 12. Curvature responses of the sandwich multimode fiber MZI in the wavelength range of 1500∼1650 nm with different GIMMF lengths of (a) 4 mm; (b) 8 mm.
In the practical curvature sensing, without affecting the dynamic range of the curvature of the sensor, it may be possible to encapsulate the sensor in a material with specific thermal optical coefficient and use the sensitivity of the characteristic peak wavelength to the refractive index to compensate its sensitivity to temperature. At this time, the sensor only needs to monitor the light intensity change of the interference valley with a narrow linewidth light source to realize the curvature sensor insensitive to temperature and RI.
4. Conclusion
A highly sensitive and temperature-independent curvature optic fiber sensor was developed using a sandwich multimode fiber Mach–Zehnder structure. The sensor was made by sandwiching a short section of GIMMF between two pieces of 1-mm SIMMFs spliced with input − SMF and output–SMF, respectively. When the length of the GIMMF of the proposed structure was short enough (≤10 mm), intensity of the interference valleys exhibited highly sensitive to the applied bending but the wavelength shift was negligible, which was opposite for the temperature, thus enabling a temperature-independent curvature sensor by only tracing the intensity variation of interference valley. Total length of the sensor could be as short as 3 mm with length of GIMMF and SIMMFs only 1mm, the maximum curvature sensitivity could reach up to -78.75 dB/m-1 in the small curvature range of 0-2.36 m-1, which was much higher than that of most of optical fiber curvature sensor to date. Furthermore, different interference valley of the proposed structure exhibited different curvature sensitivity, providing more options for the curvature sensing in practical applications. Thanks to the compact size, easy fabrication, good reproducibility and low cost, the proposed sensor has great application prospects in the fields of bending-related high-precision engineering applications by different packages, such as wearable device, small vibration signals detection, and tactile perception, and so on. In the near future, we will further improve the fiber structure, such as polishing, dislocation, corrosion, etc., to realize the vector curvature sensing.
Funding
National Natural Science Foundation of China (61875026); the Chongqing Talents Program under Grant (CSTC2021YCJH-BGZXM0128, CSTC2021YCJH-BGZXM0287); Fundamental Research Funds for the Key Research Program of Chongqing Science and Technology Commission (KJZD-K202201106); the Graduate Student Innovation Program of Chongqing under Grant (CYS21450).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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