A strain force sensor based on fiber inline Fabry-Perot (FP) micro-cavity plugged by cantilever taper was proposed. The structure was fabricated by simple and cost-effective method only including fiber cleaving, tapering and splicing. The active-length of the FP micro-cavity reached 1360 µm, while the interference length was only 3.5 µm. Owing to the ultra-long active-length and ultra-short interference length, the strain force sensitivity of the fiber inline FP micro-cavity plugged by cantilever taper reached as high as 841.59 nm/N. Besides, the proposed structure showed good linearity (99.9%) in the sensing process and small temperature crosstalk (11 pm/ ̊C). It can be used as a practical and reliable strain force sensor.
© 2017 Optical Society of America
Recently, optic fiber sensors for strain force sensing based on different optic fiber structures have been developed, such as fiber Bragg grating [1–3], long-period fiber grating [4,5], Fabry-Perot interferometer (FPI) [6–11] and Mach–Zehnder interferometer [12–14]. In these strain force sensors, the sensors based on fiber inline FP micro-cavities are particularly attractive owing to their high sensitivity, simple configuration, small cross sensitivity, and miniature sensor head [6–11].
The theoretical analysis reported by  suggested that the strain sensitivity of the fiber inline FP micro-cavity depends on the shape and dimensions of micro-cavity. To improve the sensitivity, the micro-cavities with different shapes were designed and fabricated, such as oblate spheroid , narrow cuboid  and expanded bubble [17, 18]. But the sensitivities of these fiber inline FP micro-cavities were still only 10~30 pm/µɛ (about 10~30 nm/N).
Another method to improve the strain sensitivity of the fiber inline FP micro-cavity was to separate the cavity active-length from the FP interference length and increase the active-length. The strain sensors based on the extrinsic fiber FPIs embedded in capillaries [19, 20] have been reported in the past in order to achieve such designs. But these sensors compromised the structure size, stability and tensile strength. Then the strain sensor based on the fiber inline long-active-length FP micro-cavity was proposed to overcome the shortcomings mentioned above . It was fabricated by using phosphorus pentoxide doping, hydrofluoric acid etching and fiber splicing. The reported active-length in  was 360 µm, and it can be further improved by increasing the P2O5 doping deep and extending the etching time. However, as the increasing of the active-length, the thickness of the outer wall and the diameter of the inner taper will be influenced in the etching process, which may impact on the performance of the sensor.
In this paper, a strain force sensor based on fiber inline FP micro-cavity plugged by cantilever taper with ultra-long active-length was proposed. The whole structure was fabricated by simple and cost-effective method only including fiber cleaving, tapering and splicing. More importantly, owing to the advantage of the fabrication method, the active-length of the FP micro-cavity reached 1360 µm while the FP inference length was decreased to 3.5 µm, which results in the ultra-high strain force sensitivity of 841.59 nm/N. Meanwhile, the proposed strain force sensor based on fiber inline FP micro-cavity plugged by cantilever taper was with good sensing linearity (99.9%) and small temperature crosstalk (11 pm/ ̊C).
2. Theory analysis
The diagram of the common micro-cavity-based FPI and the FPI based on the micro-cavity plugged by cantilever taper with ultra-long active-length are shown in Figs. 1(a) and 1(b) respectively. The FP interference length of common micro-cavity-based FPI equals the micro-cavity length L1. According to the interference theory of the fiber in-line FPI , the interference spectrum reaches its peak position when the following condition is satisfiedEq. (3) into Eq. (2), the stain force sensitivity can be simplified intoEq. (4) it can be seen that, if the FP interference peak close to the fixed wavelength such as 1550nm is chosen to sense the stain force, the stain force sensitivity can be regarded as a constant and it doesn’t depend on the length of the micro-cavity. But in fact, due to the surface deformation of the micro-cavity, the shape and size of the micro-cavity both influence the stain force sensitivity. That’s why the experimental sensitivity is larger than the calculation result based on Eq. (4) [15, 16]. Though the stain force sensitivity can be improved by optimizing the shape and size of the micro-cavity in FPI, the sensitivities of these fiber inline FP micro-cavities were still only 10~30 pm/µɛ (about 10~30 nm/N) [15–18].
From Fig. 1(b), the FP interference length of the FPI based on the micro-cavity plugged by cantilever taper is L1, and it is less than the hollow tube length L2. The length L3 of the cantilever taper in the hollow tube can be calculated by L2−L1. The central wavelength λm of mth order FP interference peak can be calculated byEq. (6), the stain force sensitivity of the FPI based on the micro-cavity plugged by cantilever taper can be simplified intoEq. (7) it can be seen that, if the FP interference peak close to the fixed wavelength such as 1550nm is chosen to sense the stain force, the stain force sensitivity is proportional to the value L2/L1. Therefore, the stain force sensitivity of the FPI can be improved greatly by increasing the hollow tube length L2 and decreasing the FP interference length L1.
Firstly, the cantilever taper was fabricated by using two-step arc discharge fiber tapering method. The diagram is shown in Fig. 2. The two sides of the single mode fiber (SMF) were fixed on the fiber fixtures controlled by two stepping motors respectively. The center of the SMF was heated by using arc discharge. Meanwhile, the two sides of the SMF were pulled by the stepping motors at constant speed, which is shown in Fig. 2(a). The fiber tapers with different diameters can be achieved by changing the pulling speed.
To make sure that the fiber cantilever taper can be fixed into the hollow tube with the cantilever taper parallel to the inner wall of the hollow tube, the shape of the fiber cantilever taper is needed to be designed as a plug shown in Fig. 2(d). Therefore two-step arc discharge fiber tapering method was used in this paper. In the first step of fiber tapering, the diameter of the taper was controlled to be slightly less than the internal diameter of the hollow tube (60 µm in this paper). Then the arc discharge position was moved to one side of the taper and the second step fiber tapering was done to further attenuate the fiber taper. The diagram is shown in Fig. 2(b). After the fiber cutting shown in Fig. 2(c), the fiber cantilever taper with the shape of plug was finally achieved, which is shown in Fig. 2(d). One of fiber cantilever tapers fabricated by using two-step arc discharge fiber tapering method is shown in Fig. 2(e). Form Fig. 2(e) it can be seen that, there are two diameter abrupt-changing positions on the fiber cantilever taper. The diameters of thick and thin areas of the fiber cantilever taper in Fig. 2(e) are about 60 µm and 25 µm respectively. Of course, these two values can be changed according to practical need by changing the pulling speeds in the two-step arc discharge fiber tapering processes respectively. The length of the fiber cantilever taper can be different values by changing the fiber cutting position. It is worth mentioning that, as the increasing of the taper length in single fiber tapering, the waist size of the taper got thinner and thinner at the fixed heating spot, which influenced the uniformity of the taper diameter. To achieve longer taper with uniformity diameter, we can continue to repeat similar two-step arc discharge fiber tapering shown in Fig. 2 to increase the taper length greatly.
Then, a section of silica hollow tube was spliced to the end of SMF by using the manual splicing program of the common fiber fusion splicer. The diagram is shown in Figs. 3(a) and 3(b). The splicing parameters are set as the values (a) listed in Table 1.The length of the hollow tube needs to matching with that of fiber cantilever taper to make sure that the fiber cantilever taper can be plugged into the hollow tube. The plugging position was spliced also by using the manual splicing program to achieve sealed FP micro-cavity. The diagram is shown in Fig. 3(c). The splicing parameters are set as the values (b) listed in Table 1. Both the ends of the SMF and the fiber cantilever taper form two reflecting surfaces of the FPI. One of the fabricated structure is shown in Fig. 3(d). The FP interference length L1 is about 138 µm and the hollow tube length L2 is about 1100 µm. From Fig. 3(d) we can see, the two reflecting surfaces are parallel well to each other. The fiber cantilever taper is just stuck in the hollow tube. The plugging position slightly deformed after fusion splicing, and the splicing point is firm enough.
The reflection spectrum of the fabricated structure was measured by using an optical spectrum analyzer (OSA, AQ6370B) and broad-band source (BBS, 1200 nm to 1700 nm) through a circulator. The spectrum result is shown in Fig. 4(a). It shows obvious FP inference peaks in the reflection spectrum. Then we fabricated another two structures using the same method. The FP interference length L1 and the hollow tube length L2 of these two structures are (26 µm, 810 µm) and (3.5 µm, 1360 µm) respectively. Their reflection spectra were also measured and are shown in Figs. 4(b) and 4(c). As the FP inference lengths of these three structures decrease from 138 to 3.5 μm, the spacing of the interference peaks shown in Fig. 4 increases gradually, which is in accordance well with the FPI theory . The end of the cantilever taper plugging into the FP micro-cavity with the interference length of 3.5 µm is shown in Fig. 4(d). From Fig. 4(d) we can see, the cantilever taper locates rightly in the center of the silica hollow tube, and its end surface is closely parallel to that of the SMF. The interference length of the fabricated FP micro-cavity equals the distance (only 3.5 µm) between the end surfaces of the cantilever taper and SMF.
4. Experimental results and discussions
To investigate the strain force sensitivity of the fabricated fiber inline FP micro-cavity plugged by cantilever taper, the end of the SMF containing the FP micro-cavity was loaded by different weights, which induced the strain of the SMF. The mass of the weights ranged from 5 g (giving a strain force of 0.049 N) to 40 g (giving a strain force of 0.392 N) with an interval of 5 g. The relationship between the strain force and the strain can be approximatively shown by using Hooke's Law as belowEq. (8), it can be calculated that the strain force of 1 N applied on the structure will generate the strain of about 1506 µɛ. Meanwhile, the reflection spectrum of the structure was monitored simultaneously by using the OSA and BBS mentioned before through the circulator at room temperature. By this way, the responses of three fabricated FP micro-cavities plugged by cantilever taper to strain force were all investigated.
The changes in the reflection spectra of the three structures with different strain forces are shown in Figs. 5(a)–5(c), respectively. Along with the increase of the strain force, the interference peaks in three reflection spectra all shifted to longer wavelength direction. To show the relationship between the wavelength shift and the strain force in more detail, one interference peak was chosen in each structure spectrum, and its center wavelength at different strain force was recorded. The results of the three structures were all linear fitted, which are shown in Fig. 5(d). The FP interference length L1 and the hollow tube length L2 of the structure A, B and C are (138 µm, 1100 µm), (26 µm, 810 µm) and (3.5 µm, 1360 µm) respectively. From Fig. 5(d) it can be seen that, three structures all show perfect linear response to the strain force. The linearity is 99.9%, 99.5% and 99.9% respectively. What's more, the strain force sensitivity of the fiber inline FP micro-cavity C plugged by cantilever taper reached as high as 841.59 nm/N, which equivalents the strain sensitivity of 559 pm/µɛ. This sensitivity value is about two orders of magnitude higher than that of strain force sensors based on the common fiber inline FP micro-cavities [7–9]. The detailed parameter values of three fabricated structures are shown in Table 2. From Table 2 we can see, by increasing the value of L2/L1, the measured strain force sensitivity of the structure is improved greatly. The sensitivity is approximately proportional to the value L2/L1, which is in accordance with Eq. (7).
To show the tensile strength of fiber inline FP micro-cavity plugged by cantilever taper, we continued increasing the loading weights of the structure A with an interval of 5 g. It broke at the plugging position when the mass of the loading weights reached 90 g (0.882 N). Therefore the plugging position after fusion splicing is the weakest point of the whole structure. To improve the tensile strength of the sensor, the plugging position of the structure C after fusion splicing was cut flat again, and then it was spliced to the end of another SMF. The splicing parameters are set as the values (a) listed in Table 1, but the heating current was increased to 2.5 mA. The final sensor structure C is shown in Fig. 6. The loading experiment results showed that the sensor structure C after improvement can survive until the mass of weights reached 260 g (2.548 N). The tensile strength of the proposed sensor can be improved greatly by using this method.
To investigate the crosstalk of the temperature on the strain force sensing, the fiber inline FP micro-cavity C plugged by cantilever taper was placed in air environment in a tube furnace, which was heated from 25 °C to 55 °C with the interval of about 5 °C. The relationship between the center wavelength shift of the interference peak and the temperature is shown in Fig. 7. The interference peak shifted to shorter wavelength direction as the increase of the temperature, and the temperature sensitivity is only 11 pm/°C. The experiment result indicates that the FP interference length L1 decreased as the temperature increasing, which means that the thermal expansion of the cantilever taper was a little larger than that of the silica hollow tube.
In conclusion, we proposed a strain force sensor based on fiber inline FP micro-cavity plugged by cantilever taper fabricated by fiber cleaving, tapering and splicing. Its strain force sensitivity can be improved greatly by increasing the active-length and decreasing the interference length. It can have actual application in strain force sensing owing to its ultra-high sensitivity, good linearity, small temperature crosstalk, and simple and cost-effective fabrication method.
National Science Foundation (11504070, 11574063 and 11374077); The Science and Technology Development Plan of Weihai (2015DXGJUS002); The Fundamental Research Funds for the Central Universities (Grant No.HIT.NSRIF.2016083); Discipline Construction Guidance Foundation of Harbin Institute of Technology at Weihai (WH20150209).
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