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Abstract
An optical fiber strain sensor based on capillary-taper compensation structure was proposed. The theoretical simulation by using the finite element analysis method shows a matching condition between the capillary length and the interference-cavity length to achieve the zero temperature crosstalk. Meanwhile, the strain sensitivity can also be improved greatly at the matching condition. We then set up an insertion controller system with high accuracy to make sure the interference-cavity length can match the capillary length. Finally the fiber strain sensor with both ultra-low temperature-crosstalk (0.05 pm/°C) and ultra-high sensitivity (214.35 pm/με) was achieved, and the experimental results agreed well with the calculated results. The “ladder-mode” and repeatability experiments showed that the proposed sensor was actually with the ultra-low detection limit of 0.047 µɛ.
© 2018 Optical Society of America
1. Introduction
Optic fiber strain sensors based on various categories of optic fiber structures have been proposed, such as Mach–Zehnder interferometers (MZIs) [1–3], Fabry–Perot interferometers (FPIs) [4–6], photonic crystal fibers [7–10] and fiber gratings [11–14]. These fiber structures are particularly attractive owing to immunity to electromagnetic interference, good durability and small size. The strain sensitivity is always regarded as an important research parameter [1–14]. However, in order to better articulate the capability of the sensor in actual application, the detection limit (DL) was proposed. The DL is the smallest change that can be measured accurately. The DL can be calculated by the ratio between sensitivity and resolution [15–17]. However, in actual application, many factors, including SNR, FWHM and thermal noises should also be considered [17]. Therefore, the actual DL is generally higher than the DL obtained by theoretical calculation. To get the accurate DL of the sensor, the value of DL needs to be obtained by the experimental results [18, 19]. Especially when the sensor is applied in actual uncertain environment, the temperature variation is ordinarily at a large range. The temperature sensitivity of the structure induced a wavelength shift, which has great influence on DL. In this instance, the temperature crosstalk and strain sensitivity play dominant roles in affecting the DL.
The method to improve the DL for wide temperature variation range is to decrease the temperature crosstalk and increase the strain sensitivity. However, the strain sensitivity is generally in conflict with temperature crosstalk. On one hand, many sensing structures, such as the temperature compensation sensor based on double sensing heads [20], the air–hole structure of the pure silica photonic crystal fiber [21], and air-cavity FPI structure based on cantilever [22], have been proposed to decrease the temperature crosstalk. However, the temperature crosstalk has been decreased on sacrifice of the strain sensitivity (less than 10 pm/με). Then, the DL of such fabricated strain sensors are still not improved effectively. On the other hand, the materials-coated Fiber Bragg Gratings [23, 24] and short air–cavity FP sensors [25–27] can preferably increase strain sensitivity. But the high temperature cross–sensitivity (more than 10 pm/°C) restricts further improvement of the DL. In the reported paper [28], although we have further increased the strain sensitivity up to 841.59 nm/N (about 558.8 pm/με), the temperature crosstalk is still as high as 11 pm/°C. Therefore, the sensing structure to realize ultra-low temperature crosstalk combined with the ultra-high strain sensitivity is imperative to be constructed.
In this paper, the capillary–taper temperature compensation structure was proposed to achieve ultra-low temperature crosstalk and ultra–high stain sensitivity at the same time. The thermal expansion of the structure was simulated by using finite element analysis method. The results showed the existence of length matching condition between capillary and taper can realize zero temperature crosstalk. To achieve the length matching condition accurately, the insertion controller system with the high accuracy of 0.02 µm was set up. Then, the capillary–taper temperature compensation structure with the temperature crosstalk of only 0.05 pm/°C was realized successfully. Meanwhile, owing to the inherent advantage of capillary–taper structure, its stain sensitivity is as high as 214.35 pm/με, and the actual DL of 0.047 με was confirmed by the “ladder-mode” and repeatability experiments. The DL is even better than the obtained DL in reported paper [27].
2. Principle and simulation
The schematic diagram of the sensing structure is shown in Fig. 1, where ΔL is the length of interference–cavity, L1 is the length of capillary and L2 is the length of taper. The end face of taper and single mode fiber can form Fabry–Perot cavity.
The interference–cavity can be regarded as standard Fabry–Perot cavity. Then, the center of the mth order interference peak wavelength can be expressed as [22]:
Where m is an integer, λm is the wavelength of the dip, n is the refractive index of material filled in the Fabry–Perot cavity. When the temperature T is applied on the sensing structure, the temperature crosstalk of structure can be described as:Here, the value of ∂L/∂T related with length can be obtained from the simulation, and the shape effect of material has been considered. By putting ST = 0 into the Eq. (2), the condition to realize zero temperature crosstalk can be expressed as:The finite element analysis method was utilized to simulate the thermal expansion of taper and capillary at different temperatures, respectively. The temperature effect on the sensing structure can be respectively regarded as free thermal expansion process of taper and capillary. The taper consists of smaller diameter part and larger diameter part, as shown in Fig. 1. Because the length of larger diameter part that contributes to sensing is extremely short relative to the whole active length, the effect to length matching condition can be ignored. Then, the taper and capillary can be regarded as solid and hollow cylinder in simulations, respectively. Their three-dimensional model diagrams were set up as shown in Figs. 2(a) and 2(b), respectively. The diameter and length of solid cylinder were set as 40 μm and 1000 μm, respectively. The external diameter, inner diameter and length of hollow cylinder were set as 125 μm, 50 μm and 1000 μm, respectively. The variation of temperature was set as 100 °C. The thermal expansion coefficient of taper and capillary were set as 5.50 × 10−6 /°C and 5.05 × 10−6 /°C. The simulation results are shown in Figs. 2(c) and 2(d), respectively. We can see that the capillary and taper expanded when they were heated, and the thermal expansion amount of them are 0.05033 μm and 0.05061 μm obtained from the exported simulation data, respectively.
Fig. 2 (a) Three-dimensional model diagram of the capillary. (b) Three-dimensional model diagram of the taper. (c) Simulation results of the capillary with length of 1000 μm. (d) Simulation results of the taper with length of 1000 μm.
To obtain the value of ∂L1/ ∂T1 and ∂L2/ ∂T2 at fixed lengths of capillary and taper respectively, the temperature variations were set from 100 °C to 1000 °C with interval of 100 °C at fixed structural parameters. At each temperature step, the thermal expansion amount can be calculated by the simulation. The results show that the thermal expansion amount is linear correlated with the value of temperature variation, and the slopes are the value of ∂L1/ ∂T1 and ∂L2/ ∂T2, which are both invariable for fixed length of capillary and taper, respectively. The length of capillary and taper were set from 500 μm to 1000 μm with the interval of 50μm, the values of ∂L1/ ∂T1 and ∂L2/ ∂T2 can be obtained at each length by using the same method. Finally, the relations between values of ∂L1/ ∂T1, ∂L2/ ∂T2 and length were obtained, respectively. They were both linearly fitted as shown in Fig. 3. By putting the linear relations into Eq. (3), the condition to realize zero temperature can be simplified into:
Here, we define f (L1, ΔL) as the matching function which is related with the length of capillary and taper, and when the length of capillary L1 is determined, the length of interference–cavity ΔL is uniquely identified.In the practical application, the interference spectrum is generally monitored by using the optical spectrum analyzer (OSA) and broad-band light source (BBS). The wavelength range of commercial BBS is approximate 200 nm. To make sure at least one entire interference peak locates in the wavelength range of BBS, the length ΔL of interference-cavity needs to be more than about 5 μm [29]. Based on [28], the strain sensitivity of this kind of structure is as below:
Where A is the cross-sectional area, E is the definition of Young’s modulus. Combine with Eq. (4), on the condition that f (L1, ΔL) = 0, the strain sensitivity increased with the decreasing of ΔL. Meanwhile, to achieve the structure with both zero temperature crosstalk and high strain sensitivity, the length ΔL of interference-cavity is selected as about 5~7 μm, and the corresponding capillary length L1 should be around about 1000μm. Therefore, in this paper, the capillary length L1 is chosen as 1000 μm. The corresponding interference–cavity length ΔL is calculated to be 6.19 μm from Eq. (4). By putting A = 0.01 mm2, L1 = 1000 μm, ΔL = 6.19 μm and E = 72.9 GPa into Eq. (5), the strain sensitivity is calculated to be about 228.08 pm/ɛµ, which is much higher than that of strain force sensors based on the common fiber inline FP micro-cavities [4–6]. In addition, we can see from Eq. (4) that if the shapes of both capillary and taper are determined (equate to that a1, a2, b1 and b2 are determined), the optimal stain sensitivity satisfying Eq. (4) is fixed. If the shapes of both capillary and taper are further optimized, the stain sensitivity can be higher.3. Fabrication and experiment
The sensing structure can be fabricated by three steps. In the first step, the taper was fabricated by the two-step arc discharge tapering method which has been reported in [28]. The fabricated taper is cut to produce a taper fiber tip, as shown in Fig. 4(a), we can see that, the taper fiber tip consists of two parts with different diameters of approximately 50 µm and 30 µm, and the taper with different diameters can be available by changing the pulling speed. The bigger diameter part that contributes to the sensing structure is extremely short relative to the whole active length, and it rarely affects the matching function. Besides, it must be noted that, cutting the taper is more difficult than cutting the common single-mode fiber (SMF). A new and sharp blade is better to be used to cut the taper fiber and to be cleaned in the ultrasonic cleaning machine to avoid the influence of dust. When we put the fiber taper on the optical fiber cleaver, we found that the fiber taper is more easily to bend compared with SMF. It will affect the cutting effect. Therefore, in the process of cutting, the two ends of the taper fiber need to be placed horizontally to keep the taper fiber naturally straight. Besides, the flatness of the fiber end surface at cutting position is affected by the height of the blade. Due to the smaller diameter of the taper, the distance between fiber taper and blade becomes longer than that between SMF and blade, which leads to a shallow notch on the fiber taper. Therefore, the height of the blade also need to be adjusted. Through several times practicing and testing, the suitable height has been explored in our experiments.
Fig. 4 (a) The micrograph of taper. (b) The micrograph of SMF with capillary. (c) The structure of accurately inserting controller. (d) The reflection spectra of the cavity variation with the tiny displacement. (e) The relationship between the push distance of three dimensional platform and advance distance of taper.
In the second step, a section of capillary was spliced to the end face of SMF as shown in Fig. 4(b). The external and inner diameters of capillary are 125 μm and 50 μm, respectively. In the above two steps, the lengths of the taper fiber tip and capillary can be controlled approximately into the target values (e.g. 1000 μm) by using cutting platform with the accuracy of 10 μm. And the actual length of the capillary can be measured by using the microscopic system. For example, five capillary structures were achieved by using this method, and their measured lengths are shown in Table 1. These values are all ranged from 990 μm to 1000 μm.
Table 1. Detailed parameter values of five fabricated structures
In the third step, the taper was inserted into the capillary to form the interference-cavity. To make sure the actual interference-cavity length can meet the match function, the accurate insertion controller system shown in Fig. 4(c) was set up and employed. The fusion splicer plays the roles of both collimation and fusion. The manual three-dimensional displacement platform assists to push the taper into the capillary steadily. It is worth mentioned that the high damping controller in the set up can improve the accuracy of advance distance greatly. When the three-dimensional displacement platform pushes the taper along the axial direction of the fiber for a distance, due to the effect of high damping controller, the actual variation of the inference cavity length is far less than the pushing distance of the three-dimensional displacement platform. The actual variation of the inference cavity length can be calculated by monitoring the central wavelength shift Δλm as below [29]
Where n is the refractive index of the material filled in the interference-cavity, and here n = 1. For example, the three-dimensional displacement platform continues to push from 0 µm to 90 µm with the interval of 10 µm, the interference peak shifts towards the longer wavelength direction as shown in Fig. 4(d), and the actual cavity length variations can be obtained by Eq. (6). Then, the relation between the pushing distance of the three-dimensional displacement platform and the length of the interference-cavity can be obtained by experiments as shown in Fig. 4(e). The experimental results were linear fitted. From the Fig. 4(e), we can see that, the length variation accuracy can be improved to 0.02 µm by using the method above. However, the capillary will collapse slightly after the arc discharge splicing process. Therefore, the fabrication accuracy of the interference-cavity length can reach at least 0.1 µm.In the process of insertion, to increase the insertion speed, the taper was firstly inserted without the effect of high damping controller until the cavity length is closed to the target value estimated preliminarily by using the microscope. The current actual length of the interference-cavity can be calculated accurately from Eq. (7) by using the center wavelength values λm and λm + 1 of the adjacent inference peaks in the reflection spectrum. Then, the taper was inserted continuously with higher accuracy by launching high damping using the method mentioned in the above paragraph until the cavity length reached to the target value accurately. Finally, the electrodes were placed near the end face of the capillary, and the taper fiber tip was spliced with the capillary by arc discharge between the electrodes. By using the above procedure, capillary-taper temperature compensation structure can be fabricated successfully.
One fabricated structure is shown as Fig. 5(a). The capillary and taper length of this structure was fabricated based on the matching equation. The actual length of capillary and interference-cavity are 998 μm and 6.2 μm respectively, and two reflecting surfaces of the interference-cavity are parallel well to each other. The reflection spectrum with contrast of approximately 10 dB was obtained as shown in Fig. 5(b). Then we fabricated another four different structures, and the detailed parameter values of fabricated structures were shown in Table 1. To verify the correctness of the theory, the structure B and C are with the negative matching function values and the structure D and E are with the positive matching function values. Their micrographs and reflection spectra are shown in Figs. 5(c)–5(f). We can see that the free spectrum range increases with the decreasing of the length of interference-cavity.
Fig. 5 (a) The micrograph of the structure A. (b) The reflection spectrum of the structure A. (c)-(f) The micrographs and the reflection spectra of structures B–E.
4. Experimental result and discussion
To investigate the temperature crosstalk of the fabricated structures mentioned above, the five structures were placed in the tube furnace heater, which were heated from 20 °C to 270 °C in the step of 50 °C. At each temperature step, the reflection spectra of the five structures were measured by an OSA (AQ6370B) and BBS (1200 nm to 1700 nm) through a circulator after the temperature had been steady for 20 minutes. The measured reflection spectra of the five sensing structures at each step are as shown in Figs. 6(a)–6(e), respectively. As the temperature increased by 250 °C, the interference peak of structure A hardly seems to shift at all. The interference peaks of structures B and C shifts to shorter wavelength direction for 1.19 nm and 0.75 nm respectively, while the interference peaks of structures D and E shifts to longer wavelength direction for 0.96 nm and 1.08 nm respectively. The reflection spectra changing of all the five structures are as same as the theoretical prediction mentioned above. Besides, the five structures all show perfect linear response to the temperature as shown in Fig. 6(f). The temperature sensitivities of the five structures are –0.05 pm/°C, –4.8 pm/°C, –2.5 pm/°C, 3.7 pm/°C, and 4.34 pm/°C, respectively. They generally accord with the calculated values. The temperature crosstalk of structure A is close to zero, because its capillary length and interference-cavity length approximately satisfy the matching function. In addition, the function values of f (L1, ΔL) were set from –64 to 104 with the interval of 4. The temperature crosstalk at different function values of f (L1, ΔL) can be calculated by the simulation mentioned above, and the results are shown in Fig. 6(g). From Fig. 6(g) we can see, the calculated results and experimental results are with the same changing trend.
Fig. 6 (a)–(e) The temperature response of the structure A–D. (f) The strain response of the five structures. (g) The contrast between simulation results and experiment results to temperature response.
To investigate the strain sensitivity of the structures, the free end of the SMF containing the structure was loaded by different weights, which induced the strain force of the SMF. The strain force of 1 N applied on the structure will generate the strain of about 1506 µɛ [28]. The five structures mentioned above were all tested in the experiments. The sensing structures were loaded by the weights from 0 to 9 g (giving a strain of 132.82 με) with interval of 1 N (giving a strain of 14.76 με). The relations between center wavelength shift and the strain were recorded by using the method mentioned before, and the results are shown in Fig. 7(a). We can see that five structures all show perfect linear response to the strain force. The strain sensitivities of the five structures are 214.35 pm/με, 332.98 pm/με, 234.7 pm/με, 95.35 pm/με and 84.35 pm/με, respectively, and they are approximately proportional to the value L1/ΔL. More importantly, for the structure A, the high strain sensitivity of 214.35 pm/με and low temperature crosstalk of 0.05 pm/°C can be realized at the same time. Therefore, the DL can be greatly improved in the wide temperature range.
Fig. 7 (a) The relationship between the interference wavelength dip shift and the strain for structures A–D. (b) The “ladder-mode” experiments: the structure was loaded with 0.23 με, 0.14 με, 0.047 με and 0 με, respectively to measure the reflection spectra for 20 min at each step. (c) The fluctuation of structure A without loading. (d) The repeatability experiments.
Then, to show the responses of the structure to the small strain changes, the structure A was chosen to be tested in the experiment known as “ladder-mode”. The structure A were loaded by different weights inducing the strain of 0, 0.047 με, 0.14 με and 0.23 με, respectively. At each loading weight, the structure A was kept for 20 minutes, and its reflection spectra were recorded repeatedly with the interval of 30 s. The results are shown in Fig. 7(b). We can see that the interference wavelength dip shifts to longer wavelength direction with the increasing of strain. The wavelength values of interference dip wave around certain value when the loaded weight is fixed. While the wavelength values of interference dip changed suddenly when the loaded weight is variety, and the wavelength range of interference dip with different loaded weights were separated with each other. The interference dip wavelength values of the structure A loaded by nothing were shown in Fig. 7(c). We can see that the interference dip wavelength exists a degree of fluctuation. The fluctuating range is from 1375.156 nm to 1375.166 nm. Then, the wavelength shift noise of the whole system is approximately 10 pm.
To test the repeatability of structure at tiny strain variation, the structure A is loaded by a bit of fiber with weight of 3 × 10−5 N (giving a strain of 0.047 με) and loaded by nothing periodically, and the reflection spectra were measured for twenty periods by the same method before. The results are shown in Fig. 7(d). The red points stand for the structure loaded by weight of 0.047 με, while the black points stand for the structure loaded by nothing. We can see that the wavelength shifts periodically with the periodical actions. The red point and black point in a period are separated, and there is an obvious gap between all red points and black points. The minimum space between the red points and black points is approximate 2 pm. The experimental results show the perfect stability. What’s more, the actual DL of at least 0.047 με can be confirmed in the experiment, and it also can be confirmed in Fig. 7(b). In conclusion, the actual DL of better than 0.047 με were demonstrated by the above two experiments. Assuming that the structure was used in a wide temperature variation range of 100 °C, the temperature-induced wavelength noise of structure is only 5 pm, which is equivalent to the strain noise of 0.023 µɛ. This value is smaller than the obtained DL of 0.047 µɛ confirmed by the experiments mentioned above in this paper. It means that the wide temperature variation has a little effect on the DL of proposed fiber structure in this paper. Therefore, the proposed sensor of capillary-taper structure was very suitable for measuring the tiny change accurately in the wide temperature range.
5. Conclusion
In conclusion, we proposed a strain sensor with both ultra-low temperature crosstalk and high strain sensitivity based on the capillary-taper compensation structure. The matched length condition of the structure to achieve zero-temperature-crosstalk can be obtained from the simulation, and it can be realized by using the insertion controller system. The fabricated strain sensor exhibited an excellent performance on the measurement of the strain owing to its ultra-low actual DL (0.047 με), ultra–high sensitivity (214.35 pm/µɛ), perfect linearity (99.99%) and ultra-low temperature crosstalk (0.05 pm/°C).
Funding
National Natural Science Foundation of China (11504070, 11574063 and 11374077); The Science and Technology Development Plan of Weihai (2015DXGJUS002).
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