1. Introduction

Multi-parameter sensors have become an important topic in fiber sensing. This is not only because the sensing structure can minimize the complexity, cost and size of the sensing system, but also it can solve the crossing-sensitivity issue of the sensing parameters. The principle of the multi-parameter sensors is often based on the sensing head having different sensitivities to the physical parameters. And the simultaneous measurement of the force or strain and temperature is a crucial application of optical multi-parameter sensors. Many techniques have been reported for simultaneous strain and temperature measurement. Fiber Bragg gratings (FBG) or long-period gratings (LPG) as the popular sensing elements have been widely used in the sensors, such as a grating written in the birefringence fiber [1] or the splice region of different fibers [2,3], a superstructured FBG [4], two FBGs inscription in the different fibers [5], different types FBGs [6] and so on. The FBG has the specific temperature and strain sensitivities of ~10 pm/°C and 1 pm/με, and the LPG has that of 60 pm/°C and 0.5 pm/με [7]. Besides, some sensing configurations are the combination of a FBG with Mach-Zehnder interferometers (MZIs) [8,9] or high birefringent fiber loop mirror (HiBi-FLM) [10]. In the two interferometers, the length of the sensing fiber considerably affects the sensitivities. Sensitivities of 56.8 pm/°C and 0.84 pm/με are achieved by 24 cm multi-mode fiber in [8], and 1.6 nm/°C and 25 pm/με are obtained by 12 cm HiBi fiber [10]. Such long length sensing fiber causes the sensor not compact. In addition, the FPIs are also one of the most versatile sensing devices due to their simplest configurations and microscopic sizes, among which one kind of FPIs fabricated only by a fusion splicer are demonstrated in [11–13]. The FPI in [13] exhibits a higher strain sensitivity of ~10.3 pm/με with an on-purpose splicing program, which is ~10 times higher than that of popular FBG (~1 pm/με [7]).

In recent years, another kind of photonic bandgap fiber (PBGF), which is implemented by infusing high-index tunable materials into the index-guided photonic crystal fiber (PCF), has been a most promising candidate for temperature and refractive index sensors [14–17]. According to the antiresonant reñecting optical waveguide (ARROW) theory of the PBGF [18], the position of the bandgap is decided by the diameter and the refractive index of the cladding holes. Based on the high thermal-coefficient of some materials, the transmission bandgap possesses high sensitivity to temperature, and a bandgap tuning sensitivity of ~6 nm/°C is achieved in [14]. However, the detection limit is restricted because of the broad transmission bands feature. To solve this problem, some techniques are used to introduce narrow spectral features in PBGFs, for example the LPG inscription [15], the selectively filled PCF-based coupler [16] and the bent controlled PBGF [17]. Nevertheless, the PBGF as well as the above mentioned FPI is rarely used for multi-parameter sensors.

In this paper, we demonstrate a simple dual-parameter sensor simultaneously measuring force and temperature by incorporating a FPI into a high-index-fluid-filled photonic crystal fiber (HIFF-PCF). The FPI is formed through the micro-cavity by splicing one end of the HIFF-PCF to the conventional single mode fiber (SMF) using a fusion splicer. The FP interference and bandgap effect of the HIFF-PCF are combined by a fiber loop. By following the central wavelength and the transmission loss of different interference dips, we obtain a force sensitivity of 3.25 nm/N (strain sensitivity of ~3.9 pm/με) and a temperature sensitivity of −1.94 dB/°C which is more than 46 times higher than that of −0.04249 dB/°C in [19] and −0.0261dB/°C in [4] based on intensity measurement.

2. Experimental setup and principles

The microscope image of the PCF used in our experiments is shown in the inset of Fig. 1(a) , which is fabricated by Yangtze Optical Fiber and Cable Company Ltd. of China. Its cross section includes five rings of air holes arranged in a regular hexagonal pattern and has the air holes diameter of 3.5 μm and the pitch distance of 5.8 μm. We fill the cladding air holes with a kind of high index fluid, produced by Cargille Laboratories Inc., with a refractive index of 1.52 at 589 nm at 25°C and a thermal-coefficient of −0.000407/°C. Thus, the filled PCF has higher refractive index in the cladding than that in the core, and guides light by photonic bandgap effect. The air holes of the two ends of the PCF are left without fluid for reducing the splice loss between the PCF and SMFs. The length of the HIFF-PCF is about 5 cm. A supercontinuum light source with a spectrum range from 600 nm to 1700 nm and an optical spectrum analyzer (OSA) with a highest resolution of 0.02 nm are employed for measurement.

 

Fig. 1 (a) Schematic diagram of the experimental setup. Insets are microscope image of the used PCF and the FPI with the cavity width of 18 μm and height of 40 μm. (b) Transmission spectra of the experimental setup based on the HIFF-PCF combined with the FPI (black symbol curves) and that of the HIFF-PCF (blue curves). Red curves show the reflection spectrum of the FPI.

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Firstly, we measure the transmission spectrum of the HIFF-PCF as the blue curves shown in Fig. 1(b). Two obvious bandgaps from 1456 nm to 1669 nm (bandgap 1) and from 1000 nm to 1207 nm (bandgap 2) are observed. Secondly, the left end of the PCF is spliced to a SMF by controlling splicing parameters, and a micro-cavity is achieved, as shown in the inset of Fig. 1(a). We can see the air holes of the PCF at the right of the splice point are entirely collapse due to a high arc discharge. As a result, a part of air originally inside the voids can be trapped, thus forming a spheroidal air cavity with width of 18μm and height of 40μm. The right end of the PCF is spliced to another section of SMF without air holes collapsing using a low arc discharge. Next, we put the HIFF-PCF combined with the FPI into a fiber loop consisting of an optical coupler with splitting rations of ~46:54 near 1500 nm and ~13:87 near 1100 nm, as shown in Fig. 1(a). The input light is split into two counterpropagating beams by the coupler. A part of the anticlockwise light is reflected by the FPI. The reflection spectrum is measured as the red curves shown in Fig. 1(b). We can see a stable sinusoidal interference pattern with a fringe spacing of 62 nm and a contrast of 18 dB at 1530 nm. According to FP interference principle, the fringe spacing is given by$\Delta \lambda \text{=}{\lambda }^2/2nd$. In our experiment, n and d are the refractive index of the air and the cavity width, respectively. Using the measured cavity width of 18 μm, the calculative fringe spacing is about 65 nm at 1530 nm, which is well matched with the experimental results. As to the clockwise light, it first propagates through the HIFF-PCF, undergoing the transmission loss of the HIFF-PCF, and then a part of the light is reflected by the FPI. This reflection light has high loss that it makes almost no contribution to the output spectrum of the setup. In addition, a fraction of the transmission light propagating through the HIFF-PCF can be detected at the output port. Thus the resultant output spectrum is the superimposing of the FPI reflection light and the detected transmission light, as shown in Fig. 1(b) (black symbol curves). We can see that the same FP interference dips as the red curves shown appear outside of the bandgaps and shallow dips appear in bandgap 1, while, no dips appear in bandgap 2. This is because the transmission light with higher power in bandgap 2 than that in bandgap 1 is superimposed into the FPI reflection light as a result of different splitting ratios of the coupler at the two bandgaps. In addition, the loss of the interference dips (at 1472 nm and 1200 nm) being adjacent to the bandgap edges of the HIFF-PCF are strikingly different from that being far away from the bandgap edges, this would indicates that the loss of dips are affected by the location of the bandgap edges.

3. The temperature and force sensing characteristics

The force response is investigated by bonding weight on one end of SMF spliced to the sensing head at a fixed temperature. The weight’s gravitational force provides the longitudinal force F. The temperature response is investigated by putting the unstrained sensing head into a temperature chamber.

Firstly, we investigate the central wavelength variation of a certain dip via force and temperature. Figure 2(a) shows the transmission spectra of the interference dips under different forces. The inset is the spectra of the interference dip A. It is obvious that the interference dips shift to the longer wavelength with force increasing. The variation of the central wavelength of the dip A dependence on the force from 0 to 1 N is shown as the black circled points in Fig. 2(b), and the black solid line is the linear fit. The strain sensitivity is estimated as 3.25 nm/N (R² = 0.9976). According to the relationship between the axial strain (ε) and force (F): $\epsilon \text{=}F/AE$, where A is the total glass cross-section area of the section fiber that contains the cavity, and E is the elastic modulus of fiber which is about 7.2*10⁴MPa. Thus, the strain sensitivity is about ~3.9 pm/με.

 

Fig. 2 (a) Transmission spectra of the interference dips under different forces. The inset is the dip A. (b) Characteristics of the dip A’s dependence on the force (black circled points) and temperature (blue square points). The black line is the linear fit.

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Then the temperature response of the dip A from 25°C to 70°C is also measured, as shown in Fig. 2(b). We can see the central wavelength has some small fluctuations via temperature. In [11–13], the intrinsic temperature sensitivity of the FPI, which is about 1pm/°C, is referred to, and researchers consider that the temperature-induced strain error is very low that temperature compensation is not necessary. In our experiment, due to the instability of the light source and the limit of OSA’s resolution, no specific temperature sensitivity is achieved. Yet, we can still think that the fluctuations can be neglected compared with the central wavelength variation caused by the force. Hence, we can conclude the interference dip A is almost insensitive to the temperature and linearly sensitive to the force.

Next, the sensing characteristics of the dips, which are adjacent to the bandgap edges, are investigated. According to the ARROW theory [18] and the negative thermal-coefficient of the fluid in our experiment, the bandgap shifts towards shorter wavelength when temperature increases. Thereby, the loss of the interference dip adjacent to the bandgap edge is affected by the shift of the edge. Figure 3(a) shows the output spectra of the sensing setup under temperatures from 25°C to 55°C. The specific variation of the dips’ transmission loss with temperature is shown in Fig. 3(b) using the black symbol points. It can be clearly seen that the loss of the interference dips B, C, D decrease with temperature increasing from 29 °C to 38 °C, from 38°C to 48°C and from 49°C to 57°C, respectively. In a small-scale temperature, the loss variation is approximately linear (the red lines are the linear fit), and the sensitivities are about −1.94 dB/°C, −1.96 dB/°C and −2.29 dB/°C, which gradually increase with temperature increasing. This comes from the dependence of the loss sensitivity on the bandgap shift, whose shift velocity increases with temperature increasing. Compared with the temperature sensors based on intensity measurement possessing sensitivities of −0.0261dB/°C [4] and −0.04249 dB/°C [19], our sensitivity is more than 46 times higher than them. This is also because the high shift-speed of the bandgap in the HIFF-PCF. Furthermore, if the interference dips’ space is smaller, the dip loss variation will be probably located at the linear variation area. This can be achieved via wider micro-cavity formed by controlling the arc discharge. Thus the temperature sensing will be more convenient.

 

Fig. 3 (a) Transmission spectra of the sensing setup at different temperatures. (b) Transmission losses of the dips B, C and D with the temperature, respectively. The red lines are the linear fit of the experimental results.

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The dip loss variation dependence on the force is discussed as well. Since the interference dips would shift with force changing (shown in Fig. 2), combined with a fix bandgap edge, the dips adjacent to the bandgap edge also have loss variation. Figure 4 shows the force response of dip B at a fixed temperature of 31°C. The inset is the output spectra of dip B. We can see the dip loss decreases with force increasing. The black line is the linear fit, and the linear sensitivity is −1.99 dB/N (R² = 99.45%).

 

Fig. 4 The response of the loss of interference dip B to the force at a certain temperature.

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Generally, when the force and temperature are simultaneously applied to the sensing head, the force and temperature variation ΔF and ΔT can be expressed by

Where ΔL_B and Δλ_A are the loss variation of the dip B and wavelength shift of the dip A, respectively. K_TA, K_FA represent the temperature and force sensitivities of the interference dip A, respectively, and K_{FA =} 3.25 nm/N and K_TA = 0. K_TB, K_FB represent the temperature and force sensitivity of the dips loss at B, respectively, and K_FB = −1.99 dB/N and K_TB = −1.94 dB/°C. From Eq. (1), we can determine the two parameters simultaneously by measuring the wavelength and loss change at different wavelengths and by solving the matrix equation,

4. Conclusion

We propose and demonstrate a simple dual-parameter sensor simultaneously measuring force and temperature by combining the FP interference with the bandgap effect of a HIFF-PCF. On the one hand, utilizing the high force-sensitivity and temperature-insensitivity characteristics of the FP interference dips, a force-sensitivity of 3.25 nm/N (~3.9 pm/με) is achieved, which can be further improved by controlling the shape and dimensions of the FPI [18]. On the other hand, taking advantage of the bandgap being high sensitive to the temperature, the dips’ loss has a high temperature sensitivity of more than −1.94 dB/°C, which is more than 46 times than that in [19]. Furthermore, the bandgap still can be achieved if the filling length is just 2 centimeters. This makes the proposed sensor has small size compared with the sensor based on the traditional HiBi-FLM [10]. Hence, the proposed sensor with the advantages of easy fabrication, compact structure, and high fringe contrast provides the potential application in the multi-parameter sensing.