1. Introduction

Optical fiber sensors based on Fabry-Pérot (FP) cavities exhibit several features, which make them suitable for many applications. Besides the simple configuration, these sensors are usually compact, reliable, stable and can be used in multiplexing configurations [1,2]. Depending on their geometry, FP sensors can be classified as extrinsic or intrinsic. In the first case, the FP cavity is formed in the air gap existing between two optical fibers cleaved end faces or between an end face fiber and a mirror. In the last situation, the sensor is formed by an all-fiber FP cavity whose mirrors are produced inside the fiber [3].

In 1992, Claus et al. [4] presented an extrinsic FP sensor for strain and crack opening displacement measurements. This type of configuration was also used to measure gas pressure [5] as well as strain and temperature [6]. Regarding the intrinsic configuration, several manufacturing techniques have been reported. For instance, using the femtosecond laser inscription, FP microchannels were produced and tested for temperature [7] and liquid refractive index [8] measurements. The use of a 157 nm laser to perform micromachining and produce the FP cavities has also been reported. In this case, the sensors were subjected to strain [9] and refractive index [10] variations. A different approach was proposed in 2009 by Villatoro et al. [11]. They reported on a spherical FP cavity produced by splicing a standard single mode fiber (SMF28) and an index-guiding photonic crystal fiber (PCF). A few years later, Favero et al. [12] reported the comparison between spherical and spheroidal microcavities. In both works, strain measurements were performed, and in the last a sensitivity of ~10.3 pm/με was achieved. The FP cavity formed by splicing a section of hollow-core PCF between two SMF28 was reported by Rao et al. [13]. Choi et al. [14] reported a high-temperature sensor based on two FP cavities formed by fusion splicing a short hollow-core fiber between a PCF and a piece of SMF28. Simultaneous measurement of strain and temperature using a small length of suspended core fiber spliced to the end of SMF28 was also reported [3]. More recently, Duan et al. [15] proposed the fabrication of a FP cavity by splicing a short section of SMF28 between two sections of SMF28 with a large lateral offset.

In this work, a Fabry-Perot based on hollow-core ring PCF is proposed. A simple theoretical model is used to demonstrate the dependence of strain sensitivity to the cavity length and the strain gauge length. Several sensing heads are produced and tested to strain. To the best of our knowledge, the sensitivity attained for the smallest FP cavity (~15.43 pm/με) is one of the highest reported so far for low finesse FP interferometers. The sensing head is also subjected to temperature variations.

2. Theoretical principle

The Fabry-Pérot cavity designed and tested in this work was constituted by a small section of hollow-core ring photonic crystal fiber (HCR PCF) spliced between two sections of standard single mode fiber (SMF). Strain measurements were done to a total length of L_T = L_FP + L_SMF, where L_FP stands for Fabry-Pérot cavity length and L_SMF corresponds to the SMF length. It should be noticed that this length takes into account both sections of SMF used in the sensing head fabrication. The following theoretical analysis illustrates the expected behavior of the strain sensitivity towards the total sensing head length as well as the Fabry-Pérot cavity length. The details behind the equations here summarized can be found in reference [16].

Considering that strain is applied at a constant temperature, the fringes of the FP cavity will shift according to the $\Delta {\lambda }_{FP}=k_{\epsilon (FP)}{\epsilon }_{FP}$, where ε_FP is the applied strain and k_ε(FP) corresponds to the strain coefficient. The FP cavities tested here are a few micrometers long, the same order of magnitude of the HCR PCF diameter. Thus, a small change in the length of the sensing head will have consequences in the whole HCR PCF volume. Therefore, the strain loads applied are related by Eq. (1)

Where E stands for the Young modulus of the material (which is the same for the FP cavity and the SMF), and V_FP and V_SMF are the volumes of the FP cavity and SMF, respectively. After some algebraic manipulation, one gets the relationship between the normalized strain coefficient and both FP cavity and SMF lengths:

In Eq. (2), A_SMF is the SMF area and k_ε0 corresponds to the strain coefficient when the sensing head section area is equal to the SMF section area, which was considered to be 0.05 pm/με. Numerical simulations were performed for different FP cavity lengths, as can be seen in Fig. 1 . Different single mode fibers were also considered, whose difference was the fiber diameter. So, diameters of 125 μm, 80 μm and 50 μm were analyzed, which correspond to the commercially available SMF28, SM800 and SM1500, respectively. As the FP cavity length decreases, there is a significant increase in the normalized strain coefficient (see inset Fig. 1). As the FP cavity approaches 40 μm, and decreases furthermore, there is a significant increase on the strain sensitivity.

 

Fig. 1 Theoretical response of the normalized strain coefficient with the Fabry-Pérot cavity length, for three different single mode fibers: SMF28, SM800 and SM1500.

Download Full Size | PDF

On the other hand, from the three SMF diameters considered, the SMF28 turned out to be the best choice in terms of normalized strain coefficient. Thus, this was the fiber used in the experiments.

3. Experimental results

The hollow-core ring photonic crystal fiber (HCR PCF) used in this work presents a hollow core diameter of 44.4 μm and several petal shaped holes with an azimuthal diameter of 24.4 μm. There is a 3.1 μm thick silica ring in between these two structures. The cross section image of this fiber can be seen in Fig. 2 . A small section of this fiber was spliced between two sections of standard single mode fiber (SMF28), thus constituting the Fabry-Pérot cavity. The splices were done with the manual program of the splice machine, according to the details described in [17]. In order to avoid collapsing the HCR PCF holes, a horizontal offset was done. Thus, the splices were mainly applied in the SMF28 region. The FP cavity spectral response was measured in reflection according to the experimental setup scheme also exhibited in Fig. 2. It was constituted by a broadband optical source which had a bandwidth of 100 nm at 1550 nm, an optical spectrum analyzer (OSA ANDO AQ-6315B) with 0.5 nm of resolution and an optical circulator.

 

Fig. 2 Scheme of the experimental setup. The micrographs presented are the cross section of the large hollow core photonic crystal fiber and the longitudinal image of the 207 μm long Fabry-Pérot cavity.

Download Full Size | PDF

The period of the FP cavity fringes depends on its length, according to the equation $1/{\lambda }_2-1/{\lambda }_1=1/2nL$, where λ₁ and λ₂ are the peak wavelengths of two adjacent fringes, n is the medium effective refractive index where light is travelling and L corresponds to the FP cavity length.

The average effective refractive index was estimated to be 1.0023 for a wavelength operation at 1550 nm. Four sensing heads were made, with different FP cavity lengths. The spectral behavior is shown in Figs. 3(a) -3(d). The smallest sensing head was 13 μm long and presented only one of interferometer peaks. The remaining sensing heads, which were 35 μm, 207 μm and 906 μm long, exhibited an interferometric period of 35.30 nm, 6.03 nm and 1.30 nm, respectively. All sensing heads were characterized in strain, at room temperature, being subjected to the same test conditions. Thus, the fiber was attached to a translation stage with a resolution of 1 μm. The experiment was done with a total length, composed by SMF28 and the HCR PCF, of ~700 mm. Figures 3(a)-3(d) show the spectral behavior of the different sensing heads as strain is applied. The shift towards longer wavelengths (red shift) indicates that there is an increase in the optical path with strain. The wavelength responses of the different sensing heads are exhibited in Fig. 4(a) . From this figure it becomes clear that the sensing head length highly influences the strain sensitivity. In fact, the smaller the sensing head, the higher its sensitivity. For the 906 μm long sensing head, a sensitivity of 3.12 pm/με was attained, whereas for the 207 μm long, a sensitivity of 3.79 pm/με was achieved. However, for the 35 μm long sensing head, the sensitivity was doubled, being of 6.16 pm/με. Decreasing even further the cavity length, to 13 μm, a sensitivity of 15.43 pm/με was attained. Thus, by choosing the appropriate FP cavity length, it is possible to monitor the sensitivity most suitable for the application in question.

 

Fig. 3 Spectra of the four different sensing heads. The FP cavity lengths are a) L_FP = 13 μm, b) L_FP = 35 μm, c) L_FP = 207 μm, d) L_FP = 906 μm. The spectrum shift with the applied strain is also present for each sensing head.

Download Full Size | PDF

 

Fig. 4 (a) Wavelength variation upon applied strain, for the four sensing heads. (b) Variation of sensitivity with the FP cavity length, considering both theoretical curve and experimental values; inset: photograph of the 13 μm long sensing head.

Download Full Size | PDF

Figure 4(b) presents the measured sensitivities as a function of the FP cavity length (blue dots) and the theoretical behavior previously studied (gray line). There is a good agreement between both results.

Once the influence of the FP cavity length on the strain sensitivity was studied, a different theoretical and experimental study was performed. Thus, using the same equations as before, the strain sensitivity was estimated as a function of the total fiber length. As the total length increases, there is an enhancement of the sensitivity (see the gray line in Fig. 5(b) ). However, the variation is only 0.12 pm/με for a total length increase of ~54 mm. Thus, the total length should be taken in account to improve the sensitivity; however, this is not the most important parameter for this matter.

 

Fig. 5 (a) Wavelength variation upon applied strain, for the 207 μm long FP cavity, considering three different total lengths: L_T = 706 mm, L_T = 342 mm and L_T = 170 mm. (b) Variation of sensitivity with the total length, considering both theoretical curve and experimental values.

Download Full Size | PDF

Experimentally, the same sensing head, with a FP cavity length of 207 μm, was subjected to strain with a total length of 706 mm, 342 mm and 170 mm. The results are shown in Fig. 5(a). The behavior is similar and the sensitivities obtained are close to each other, as theoretically expected: 3.79 pm/με, 3.75 pm/με and 3.67 pm/με for a length of 706 mm, 342 mm and 170 mm, respectively. Figure 5(b) presents the strain sensitivity obtained experimentally, which is in good agreement with the theoretical curve also presented in the same Figure.

The same sensing head was placed inside a tubular oven, and subjected to temperature variations from the room temperature (~26 °C) until 83 °C. The error associated with the temperature readings was smaller than 0.1 °C. The wavelength dependence towards this measurand is shown in Fig. 6(a) and 6(b). From this figure, it can be stated that this sensing head is insensitive to temperature variations, as the sensitivity was only of 0.81 pm/°C and is similar to a silica tube [18]. However, for a correct compensation it is possible to use two different cavities: one similar to the cavity presented in this work and the other obtained by cutting the SMF with a small length based on the configuration proposed by Rao et al [19].

 

Fig. 6 a) Spectra of the 207 μm long sensing head when subjected to temperature variations. b) Wavelength dependence with temperature.

Download Full Size | PDF

The strain sensitivities of different cavity structures are presented in Table 1 . Comparing this new structure with the ones already reported some advantages are evidenced. The FP cavities response to strain are reported to be independent of the cavity size. However, in this work there is a remarkable dependence, which is shown both theoretically and experimentally. In the case of hollow core PCF or silica tube based structures, intermodal interference can occur [20,21]. Nevertheless, in this case the interference does not depend on the cavity size. Besides, comparing this new structure with a silica tube with similar dimensions, it presents higher sensitivity to strain due to its dependence with transversal area and the cavity length. The small holes around the central large one allow to significantly enhance the sensitivity towards this measurand. Finally, with this two-wave interferometer the best strain sensitivity has been attained, to the best of our knowledge. Relatively to the temperature sensitivity, it is similar to the one obtained with a silica tube based configuration [18].

Table 1. Strain sensitivity for different cavities structure

View Table

4. Conclusion

Summarizing, a study of the Fabry-Pérot (FP) cavity length dependence towards strain measurements was performed. The FP cavity was based on a hollow-core ring PCF and its manufacturing was quite simple. The two-wave interferometer obtained presented an increase of strain sensitivity as the FP cavity was reduced. The 13 μm long FP cavity exhibited a sensitivity of 15.43 pm/με, which is one of the highest values reported so far. A study of the dependence of the strain sensitivity upon total length variation was also done. Even though this value was not highly influenced by the mentioned parameter, higher total lengths originated better strain sensitivity. When compared to other papers, this structure has achieved an increase of ~50% of strain sensitivity. This configuration can be used to measure different parameters, namely pressure, axial deformation as well as other parameters with indirect measurement to strain. Finally, the FP cavity exhibited low thermal sensitivity.