1. Introduction

In-fiber Fabry-Perot interferometers (FPIs), also referred to in literature as in-line FPIs or intrinsic FPIs, are formed by two parallel surfaces perpendicular to the outer surface of the fiber, and have been successfully used in several sensing applications. Because they are fiber-based, these sensors can tolerate temperature variations, high pressure and strain; they are less affected by corrosion, while still maintaining their physical integrity [1,2]. They are compact and usually have simple configurations [3,4]. Several technologies have been introduced to construct in-fiber FPIs, such as simply placing a coating at the end of the fiber [5], chemical etching [6] and splicing technology [7]. Islam et al. provide a thorough review of optical fiber FPIs and their applications [8].

In-fiber FPIs can be used in most of the applications where Fiber Bragg Gratings (FBGs) are used for direct or indirect sensing of physical quantities such as strain, pressure, acceleration and magnetic fields; however, in-fiber FPIs have been demonstrated to have about one order of magnitude lower sensitivity to temperature than FBGs (1.1 pm/°C [9] versus 10 pm/°C [10], respectively). The strong temperature dependence presented by FBGs has been explored in several temperature sensing applications, but may introduce cross-noise when the application involves sensing of another quantity. For this reason, FBG sensors often need some type of temperature compensation scheme [11–13], which usually increases the complexity of the system.

In this paper, we discuss an in-fiber FPI built by splicing a short section of capillary optical fiber between two single mode fibers to create a cylindrical air-cavity inside the fiber [4]. The in-fiber FPI was tested as a strain sensor, showing desirable high response to axial strain and low temperature sensitivity. To build the magnetic field/force sensors, we used two different configurations that previously had been used to build FBG-based sensors, but by placing the FPI where the FBG had been used. For the first configuration (for magnetic field sensing), the FPI was attached to the surface of a rectangular-shaped magnetostrictive material [14]. For the second configuration (for magnetic force sensing), the fiber was inserted inside a small magnet [15].

2. FPI construction and characterization

A Fujikura fusion splicer, model FSM-30S, was used to splice short sections (25 μm - 650 μm) of capillary fiber between two standard single mode fibers (SMF-28), resulting in cylindrical air-cavities. The capillary fiber used had outer diameter equal to 125 µm and a central hole with diameter equal to 75 μm (inner walls with thickness equal to 25 μm). The procedure consisted of splicing a long section of the capillary fiber to a single mode fiber, cleaving the capillary fiber under an optical microscope to achieve the length desired for the air-cavity, and then splicing the cleaved side of the capillary fiber to another single mode fiber. The repeatability for air-cavity length obtained was found to be good, as long as the relevant parameters for the splicer were used with the optimum values (arc and pre-arc power, time, splicing angle, etc.). Figures 1(a) and 1(b) shows images of typical air-cavities obtained, with length (L) of 25 µm and 200 µm, respectively.

 

Fig. 1 Air-cavities of length of (a) 25 µm and (b) 200 µm (microscope image). (c) Back-reflected signal for an in-fiber FPI formed by an air-cavity of 60 µm. (d) Back-reflected signal for an in-fiber FPI of air-cavity of 25 µm shifting with applied longitudinal strain.

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The signal back-reflected by an in-fiber FPI has the typical interference pattern shown in Fig. 1(c). The Free Spectral Range Δλ_FSR is related to the length L of the air-cavity by

According to Eq. (2), we can expect a lower sensitivity to temperature changes for the in-fiber FPI when compared to FBGs because the wavelength shift with temperature for the FPI is proportional to the thermal expansion coefficient α, whereas for the grating the dominant contribution is from the thermo-optic effect λ₀(1/n)(δn/δT)ΔT, where (δn/δT) is about an order of magnitude greater than α [16].

We measured the temperature sensitivity of our FPI sensors built with different air-cavity lengths (25 μm, 100 μm, 150 μm, 160 μm and 200 μm) with a tubular furnace (MicroTube, model FE50RPN) with uncertainty in temperature of the order of 0.1°C and an optical interrogator (FiberSensing, FS42 BraggMeter) with wavelength accuracy of 1 pm over the range from 1510 nm to 1590 nm. The wavelength shift ${\lambda }_0^C$ was obtained as a function of temperature. All air-cavities lengths tested exhibited temperature sensitivity in the range between 0.8 pm/°C and 1.1 pm/°C. which is similar to the results reported for a silica capillary tube [17]. Figure 2(a) shows the wavelength shift for the FPI with air-cavity of 25 μm (sensitivity ~0.8 pm/°C). Considering solely the effect of the thermal expansion for fused silica, α = 0.55 x 10⁻⁶/°C [16], and using Eq. (2) and λ = 1541 nm, for example, the calculated temperature response is 0.85 pm/°C which is within our experimental error.

 

Fig. 2 (a) Wavelength shift as a function of temperature for an FPI of air-cavity length equal to L = 25 μm (${\lambda }_0^C$) and for a typical FBG (Δλ^B). (b) Longitudinal strain applied to the in-fiber FPI: wavelength shift (${\lambda }_0^C$) as a function of applied strain for air-cavities with length equal to 25 µm, 55 µm and 150 µm.

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For comparison, Fig. 2(a) also shows the Bragg wavelength shift for an FBG tested at the same time, where the sensitivity was ~12 pm/°C, inside the typical range found in the literature [10]. Note that all FBGs used in the experiments in this paper were written on photosensitive fiber, and exhibited typical FBG temperature and strain sensitivity. A 1cm long section of coating was removed before the FBGs were written, and the fibers were not recoated.

For the strain characterization, a short section of fiber on each side of the air-cavity was uncoated; one side was glued to a fixed stage while the other side was glued to a translation stage (adhesive Loctite® 416 was used), as can be seen in the inset of Fig. 2(b). Longitudinal strain was applied to the fiber by moving the stage, while the reflected signal was monitored by an optical interrogator (Micron Optics, model sm125-200) with wavelength accuracy of 10 pm from 1520 nm to 1570 nm. The graph in Fig. 2(b) shows the wavelength shift for air-cavities of 3 different lengths with applied strain from 0 µɛ to 1200 µɛ. As can be seen, ${\lambda }_0^C$ shifts linearly with strain.

The strain characterization of our air-cavities showed that shorter air-cavities have higher strain sensitivities (9.5 pm/με for L = 25 μm, 6.6 pm/με for L = 55 μm, and 4.8 pm/με for L = 150 μm), with a length dependence behavior similar to [18], where the relationship between the strain and the FP cavity length is demonstrated. Also, typical strain sensitivities reported for FBGs (~1.0 pm/με [19]) are lower than the sensitivities obtained for our in-fiber FPIs with the air-cavities lengths tested. Regarding the mechanical resistance of our air-cavities, they were tested with strain over 2000 µɛ and did not show any sign of damage.

Cavities with different geometries and much more elaborated fabrication processes have been built [9, 20, 21]. Coating and pre-treating the tip of the fiber, the use of photonic crystal fibers, and creating cavities by means of air bubbles can increase the sensitivities. All of these techniques are aiming at creating an air-cavity with minimum length and minimum wall thickness, since the sensitivity also increases inversely with the cross-sectional area of the fiber. The best sensitivity for an in-fiber FPI reported so far is for a cavity wall thickness of 1 µm: 43 pm/µɛ for a cavity length of 61 µm [21]. Nevertheless, our device presents the simplest fabrication technique, and good sensitivity with better controllability during the manufacturing of the air-cavity.

3. Magnetic field sensors

Magnetic field sensors based on fiber optics and different techniques have been investigated, among which Fabry Perot interferometry with extrinsic [22–24] and intrinsic cavities. Sensors using extrinsic cavities may present high sensitivity to magnetic fields by using magnetic fluids [25] and magnetostrictive materials [26] as sensing elements, reaching sensitivity up to 117 pm/mT or resolution of 50 nT for some cases. Intrinsic FPIs can be formed by building an air-cavity contained in the fibers such as hollow-core or photonic crystal fibers [3, 27–29] or by creating spherical air-bubbles inside the fibers during the fusion splice [9, 30, 31].

In this work we propose two configurations for magnetic field sensors based on the intrinsic FPI discussed in Section 2 of this paper. We believe our FPI presents advantages when compared to other techniques used for magnetic field sensing because its construction method is straightforward, yielding reliable sensors with good sensitivity to strain and low sensitivity to temperature.

The first magnetic field sensor proposed is shown schematically in Fig. 3(a). The sensor is constructed by attaching a section of the optical fiber containing the in-fiber FPI to a 4 mm × 4 mm × 20 mm cuboid of TX (Tb_0.3Dy_0.7Fe_1.92), a magnetostrictive material [14, 32], as shown in Fig. 3(b). The cuboid is then placed inside the Teflon® case. For comparison, an FBG was also attached to the TX sample, next to the in-fiber FPI. Both FPI and FBG were placed close to each other and in the center of the cuboid. Adhesive Loctite® 416 was used.

 

Fig. 3 (a) Schematic of the magnetostrictive sensor built with the FPI. (b) Photograph of TX with the FBG and FPI attached. (c) Wavelength shift as a function of magnetic field applied for an FPI (${\lambda }_0^C$) and an FBG (Δλ^B) attached to a TX sample of size 4mm x 4mm x 20mm.

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The device was tested by placing it in the central region of an electromagnet (GMW Magnet Systems 3470), such that the in-fiber FPI and the FBG were located as close as possible to the center of the spatially uniform magnetic field. A Hall-effect based magnetometer (F.W. Bell 5080) was used to measure the applied field to the sensing element. Figure 3(c) shows typical results obtained for the samples tested. The variables monitored in this test were ${\lambda }_0^C$ for the in-fiber FPI and Δλ^B for the FBG. The wavelength shift of the reflected signal is shown for applied magnetic fields from approximately 2 mT to 80 mT for an FPI with air-cavity length of 40 μm together with an FBG centered at 1523 nm. As can be seen, a sensitivity of 44 pm/mT was obtained for our FPI, which is more than four times the sensitivity obtained for the FBG. Several samples were tested with different air-cavity lengths. As with the strain results obtained in the previous section, the sensitivity to magnetic field increased as the air-cavity length decreased.

Note that the strong nonlinearity observed in Fig. 3(c) is due to the original magnetostrictive response of the TX sample. A more linear response can be obtained by applying a determined amount of pre-stress to the sample [33]. Nevertheless, in order to work on the maximum sensitivity range a biasing field must always be present. Also, it should be mentioned that all samples were tested for negative and positive fields. Only positive field values are shown in the graph of Fig. 3(c) because, since, magnetostriction is a unipolar phenomena, both positive and negative values of magnetic field generate a positive magnetostriction response. However, the presence of a biasing field will enable us to discriminate when a positive or negative magnetic field value is applied to the sensor.

The second type of device built was a magnetic force sensor that transfers magnetic force into strain. It was built by gluing a small cylindrical magnet, which had been magnetized in the axial direction, to the loose end of the optical fiber containing the FPI. SmCo magnets (Logimag, Ltd.) with 3.0 mm in diameter and 5.0 mm in length were used. A small hole in the center was drilled in the magnet for one end of the fiber to be inserted into and glued. As observed in the schematic in Fig. 4(a), the optical fiber and magnet were encapsulated by a Teflon® cylinder with a guiding cavity. The Teflon® cylinder served three purposes: to protect the FPI, to minimize friction, and to keep unwanted ferromagnetic parts away from the magnet. The loose end of the fiber was passed through an acrylic support and glued to it, so that the FPI was located between the acrylic and the magnet. This device can also be adapted to detect corrosion in ferromagnetic structures in the same way as was done by using Fiber Bragg Gratings [15].

 

Fig. 4 (a) Schematic of the magnetic force sensor built with the in-fiber FPI. (b) Photograph of the sensor. (c) Wavelength shift as a function of distance from a ferromagnetic plate for the magnetic force sensor.

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The magnetic force sensor was tested by moving a 50 mm × 25 mm × 6 mm steel plate towards the sensor in order to increase the magnetic force, therefore also increasing the strain to which the optical fiber containing the FPI was subjected. The results are shown in Fig. 4(c). For an air-cavity of 200 µm, the calibration obtained was equal to 1.82 nm/N. The solid line is the magnetic force calculated by a finite element model (FEM) and the circles are the FPI measurements. This force sensor presented a better sensitivity than the one using an FBG (1.3 nm/N) [15].

4. Conclusions

An in-fiber FPI based on capillary optical fibers was constructed and characterized in terms of its temperature and strain sensitivity. The FPI consisted of a simple component made by a section of capillary optical fiber spliced between two pieces of single mode optical fiber. The response of a typical air-cavity of length approximately equal to 25 µm was about 9.5 times higher than the response of a typical FBG to axial strain variations, whose results reported in the literature is about 1 pm/με and about 10 times lower than the response of a typical FBG to temperature variations. The lower response to temperature of this type of FPI is advantageous in environments with variations in temperature.

The low temperature sensitivity offered by the FPI makes it a very attractive strain and magnetic field (or Force) sensor that does not require temperature compensation in contrast to fiber sensors based on FBG. Sensors based on our in-fiber FPI can be simple and reproducible devices that are easy to manufacture without the need for special alignment. With these motivations, magnetic field sensors were built with the FPIs together with a magnetostrictive material and with a SmCo magnet. We demonstrated a viable, easy to build, alternative for magnetic sensors using optical interrogation systems that presented a better sensitivity than sensors based on FBGs.