Magnetic field and temperature dual-parameter sensor based on nonadiabatic tapered microfiber cascaded with FBG

A kind of double-parameter sensor based on magnetic-fluid-coated nonadiabatic tapered microfiber (NTF) cascaded with fiber Bragg grating (FBG) is proposed and experimentally demonstrated. Simultaneous measurement of magnetic field and temperature is realized by monitoring the variation of NTF interference spectrum and FBG characteristic dip. In the magnetic field range of 0-18 mT, the highest magnetic field sensitivity can reach 1.159 nm/mT. The maximum temperature sensitivity is up to -1.737 nm/°C. The proposed magnetic-fluid-coated NTF interferometer cascaded with FBG will find extensive application prospect due to its high sensitivity, easy fabrication, compactness, strong robustness, and low cost.


I. INTRODUCTION
Compared with the traditional singlemode-multimodesinglemode (SMS) structure, tapered microfiber is an effective way to reduce fiber diameter and increase the interaction between evanescent field and the surrounding environment, which can lead to increase in sensitivity [1][2][3]. In addition, the structure is compact and easy to manufacture. The sensing characteristics of tapered microfiber have been extensively studied in various fields including current sensing [4], water pollution monitoring [5], optoacoustic emitter [6], humidity measurement [7], refractive index measurement [8][9][10], temperature sensing [11][12][13], and magnetic field sensing [14], [15]. Tapered microfiber can be divided into adiabatic tapered microfiber (ATF) and nonadiabatic tapered microfiber (NTF) [16], [17]. NTF has a large taper angle variation and the cladding mode excited in the cone region is coupled with the core mode. But for ATF, the taper angle changes very small, and the coupling does not occur in the cone region.
Magnetic field sensors have been widely used in many scientific and industrial applications, including biomedical detection, aviation industry, space and geophysical research. Several fiber optic magnetic field sensors based on different sensing technologies have been reported, including Faraday effect [18,19], and magnetostrictive materials [20][21][22][23][24]. Nevertheless, in certain cases, the integration process of this type of material with the optical fiber is not easy. In recent years, sensors based on magnetic fluid (MF) have been widely studied. MF is a kind of stable colloidal solution, which is composed of nanometer magnetic solid particles, carrier solution and surfactant. It not only has the fluidity of liquid but also has the magnetic properties of magnetic materials. It is widely used for designing various new-fashioned fiber-optic magnetic field sensors. The employed structures include tapered photonic crystal fiber [25], side-polished fiber [26], fiber F-P cavity [27], FBG [28][29][30][31], and long period gratings (LPGs) [32][33][34][35]. These structures are complicated and expensive to make. However, NTF is easy to manufacture and low-cost. Besides, magnetic field sensor based on NTF can significantly improve the sensitivity. In 2014, Layeghi has already proposed a magnetic field sensor based on NTF [14], but the magnetic field sensitivity is relatively low. In this work, the magnetic field sensitivity is improved by about 16 times after parameter optimization.
On the other hand, the refractive index of MF also varies with temperature. Therefore, the temperature crosssensitivity of fiber-optic magnetic field sensor based on MF cannot be ignored. In most cases, magnetic field and temperature should be measured simultaneously. In 2014, a novel fiber-optic F-P magnetic field sensor was proposed by Zhao et al [36]. In 2020, a photonic crystal fiber cascaded grating structure was proposed by Wang et al [37]. The temperature cross-sensitivity of the two sensors can be well eliminated, but they are difficult to fabricate.
In this work, a composite magnetic field sensor based on MF-coated NTF cascaded with FBG is proposed. The FBG is insensitive to magnetic field, which is used to solve the problem of temperature cross-sensitivity. Meanwhile, the NTF structure enables the high magnetic field and temperature sensitivity.

II. SENSING PRINCIPLE
The sensing principle of the NTF structure is based on the optical path difference between the core mode and cladding mode. As shown in Figure 1, the incident light reaches the first descending cone region and excites cladding mode at the uniform waist region. At the ascending cone region, the cladding mode is recoupled to the fiber core. The structure can be considered as a mode interferometer. Because the propagation constants of core mode and cladding mode are different, the comb spectrum is generated at the output. The output intensity of the interferometer can be expressed as [38], [39] core 2 cos( ) clad core clad where core  and clad  are the intensities of the fundamental core mode and cladding mode, respectively.  represents the phase difference between the core mode and cladding mode, which can be expressed as where  represents the wavelength of the incident light, and L is the uniform waist length. eff n  is the effective refractive index difference between the core mode and cladding mode, which is given as When the external magnetic field intensity changes, the refractive index of MF also changes [40]. When the refractive index of MF increases, core eff n and clad eff n also increase, but the increase of core eff n is much larger than that of clad eff n [12]. Therefore, the effective refractive index difference between the two modes Similarly, when the ambient temperature changes, the refractive index of MF also changes [40], [42]. When the temperature increases, the refractive index of MF decreases, which leads to the reduction of core n and clad n . Therefore, the effective refractive index difference between the two modes (2 m 1) (2 m 1) 2n When the MF-coated NTF is cascaded with a FBG, the Bragg transmission valley is expressed as [43] 2 core where  represents the period of FBG. core eff n is independent of the external environment. Therefore, the transmission spectrum of FBG is insensitive to magnetic field change. However, the change of temperature will affect the transmission, the Bragg wavelength shift caused by temperature can be expressed as

A. FABRICATION AND CHARACTERIZATION
The sensing structure consists of MF-coated NTF and FBG. The NTF is obtained by singlemode fiber taper. The core/cladding diameter of SMF is 9/125 μm. The detailed fabrication is divided into two steps: firstly, cupped fiber taper is made by discharging with the optical fiber fusion splicer (AV6471); then the cupped fiber taper is placed on the fiber-pulling machine. Hydrogen flame is employed to further taper the fiber. Finally, the NTF is obtained. Through setting different tapering parameters, such as discharge power (30 bit-100 bit), discharge time (1 sec-6 sec), and pulling speed (300 μm/s-900 μm/s), three sensing structures with different taper lengths are obtained. In order to avoid possible bending and fracture of the tapered fiber, the three structures are first fixed in quartz groove, and then encapsulated in tube filled with MF. Both ends of the simple tube are sealed with UV glue to prevent the flowing of MF. The employed water-based MF is EMG605, which is provided by Ferrotec Co., LTD. The MF is diluted with distilled water. The refractive index of the final MF is 1.339, which is measured with a refractometer (A670, Hanon, China). Then, the packaged NTF is cascaded with a FBG, which is provided by Henan Minghai Optoelectronic Technology Co., LTD. The central wavelength of the FBG is 1550 nm, and the grating length is 10 mm. The waist diameter of the three NTFs was kept at 5 μm and the interference arm lengths were 3 mm, 4 mm and 5 mm, respectively. The corresponding NTFs are referred as Taper 1, Taper 2 and Taper 3. Their micrographs are shown in Figure 2

B. EXPERIMENTAL DETAILS
The experimental setup for measuring the magnetic field and temperature sensing properties of the as-fabricated devices is shown in Figure 3. The sensing structure is connected to the super continuous broadband light source (SBS, Wuhan Yangtze Soton Laser Co., Ltd., Wuhan) and the optical spectral analyzer (OSA, Yokogawa AQ6370C). The light emitted from SBS has a wavelength range of 700-1700 nm. The resolution of OSA is set at 0.2 nm. The direction of magnetic field is perpendicular to the optical fiber axis. The intensity of magnetic field is adjusted by changing the supply current. For temperature test, the sensing device is placed in a columnar temperature control oven (LCO 102 LONG, ECOM Ltd., Czech Republic). The temperature adjustment resolution is 0.1 ℃.

IV. RESULTS AND DISCUSSION
The typical transmission spectrum of the sensing structure (Taper 1 cascaded with FBG) under zero magnetic field is shown in Figure 4. The maximum wavelength shift sensitivity occurs for the dip at around 1311 nm (referred as Dip 1), which is selected for the subsequent analysis. The dip at round 1550 nm (referred as Dip 2) has a large extinction ratio, which is the FBG characteristic dip.

FIGURE 5. (a)Transmission spectra of the sensing structure (Taper 1 cascaded with FBG) at different magnetic field intensities. The inset is the enlarged transmission spectra at the FBG wavelength; (b) Wavelength of Dip 1 and Dip 2 as a function of magnetic field. (c) Transmission spectra of the sensing structure (Taper 1 cascaded with FBG) at different temperatures. The inset is the enlarged transmission spectra at the FBG wavelength; (d) Wavelength of Dip 1 and Dip 2 as a function of temperature.
The transmission spectra of Taper 1 cascaded with FBG under different magnetic field intensities are shown in Fig.  5(a). The mode interference dip (viz. Dip 1) drifts towards long wavelength with the magnetic field and the maximum drift reaches 18.647 nm. While the FBG dip (viz. Dip 2) is insensitive to magnetic field. When the external magnetic field intensity increases from 0 mT to18 mT, the refractive index of MF increases. The obtained experimental results are consistent with the aforementioned theoretical analysis. The magnetization saturation of MF used in the experiment is 20 mT. So, when the magnetic field continues to grow, the wavelength shift is not obvious at higher magnetic field. Fig.  5(b) explicitly depicts the relationship between dip wavelength and magnetic field intensity. After linear fitting, the magnetic field sensitivity is obtained to be 1.159 nm/mT. Fig. 5(c) is the transmission spectra of the sensing structure (Taper 1 cascaded with FBG) at different temperatures. It can be found that Dip 1 drifts towards short wavelength with temperature, while Dip 2 drifts towards long wavelength with temperature. As the temperature increases, the refractive index of MF decreases, which is contrary to the case for magnetic field increase [40]. The obtained experimental results are also consistent with the aforementioned theoretical analysis. Fig. 5 (d)   Similarly, experimental results for Taper 2 cascaded with FBG are obtained and plotted in Figure 6. The magnetic sensitivity of Dip 1 is 0.958 nm/mT. The temperature sensitivities of Dip 1 and Dip 2 are -0.890 nm/℃ and 0.010 nm/℃, respectively.
Finally, the experimental results for Taper 3 cascaded with FBG are shown in Fig. 7. The magnetic field and temperature sensitivities of Dip 1 are 0.390 nm/mТ and -0.770 nm/℃, respectively. The temperature sensitivity of Dip 2 is 0.010 nm/℃.
To be clear, Table 1 summarizes the maximum sensitivities of the as-fabricated three sensing structures. It can be seen from Table 1 that the magnetic field and temperature sensitivities of Taper 1 cascaded with FBG are higher than those of the other two. For the three tapers, their smallest waist diameters are the same (i.e. 5 μm), but their steepness for the tapering region becomes smaller from Taper 1 to Taper 3. Theoretically, the shift of wavelength is greater for the structure with longer interference arm (see (4) and (5)) at the same conditions. But the experimental results indicate that the structure with shorter interreference arm length has a higher sensitivity. Thus, it can be concluded that the steepness has a greater influence on the sensitivity. The steeper the taper is, the greater their sensitivity will be.
For comparison, Table 2 lists the sensing performance of various dual-parameter measurement structures. Among these structures, the magnetic field sensitivities mentioned in Refs. [37], [44] and [45] are relatively high, but they have high fabrication cost. Comparing with the structures reported in Refs.
[2], [36], [46] and [47], the structure proposed in this work has a higher sensitivity for both magnetic field and temperature measurement and the fabrication cost is low.

V. CONCLUSION
In conclusion, a kind of optical microfiber sensor for simultaneously measuring magnetic field and temperature is proposed. The experimental results show that the steepness of the NTF has a greater influence on the sensitivity. The maximum magnetic field and temperature sensitivities are obtained to be 1.159 nm/ mT and -1.737 nm/℃, respectively. The advantages of the proposed sensors are simple in structure, low-cost and easy fabrication. The problem of temperature crosstalk can be overcome effectively by using the sensitivity matrix.