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Abstract
A novel, compact, and easy fabrication vector magnetic field sensor has been proposed and investigated. The proposed sensor consists of a U-bent single-mode fiber fixed in a magnetic-fluid-filled vessel. Neither mechanical modification nor additional fiber grating is needed during the sensor fabrication. The results show that the response of magnetic fluid to magnetic field can be used to measure the direction and intensity of magnetic field via whispering gallery modes supported by the U-bent fiber structure with suitable bending radius. The sensitivity of direction is 0.251 nm/°, and the maximum magnetic field intensity sensitivity is 0.517 nm/mT. Besides, the results of this work prove the feasibility for realizing vector magnetic sensors based on other bending structures (such as bending multimode interference, bending SPR structure) in the future.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber sensors are recognized as one of the important devices for monitoring many physical parameters, such as temperature, displacement, curvature and refractive index (RI) [1–3]. Besides their well-known advantages (such as easy fabrication, high integration and compactness, high precision, survivability under challenging environment, and low cost), they also have good compatibility with nanomaterials. Hence, many novel optical fiber sensors combined with nanomaterials have been proposed [4,5].
Magnetic fluid (MF) is a kind of nanomaterial, which is stable colloid composed of surfactant coated magnetic nanoparticles and carrier liquid. MF has unique optical properties, especially dichroism, birefringence, Faraday effect and tunable RI under magnetic field. It shows potential applications in magnetic field detection. Therefore, many MF-based optical fiber magnetic field sensors using different sensing structures and principles were proposed, e.g. MF coated optical fiber multimode interferometer [6,7], tapered fiber [8,9], fiber surface plasmon resonance (SPR) [10,11], MF-filled Fabry-Perot interferometer [12,13] or microstructured optical fibers (MOFs) [14,15]. Moreover, anisotropic nanochain-clustering of magnetic nanoparticles within MF around optical fiber under different orientations of magnetic field was investigated in 2016 [16]. Then, spectral response of MF-coated optical fiber under different orientations of magnetic field has gradually become the focus of researchers. However, in order to achieve the vector magnetic field measurement, it is generally necessary to make the optical fiber structure asymmetric in geometry or RI. Obviously, this puts forward a higher requirement for processing the optical fiber. The processed fiber structures include D-shaped fiber [17–21], lateral-offset fusion [22,23], microfiber coupler (MFC) [24,25], fiber grating [16,26,27], tapered fiber [28,29]. Generally, those structures and methods may add the complexity of fabrication and increase the processing cost. Furthermore, most of the mechanical processing will make fiber more fragile and raise the uncertainty during fabrication [30]. Thus, to overcome these limitations, other alternative routes for sensing vector magnetic field is considerably important.
Among many schemes of optical fiber sensors, a simple and convenient one is the bent single-mode optical fiber (SMF). By bending the SMF to a U-shaped structure with sufficiently small radius, part of optical beam will transfer to the cladding and be guided along the outer surface of the cladding as whispering gallery mode (WGM). The WGM mode’s propagation constant depends on the RI of the medium near the outer surface. Recently, many sensors based on WGM in bent optical fiber have been investigated experimentally and theoretically [31–34]. In the field of magnetic field measurement, Liu and Chen et al. conducted a series of studies on MF-based U-bent SMF sensors [35–37]. Their works mainly focus on sensing the scalar magnetic field intensity. The response to the orientation of magnetic field, viz. sensing the vector magnetic field, has not been explored yet.
In this work, U-bent SMF was proved to have potential application in vector magnetic field sensing. The scheme is implemented by bending the SMF into a cylindrical vessel. The inner diameter of the cylindrical vessel can be regarded as the bending diameter of the SMF. At the same time, cylindrical vessel could be the container for MF naturally. Compared with other vector sensing structure, this scheme elegantly avoids the need for breaking the mechanical integrity of the optical fiber, and its low cost of manufacturing is more conducive to pragmatic applications. Besides, U-bent structure forms the reflection-like and probe-type configuration, which is very helpful for magnetic field detection in narrow space.
2. Fabrication and sensing principle
Figure 1(a) shows the schematic diagram of the vector magnetic field sensor proposed in this work. SMF (core/cladding diameter is 9.2/125 μm) is passively bent to fit into three MF-filled cylindrical vessels with different diameters. It has been reported that, for intensity demodulated macrobending refractive index sensor, the optimum bend diameter is 11.0 mm for 1550 nm [38]. Meanwhile, it needs to avoid the fiber core cracking by bending with too small diameter. Thus, we made three sensors with bend diameter of around 13.0 mm, 11.0 mm, 9.0 mm, respectively (the actually measured bend diameters are 13.04 mm, 11.08 mm, 8.90 mm, respectively). The bending radius R of SMF is about half of the diameter of the vessel. The part of the fiber attached to the inner surface of the vessel is fixed with UV glue to keep the fiber stable. Experiments indicate that this structure configuration has good fabrication repeatability. The RI response of U-bent SMF is measured experimentally and the results are shown in Fig. 1(b). A series of interference dips can be observed in the transmission spectra. Figure 1(b) indicates that Sensor 2 with optimum bend diameter (around 11.0 mm) has the deepest interference dip near 1550 nm, which means the light intensity of cladding mode is largest among all the three sensors. When the RI of the external solution increases, all dips redshift. The sensitivity of all dips in the range of 1500 to 1600 nm are about 200-240 nm/RIU. Then, MF is packed in the vessels. The selected MF is water-based MF with surfactant-coated Fe3O4 nanoparticles (provided by Hangzhou Jikang New Materials Co., LTD, Hangzhou, China), the particle size is 10 nm. The RI of MF is adjusted by deionized water. In this study, the RI of MF applied is about 1.357 (measured by a refractometer A670, Hanon, Jinan, China). The corresponding transmission spectra of the U-bent SMF sensor in air and MF are shown in Fig. 1(c). MF with higher concentration (larger RI) may be more sensitive to magnetic field. However, for the U-bent fiber in MF with higher RI, the interference dips may not be observed visibly under relatively high magnetic field, which is due to the leaking of cladding mode. This has been verified in our experiment and the results is shown in Fig. 1(d).
Fig. 1. (a) Schematic diagram of U-bent SMF vector magnetometer. (b) Transmission spectra of the U-bent SMF immersed in solution with different RIs. (c) Transmission spectra of the U-bent SMF sensor in air (black line) and in MF (red line). (d) Transmission spectra of Sensor 1 in MF with high RI (1.373) under 0 mT and 30 mT magnetic field. The magnetic field is applied perpendicular to the bent plane. Inset shows the schematic diagram of the leaking of cladding mode.
A bent fiber with bending radius R [see Fig. 2 (a)] can be considered as an equivalent straight waveguide (ESW) by conformal transformation [32,39]. As shown in Fig. 2(b), the effective refractive index (ERI) of ESW can be described by equation ${n_{esw}} = n({x,y} )({1 + {x / R}} )$, where $n({x,y} )$ is the original RI profile of the straight fiber. Obviously, the outer portion of the fiber has higher ${n_{esw}}$. Therefore, the outer surface of cladding can be considered as a waveguide, which causes the tendency of the core mode shifting to the outer portion. The corresponding numerical simulation is shown in Fig. 2(c). The input optical beam from straight SMF will be split into two optical paths (i.e., core mode and WGM) to form a Mach-Zehnder interferometer. According to the interference theory, the spectra can be expressed as [32,36]:
where ${I_{core}}$ and ${I_{WGM}}$ represent the light intensity of core mode and WGM, respectively. $\varphi $ is the phase difference between the core mode and WGM, which can be expressed as where L is the length of the bent SMF, $\varDelta n$ is the difference between the ERI of core mode and WGM. When $\varphi $ equals even times of $\pi $, the transmission light intensity will be maximum. In this case, L will be integer times of ${\lambda / {\varDelta n}}$. Similarly, when $\varphi $ equals odd times of $\pi $, the transmission light intensity will be minimum, where the dip ${\lambda _{dip}}$ happens. Therefore, the dip wavelength can be expressed as where m is an integer. Equation (3) indicates that the change of $\varDelta n$ will lead to the shift of interference dip wavelength. Thereby, RI change of the ambient environment will affect the resonance dip wavelength.Fig. 2. (a) Geometry of bent fiber. (b) Refractive index profile (y = 0) of a straight fiber (black line) and effective straight waveguide (red line). (c) Electric field amplitude distribution of a typical WGM supported by the bent SMF (R=7.5 mm) at 1580 nm. (d) Electric field amplitude distribution of bent 2D slab waveguide structure (R=7.5 mm) at 1580 nm (not shown to scale). (e) Schematic of the light ray within bent SMF.
In addition, without losing generality, an effective 2D slab waveguide model with similar SMF parameters is employed to demonstrate the light propagation within the bent structure [40]. The simulation result is shown in Fig. 2(d). Figure 2(d) reveals that the coupling between the core mode and WGM is clearly periodic with a period of ${\lambda / {\varDelta n}}$. This phenomenon can be simplified phenomenologically by the propagation of geometric light ray as shown in Fig. 2(e), which is in accord with the case of Mach-Zehnder interferometer.
For all the WGMs supported by this waveguide, the low ERI (high order) WGMs are hard to be generated. The reason is that the inner portion of the structure has no mode field distribution as shown in the simulation [see Fig. 2(d)]. Only those WGMs with ERI slightly higher than that of the fundamental mode (FM) of the straight SMF can be generated efficiently [30,40]. When the RI of the external solution increases, the ERI of those generated WGMs will also increase [32], while the ERI of the core mode approximately remain constant. So, the $\varDelta n$ will increase with the RI of the external solution. Thus, the dip wavelength redshifts with the RI of the external solution, which is in agreement with the experimental results shown in Fig. 1 (b).
For magnetic field measurement, MF is treated as magnetic field sensitive material. A series of experiments verify that the nanoparticles will rotate and interact with each other under certain magnetic field [16,23,41]. The magnetic nanoparticles within MF will form nanochain-clusters around fiber [see Figs. 3(b) and 3(c) below], which is dependent of the intensity and orientation of the magnetic field. As a result, the ERI of asymmetric optical modes (i.e. WGMs in this work) can be influenced by both the intensity and direction of the magnetic field, which is the basic principle for vector magnetic field sensing.
Fig. 3. (a) Experimental setup of the vector magnetic field sensing system. (b) Schematic diagrams of the direction. Bottom panels of (b) are 3D models of the nanochain distribution.
3. Experimental details and discussion
The experimental setup of the vector magnetic field sensor is illustrated in Fig. 3. A light source with highly stable output emitting light covering wavelength range of 1450-1650 nm is employed. The sensor is fixed on a rotating stage and placed in the center of the electromagnet. The magnetic field strength is adjusted by changing the magnitude of the supply current and calibrated by a gauss meter.
To verify the vector magnetic field sensing property, the intensity of magnetic field is fixed at 30 mT while rotating the stage from 0° to 360° with a step of 10°. The 0° and 90° represent the conditions when the plane of U-bent SMF is perpendicular and parallel to the magnetic field, respectively. The schematic diagrams of the direction are illustrated in Fig. 3(b).
Figure 4 shows the transmission spectra of the as-fabricated three sensors under different orientations of magnetic field. Obviously, all spectra vary periodically with the magnetic field direction ranging from 0° to 360°. Considering the periodicity, Fig. 4 only displays the spectra for the magnetic field direction in the ranges of 0°-90° and 90°-180°. Specifically, when the orientation angle increases from 0° to 90° and 180° to 270°, all dips blueshift until reach the minimum wavelength. In contrast, when the orientation angle increases from 90° to 180° and 270° to 360°, all dips redshift until reach the maximum wavelength. In addition, at 90° or 270° direction, the shift of the spectra is relatively slight.
Fig. 4. Transmittance spectral response to magnetic field direction under magnetic field intensity of 30 mT. Inset of sensor 2 shows the transmission at 0° and 90° directions.
The above phenomenon can be explained by the anisotropic nanochain-clustering of magnetic nanoparticles within MF around the optical fiber as shown in Fig. 3(b). For U-bent SMF, the WGMs propagate along the outer surface of the cladding. Thus, the ERI of WGMs mainly depends on the surrounding environment near the outer surface. When the magnetic field direction is perpendicular to the plane of U-bent SMF [left panel of Fig. 3(b)], the magnetic nanoparticles are concentrated at the outer surface of the cladding, which causes the increase of ERI of WGMs. When the magnetic field direction is parallel to the plane of U-bent SMF [right panel of Fig. 3(b)], the magnetic nanoparticles are distributed at both sides of the plane. On the meridian plane of the bent region, the distribution of magnetic nanoparticles is not uniform. For example, at the beginning and end of the bent region, the concentration of the magnetic nanoparticles is low. However, at the middle region of the bent region, the magnetic nanoparticle concentration is high. These low and high concentration distributions lead to the opposite effect on ERI of WGM, which causes the very small change of ERI at this configuration, i.e. 90° or 270° direction. So, the spectral shift is slight at these specific directions.
However, sensor 2 may not be suitable for vector magnetic field sensing. Figure 4(c) shows that only one dip can be observed near 1570 nm at 0°. As the direction angle increases, two dips can be observed until 90° direction. Then, as the direction angle continues to increase, two dips redshift together and mix into one dip again at 180° direction [Fig. 4(d)]. This crosstalk phenomenon between dips should be avoided in magnetic field sensing. The reason for the occurrence of crosstalk may be due to the small interval between two dips, which is only about 20 nm for sensor 2. The small interval could be assigned to the strong coupling between FM and WGM, which leads to the anticrossing effect of the supermodes and then causes the change of $\varDelta n$ [40]. Meanwhile, when the direction is close to 0° and 180°, the dips are getting shallower, which reduces the resolution. This also contributes to the crosstalk phenomenon.
Besides, the response of the as-fabricated three sensors to magnetic field intensity was characterized by fixing the magnetic field orientation at 0° and 90°, respectively and then increasing the intensity of magnetic field with a step of 5 mT. The experimental results are shown in Fig. 5. All dips of the three sensors redshift and blueshift with the increase of magnetic field intensity at 0° and 90°, respectively. However, it is clear that the interval between dip 1 and dip 2 for sensor 2 is getting smaller when the magnetic field increases from 0 mT to 5 mT. When the magnetic field intensity is in the range of 10 mT to 30 mT, only one dip can be observed, which is due to the mixing of two dips (i.e. crosstalk phenomenon). This is similar to the case when conducting magnetic field direction detection [Fig. 4(c)]. So, avoiding crosstalk phenomenon is important for vector magnetic field sensing, which implies, within a certain wavelength region, not all structures with random bending radius are suitable for vector magnetic field sensing.
Fig. 5. Transmittance spectral response to magnetic field intensity at two specific directions (0° and 90°, respectively).
According to the above analysis, only sensor 1 and sensor 3 among the three as-fabricated sensors are suitable for vector magnetic field sensing. The sensing performance of sensor 1 and sensor 3 are shown in Fig. 6. Dip 2 of sensor 1 has the highest intensity sensitivity at 0°, which is 0.517 nm/mT. Its highest direction sensitivity is estimated to be 0.251 nm/°, which is calculated by averaging the four sensitivities corresponding to the orientation angle ranging from 10° to 50°, 130° to 170°, 190° to 230°, and 310° to 350°, respectively [see Fig. 6(e)]. The variation of dip wavelength as a function of magnetic field orientation angle for other three dips is also plotted in Fig. 6(e). The directional response is mainly caused by the beginning and end parts of the bent SMF. The RI change within the “transition region” between nanochain-clustering and non-clustering areas is largest with the magnetic field direction. When the “transition region” is around the sensitive parts of the WGMs [top side of Fig. 2 (c), the direction sensitivity is high. On the contrary, if the “transition region” is around the insensitive parts (left and right sides of Fig. 2 (c)], the direction sensitivity is low. Considering the 0.02 nm resolution of the commercial OSA, the maximum resolution for intensity detection and direction detection are about 0.04 mT and 0.08°, respectively.
Fig. 6. (a) and (c) Shift of dip wavelength with magnetic field direction for sensor 1 and sensor 3. (b) and (d) Shift of dip wavelength with magnetic field intensity at 0° and 90°. (e) Dip wavelength as a function of magnetic field orientation angle and the linear fitting.
For comparison, Table 1 lists the sensing structures, fabrication methods and sensing performance of the related vector magnetic field sensors. As the direction sensitivity is dependent of the intensity of magnetic field, the maximum intensity sensitivity is adopted for comparison. The mainly adopted structures and fabrication methods include D-shaped fiber drawn from specially shaped prefabricated rods or fabricated with mechanical polishing system, lateral-offset fusion through adjusting related fusion parameters, MFC by flame heating two tapered fibers together, fiber grating inscribed in H2-loaded fiber with UV. Compared with other structures and fabrication methods, the U-bent SMF employed in this work is relatively easy to realize and possesses good mechanical strength. Moreover, it is obvious from Table 1 that the magnetic field sensor based on SPR effect has the advantage of high sensitivity. Thus, U-bent SPR sensor is promising for highly sensitive vector magnetic field sensing in the future. Finally, we would like to point out that there are some fabrication techniques suitable for extending the range of bend diameter of U-bent SMF, such as electric arc-discharge and flame-assisted bending [42,43]. This may be helpful for further improving the sensitivity and compactness of the sensor.
Table 1. Sensing performance of various optical fiber vector magnetic field sensors.
4. Conclusions
In conclusion, U-bent SMF fixed in a magnetic-fluid-filled vessel is proved to be a suitable structure for vector magnetic sensing. Meanwhile, by comparing the structures with different bending radiuses, it is proved that not all U-bent radiuses are suitable for vector magnetic field sensing. Among the three as-fabricated sensors, the one with R=5.54 mm is not appropriate for vector magnetic field sensing. For other two vector magnetic field sensors, the most sensitive dip (dip 2 of sensor 1) is chosen for interrogating magnetic field. The direction and intensity sensitivities can reach 0.251 nm/° and 0.517 nm/mT, respectively. The proposed sensor has the advantages of easy fabrication and high mechanical strength, which has the potential applications in various fields.
Funding
National Natural Science Foundation of China (62075130, 61675132); Shanghai Shuguang Program (16SG40); Shanghai Talent Development Fund (201529); State Key Laboratory of Advanced Optical Communication Systems and Networks. Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication (SKLSFO2014-05).
Disclosures
The authors declare no conflicts of interest.
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