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Abstract
All-fiber-optic magnetic field sensor integrated with magnetic fluid has been investigated for decades, accompanied by the commitment to vectorization, miniaturization, integration and solving the temperature cross-sensitivity caused by thermo-optic effect of magnetic fluid. A kind of dual-channel-in-one temperature-compensated all-fiber-optic vector magnetic field sensor was proposed and investigated theoretically in this work. Three optical surfaces, including two sensing surfaces (plated with gold film of 40 nm thickness and then coated with magnetic fluid and polydimethylsiloxane, respectively, referred as CH1 and CH2) and one reflective surface, were integrated on a single-mode fiber tip to facilitate the dual-channel-in-one design. The Kretschmann configurations were formed by the waveguide fiber, gold film and functional materials at the sensing surfaces (CH1 and CH2). Surface plasmon resonance was excited in different wavelength bands corresponding to CH1 and CH2. Attenuation wavelengths corresponding to CH1 and CH2 depend on the magneto-induced and temperature-induced refractive index change of functional materials, respectively, which makes the temperature-compensated magnetic field sensing possible. The non-centrosymmetric evanescent field generated by micro-fiber-tip-prism enables the vector magnetic field sensing. Especially, the length of the sensing area is only 115.5 µm, which achieves ultra-integration and miniaturization. The current work provides a novel scheme for designing all-fiber-optic vector magnetic field sensing based on magnetic fluid and demonstrates the realization of lab-on-a-fiber and then promotes the industrial application of all-fiber-optic vector magnetic field sensing devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Due to its magneto-induced refractive index (RI) modulation, magnetic fluid (MF) has been widely used as magnetic field indicator in all-fiber-optic magnetic field sensing field. MF is composed of magnetic nanoparticles (MNPs) coated with surfactant and then dispersed in a suitable carrier liquid. MNPs are magnetized and redistributed under an external magnetic field [1,2], which in turn affects the RI of MF [3–5]. In 2011, Chen et al. realized fiber-optic magnetic field sensing by immersing optical fiber in MF for the first time [6]. After that, various MF-based magnetic field sensing schemes configured with optical fiber interferometers based on mode interference and resonant cavity structures have been proposed, such as Mach–Zehnder interferometer (MZI) based on taper fiber [7,8], offset fusion [9–12], core mismatch [13] or U-bend structure [14,15], whispering gallery mode (WGM) resonance structure based on fiber ring resonator [16–18], etc. However, the fiber-optic interferometer and resonator-based magnetic field sensing scheme suffer from low sensitivity due to the low evanescent field intensity, which leads to the small effect of the analyte′s RI on the effective mode RI of the sensing light [19]. While for the fiber-optic microcavity-based Fabry-Pérot (F-P) resonators [20–24], the sensing light directly propagates through the MF, which is conducive to achieve relatively high sensitivity. Recently, Zhao et al. proposed the F-P resonator combined with Vernier effect and MF [25]. The ultra-high magnetic field intensity sensitivity was achieved. But, the small free spectral range (FSR) limits the magnetic field sensing range of the sensor and the sensing light directly propagating inside the MF leads to a large insertion loss.
Surface plasmon resonance (SPR) effect has the characteristics of high sensitivity to analyte′s RI and easy demodulation of spectral signals, which facilitate its sensing application. In 2018, Zhou et al. realized the all-fiber magnetic field sensing based on SPR effect for the first time. The high magnetic field intensity sensitivity and large sensing range were obtained [26]. However, the deficiency is the inability to sense magnetic field direction. In 2017, Yin et al. used the dislocation fusion structure to generate a non-centrosymmetric evanescent field, so that the sensing area is only sensitive to the RI change in a specific direction, thereby all-fiber vector magnetic field sensing is realized [27].
In order to meet the needs of practical applications, e.g., magnetic field sensing in narrow areas and accurate measurement of gradient magnetic fields [28], miniaturization and integration requirements are put forward for the fiber-optic vector magnetic field sensor. In particular, magnetic field with high gradient characteristics varies greatly in space and then the traditional sensors with large sensing size cannot provide accurate measurements, i.e., the spatial resolution is insufficient. To realize the miniaturization, we previously proposed a scheme for vector magnetic field sensing using a wedge-shaped fiber head combined with MF and SPR [29]. The sensing area length is only 615 µm.
On the other hand, the schemes for solving the temperature-magnetic field cross-sensitivity problem caused by the thermo-optic effect of MF were proposed by other authors, which includes nonadiabatic tapered microfiber cascaded with a fiber Bragg grating [30]. However, in order to ensure the reflection quality of FBG, it′s length is usually centimeter scale, and its temperature sensitivity is relatively low. In our previous work, we proposed to use a 2 × 2 fiber coupler in parallel to merge two SPR-based sensing probes, viz. a wedge-shaped fiber-optic magnetic field sensing probe and a multimode-no-core fiber temperature sensing probe [19], which greatly improved the temperature sensing sensitivity.
This work proposes and theoretically investigates a novel sensing scheme for temperature-compensated all-fiber-optic vector magnetic field sensing. The designed two sensing surfaces are tactfully integrated on the single fiber-end, which is plated with gold film to compose the fiber-core—gold film—functional-material Kretschmann structure for exciting SPR effect. This is the basic sensing principle of the proposed device. The length of the sensing area is only 115.5 µm. The dual-channel-in-one design contributes greatly to the performance enhancement of the proposed sensor. The high integration and ultra-miniaturization are easily realized and expands its application scenario, such as in narrow space and at high gradient magnetic field.
2. Sensing principle
In order to understand the sensing principle more intuitively and reduce the calculation workload, the object under study is simplified to a two-dimensional waveguide structure model. Figure 1 shows the schematic of the proposed SPR-based temperature-compensated all-fiber-optic vector magnetic field sensing tip and its simulation model. The redundant parts (out of the rectangular area) are abandoned in the simulation model to improve the computational efficiency. The sensing channel 1 and 2 (referred as CH1 and CH 2) are coated with MF and polydimethylsiloxane (PDMS), respectively. The incident light excites SPR successively at the two sensing surfaces coated with different functional materials. Then, the light from sensing channel 2 impinges on the reflective surface normally and is retroreflected by it. Through specific design [α1 = α2, 2(α1 + α2) + β = 90°], the retroreflected light will go the same path the incident light has passed. This dual-channel-in-one design is intrinsically miniature and integrative. Although the incident angle on CH1 and CH2 are equal (α1 = α2), the reflectance spectrum has two attenuation dips assigned to the two reflective surfaces. This is due to the RI difference between different functional materials [31].
Fig. 1. Schematic of the proposed dual-channel-in-one temperature-compensated all-fiber-optic vector magnetic field sensor and the simulation model.
Attenuation dip wavelength corresponding to CH1 and CH2 can be modulated by the coated MF and PDMS, whose RI are magnetic-dependent and temperature-dependent, respectively. Thus, magnetic field and temperature can be detected by monitoring the variation of SPR attenuation dip wavelength stemming from CH1 and CH2.
2.1 Fundamental of SPR sensing
SPR refers to the resonance energy coupling phenomenon between the guided mode in the waveguide and the surface plasmon wave (SPW) [32]. When phase matching is satisfied, that is the propagation constant of guided mode (βin) matches that of SPW (βsp), the SPR phenomenon occurs and then part of the incident optical energy is converted into SPW resonance energy and the dip appears in the reflection spectrum. It can be expressed as [33]
2.2 Functional materials
In order to sense other physical quantities, it is necessary to use various functional materials to convert their change into RI change, which is easy to be detected through demodulating the SPR attenuation wavelength. Benefiting from the non-centrosymmetric evanescent field of the designed sensing probe and its micron-scale size, the use of MF as the functional material may maximize the advantages of vectorization, miniaturization and integration for magnetic field sensing application [19,29].
2.2.1 Magnetic-sensitive material: magnetic fluid (MF)
Under external magnetic field, MNPs within MF will be subjected to the interaction between magnetic moment and external magnetic field, as well as the interaction between magnetic moments. As a result, MNPs will form chains along the magnetic field direction and aggregate around the immersed fiber at the areas tangential or parallel to the magnetic field direction, which leads to the increase of local RI [3,4,36,37].
As shown in Fig. 2, when the magnetic field direction is parallel to the sensing surface of the proposed probe (θ = 0°), the MNPs aggregate near the sensing surface, which results in increase of the local RI, and vice versa (θ = 90°), the RI decreases. As a result, vector magnetic field can be measured by monitoring the SPR attenuation wavelength assigned to the magneto-induced RI change of MF.
Fig. 2. Top view of the distribution of MNPs around the proposed sensing structure at different magnetic field directions.
To verify the above analysis, Monte Carlo method was employed to numerically calculate the distribution of MNPs under external magnetic field. A restricted region, where the MNPs cannot enter has been introduced in the calculation model, which represents the immersed fiber-optic sensing probe (see Fig. 3).
Fig. 3. Simulation results of MNPs′ distribution around a restricted area under different external magnetic fields. (a) Circularly restricted area without external magnetic field; (b) Circularly restricted area under external magnetic field at θ = 90° direction; (c) D-shaped restricted area for θ = 90°; (d) D-shaped restricted area for θ = 0°.
To calculate the distribution of MNPs with Monte Carlo method, a random motion of each particle at a randomly distributed original position P0 is introduced. The q-th motion will generate a new position of MNP Pq, corresponding to an overall potential energy value Eq. If Eq < Eq−1, the motion is valid, else the motion with a probability of exp[(Eq−1 – Eq) / kT] is effective [38–40]. The probability is set to prevents Eq from entering an extremely low value, which may cause the system fail to break through the potential barrier brought by the extreme value, thus to enter a lower potential energy state. The cycle repeats until Eq no longer changes significantly.
The potential energy in MF mainly includes: the energy of interaction between particle i and external magnetic field ui(B), the energy of magnetic dipole-dipole interaction uij(m), and the interaction energy due to the overlapping of the surfactant layers uij(v). Refer the vector of magnetic moment of particle i and magnetic induction intensity as mi (m = |mi|) and B (B = |B|), and approximate the MNPs as a series of identical spheres, the above potential energy can be expressed as follows [2]
The intrinsic magnetic moment of MNPs with diameter d = 10 nm employed in the numerical calculation is m = 2.32 × 10−19 A/m2, the number of surfactant molecules per unit area N = 1 × 1018 m−2, the temperature T = 300 K, the magnetic induction intensity B = 100 mT. Limited by the computer performance, the following measures were adopted: 1). Only 400 particles with 5% concentration (area fraction) in a rectangular area were calculated; 2). Periodic boundary condition was settled, which will remove the particles beyond the range of calculation boundary and re-insert them at the opposite boundary; 3). Introduce the cut-off radius Rc = 10d, which will consider the interaction force to be zero when the distance between particles exceeds the cut-off radius.
After 50,000 Monte Carlo steps, the simulation results are shown in Fig. 3 (refer to Visualization 1 for the calculation process). The MNPs exhibit random agglomeration phenomenon without the external magnetic field and are uniformly distributed around the circular restricted region [Fig. 3(a)], while the MNPs form nanochain-clusters along the magnetic field direction under external magnetic field, and the agglomeration occurs near the position where the external magnetic field direction is tangent to the restricted region, and the dilution is near the position where magnetic field is perpendicular to the restricted region [Fig. 3(b)]. This phenomenon can be explained that, in the vicinity of the position where the magnetic field is perpendicular to the circular restricted region, the interaction between particles is weakened due to the blocking of the restricted region. This will result in the aggregation of MNPs at other region with more particles and stronger interaction force. The same conclusion applies to the D-shaped rejection region [Figs. 3(c) and 3(d)].
It is important to note that the total area of the calculated region depends on the number of particles in the case where the diameter and area fraction of the MNPs are determined as S = Total area of 400 MNPs / 5%. The calculation area is set as a square, so its side length is $\sqrt S $, and the radius of the restricted area introduced in the calculation is ${{\sqrt S } / 4}$, which is much smaller than the actual fiber size. Therefore, the calculation results can only show the regularity of the MNPs under the action of external magnetic field. It is impossible to truly restore the actual situation. However, comparing the calculation results with the experimental results in Refs. [27,36], which introduced an air bubble into a MF film to simulate the distribution of MNPs around the optical fiber (air bubble), the regularity of the calculation results and the experimental results are highly consistent, which is in good agreement with the phenomenological analysis shown in Fig. 2 and other reported experimental results as well.
2.2.2 Temperature-sensitive material: polydimethylsiloxane (PDMS)
PDMS is a kind of polymeric material whose RI changes with temperature remarkably. According to Ref. [41], the RI variation of PDMS can be expressed as
Considering the dispersion of PDMS, the value of nP0 as a function of wavelength is obtained from Ref. [42] (the ratio of main agent to curing agent is 20:1). The analytical function of dispersion adopted for the numerical calculation is obtained as follows through fitting the data in Ref. [42]
Thus, temperature can be measured by monitoring the shift of SPR attenuation wavelength assigned to the temperature-induced RI change of PDMS.
2.3 Dual-channel-in-one sensing principle
Single mode optical fiber is employed and the incident angle on CH1 (α1) and CH2 (α2) are considered to be constant. The grinding angles of the reflective surfaces are set to satisfy 2(α1 + α2) + β = 90°, which ensures the optical path is closed, i.e., all-channel-in-one scheme (see Fig. 1). In this work, α1 = α2 = 10°, β = 50° and the thickness of gold film is 40 nm.
The RI of MF nMF = 1.340 (functional material for CH1) and that of PDMS nPDMS = 1.395 (functional material for CH2). The reflectance spectra are calculated based on the transfer matrix method with MATLAB [32,43] and the optical field distribution are simulated with COMSOL. The corresponding results are shown in Fig. 4. As the RIs of MF and PDMS functional materials (and fiber core and cladding as well) are different, the excited SPR for CH1 and CH2 lies in different wavelength bands. For CH1, the fiber core-gold film-MF structure excites an obvious SPR effect at around 665 nm [see Fig. 4(b) for the obvious SPW field on CH1]. However, for CH2, the cladding layer-gold film-PDMS structure excites SPR at around 1076 nm [see Fig. 4(b) for the obvious SPW field on CH2].
Fig. 4. Simulation results of the proposed dual-channel-in-one sensing structure. (a) Reflectance spectra (MATLAB); (b) Optical field distribution (COMSOL).
3. Vector sensing model
For investigating the vector magnetic field sensing properties, the analytical expressions for the MF′s RI with magnetic induction intensity and direction are necessary.
The magnetic-field-intensity-dependent RI of MF can be expressed with the Langevin-like function [44,45]
The experimental data in our previous work [29] were based on the structure of wedge-shaped multimode optical fiber coated with gold film. The structures designed in this work and in the cited work are all based on wedge-shaped fiber. The only difference is that the wedge-shaped fiber of this work has two sensing channels, but the magnetic field sensing channel (part) is the same for both structures. Thus, the effect of MNPs distribution will be similar for both devices. In addition, the wedge-shaped structure is almost insensitive to magnetic field when the magnetic field direction is perpendicular to the sensing surface, but it has high sensitivity to magnetic field when the sensing surface is parallel to the magnetic field direction. In order to obtain a reasonable magneto-induced refractive index response function of MF, the experimental data for the sensing surface parallel to the magnetic field direction were quoted and fitted with Eq. (9) to obtain the suitable fitting coefficients: nc = 1.371 and ns = 1.391 [see Fig. 5(a)].
Fig. 5. Experimental data and employed RI of MF as functions of magnetic field intensity and direction. (a) Fitting to the experimental data for RI change of MF with magnetic induction intensity; (b) Employed function of RI-magnetic induction intensity; (c) Fitting to the experimental data for RI change of MF with magnetic field direction (B = 15.5 mT); (d) Employed function of RI-magnetic field direction (B = 10 mT).
For magnetic field direction change, we have previously reported the following analytical expression [19]
It is noticed that the maximum RIs of MF in Figs. 5(a) and 5(c) approach that of PDMS, which will increase the crosstalk possibility between CH1 and CH2. Therefore, for our simulations, the values of nc, ns and n0 are modified to 1.360, 1.386 and 1.340 with the achieved Langevin-like functions, respectively [see Figs. 5(b) and 5(d)]. This will reduce the initial and maximum RIs of MF and avoid the crosstalk. In practice, this can be easily achieved by diluting the MF.
According to the above-mentioned theoretical basis and analysis, the miniature dual-channel-in-one temperature-compensated vector magnetic field sensor can be obtained through monitoring the reflection spectrum.
4. Sensing performance and discussion
Figure 6 shows the spectral response of the proposed sensor to ambient temperature in the range of 280-330 K. The SPR attenuation wavelength corresponding to CH1 and CH2 redshifts and blueshifts with the ambient temperature, respectively [see Fig. 6(b)]. The maximum and minimum temperature sensitivities of CH2 are −5.91 and −3.35 nm/K, which are significantly higher than that of CH1 (0.57 nm/K). This is due to the higher thermo-optic coefficient of PDMS. The great difference in sensitivity between the two channels is conducive to resolve the temperature cross-sensitivity issue.
Fig. 6. Spectral response of the proposed sensor to ambient temperature (a) and the corresponding SPR wavelength as a function of ambient temperature (b).
Figure 7 shows the spectral response of the proposed sensor to magnetic induction B with the intensity in the range of 0-22 mT. The SPR attenuation wavelength of CH1 exhibits a significant red-shifted response. The nonlinear response of CH1 resembles the Langevin-like function, which is consist with the prediction by Eq. (9).
Fig. 7. Spectral response of the proposed sensor to magnetic induction intensity (a) and the corresponding SPR wavelength as a function of magnetic induction intensity (b).
Figure 7 displays that the SPR attenuation wavelength of CH2 is almost insensitive to magnetic field intensity, which is in good agreement with the above-mentioned theoretical analysis.
Similarly, Fig. 8 shows the spectral response of the proposed sensor to magnetic field direction (at B = 10 mT), which indicates that CH1 shows great sensitivity to magnetic field direction. The maximum sensitivity occurs at θ = 90° or 270°, which agrees with the theoretical analysis.
Fig. 8. Spectral response of the proposed sensor to magnetic field direction (a) and the corresponding SPR wavelength as a function of magnetic field direction (b).
According to Figs. 7(b) and 8(b), CH2 has slight SPR attenuation wavelength shift when θ = 90°/270° and at high magnetic field intensity. In that case, CH1 has already experienced a large-scale wavelength shift, the working bands of CH1 and CH2 are substantially close. Therefore, it is judged that the response of CH2 to magnetic field is caused by the crosstalk of the two channels. The influence of crosstalk between the two channels can be reduced through adjusting the initial refractive index of PDMS (by changing the ratio of the main liquid of PDMS to the curing agent [42]), then the working band interval between the two channels becomes larger and the cross-talking can be avoided.
Finally, for realizing the sensor pragmatically, the suggested fabrication processes are shown in Fig. 9, which include: (1). Grinding and polishing the reflective surface; (2). Plating gold film on the reflective surface (as reflector); (3). Grinding and polishing the sensing surface of CH2; (4). Plating gold film with thickness of 40 nm on the sensing surface of CH2; (5). Applying PDMS and waiting for curing; (6). Grinding and polishing the sensing surface of CH1; (7). Plating gold film with thickness of 40 nm on the sensing surface of CH1; (8). Filling MF into a plastic tube. Then, the dual-channel-in-one temperature-compensated all-fiber-optic vector magnetic field sensor is realized.
5. Conclusion
In conclusion, an integrated temperature-compensated all-fiber-optic vector magnetic field sensing scheme based on SPR effect has been proposed. The sensing performance and fabrication processes and feasibility have been studied and discussed in details. The proposed dual-channel-in-one sensing scheme integrates vector magnetic field and temperature sensing on a fiber probe of about 115.5 µm length with high sensitivities. It tactfully solves the temperature cross-sensitivity problem of optical fiber magnetic field sensor devices. It is believed that this sensing scheme may provide a positive reference for the development of photonic devices with the advantages of integration, miniaturization, vectorization and multi-function.
Funding
National Natural Science Foundation of China (61675132, 62075130); Shanghai Shuguang Program (16SG40).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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