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Abstract
In order to meet the demand for large-scale magnetic field testing, this paper proposes a D-shaped magneto-refractive photonic crystal fiber (MRPCF) based on surface plasmon resonance (SPR) by using the erbium-doped materials. The four different structures of Models A, B, C, and D are designed by changing the diameter, the position, and the number of layers of the air holes, and the corresponding magnetic field sensing characteristics are analyzed. The results show that in the magnetic field range of 5–405 mT, the magnetic field sensitivities of Models A, B, C, and D are 28 pm/mT, 48 pm/mT, 36 pm/mT, and 21 pm/mT, respectively. Meanwhile, the figure of merit (FOM) of the four MRPCF-SPR sensors is investigated, which have FOMs of 4.8 × 10−4 mT-1, 6.4 × 10−4 mT-1, 1.9 × 10−4 mT-1, 0.9 × 10−4 mT-1. Model B has higher sensitivity and larger FOM. In addition, the effect of the structural parameters of Model B on the sensing performance is also studied. By optimizing each parameter, the magnetic field sensitivity of the optimized Model B is increased to 53 pm/mT, and its magneto-refractive sensitivity and FOM are 2.27 × 10−6 RIU/mT and 6.2 × 10−4 mT-1, respectively. It shows that the magneto-refractive effect of MRPCF can be effectively enhanced by optimizing the structural design of fiber. The proposed MRPCF is an all-solid-state fiber, which solves the instability problem of the magnetic fluid-filled fiber and reduces the complexity of the fabrication process. The all-solid-state MRPCF can be used in the development of quasi-distributed optical fiber magnetic field sensors and has broad applications in the fields of geological exploration, earthquake and tsunami monitoring, and military navigation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The measurement of magnetic fields can be achieved by magnetic field sensing, which is widely used in many fields such as industrial detection [1], national defense technology [2], biological imaging [3], navigation [4], marine underwater detection [5], bridge engineering [6], and smart grids [7]. Magnetic field sensors can be divided into two categories: electrical and optical. At present, the development of electrical magnetic field sensors is relatively mature, such as atomic magnetometers [8], giant magneto-impedance [9], and flux magnetometers [10]. However, most of them are point-based detection, and are not easy to integrate. For large-scale sea or equipment monitoring, an additional mobile platform is required. While the optical magnetic field sensors have the advantages of small size, low cost, corrosion resistance, anti-electromagnetic interference, and easy integration. They have great potential in the application of large-scale quasi-distributed magnetic field monitoring [11,12]. Therefore, optical magnetic field sensors have received extensive attention in various application fields. According to the sensing mechanism, optical fiber magnetic field sensors mainly include magnetostrictive effect [13], Faraday rotation effect [14], and magneto-refractive effect [15–17]. Among them, the sensor based on magneto-refractive has the advantages of easy manufacture, simple system, high sensitivity, and the ability to meet large area testing. Therefore, researchers have carried out extensive research on it.
In the current research on the sensors of magneto-refractive effect, the magnetic sensitive material used is magnetic fluid (MF). The modulation of magneto-refractive is achieved by using an optical fiber encapsulated with MF or filling air holes in the fiber with MF. In 2013, H. Wang et al. [18] proposed a sensing structure based on MF and singlemode-multimode-singlemode (SMS) fiber with magnetic field sensitivity of -16.86 pm/Oe. In 2021, M. Yuan et al. [19] designed a magnetic field sensor combined with microfiber coupler and MF, the sensitivity reaches -97.856 nm/mT. In 2021, Y. Zhang et al. [20] proposed a dual-parameter sensor based on MF-coated nonadiabatic tapered microfiber with fiber Bragg grating, the magnetic field sensitivity and the temperature sensitivity are 1.159 nm/mT and -1.737 nm/°C. In 2022, Z. Hao et al. [21] designed a wedge-shaped fiber vector magnetic field sensor using the combination of surface plasmon resonance and MF, with the maximum refractive index sensitivity and magnetic field sensitivity of 6692 nm/RIU and 11.67 nm/mT. Although MF has good optical magneto-refractive properties, it is volatile, cannot work for a long time, has high absorption loss, and is susceptible to temperature crosstalk [22]. To meet the requirements of the development of long-distance magneto-refractive fibers, it is necessary to break through the technology of directional filling and high-quality fusion splicing. As a result, researchers begin to propose the magneto-refractive effect of magnetic material-doped fibers. In 2021, Y. Dong et al. [23] proposed an Er/Yb co-doped fiber (EYDF) and studied its magneto- refractive properties. Compared with single-mode fiber (SMF), EYDF has a larger magnetic moment and the magneto-refractive sensitivity of EYDF is measured to be 3.8279 × 10−5 RIU/Gs. In 2021, S. Liu et al. [24] also proposed an Er-doped fiber and measured its magneto-refractive sensitivity of 4.838 × 10−6 RIU/mT using an experimental system based on Mach-Zehnder interferometer. The magnetic material-doped fiber can overcome the shortcomings of MF. However, due to the limited variety of available materials, it is still necessary to develop high-quality magneto-refractive fibers. In addition, the use of doped fiber for magnetic field sensing has been less studied and its sensitivity needs to be further improved.
In recent years, photonic crystal fiber (PCF) sensors based on surface plasmon resonance (SPR) have become popular for research [25,26], which have broad application prospects in the sensing field. SPR is a phenomenon of resonance between electromagnetic wave (EW) and surface plasma wave (SPW) generated by free electrons on metal surface, which is sensitive to the change of the refractive index of the medium. Surface plasmon polaritons (SPP) can improve the Faraday rotation effect [27], which can enhance the magneto-refractive effect to a certain extent. And SPP can also enhance the surface wave to improve the sensitivity. The SPR-based optical fiber sensors not only have high sensitivity, but also have the advantages of wide detection range and label-free detection [28,29]. In addition, compared with traditional fibers, PCF is a new type of fiber with design flexibility and freedom, and its internal air holes can be arranged periodically or randomly. The structure and arrangement of different air holes can guide the transmission of specific modes, which allows the distribution of the evanescent field in the fiber to be regulated, and thus effectively controlling the sensing properties of PCF-SPR sensors [30–32].
Above mentioned background, this paper combines different structures of PCF-SPR sensor with doped magnetic materials, which provides an effective way for the development of high-performance magneto-refractive fibers and high-sensitivity magnetic field sensing. This paper proposes four different D-shaped erbium-doped magneto-refractive PCF (MRPCF) structures of Models A, B, C, and D. The sensing characteristics are analyzed by finite element analysis. The results show that in the magnetic field range of 5 - 405 mT, the magnetic field sensitivities of Models A, B, C, and D are 28 pm/mT, 48 pm/mT, 36 pm/mT, and 21 pm/mT, respectively. The FOMs are 4.8 × 10−4 mT-1, 6.4 × 10−4 mT-1, 1.9 × 10−4 mT-1, 0.9 × 10−4 mT-1. In addition, it is also carried out structural optimization analysis. The magnetic field sensitivity, magneto-refractive sensitivity, and FOM of the optimized Model B are 53 pm/mT, 2.27 × 10−6 RIU/mT, and 6.2 × 10−4 mT-1, respectively. The designed MRPCF can realize magnetic field sensing without filling with magnetic fluid, which has the advantages of cost saving and flexible design, and has great potential in the fields of navigation and environmental monitoring. Besides, the performance analysis of different structures of MRPCF provides a reference for designing the sensors with higher sensitivity.
2. Structure and theory
The proposed structures of MRPCF are Models A, B, C, and D, and the cross-sections are shown in Fig. 1(a)–1(d). All models are D-shaped with gold plating on the side polished surface. The thickness of the gold layer is represented by h. Model A consists of three layers of air holes, with the central air hole missing. D = 4 µm represents the diameter of large air holes. Model B is designed by reducing the innermost air holes of Model A, and the diameter of small air holes is d = 2.7 µm. In Model C, a small air hole is placed in the center with missing air holes on both sides. Model D has four layers of air holes, and the diameter of the air holes is represented by d1 = 2.9 um. The spacing of air holes for Models A, B, and C is Λ = 4.5 µm, and that for Model D is Λ1 = 3.5 µm. The outermost layer is provided with perfectly matched layer (PML) to absorb excess energy. The fabrication of MRPCF can be realized by chemical vapor deposition (MCVD) process and atomic layer deposition (ALD) technology [24]. The Er2O3 and Al2O3 doped layers are deposited in the silica, and then the preform is fabricated by stacking, punching, and drilling [33]. Besides, the gold layer is coated on the side polished surface by chemical deposition coating or magnetron sputtering [34].
Fig. 1. Cross section of the proposed D-shaped MRPCF magnetic field sensor. (a) Model A; (b) Model B; (c) Model C; (d) Model D.
The dispersion relation of silica can be defined by the Sellmeier equation [35] as:
The dielectric constant of the doped fiber material becomes anisotropic [36,37], so the property can be expressed as:
The dielectric constant of gold can be expressed by the Drude–Lorentz model [38]:
In this paper, the gold layer is used to stimulate SPR. When SPR occurs, the coupling between modes is generated. The coupled mode theory [39] can be expressed as:
In order to investigate the sensing performance of the proposed sensor, this paper adopts the method of analyzing the confinement loss of the core mode. The confinement loss can be represented by the following relation [40]:
This paper adopts the method of wavelength demodulation to analyze the change of spectrum. When the external magnetic field changes, the refractive index of the doped fiber also changes. It causes the resonance wavelength to shift, resulting in a drift in the loss spectrum. The magnetic field sensitivity of the sensor is obtained by calculating the drift of the loss spectrum [41], which can be expressed as:
where Δλpeak is the variation of resonance wavelength and ΔB is the variation of external magnetic field.The figure of merit (FOM) can also be used to evaluate the sensing performance of the sensor [42], and its expression is:
where SB denotes the magnetic field sensitivity and FWHM represents the full width at half maximum.The magnetic field resolution can be used to measure the test accuracy of the sensor, and its expression is:
where Δλmin represents the minimum resolution of the spectrum and is set to 0.02 nm.3. Simulation and analysis
3.1 Performance analysis of different structures
In this paper, the sensing characteristics of the designed MRPCF are investigated using the finite element analysis method of COMSOL. The mode characteristics of the sensor are first analyzed to determine the direction of polarization. Figure 2 shows the loss spectrum for the x-polarized and y-polarized core modes of Model A, Model B, Model C, and Model D. It can be seen that the resonance peaks of y-polarized core mode of the four models are sharper and the loss peak is larger. Besides, the electric field distributions at the wavelength corresponding to the loss peak indicate that the y-polarized core mode has more energy coupling with SPP mode, and its coupling strength is greater than that of x-polarization, which is more conducive to the excitation of SPR. Therefore, this paper chooses to study the sensing characteristics of the proposed MRPCF in the y-polarized core mode.
Fig. 2. Loss spectrum of (a) x-polarized and (b) y-polarized fiber core mode of Model A, Model B, Model C, and Model D.
Figures 3(a)–3(d) show the dispersion relation of the y-polarized core mode and SPP mode, and the loss spectrum for the four models, respectively. The black and red lines represent the real part of the effective refractive index of y-polarized core mode and SPP mode, respectively, and the blue line represents the variation of loss with wavelength. The real part of the effective refractive index decreases with increasing wavelength for both the core mode and the SPP mode. The intersection of two curves at a certain point indicates that the real parts of the two effective refractive indices are equal. At this time, the phase matching condition is satisfied and the resonance occurs between the two modes to excite the SPR effect, resulting in a sharp peak on the loss spectrum [43]. From Fig. 3, it can be seen that Models A, B, C, and D excite SPR at 1566 nm, 1772 nm, 1825 nm, and 1796 nm, respectively.
Fig. 3. Dispersion relationship between y-polarized fiber core mode and SPP mode for (a) Model A, (b) Model B, (c) Model C, and (d) Model D, and the loss spectrum of the proposed sensor.
Figures 4(a)–4(h) show the electric field distributions of the y-polarized core mode and SPP mode for Models A, B, C, and D. The energy of the core mode is mainly confined to the defect channel in the center, while the energy of the SPP mode is concentrated at the surface where the dielectric and metal layers interact. When resonance occurs, the energy of the optical field is transferred from the core mode to the SPP mode. Besides, the four models exhibit different electric field distributions. This is because the structure of the air hole arrangement of each model is different, resulting in different energy of the core mode generated during the propagation of light.
Fig. 4. Electric field distribution for different modes of Model A, Model B, Model C, and Model D. (a-d) y-polarized fiber core mode; (e-h) SPP mode.
In this paper, the magnetic field response characteristics of the proposed MRPCF-SPR sensor are investigated. Figure 5 shows the experimental setup of the sensor. The incident light from the broadband light source (BBS) enters the polarization controller through the single-mode fiber (SMF), and then enters the MRPCF sensing device. The magnetic coil is used to generate a uniform magnetic field in the sensing area. The variation in the loss spectrum caused by different magnetic fields is observed by an optical spectrum analyzer (OSA). Finally, the analysis of magnetic field response is performed on a computer (PC).
The loss spectrum of the y-polarized core mode for the four models at magnetic field strength of 5 - 405 mT is shown in Fig. 6. The resonance wavelengths of the four models all redshift as the magnetic field increases. This is because the effective refractive index of MRPCF increases with the increase of the magnetic field [24]. It affects the strength of the coupling between the core mode and SPP mode, causing the phase matching condition to change, which makes the loss spectrum redshift. The resonance wavelength of Model A moves from 1566 nm to 1577 nm, that of Model B from 1772 nm to 1791 nm, that of Model C from 1825 nm to 1839 nm, and that of Model D from 1796 nm to 1804 nm. It can be found that Model B has the largest wavelength shift among them. Figure 7 depicts the relationship between different magnetic fields and resonance wavelengths for each model, and the fitting results show good linearity. According to Eq. (9), in the magnetic field range of 5 - 405 mT, the magnetic field sensitivities of Models A, B, C, and D are 28 pm/mT, 48 pm/mT, 36 pm/mT, and 21 pm/mT, respectively. At the same time, we also calculate the FOM of the sensor using Eq. (10). The FOMs of the four models are 4.8 × 10−4 mT-1, 6.4 × 10−4 mT-1, 1.9 × 10−4 mT-1, 0.9 × 10−4 mT-1, respectively. It is found that Model B has the best sensing performance among the four models.
Fig. 6. Influence of different magnetic field intensity on the loss spectrum of (a) Model A, (b) Model B, (c) Model C, and (d) Model D.
Fig. 7. The fitted results of resonant wavelength of y-polarized fiber core mode with different magnetic field intensity for Model A, Model B, Model C, and Model D.
3.2 Optimization analysis
Based on the above research, this paper continues to optimize the structural parameters of Model B. The effect of the diameter of small air holes on the sensor is first analyzed. Figure 8(a) shows the loss spectrum of the proposed sensor for different d. It can be seen that with the increase of d, the resonance wavelength blueshifts and the peak loss gradually increases. This is because when d increases, the effective refractive index of the SPP mode decreases, resulting in the resonance wavelength blueshifts. In addition, the increase of d makes the core mode closer to the metal dielectric layer and the coupling effect between the modes is stronger, resulting in a larger loss peak. When d is 2.4 µm, 2.5 µm, 2.6 µm, 2.7 µm, and 2.8 µm, the loss peaks are 309.1 dB/cm, 400.0 dB/cm, 405.2 dB/cm, 412.1 dB/cm, and 419.2 dB/cm, respectively. It can be found that the loss peak increases sharply when d changes from 2.4 µm to 2.5 µm in Fig. 8(b). When d is 2.5 - 2.8 µm, the change in loss is smaller. The FWHM of the sensor with different d is shown in Fig. 8(c). The FWHM is the narrowest at d = 2.5 µm. Therefore, the optimized value of d is 2.5 µm.
Fig. 8. (a) Influence of different d on the loss spectrum for Model B, (b) the loss peak and (c) the FWHM at different d.
The influence of the diameter of large air holes on the loss spectrum is shown in Fig. 9(a). As D increases, the resonance wavelength blueshifts and the loss peak remains almost constant. When D is 4.2 µm, the loss peak starts to decrease. Because the increase of D reduces the effective refractive index near the fiber core, allowing the effective refractive index difference between the fiber core and cladding to increase, which is beneficial to the propagation of light in the fiber core. However, when D is too large, it may cause the energy leakage of core mode and lead to the loss peak reduction. From Fig. 9(b), the loss peaks of different D are 391.5 dB/cm, 392.5 dB/cm, 400.0 dB/cm, 273.5 dB/cm, and 212.5 dB/cm, respectively. Figure 9(c) shows the influence of different D on the FWHM. When D = 4 µm, the loss peak is the largest and the FWHM is the narrowest. So we choose the size of D to be 4 µm.
Fig. 9. (a) Influence of different D on the loss spectrum for Model B, (b) the loss peak and (c) the FWHM at different D.
The optimization of the spacing of the air holes is shown in Fig. 10(a). When Λ increases from 4.4 µm to 4.6 µm, the resonance wavelength redshifts and the loss peak decreases. Since the effective refractive index of SPP mode increases with the increase of Λ, the resonance wavelength redshifts. At the same time, the smaller the spacing of the air holes makes the arrangement of the air holes close to each other, which leads to the stronger the energy of core mode, and thus the loss peak increases. When the Λ is 4.4 µm, 4.45 µm, 4.5 µm, 4.55 µm, and 4.6 µm, the loss peaks are 413.2 dB/cm, 403.5 dB/cm, 400.0 dB/cm, 387.3 dB/cm, and 387.5 dB/cm, respectively. In Fig. 10(b), it can be found that the variation of the loss peak caused by the change of Λ is not large, so we consider that different Λ has little effect on the transfer of coupling energy between modes. The FWHM of the sensor with different Λ is shown in Fig. 10(c). The FWHM is relatively narrow when Λ = 4.5 µm. Therefore, we choose Λ = 4.5 µm.
Fig. 10. (a) Influence of different Λ on the loss spectrum for Model B, (b) the loss peak and (c) the FWHM at different Λ.
The thickness of the gold layer also has a great influence on the sensing performance. Figure 11(a) shows the loss spectrum of the proposed sensor at different h. As h increases, the resonance wavelength blueshifts. When h is 40 nm, 45 nm, 50 nm, 55 nm, and 60 nm, the loss peaks are 315.6 dB/cm, 358.5 dB/cm, 400.0 dB/cm, 382.7 dB/cm, and 369.9 dB/cm, respectively. The loss peak first increases and then decreases from the Fig. 11(b). This is because when h increases, more free electrons are generated on the metal surface, which makes the coupling effect between the core mode and SPP mode stronger. It leads to more energy being transferred from the core mode to SPP mode, resulting in a larger loss peak. However, if the thickness of the gold layer is too large, it is difficult for the core mode to penetrate the dielectric layer in the form of an evanescent wave [44], which weakens the strength of the SPP mode on the metal surface, thus the loss peak decreases at h = 55 nm. When h is 50 nm, the FWHM is the narrowest from the Fig. 11(c). Therefore, h = 50 nm is the optimal value.
Fig. 11. (a) Influence of different h on the loss spectrum for Model B, (b) the loss peak and (c) the FWHM at different h.
By optimizing and analyzing the structural parameters, the optimized Model B has structural dimensions of d = 2.5 µm, D = 4 µm, Λ = 4.5 µm, and h = 50 nm. The magnetic field response is shown in Fig. 12(a). As the magnetic field increases from 5 mT to 405 mT, the resonance wavelength redshifts and the loss peak decreases. From the fitting results in Fig. 12(b), it can be calculated that the magnetic field sensitivity of the optimized Model B is 53 pm/mT, which is 5 pm/mT higher than that before optimization, and its FOM is 6.2 × 10−4 mT-1. It shows that the optimization analysis of structural parameters and the selection of suitable values for the parameters can effectively improve the sensing performance of the sensor. Besides, the relationship between the effective refractive index of the sensor and the magnetic field at 1550 nm is also studied, as shown in Fig. 12(c), and the magneto-refractive sensitivity is 2.27 × 10−6 RIU/mT. According to Eq. (11), the magnetic field resolution of sensor is 0.38 mT.
Fig. 12. (a) Influence of different magnetic field intensity on the loss spectrum, and the fitted results of (b) resonance wavelength and (c) refractive index (at 1550 nm) of y-polarized fiber core mode with different magnetic field intensity for the optimized Model B.
4. Discussion
Finally, this paper summarizes the sensing performance of the proposed MRPCF-SPR sensor, as shown in Table 1. The magnetic field sensitivity of Model B is improved after parameter optimization. It shows that the different structures formed by the different arrangements of air holes have an impact on the performance indicators of the sensor. In addition, the influence of the fabrication tolerance of the sensor on the sensing performance of optimized Model B is analyzed, as shown in Table 2. It can be found that when the tolerance of the structural parameters is 2%, the amount of change in the sensitivity of the sensor is not significant. Therefore, the sensor proposed in this paper has good fabrication tolerance, and the slight deformation of optical fiber caused in actual fabrication has little impact on the sensor performance. The research in this paper shows that the wavelength sensitivity of the magneto-refractive fiber can be effectively improved by changing the structural design of the fiber and the introduction of SPR. The magneto-refractive wavelength regulation signal of MRPCF can be connected to the interferometer to convert the wavelength signal into a phase signal, which can further improve the magnetic field detection accuracy of the sensor. In addition, some materials with better magneto-refractive effect can be used for the design of sensor devices. The materials such as PbS, Er/Yb, Tb2O3, etc. can be doped in the optical fiber to achieve improved sensitivity of the magnetic field sensor.
Table 1. Performance comparison of four models of the proposed MRPCF-SPR magnetic field sensor
Table 2. Error in the sensitivity of optimized Model B with different tolerance Δt
5. Conclusion
In this paper, a D-shaped MRPCF based on SPR is proposed and four different structures are designed. The effect of different structures on the sensing performance is analyzed by studying the performance indicators of the sensor. The results show that in the magnetic field range of 5 - 405 mT, the magnetic field sensitivities of Models A, B, C, and D are 28 pm/mT, 48 pm/mT, 36 pm/mT, and 21 pm/mT, respectively. The FOMs of the sensors are 4.8 × 10−4 mT-1, 6.4 × 10−4 mT-1, 1.9 × 10−4 mT-1, 0.9 × 10−4 mT-1, respectively. Model B has the best sensing performance among the four models. In addition, we also discuss the influence of d, D, Λ, and h on the sensing performance of Model B. The magnetic field sensitivity of the optimized model B is improved to 53 pm/mT, and its magneto-refractive sensitivity and FOM are 2.27 × 10−6 RIU/mT and 6.2 × 10−4 mT-1, respectively. Therefore, by changing different structures of fiber, the magneto-refractive effect of the sensor can be improved, thereby enhancing the sensing performance. It has a very important guiding significance for the design of optical fiber devices. The proposed MRPCF not only has a simple process, but also does not need to be filled with magnetic fluid. It can meet the requirements of miniaturized, integratable, low-cost magnetic field detection, and has strong environmental adaptability, which is important for the realization of underwater magnetic field monitoring.
Funding
National Natural Science Foundation of China (61661004, 61775238, 62275269); Science and Technology Major Project of Guangxi (2020AA21077007, 2020AA24002AA); Guangdong Guangxi Joint Science Key Foundation (2021GXNSFDA076001); Project of State Key Laboratory of Transducer Technology of China (SKT2001).
Acknowledgments
The authors would like to thank the support of the laboratory and university.
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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