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Abstract
In this paper, an optical fiber magnetic field and temperature sensor based on an optical microfiber coupler (OMC), Polydimethylsiloxane (PDMS), and magnetic fluid (MF) is proposed, and its magnetic field and temperature sensing characteristics are analyzed theoretically and verified experimentally. Based on the OMC and using MF as the sensing medium, the sensor can respond to the magnetic field and temperature respectively after encapsulated by PDMS. The experimental results show that the maximum magnetic field sensitivity is 96.8 pm/Oe, and the maximum temperature sensitivity is 919.1 pm/°C. To overcome the cross-sensitivity of the magnetic field and temperature of the sensor, the sensitivity matrix is established and demodulated. In addition, we discuss the optimization of the sensitivity demodulation matrix by the size design of the PDMS package and the OMC structure. The proposed two-parameter sensor in this article has the advantages of high sensitivity, low cost, small volume and high integration, which is of great significance for the multi-parameter sensing of basic physical parameters such as magnetic field and temperature.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The magnetic field is an essential fundamental parameter to be monitored in the development and management of the ocean. We can use magnetic field sensors to detect magnetic anomaly environment monitoring under the sea, such as submarine pipeline detection [1,2], underwater archaeological activities [3], current sensing [4] and ocean mineral exploration [5], etc. The magnetic field sensors can be divided into the electrical magnetic field sensor and the optical fiber sensor according to the sensing medium. The electrical magnetic field sensors have some disadvantages such as large volume, high cost, weak anti-electromagnetic interference ability and requiring an additional temperature control system. If we want to achieve large-area sea monitoring, they need to be installed on a mobile monitoring platform. Compared with them, the optical fiber sensors have the advantages of small size, low cost, strong environmental adaptability and so on. Therefore, the research of optical fiber magnetic field sensors is of great significance to the development and application of magnetic field monitoring technology.
According to the sensing mechanism, optic fiber magnetic field sensors can be divided into different types. These sensing mechanisms include magneto-optical material [6,7], the magnetostrictive effect [8], and magnetic fluid [9,10]. Amirsolaimani [7] developed a magnetic field sensor based on magneto-optic effect by using magneto-optic materials with high Verdet value, which had a sensitivity of 20 fT/√Hz. Although its sensitivity is extremely high, the manufacturing process of the magneto-optic materials used was relatively complex. Chen [8] used the magnetostrictive material Terfenol-D combined with piezoelectric (PZT) ceramics to fabricate a sensor to measure the magnetic field and the sensitivity of 0.036 V/µT was obtained, which can be used for intermediate magnetic (geomagnetic) magnitude of magnitude sensing, such as navigation and magnetic switch. However, their experimental set was complicated and the sensor had the hysteresis phenomenon. Xia [9] developed a refractive index control magnetic field sensor combined FBG with Fabry-Perot (F-P) cavity, and obtained the sensitivity of 23–53 pm/Oe. It has the advantages of small volume and temperature compensation, but the sensitivity is low. The refractive index control magnetic field sensor developed by Tian [10] is based on optical microfiber (OM) and MF-filling structure, and the magnetic field sensitivity of 24.4 pm/Oe was obtained, which is also suitable for strong magnetic magnitude sensing, but the influence of temperature on the sensor has not considered. Moreover, because MF is sensitive to both magnetic field and temperature [11], we choose MF as the sensing medium for our two-parameter sensor.
In order to meet the application requirements of geomagnetic sensing, the sensitivity of the refractive index control sensor based on MF needs to be further improved. And the problem of cross-sensitivity of multiple parameters must be solved in practical application. Multi-parameter cross-sensitivity demodulation schemes are usually solved by sensitivity matrix. For example, Xia's FBG two-parameter demodulation scheme has two temperature sensing regions, and FBG is used for compensation after demodulation, which limits the function of multi-parameter sensing.
Because OMC has a large proportion of evanescent field transmission characteristics [12], its transmitted light field directly interacts with the material around the OMC waist region, which has a positive effect on the improvement of sensitivity. For our OMCI reflective structure compared to the traditional transmission structure, the light can be transmitted twice in the OMC waist region to form a quasi-resonant structure, which can generate multiple interference dips on the spectrum and improve the sensor sensitivity.
In view of this, based on OMC and MF as the sensing medium and Michelson interferometer (MI) theory, we developed an OMCI optical fiber magnetic field and temperature sensors with refractive index control, and PDMS was used to make the sensor package shell. The sensing mechanism, packaging design, and experimental test were also studied. Besides, the interference groove envelope is formed within a certain range of MI arm difference (5∼30 mm) [13], which is conducive to tracking specific wavelengths (the dips or peaks of the wavelength).
For the proposed two-parameters sensor, its output spectrum can generate over two dips. By using these dips to calibrate the experimental sensitivity of magnetic field and temperature, respectively, a two-dimensional sensitivity matrix can be established. In addition, as the magnetic field and temperature rise respectively, the waveform shifts direction of its output spectrum is different when the sensor works, which is more conducive to the demodulation of the two parameters. The proposed magnetic field sensor can accurately demodulate the temperature without compensation.
In addition, Due to the high thermal expansion coefficient and low Young's modulus, PDMS is used in temperature sensing materials or some substrate materials. Compared with the above sensors, the most significant advantage of ours is that it can demodulate the magnetic field and temperature, and it can optimize the sensitivity matrix by changing the volume of PDMS or the radius of OMC. And beyond that, the proposed sensor has the advantages of high sensitivity, small volume and simple manufacturing process, which is an effective way to realize the integration of magnetic field regionalization detection equipment. It is of great significance for industrial applications such as non-contact switch, current measurement, magnetic storage reading, and has great potential in the application of marine environmental monitoring.
2. Principle and Structure design
2.1 Principle
The OMC we use is made of two single-mode fibers (SMF) melted and tapered, and it comprises four ports, two tapered transition regions and a waist region. We connected Port 3 and Port 4 with Faraday rotary mirrors (FRMs) respectively to form the OMCI component, and it effectively improves the integration and compactness of the device, as shown in Fig. 1. The transmission spectrum of the OMC is not only similar to the interference phenomenon of conventional interferometers but also regulated by the transmission characteristics of the OMC itself. In addition, compared with common coated reflectors, Faraday rotary mirrors can reduce the polarization fading effect caused by the birefringence effect of single-mode fiber.
According to the OMC coupling theory, Port 1 is the input port and Port 2 is the output port. The optical power reflected from Port 3 and Port 4 back to the waist region can be respectively expressed as [14]:
P1 is the input power of Port 1, P3 and P4 are the output power of Port 3 and Port 4, respectively. L is the coupling length, the uniform waist region and part of the conical transition region play a leading role in the coupling characteristics of the whole OMC. The coefficient C is the coupling strength. C can be expressed as [15]:In the Eq. (3), $V=[(2\pi R)/\lambda](n_{2}^{2}-n_{3}^{2})^{1/2}$ is the normalized frequency, and λ represents the wavelength of the incident light, R represents the radius of OMC. n2 and n3 represent the refractive index of optical fiber cladding and MF, respectively. After the beam splitting process in the waist region for the first time, the light interferes by reflecting to the uniform waist area through the Faraday rotating mirrors of Port 3 and Port 4, then the output power P2 of Port 2 can be expressed as [13]:
wherein, $\phi = 2\pi {n_2}\Delta {l_a}{\rm{/}}\lambda $ represents the phase difference of the interference, $\Delta {l_a} = {l_2} - {l_1}$ represents the arm difference of the interferometer. Therefore, P2 changes as n3 rises or falls. The n3 as the refractive index of the MF can be expressed by the Langevin model function as [11]:2.2 Structure of the sensor
The structure of the sensor is shown in Fig. 2. It is mainly composed of sensing region and reflection region. The sensing region was composed of OMC, cuboid PDMS (Dow Corning, USA) and diluted MF (Jixing, Hangzhou). After the OMC waist area is surrounded by the magnetic fluid, both the entire OMC waist area and the MF are well encapsulated inside the rectangular PDMS (72 mm × 5 mm × 10 mm). In the reflection region. Port 3 and Port 4 were connected with Faraday rotation mirrors.
3. Verification and testing
3.1 Experiments of magnetic field sensing
In order to verify the above theoretical analysis results, we experimental test the magnetic field sensing performance, and the measurement system is shown in Fig. 3(a) and 3(b). The system mainly includes an amplified spontaneous emission source (ASE, 1520∼1620 nm), an optical spectrum analyzer (OSA, 600∼1700 nm, Yokogawa, Japan, AQ6370D), a Helmholtz coil (CHY12-500), a DC power supply (CH-F2030), a Gaussmeter (CH-1800) and a personal computer (PC) for signal processing. The ASE light source is connected to Port 1, the spectrum analyzer is connected to Port 2, and the DC power supply is used to drive the Helmholtz coil to generate a stable DC magnetic field. The OMC uniform waist radius (R) was 3 µm and waist coupling length (L) was 7 mm to manufacture the sensor as sample 1, and the arm difference of the interferometer was controlled as Δla ≈ 8 mm.
First of all, We calibrated the magnetic field intensity of the DC magnetic field generated by the Helmholtz coil using the Hall probe (HCHD801F). After calibration, sample 1 was placed in a Helmholtz coil, as shown in Fig. 3(b), and the magnetic field intensity was set to rise from 0 Oe to 50 Oe at 28.6°C. The magnetic field interval intensity was 10 Oe for each recording, and the interval was 10 min for each recording. The output spectrum of Port 2 was observed on OSA and the resolution of OSA is 0.02 nm, as shown in Fig. 4. By tracking the dips of the output spectrum in Fig. 4(a), we can see that it has the redshifts as the magnetic field increases. Because n3 rises with the increase of the magnetic field [11], and the evanescent field generated in the OMC waist region is very sensitive to the increase of the n3, so the interference dips shifts with the change of the magnetic field. Magnetic field sensitivity SB can be expressed as [16]:
Δλdip represents the drift of dip, and ΔB represents the variation value of the operating magnetic field intensity. Based on the above experimental results, we successfully realized the magnetic field sensing function of the sensor. According to the fitting curve in Fig. 4(b), the magnetic field sensitivity of sample 1 was obtained as SB1-dip1 = 79.0 pm/Oe and SB1-dip2 = 96.8 pm/Oe.
Fig. 4. (a)The relationship between the sensor output spectrum and the changing magnetic field from 0 Oe to 60 Oe for sample 1.(b)Linear fitting of wavelength shifting for the magnetic response.
3.2 Simulation of temperature sensing characteristics
As seen from Eq. (5), the variation of the refractive index of magnetic fluid is related to both magnetic field and temperature changes. According to the previously reported work [17], n3 were 1.340, 1.328 and 1.316 at 20°C, 70°C and 120°C respectively. So the relation of the refractive index of magnetic fluid n3 and T can be expressed as the following fitting curve equations:
Because the refractive index of the magnetic fluid can be adjusted by T, the temperature sensing can be realized without changing the sensor package structure. To verify the temperature sensing characteristics of the sensor, according to Eqs. (1–5) and (7), we conducted simulation analysis on the temperature responses of OMC under different structural parameters (R and L) without considering the influence of PDMS packaging on the response results.
Under the same L, the corresponding characteristic peaks in the output spectra of Fig. 5(a)–5(c) drift with the temperature changing, the temperature sensitivity of 524.7 pm/°C, 431.1 pm/°C and 365 pm/°C were obtained at R = 2.5 µm, R = 3 µm, R = 3.5 µm, respectively. Because the OMC waist region is sensitive to the change of n3 around it, and n3 significantly decreases with the increase of temperature, resulting in the specific wavelength (peaks) shifts in the output spectrum. It is worth noting that, according to the figure of the fitting curve in Fig. 6(a), temperature sensitivity decreases with the increase of R under the same L condition (2.5 µm ≤ R ≤ 3.5 µm). Because the energy proportion of evanescent field decreases with the increase of radius [18], OMC with a smaller radius was more sensitive to the change of n3, results in a correlation between temperature sensitivity and the length of the waist radius.
Fig. 5. Simulation output spectrum corresponding to different OMC radiu without PDMS package when L = 8 mm. (a) R = 2.5 µm. (b) R = 3 µm. (c) R = 3.5 µm.
Fig. 6. (a) The fitting curve of the output spectrum for temperature simulation without PDMS package when L = 8 mm at R = 2.5 µm, R = 3 µm and R = 3.5 µm. (b) The fitting curve of the output spectrum for temperature simulation without PDMS package when R = 3.5 µm at L = 6.5 mm, L = 8 mm and L = 9.5 mm.
In addition, we simulated the corresponding output spectra of OMC sensors with different lengths of waist region under the same radius (R = 3.5 µm) of OMC waist region. In this simulation, when L = 6.5 mm, L = 8 mm, and L = 9 mm, the sensor obtained temperature sensitivity of 379.7 pm/°C, 365 pm/°C, and 363.9 pm/°C, respectively, shown in the fitting curve in Fig. 6(b). It was observed that the temperature sensitivity of the sensor was almost constant with the increase of L (6.5 mm ≤ L ≤ 9.5 mm). In the case of a certain waist radius, the proportion of energy transmitted by the evanescent field remains unchanged, so changing the length of L has no significant influence on the temperature sensitivity of the sensor.
3.3 Experiments of temperature sensing
We have verified the correlation between R and the temperature sensitivity of the sensor through theoretical simulation. To further verify the temperature sensing characteristics of the sensor, we conducted a temperature test experiment on sample 1. The experimental system is composed of an Amplified Spontaneous Emission source (ASE, 1520∼1620nm), optical spectrum analyzer (OSA, 600∼1700 nm, Yokogawa, Japan, AQ6370D), conductivity meter (WS-A1521), temperature-controlled water tank (KQ2200DE) and personal computer (PC) for signal processing, as shown in Fig. 7(a) and 7(b). The capacity of the water tank is about 2 liters.
To avoid the error caused by uneven heating in the process of the experiment, this experiment uses the method of natural cooling to carry out the temperature sensing experiment. We put sample 1 into the temperature-controlled water tank, heated it slowly to 28.6°C and kept it for 10 minutes. After turning off the heating equipment, we record the output waveform corresponding to different temperatures. The output spectrum obtained from the experimental record is shown in Fig. 8(a).
Fig. 8. (a) The relationship between the sensor output spectrum and the changing magnetic field from 28.6 °C to 25.4 °C at 0 Oe for sample 1. (b) Linear fitting of wavelength shifting for temperature response.
It can be seen that the two dips in the output spectrum have blue shifts with the increase of temperature. Temperature sensitivity ST can be expressed as [14]:
Δλdip or peak represents the shifts amount of the dip or peak, and ΔT represents the temperature change corresponding to Δλdip or peak. According to the fitting curve in Fig. 8(b), the two characteristic peaks of sensor sample 1 achieve the temperature sensitivity of ST1-dip1 = −919.1 pm/°C and ST1-dip2 = −903.0 pm/°C respectively.In order to verify the effect of R and L on temperature sensitivity, we made sample 2 with R = 2.8 µm and L = 7 mm, sample 3 with R = 2.8 µm and L = 8 mm, and sample 4 with R = 3.3 µm and L = 8 mm. Their arm difference is all controlled to Δla ≈ 8 mm and their PDMS package volume is the same (104 mm × 8 mm × 12 mm).
Then, we carried out temperature sensing experimental tests on samples 2, 3 and 4. The measurement process was the same as the measurement conditions of sample 1, and their temperature output spectra and fitting curves were obtained as shown in Fig. 9(a)–9(c) and Fig. 10(a)–10(c), respectively. The maximum temperature sensitivity of samples 2, 3 and 4 is ST2-max = - 772.4pm/°C, ST3-max = - 815.0pm/°C and ST4-max = - 110.9 pm/°C, respectively.
Fig. 9. The temperature responses of the samples with different OMC structural parameters. (a) R = 2.8 µm, L = 7 mm; (b) R = 2.8 µm, L = 8 mm; (c) R = 3.3 µm, L = 8 mm.
Fig. 10. Fitting curves of output spectrum of temperature response at different OMC structural parameters in experiments. (a) R = 2.8 µm, L = 7 mm; (b) R = 2.8 µm, L = 8 mm; (c) R = 3.3 µm, L = 8 mm.
Under the same L, we found that the temperature sensitivity of sample 3 was significantly higher than sample 4. In addition, there is no significant difference in the highest temperature sensitivity between sample 2 and sample 3 (they have the same OMC radius). Given this, it is shown that R plays a major role in regulating temperature sensitivity under the condition of the same PDMS package volume. The experimental results are consistent with the above mentioned theoretical analysis results.
3.4 Two-parameter demodulation
We have known that sensors can respond to the variation of magnetic field and temperature, respectively. However, existing sensors always have the demodulation problem of multi-parameter sensing, and how to realize cross-sensitive demodulation has become an urgent problem to be solved in the practical application of optical fiber sensors. To solve the simultaneous demodulation of magnetic field and temperature, the sensitivity matrix needs to be solved by inverse calculation. In this paper, we optimized the R and L of OMC to make the output spectrum of the sensor have two or more characteristic dips. We calibrated the sensitivity of the magnetic field and temperature response respectively by tracking the two dips, and then constructed the sensitivity matrix, which can be expressed as follows:
For sample 1, Δλdip1 and Δλdip2 represent the shifts amount of the dip1 and dip2, respectively, and ΔB and ΔT correspond to the demodulated magnetic field intensity and temperature changes, respectively. Therefore, Eq. (9) can be further expressed as:
It can be seen from Eqs. (9) and (10) that the key to realizing two-parameter demodulation is to construct a sensitivity matrix and carry out the high-precision inversion operation.
In order to further verify and demodulate the sensitivity matrix, the dips at 0 Oe in Fig. 4.(a) and the dips at 28.6°C in Fig. 8.(a) respectively correspond to the output spectrum as the reference spectrum of magnetic field and temperature demodulation, and the known value (Δλdip1 and Δλdip2) were brought into the matrix so that we can demodulate ΔB and ΔT respectively. The demodulation results are shown in Table 1 and Table 2, respectively.
Table 1. Demodulation results of temperature
Table 2. Demodulation results of magnetic field intensity
It can be seen that the sensitivity matrix is successfully used for the demodulation of the magnetic field and temperature sensing. For the demodulation results of temperature sensing as shown in Table 1, and the mean absolute deviation is very small (MAD1 is 0.0253 °C), which has very little impact on the temperature demodulation results. However, the demodulation results of magnetic field sensing have some inadequacy (MAD2 is 2.5954 Oe), as shown in Table 3. The demodulation results are more accurate at 30 Oe and 40 Oe, but have a slightly larger deviation of 10 Oe and 20 Oe, as shown in Table 2. This may be due to a poor degree of fitting for the magnetic field sensing (the dips shifts recorded every 10 Oe interval is not linear enough) or some system errors in the magnetic field generation and calibration equipment. In addition, for the response data of the basic parameter sensor used to construct the sensitivity matrix, the number of measurement times is limited and there are systematic deviations in the testing process, it is expected to further improve the accuracy by increasing the amount of data tested.
Table 3. Mean absolute deviation (MAD) of demodulation results
4. Discussion
In summary, the sensitivity matrix we build involves the sensitivity of magnetic field and temperature sensing. Each dip has a different magnetic field or temperature sensitivity, which are the key to matrix optimization as the coefficients of binary first-order equations.
We summarized the relationship between OMC structural parameters (R or L), PMDS package volume, and temperature sensitivity, as shown in Table 4. In the case of the same L, the temperature sensitivity of sample 1 is better than sample 2, which is contrary to the simulation results above. The reason is that PDMS has a high thermal expansion coefficient, and its volume expands as the temperature rises, thus this process squeezing the MF around the OMC waist region, reducing the volume of the MF, and increasing the density of the MF. Because the PDMS package volume of sample 1 is smaller than sample 2, under the change of unit temperature, the expansion degree of PDMS in sample 2 is larger than sample 1, resulting in higher MF density in sample 2. However, the increase of density in MF will increase n3 [19] and inhibit the decreasing effect of temperature rise on n3 (As seen from Eq. (7), n3 decreases as the temperature increases). Therefore, the temperature sensitivity of sample 1 is higher than that of sample 2 in the experiment.
Table 4. Effect of PDMS package volume on temperature sensitivity
As a result, changing the radius of OMC and reducing the volume of PDMS can improve the temperature sensitivity of the sensor, and thus optimize the demodulation of the sensitivity matrix.
We also summarized the performance of other magnetic field sensor structures, as shown in Table 5. Compared with other works, the two-parameter sensor we proposed not only realizes the high sensitivity, but also the tunable effect of PDMS on temperature sensitivity is verified by experiments, and through multiple wavelength demodulation methods to achieve the demodulation of sensitivity matrix, it is of great significance to complete the calibration of the sensor before each operation. It is worth noting that, compared with Xia's demodulation scheme based on FBG and F-P cavity, the proposed sensor has only one sensing region, which is different from their piecewise compensation structure (more than two sensing regions). Moreover, the proposed sensor does not require temperature compensation and can accurately demodulate the temperature value.
Table 5. Comparison of properties of magnetic field and temperature sensor reported in other literatures.
In addition, the interference arm region has considerable integration performance. Due to the variation of interference arm difference caused by the expansion of pressure-sensitive or salt-sensitive materials, the fringe spacing in the envelope of interference wave peak or interference wave trough changes [14]. In this way, it is expected that the sensing parameters can be extended or compensated. Therefore, using the response of the OMCI interference arm to the parameters is expected to improve the demodulation accuracy and reduce the dimensionality of matrix operations. Within the allowable range of deviation, add the interference arm as the second sensing unit, thereby increasing the number of parameter detection (such as pressure, humidity, salinity, etc.), or use the interference arm as the temperature compensation unit.
5. Conclusions
In conclusion, we have proposed and demonstrated a two-parameter sensor based on OMCI, MF and PDMS. In addition to verifying the response of the sensor to the magnetic field, we also analyzed the temperature sensing characteristics of the sensor through simulation and experimental tests, and perform the demodulation of the sensitivity matrix successfully. The experimental results show the proposed sensor achieves the highest magnetic field sensitivity of 96.8 pm/Oe and the highest temperature sensitivity of -919.1 pm/°C. The temperature sensitivity of the sensor can be optimized by changing the volume of the PDMS package or the radius of the OMC to select the sensitivity suitable for the demodulation matrix. The sensor has the advantages of small volume, low cost and high sensitivity, and the flexible structure is easy to integrate with other optical devices. It is expected to further realize the geomagnetic magnitude sensing, which has important significance for the development of marine applications such as underwater magnetic field networking detection and marine magnetic anomaly monitoring.
Funding
National Natural Science Foundation of China (Grant Nos. 61805278, Grant Nos. 61661004); State Key Laboratory of Industrial Control Technology (Guangxi Science AB1850043); Project of State Key Laboratory of Transducer Technology of China (No. SKT2001).
Acknowledgments
Y. Yu and Z. R. Zhang are both corresponding authors, and contribute equally in this paper. We thank the College of Meteorology and Oceanography in National University of Defense Technology for providing manufacturing equipment for OMC, and thank College of Liberal Arts and Sciences in National University of Defense Technology for testing the sensors.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
References
1. R. Grossinger, F. Keplinger, N. Mehmood, J. H. Espina-Hernandez, J. Araujo, C. Eisenmenger, K. Poppenberger, and J. M. Hallen, “Magnetic and Microstructural Investigations of Pipeline Steels,” IEEE Trans. Magn. 44(11), 3277–3280 (2008). [CrossRef]
2. F. Wang, Y. Song, L. Dong, C. Tao, and X. Lin, “Magnetic Anomalies of Submarine Pipeline Based on Theoretical Calculation and Actual Measurement,” IEEE Trans. Magn. 55(4), 1–10 (2019). [CrossRef]
3. L. V. Eppelbaum, ““Study of magnetic anomalies over archaeological targets in urban environments,” Physics and Chemistry of the Earth Parts A/B/C 36(16), 1318–1330 (2011). [CrossRef]
4. Q. Xu, X. Liu, K. Zhu, P. W. T. Pong, and C. Liu, “Magnetic-Field-Sensing-Based Approach for Current Reconstruction, Sag Detection, and Inclination Detection for Overhead Transmission System,” IEEE Trans. Magn. 55(7), 1–7 (2019). [CrossRef]
5. B. Heincke, R. Jackisch, A. Saartenoja, H. Salmirinne, S. Rapp, R. Zimmermann, M. Pirttijärvi, E. Vest Sörensen, R. Gloaguen, L. Ek, J. Bergström, A. Karinen, S. Salehi, Y. Madriz, and M. Middleton, “Developing multi-sensor drones for geological mapping and mineral exploration: setup and first results from the MULSEDRO project,” GEOL SURV DEN GREENL 43 (2019).
6. L. Sun, S. Jiang, and J. R. Marciante, “All-fiber optical magnetic-field sensor based on Faraday rotation in highly terbium-doped fiber,” Opt. Express 18(6), 5407 (2010). [CrossRef]
7. B. Amirsolaimani, P. Gangopadhyay, A. P. Persoons, S. A. Showghi, L. J. LaComb, R. A. Norwood, and N. Peyghambarian, “High sensitivity magnetometer using nanocomposite polymers with large magneto-optic response,” Opt. Lett. 43(19), 4615–4618 (2018). [CrossRef]
8. F. Chen and Y. Jiang, “Fiber optic magnetic field sensor based on the TbDyFe rod,” Meas. Sci. Technol. 25(8), 085106 (2014). [CrossRef]
9. J. Xia, F. Wang, H. Luo, Q. Wang, and S. Xiong, “A Magnetic Field Sensor Based on a Magnetic Fluid-Filled FP-FBG Structure,” Sensors 16(5), 620 (2016). [CrossRef]
10. H. Tian, Y. Song, Y. Li, and H. Li, “Fiber-Optic Vector Magnetic Field Sensor Based on Mode Interference and Magnetic Fluid in a Two-Channel Tapered Structure,” IEEE Photonics J. 11(6), 1–9 (2019). [CrossRef]
11. Y. F. Chen, S. Y. Yang, W. S. Tse, H. E. Horng, C. Hong, and H. C. Yang, “Thermal effect on the field-dependent refractive index of the magnetic fluid film,” Appl. Phys. Lett. 82(20), 3481–3483 (2003). [CrossRef]
12. Y. Yu, Q. Bian, Y. Lu, X. Zhang, J. Yang, and L. Liang, “High Sensitivity All Optical Fiber Conductivity-Temperature-Depth (CTD) Sensing Based on an Optical Microfiber Coupler (OMC),” J. Lightwave Technol. 37(11), 2739–2747 (2019). [CrossRef]
13. L. Zhou, Y. Yu, H. Huang, Y. Tao, K. Wen, G. Li, J. Yang, and Z. Zhang, “Salinity Sensing Characteristics Based on Optical Microfiber Coupler Interferometer,” Photonics 7(3), 77 (2020). [CrossRef]
14. L. Zhou, Y. Yu, L. Cao, H. Huang, Y. Tao, Z. Zhang, J. Wang, J. Yang, and Z. Zhang, “Fabrication and Characterization of Seawater Temperature Sensor with Self-Calibration Based on Optical Microfiber Coupler Interferometer,” Appl. Sci. 10(17), 6018 (2020). [CrossRef]
15. L. Luo, S. Pu, J. Tang, X. Zeng, and M. Lahoubi, “Highly sensitive magnetic field sensor based on microfiber coupler with magnetic fluid,” Appl. Phys. Lett. 106(19), 193507 (2015). [CrossRef]
16. F. Wei, A. K. Mallik, D. Liu, Q. Wu, G. Peng, G. Farrell, and Y. Semenova, “Magnetic field sensor based on a combination of a microfiber coupler covered with magnetic fluid and a Sagnac loop,” SCI REP-UK 7 (2017).
17. Y. Miao and J. Yao, “Temperature sensitivity of microstructured optical fiber filled with ferrofluid,” Optical Fiber Technology 55, 102161 (2020). [CrossRef]
18. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025 (2004). [CrossRef]
19. S. Y. Yang, Y. F. Chen, H. E. Horng, C. Hong, W. S. Tse, and H. C. Yang, “Magnetically-modulated refractive index of magnetic fluid films,” Appl. Phys. Lett. 81(26), 4931–4933 (2002). [CrossRef]
20. X. Li, X. Zhou, Y. Zhao, and R. Lv, “Multi-modes interferometer for magnetic field and temperature measurement using Photonic crystal fiber filled with magnetic fluid,” Optical Fiber Technology 41, 1–6 (2018). [CrossRef]
21. J. Wang, L. Pei, J. Wang, Z. Ruan, J. Zheng, J. Li, and T. Ning, “Magnetic field and temperature dual-parameter sensor based on magnetic fluid materials filled photonic crystal fiber,” Opt. Express 28(2), 1456 (2020). [CrossRef]
22. H. Huang, Z. Zhang, Y. Yu, L. Zhou, Y. Tao, G. Li, and J. Yang, “A Highly Magnetic Field Sensitive Photonic Crystal Fiber Based on Surface Plasmon Resonance,” Sensors 20(18), 5193 (2020). [CrossRef]
23. L. Mao, S. Pu, D. Su, Z. Wang, X. Zeng, and M. Lahoubi, “Magnetic field sensor based on cascaded microfiber coupler with magnetic fluid,” J Appl Phys 120(9), 093102 (2016). [CrossRef]
24. J. Zhang, X. Qiao, H. Yang, R. Wang, Q. Rong, K. Lim, and H. Ahmad, “All-fiber magnetic field sensor based on tapered thin-core fiber and magnetic fluid,” Appl. Opt. 56(2), 200 (2017). [CrossRef]
25. S. Pu, L. Mao, T. Yao, J. Gu, M. Lahoubi, and X. Zeng, “Microfiber Coupling Structures for Magnetic Field Sensing With Enhanced Sensitivity,” IEEE Sensors J. 17(18), 5857–5861 (2017). [CrossRef]
26. W. Wang, H. Zhang, B. Li, Z. Li, and Y. Miao, “Optical fiber magnetic field sensor based on birefringence in liquid core optical waveguide,” Optical Fiber Technology 50, 114–117 (2019). [CrossRef]
