A simple and compact magnetic field and temperature dual-parameter sensor is proposed, which is based on a sandwich structure consisting of a section of hollow core Bragg fiber (HCBF) filled with magnetic fluid (MF) and two sections of single-mode fiber (SMF). The corresponding relationship between the resonant dip with different periods in the transmission spectrum and specific anti-resonant (AR) mode in the HCBF is determined. The resonant dips based on different AR modes shift differently when the magnetic field intensity and temperature change. Then, the simultaneous measurement of the magnetic field intensity and temperature can be achieved by utilizing a cross matrix. The experimental results show that the maximum magnetic field sensitivity in the range of 0-12 mT is 86.43 pm/mT, and the maximum temperature sensitivity in the range of 20-60 ℃ is 17.8 pm/℃. The proposed sensor has the advantages of compact structure, easy fabrication and low cost, thus, it has great potential applications in the field of simultaneous sensing of magnetic field intensity and temperature in complex environments.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Magnetic field measurement is essential in many fields, such as bridge monitoring, power equipment monitoring, military engineering and biomedical engineering [1–3]. Optical fiber-based magnetic field sensors are widely used in magnetic field sensing due to the unique advantages of optical fiber sensors, such as compact structure, high sensitivity, and short response time [4–7]. Magnetic fluid (MF), as a special functional material in the form of nano-sized magnetic particles, is wrapped in a surfactant and uniformly dispersed in a base fluid to form a stable colloidal solution. MF has both the fluidity of liquids and the magneto-refractive properties of magnetic materials. It is often combined with optical fiber sensors and used for magnetic field sensing [8–10]. The refractive index (RI) of MF is not only affected by the magnetic field but also by the ambient temperature [11–13]. Thus, to obtain more accurate measurement results, it is necessary for simultaneously measure the magnetic field and temperature. In 2016, a magnetic field and temperature dual-parameter sensor with no-core fiber was proposed. The no-core fiber was sealed in a capillary with MF for magnetic field sensing. Different dips in the transmission spectrum have different sensitivities to the magnetic field and temperature: the maximum sensitivities of the magnetic field and temperature are 74.3288 pm/mT and 286.67 pm/℃ , respectively. Gao et al. proposed a dual-parameter sensor based on a hollow core photonic crystal fiber (PCF), in which two air holes in the air-ring cladding were injected with MF and alcohol, respectively. The sensitivity of this sensor is 810 pm/mT, and within the range from 30 to 80 ℃, the standard wavelength difference is only 0.02 nm . Subsequently, Wang et al. proposed a magnetic field and temperature sensor based on the cascade structure of the PCF and fiber Bragg grating (FBG), where MF was injected into the PCF to achieve magnetic field sensing. The maximum magnetic field sensitivity and temperature sensitivity of the PCF are 924.63 pm/mT and 162.55 pm/℃, respectively . Although the above-mentioned sensors can effectively measure the magnetic field and temperature simultaneously, the fabrication process of these sensors is complicated, and they are expensive.
Hollow core fiber (HCF) is a kind of optical fiber based on anti-resonant (AR) reflecting guidance. Its particular hollow core structure can inject liquid into the optical fiber for sensing [17–19]. As the simplest structure among HCFs, the capillary fiber is often used in combination with MF for magnetic field sensing [20,21]. However, because the cladding of the capillary fiber is composed of a single RI medium, the transmission loss of the capillary fiber is large, and the visibility of the transmission spectrum is low , and the measurement results are affected. Recently, Wang et al. designed and fabricated a new type of hollow core Bragg fiber (HCBF) with an inner diameter of 32 μm, whose cladding is alternatively composed of two RI media, and the experiment result indicates that the transmission loss of the HCBF is only 3.48 dB/cm . In 2020, a dual-parameter sensor of temperature and strain based on this new type of HCBF was proposed. The experiment results showed that owing to the low transmission loss of the HCBF, the contrast of the transmission spectrum obtained by the sensor based on the HCBF is much higher than that of the capillary fiber .
In this paper, a magnetic field and temperature dual-parameter sensor based on a new type of HCBF is proposed and demonstrated. The formation mechanism of the transmission spectrum of the single-mode fiber (SMF)-HCBF-SMF structure was analyzed. We also explain the reason for the redshift of the transmission spectrum when the intensity of the external magnetic field increases and the direction of the magnetic field is perpendicular to the axial direction of the sensor. Finally, the simultaneous dual-parameter sensing of the magnetic field and temperature is realized by utilizing a cross matrix. Owing to the low transmission loss of the HCBF, the visibility of the transmission spectrum based on the HCBF is high, which improves the accuracy of measurement results. The sensor proposed in this paper has many advantages, such as low cost, easy fabrication, and a simple structure.
2. Sensor structure and sensing principle
We designed and implemented a magnetic field and temperature dual-parameter sensor based on two AR modes by combining the fillable property of the HCBF and the magneto-refractive property of the MF. The HCBF as the sensing fiber consists of a hollow core with an inner diameter of 32 μm and four periods of high and low index claddings, where the refractive indices (RIs) of high and low index layers are 1.454 and 1.444, and their thicknesses are 1.06 μm and 3.07 μm, respectively. The outer diameter of HCBF is 125 μm. The RI distribution of the HCBF is measured using the SHR-1802, which is a 3-D RI profiler of optical fibers developed by our laboratory based on digital holography , as shown in Fig. 1(a). The RI of the RI matching liquid used in the measurement is 1.462 at the wavelength of 589 nm. The illustrations in the upper left and right corners are the 2-D distribution diagram of the RI and cross-section micrograph of the HCBF. The sensor comprises two sections of the SMF and a section of the HCBF, as shown in Fig. 1(b). Many modes other than the fundamental mode are excited at the first splicing point, owing to the mode field mismatch between the SMF and HCBF. Because the RI of the HCBF cladding is greater than that of the core, light tends to the cladding after entering the HCBF, and the cladding of the HCBF is equivalent to a Fary-Perot (F-P) etalon. The light that meets the resonant condition of the F-P etalon passes through the cladding and leaks to the outside. In contrast, the light that does not meet the resonant condition is reflected and continues forward, which is called AR reflecting guidance.
The resonant wavelength of the HCBF used in this study can be expressed as 1). According to Eq. (1), the position of the resonant wavelength and the value of the FSR in the transmission spectrum changes with the RI of the HCBF.
Simulations were carried out by using the Rsoft software with the BeamProp method to analyze the transmission characteristics of the SMF-HCBF-SMF sensor. To minimize calculation time, all simulations in this study were carried out with 2-D models, which is valid due to the symmetrical structure of the fiber. The RIs of the SMF core and cladding were set to 1.468 and 1.4628, respectively. The core and outer diameters were 9 μm and 125 μm, respectively. The parameters of the HCBF were the same as those of the actual HCBF used. The lengths of SMF and HCBF were set to 1000 μm and 3000 μm, respectively. The beam propagation results of the SMF-HCBF-SMF structure are shown in Fig. 2(a). It can be seen that because the core diameter of the HCBF is much larger than that of the SMF, when light enters the HCBF from the lead-in SMF, it will enter the core of the HCBF and excite core modes. When light is transmitted in the HCBF, a self-imaging effect similar to the multimode fiber appears during the transmission process. The transmission spectrum was simulated further understand the transmission characteristics of the SMF-HCBF-SMF sensor, as shown in Fig. 2(b). The transmission spectrum is a noticeable AR spectrum. The wavelength of the periodic dips in the spectrum corresponds to the resonant wavelength of the cladding F-P cavity. Most of the light at these wavelengths that is transmitted in the HCBF leaks to the outside. However, it can be seen from the figure that not just one, but two sets of periodic dips alternately appear in the transmission spectrum. The FSRs of the two sets of periodic dips around 1500 nm are 23.2 nm and 23.4 nm, respectively, which are consistent with the 23.32 nm calculated using Eq. (1). It is proved that these two sets of dips with different periods are both produced by AR mechanism.
To investigate the formation of the two sets of periodic dips in the transmission spectrum, the modes transmitted in the SMF-HCBF-SMF structure were analyzed. The energy ratio of each excited mode in the HCBF can be obtained when the excitation source of the HCBF is the fundamental mode of the SMF, the main excited modes are LP01 and LP02, and their energy ratio are 67.5% and 25%, respectively. The excited modes were set as the excitation source of the HCBF-SMF structure, and the transmission spectrum was simulated and compared with Fig. 2(b). Because the energy of the other modes is relatively low, this study only uses LP01 and LP02 modes as the HCBF-SMF excitation source, and the power of both modes is normalized. Figure 3(a) shows the simulation results of beam propagation when the LP01 mode is used as the excitation source. Figure 3(b) shows the transmission spectrum when the LP01 mode is used as the excitation source, and the inset shows the field distribution of the LP01 mode at 1543 nm, which corresponds to the AR wavelength of the LP01 mode. The measured FSR of the resonant wavelength around 1500 nm was 23 nm, which is consistent with the FSR in Fig. 2(b). Figure 3(c) shows the simulation results of beam propagation when the LP02 mode is used as the excitation source. Figure 3(d) shows the transmission spectrum when the LP02 mode as the excitation source, and the inset is the field distribution of the LP02 mode at 1549 nm, which corresponds to the AR wavelength of the LP02 mode. The measured FSR of the resonant wavelength around 1500 nm is 23.2 nm, which is consistent with the FSR in Fig. 2(b). In addition, the FSR corresponding to each mode can be calculated by setting n0 in Eq. (1) as the real part of effective RI of the mode. The real part of the effective refractive indices of LP01 mode and LP02 mode in HCBF are obtained by above simulation, which are 0.9997 and 0.9974 respectively. Correspondingly, their FSR are calculated as 23.32 nm and 23.37 nm, which agrees well with the simulation results of 23 nm and 23.2 nm in Fig. 3. Since the effective RI of the LP01 mode is close to that of HCBF core, the FSR calculated by Eq. (1) is basically the same.
To better match the two sets of AR interference spectrum in Fig. 2(b) with the excited modes in HCBF, the dip wavelengths of the two sets of AR interference spectrum, and the dip wavelengths in the transmission spectra based on the LP01 and LP02 modes in Figs. 3(b) and (d) are mapped one-to-one, respectively, and the dips in the transmission spectrum from left to right are marked as 1, 2, 3, …, 8, as shown in Fig. 4. The resonant wavelength of the AR 1 in Fig. 2(b) is consistent with the resonant wavelength of the transmission spectrum based on the LP01 mode. The wavelength difference between the corresponding dips is most prominent at the 8th dip, which is 0.4 nm. Moreover, the resonant wavelength of the AR 2 is consistent with the resonant wavelength of the transmission spectrum based on the LP02 mode. The wavelength difference between the corresponding dips is prominent at the 2nd dip, which is 2.4 nm. Therefore, we can determine that in the transmission spectrum of the SMF-HCBF-SMF structure, the AR 1 interference spectrum is caused by an AR reflection of the LP01 mode, and the AR 2 interference spectrum is caused by an AR reflection of the LP02 mode. Because the energy ratio of the LP01 mode is larger than that of the LP02 mode, the contrast of the interference spectrum of the LP01 mode is greater than that of the interference spectrum of the LP02 mode.
The above simulation results show that the transmission spectrum based on HCBF is an AR interference spectrum instead of a band-gap spectrum. As the length of the HCBF increases, the transmission losses corresponding to different wavelengths increase with different speeds . Certain wavelengths can no longer transmit light when the fiber length is greater than 7 cm. However, under the same length, the loss corresponding to certain wavelengths is relatively small, and the transmission spectrum forms a noticeable band-gap spectrum. However, when the length of the HCBF is small, the transmission spectrum only shows the characteristics of a significant loss at specific wavelengths, and does not form a band gap spectrum. The transmission spectrum is more consistent with the characteristics of the AR interference spectrum, that is, the wavelength with a significant loss corresponding to the resonant wavelength. Because the length of the HCBF used in this study is within 1cm, the obtained transmission spectrum is an AR interference spectrum instead of a band-gap spectrum.
The RI of the MF is related to changes in the magnetic field and temperature. As the RI of the MF changes, the wavelength of the dip in the transmission spectrum shifts. The wavelength shift can be expressed as 
3. Sensor fabrication and experiment setup
MF is a material with both magneto-refractive and fluid characteristics, and the capillary effect can be used to inject MF into the core of the HCBF to complete the measurement of magnetic field intensity. To ensure that the MF will not evaporate due to splicing discharge and the flatness of the splicing point, MF filling will be realized in several steps to ensure no MF exist at either end of HCBF. First, MF is filling a HCBF thanks to capillary effect. The MF injection will stop before the HCBF is fully filled. And the clean HCBF end-face will be spliced with one SMF using a fusion splicer (FITEL, S179). Then the SMF-HCBF structure will be cut at desired length utilizing a precision optical fiber cleaver. Alcohol will be applied for the other end-face cleaning and another SMF will be fusion spliced to the HCBF. As such, there is no MF at both ends of the HCBF. The splicing parameter (discharge intensity is 4 bit, discharge duration time is 40 ms, and the gap between two fibers is 10 μm) is optimized to avoid the collapse of the core of the HCBF during splicing. The side micrograph of the MF-filled HCBF and the splicing point are shown in Fig. 5(a). The length of the HCBF was 3 mm, and the MF used in this study was EMG 805 (Ferrotec). It can be seen from Fig. 5(a) that the HCBF core expanded at the splicing point at the left end. This is because the right end is spliced with the SMF closely, and the pressure in the HCBF becomes larger when the left end is spliced with the SMF. Since light enters the HCBF and transmits approximately 200 μm before AR effect occurs , the expansion of the HCBF only at the splicing point will not affect the transmission characteristics of the light.
A schematic diagram of the experimental setup is shown in Fig. 5(b). The SMF-MF-filled HCBF-SMF sensor was placed in a magnetic field controlled by an external current source, and the direction of the magnetic field was perpendicular to the axis direction of the HCBF. A Gauss meter (F.W. BELL, 8030) with a minimum resolution of 0.1 Gs was placed in the magnetic field to calibrate the magnitude of the magnetic field in real-time. Light was emitted from the broadband light source (Amonics, ASLD-CWDM-5) into the lead-in SMF (Corning, SM-28), and the output light was received by an optical spectrum analyzer (OSA) (Yokogawa, AQ6370), which has a minimum resolution of 0.02 nm.
4. Results and discussion
The magnetic field sensing experiment was performed at room temperature, and the transmission spectra at different magnetic field intensities are shown in Fig. 6(a). From the previous analysis, it can be seen that the interference spectra of dips 1 and 2 are mainly formed by AR modes of the LP01 and LP02, respectively. Zooming in on dips 1 and 2, we find that the position of dip 1 hardly changes when the magnetic field changes while the position of dip 2 exhibits a redshift with the increase in the magnetic field, as shown in Fig. 6(b) and Fig. 6(c).
Because of the light absorption of the MF, only a small amount of MF was injected into the HCBF in our experiment. Owing to the sensitivity of MF to the magnetic field, the RI of the MF changes when the magnetic field changes. When the MF-filled HCBF is spliced into the SMF, the heating of the fusion splicer causes the MF in the HCBF to move, and then the MF will mostly adhere to the inner wall of the HCBF. Hence, the injected MF was equivalent to a cladding of the HCBF. Generally, the refractive index of magnetic fluid depends on the relative orientation of the light transmission and the magnetic field  or the external electric field and the magnetic field . It can be observed from Ref.  that, when the applied magnetic field direction is perpendicular to the light transmission direction, the RI of the MF will decrease with the increase in magnetic field intensity. However, when the applied magnetic field direction is parallel to the light transmission direction, the RI of the MF increases with an increase in magnetic field intensity. Moreover, according to Ref. , when the light transmission direction is parallel to the applied magnetic field direction, the MF is more sensitive to changes in the magnetic field.
Because the RI of the HCBF cladding is greater than that of the core, light is refracted at the core-clad interface and enters the cladding. The transmission trajectory of the core mode in HCBF is shown in Fig. 7. The relationship between incident angle θ1 and longitudinal propagation constant β and wave vector n0k0 can be expressed as 
When the fundamental mode of SMF is set as the excitation source in simulation at the wavelength of 1550 nm, the real part of effective refractive index of LP01 mode and LP02 mode in HCBF are obtained, which are 0.9997 and 0.9974 respectively. By taking the effective refractive index of LP01 mode and LP02 mode into the Eqs. (3) and (4), the transverse propagation constants kt of LP01 mode and LP02 mode can be obtained as 0.0992×106 and 0.2919×106, respectively. The transverse propagation constant kt of LP02 mode is greater than that of LP01 mode, which can indicate that the component of LP02 mode parallel to the magnetic field direction is greater than that of LP01 mode.
Hence, the wavelength of dip 1 does not change significantly as the applied magnetic field intensity changes, while the wavelength of dip 2 will have a significant redshift. A linear fitting on dip 2 under different magnetic field intensity in the range of 0-12 mT is performed, as shown in Fig. 6(d), where the sensitivity is 86.43 pm/mT, and R2 is 0.96368.
The temperature response of the sensor was also tested by placing the sensor in a temperature-controlled chamber. The temperature was increased from 20 to 60 ℃ in steps of 10 ℃. The evolution of the transmission spectrum is shown in Fig. 8(a). Dips 1 and 2 selected in Fig. 8(a) are the same as those in Fig. 6(a), and the temperature responses of the dips 1 and 2 are shown in Figs. 8(b) and 8(c), where both dips exhibit a redshift with increasing temperature. Comparing the two dips by linear fitting, as shown in Fig. 8(d), the temperature sensitivity of dip 1 is 17.8 pm/℃, and its R2 is 0.95025, while the temperature sensitivity of dip 2 is 17 pm/℃, and its R2 is 0.80968. Thus, the sensitivity of the two dips to temperature is practically the same. Because the thermo-optical coefficient of the MF is much smaller than the magneto-optical coefficient, the sensitivity of the MF to the temperature is much smaller than that of magnetic field. Because the R2 of dip 1 is higher than that of dip 2, the temperature sensitivity of dip 1 is taken as the temperature sensitivity of the sensor.
Because the SMF-MF-filled HCBF-SMF sensor has different sensitivities to magnetic field intensity and temperature, the simultaneous sensing of magnetic field and temperature can be achieved through a cross matrix. When different magnetic fields and temperatures are simultaneously applied to the HCBF-based sensor, the wavelength shifts of dips 1 and 2 can be expressed as
The change in the magnetic field intensity and temperature can be expressed as the following matrix:
Therefore, the magnetic field intensity and temperature can be monitored simultaneously by detecting the dip wavelength shift of the two AR interference spectra.
In addition, the stability of the proposed sensor was measured by continuously recording the sensor’s dip shift for 1 hour. To eliminate the influence of surrounding environmental change, sensor was placed into a temperature-controlled chamber with temperature set as 25 ℃. The variances of wavelength shift corresponding to dip1 and dip 2 were 0.0157 nm and 0.0467 nm, respectively. The sensor was also placed under fixed magnetic field to study the stability of sensor under magnetic field. Variances of wavelength shift corresponding to dip 1and dip 2 were 0.0164 nm and 0.0582 nm, separately. It is also observed the variances of dip 1 and dip 2 were relatively larger when under magnetic field that the one with no magnetic field. It could be related to the environmental change including lab temperature change and magnetic field variation in 1 hour period. Nonetheless, the small variances indicate the good stability of our proposed sensor.
In summary, we propose an in-lined optical fiber sensor formed by splicing a section of MF-filled HCBF between two SMFs to measure the magnetic field intensity and temperature simultaneously. The relationship between dips of different periods in the transmission spectrum of the SMF-HCBF-SMF structure and the AR modes of the HCBF is determined. Because of the similarity between the structure of the HCBF used in this study and ordinary hollow core fibers, this conclusion can be used to explain similar phenomena in the transmission spectrum of other hollow core fibers. We also explained why the transmission spectrum exhibits a redshift when the magnetic field intensity increases and the direction of the magnetic field is perpendicular to the axis of the sensor. Two resonant dips caused by different AR modes are used to simultaneously measure the magnetic field intensity and temperature, and the sensitivities of magnetic field and temperature are 86.43 pm/mT and 17.8 pm/℃, respectively. Although the magnetic field sensitivity of the sensor we proposed is relatively low when compared to Refs. [1,6,16], simultaneous measurements of both magnetic field and temperature could be achieved. Thanks to its simple structure, easy fabrication and simple subsequent processing of measurement results, this proposed sensor could be applied in fields that require multi-parameter measurements including magnetic field and temperature.
National Natural Science Foundation of China (61735009, 61875116, 61875118, 62022053); 111 Project (D20031); Advanced Optical Waveguide Intelligent Manufacturing and Testing Professional Technical Service Platform of Shanghai (19DZ2294000).
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from authors upon reasonable request.
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