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Abstract
What we believe is a novel dual-channel whispering gallery mode (WGM) sensor for concurrently measuring bidirectional magnetic field and temperature is proposed and demonstrated. Two sensing microcavities [magnetic fluid (MF)-infiltrated capillary and polydimethylsiloxane (PDMS)-coated microbottle, respectively, referred as Channel 1 (CH1) and Channel 2 (CH2)] are integrated into a silica capillary to facilitate the dual-channel design. Resonant wavelengths corresponding to CH1 and CH2 mainly depend on the change in the magneto-induced refractive index and the change in the thermo-induced parameter (volume and refractive index) of the employed functional materials, respectively. The MF-infiltrated capillary enables bidirectional magnetic field sensing with maximum sensitivities of 46 pm/mT and -3 pm/mT, respectively. The PDMS-coated structure can realize the temperature measurement with a maximum sensitivity of 79.7 pm/°C. The current work possesses the advantage of bidirectionally magnetic tunability besides the temperature response, which is expected to be used in field such as vector magnetic fields and temperature dual-parameter sensing.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, optical resonators have played a major role in modern optics. Compared with interference resonators based on optical fibers, optical resonators exhibit higher sensitivity and have been widely applied in various fields, such as micro-nano photonics, integrated optics, and quantum optics [1–7]. Generally, common optical microresonators can be divided into the following three types: Fabry–Pérot (FP) resonators, photonic crystal resonators, and whispering gallery mode (WGM) resonators. Compared with the other two microresonators, WGM microstructure sensors have higher values of quality factor (Q-factor), extremely smaller mode volumes, simpler preparation and integration. Accordingly, they are implemented in various sensing applications such as biology, gas, temperature, magnetic field, etc [8–16]. Generally, most WGM microstructures need to be combined with some key functional/sensitive materials, such as magnetic fluid (MF) and polydimethylsiloxane (PDMS), to achieve magnetic field and temperature measurement.
MF is a kind of special magneto-optical material that consists of surfactant-coated magnetic nanoparticles (MNPs) and carrier liquid. It has both the fluidity of liquid and tunable optical properties, including tunable refractive index (RI), tunable transmission loss, and tunable birefringence, so it has been extensively applied in designing magnetic field sensors [17–22]. However, in practical measurement situations, magnetic field and temperature often occur simultaneously. Most optical fiber magnetic field sensors based on MF are sensitive to temperature change, which often leads to the inaccuracy of magnetic field measurement. Therefore, with the continuous deepening of research, single-parameter magnetic field sensors are unable to meet the needs of modern society [23].
In 2012, Zu et al. proposed a magnetic field sensor based on MF and Mach–Zehnder interferometer. The achieved sensitivity and resolution of the sensor are 2.367 pm/Oe and 4.22 Oe, respectively. The magnetic field sensor is insensitive to temperature variation with a temperature coefficient of only 3.2 pm/°C [24]. In 2019, Wei et al. proposed a temperature-compensated magnetic field sensor based on a ring erbium-doped fiber laser combined with a fiber Bragg grating (FBG) and a Sagnac loop containing a microfiber coupler (MFC) and MF. The maximum experimentally demonstrated sensitivity of the magnetic field and temperature determined from the spectral shifts of two laser peaks are 102 pm/mT and 18 pm/°C, respectively [25]. In 2019, Ying et.al. studied a magnetic field and temperature sensor based on a D-shaped photonic crystal fiber using surface plasmon resonance and directional resonance coupling methods [26]. In 2023, Liu et al. fabricated a spherical-multi mode fiber-thin core fiber-sphere sensor structure. The sensitivity was significantly higher than that of a corresponding Mach-Zehnder interferometer based on a sphere-thin core fiber-sphere sensing structure [27]. In addition, temperature and magnetic field optical fiber sensing structures also include tapered all-solid waveguide-array fiber (WAF) [28], optical fiber structure with cascaded fiber Bragg grating (FBG) [29–32], fiber-loop shape structure [33,34], U-bent fiber structure [35] and FP structure [36,37]. Generally, those structures have limitations in manufacturing processes and have difficulty in meeting the requirements of miniaturization and integration. Thus, to overcome these limitations, other alternative routes for simultaneously sensing magnetic fields and temperatures are considerably important.
In this work, we first carry out a systematic study of the distribution characteristics of MNPs in the microcavity with dynamic simulation and experimental observation. Then, MF and PDMS are used as the key sensitive materials. The composite microcylindrical and microbottle cavities are integrated into a capillary tube. The WGM of the microcylindrical and microbottle cavities are efficiently excited by adjusting the coupling position between the microcavities and the tapered fibers. The magnetic field and temperature dual-parameter measurement is realized. Compared with other vector magnetic field sensing structures, this sensing structure avoids conventional problems like fiber fragility, manufacturing complexity, and high cost. It is expected to promote the development of sensor miniaturization and integration in designing temperature-compensated fiber-optic vector magnetic field sensing based on WGM.
2. Fabrication
As shown in Fig. 1, the detailed fabrication process is divided into the following steps: Step 1 Infiltration process: A hollow capillary tube with an initial outer (inner) diameter of 125 µm (75 µm) is employed [Fig. 1(a)]. Drop one end of the capillary tube into MF. The MF will infiltrate the capillary tube under the influence of capillary force [Fig. 1(b)]. Step 2 Eetching process: After two ends of the MF-infiltrated capillary are sealed with UV glue, it is inserted into the hydrofluoric (HF) acid solution for about 40 minutes to obtain a microcylindrical resonance (MCR) cavity [Fig. 1(c), see the red frame labeled as Channel 1(CH1)]. The final diameter of the etched region is 86 µm, and the wall thickness is 5.5 µm. Step 3 Adhering process: Drop PDMS solution onto the etched capillary. The PDMS solution will be attached to the external surface of the capillary and form an additional microbottle. Then, the PDMS microbottle resonance (MBR) cavity with a maximum diameter of 227.9 µm is obtained [Fig. 1(d), see the green frame labeled as Channel 2(CH2)]. Compared with the conventional hot extrusion and spherical cavity-pressing methods, longer and flatter MBR cavities can be easily obtained via this method, which does not employ any electric motors or discharge technology. It possesses the advantages of simple fabrication and resource-saving.
Fig. 1. Fabrication processes of the MCR and MBR cavities and their corresponding microscopic images: (a) the employed capillary tube, (b) MF-infiltrated capillary tube, (c) HF acid-etched capillary tube and formation of MCR cavity, (d) PDMS attached to the external surface of the capillary and formation of MBR cavity.
The employed hollow capillary tube is provided by Minghai Optoelectronics Technology Ltd. Co. (Henan, China). The employed MF is water-based MF with surfactant-coated 10-nm-diameter Fe3O4 nanoparticles (provided by Hangzhou Jikang New Materials Ltd. Co., Hangzhou, China). The initial volume fraction of MNP within MF is 33%. The volume fraction applied in this work is 9.7%, and the RI of MF is around 1.37 [diluted with distilled water and measured by a refractometer (A670, Hanon, Jinan, China)]. The employed PDMS solution is fabricated by mixing the elastic polymer (Sylgard 184-A) and the curing agent (Sylgard 184-B) with a ratio of 10:1.
3. Sensing principle
Figures 2(a) and 2(b) show the schematic diagrams of the fabricated MCR and MBR cavities coupled with two tapered single-mode fibers (SMFs, core/cladding diameter of 105.5/125 µm) under different magnetic field directions. Figure 2(c) is the microscope image of the dual-channel sensor. Figure 2(d) shows the typical optical photograph indicating the coupling between the MBR cavity and the tapered fiber within a high-input power laser. These verify the effective coupling between the microcavity and the tapered microfiber.
Fig. 2. Schematic diagram of the proposed dual-channel sensor under different magnetic field directions: (a) perpendicular to the capillary axis, (b) parallel to the capillary axis, and microscope image of the dual-channel sensor (c), and a typical optical photograph indicating the coupling between the MBR cavity and the tapered fiber within a high input power laser (d).
The operating principle of the sensing structure is based on monitoring the WGM resonant wavelength shift. When the incident light enters the tapered region of the SMF, the WGMs can be effectively excited through the evanescent coupling between the tapered microfiber and the MCR and MBR cavities. The following equation can describe WGM resonant wavelength
where an integer is the resonant wavelength, refers to the effective refractive index (ERI), and represents the outer radius of the microcavity.For CH1, the microcavity radius is fixed. The relationship between resonance wavelength shift and ERI change is expressed as
Equation (2) indicates that the resonant wavelength will shift with the variation of ERI.
In this work, MF is mainly employed as the magnetic field-sensitive material, which possesses both the magnetic properties of solid magnetic materials and the fluidity of liquid materials. Under a zero magnetic field, the MNPs within MF are dispersed randomly into a carrier liquid. However, when the magnetic field is applied, the MNPs within MF are rapidly magnetized. Due to the dipolar interaction of inter-nanoparticles, the MNPs favor agglomeration along the magnetic field direction and form chain-like structures [38,39], resulting in liquid-phase separation and a certain transformation in their equivalent dielectric constant. The formula for the equivalent dielectric constant is given as [40]
For CH2, the thermal effect causes the temperature-induced change in RI and the outer radius of the PDMS-coated microbottle. Thus, the resonance wavelength shift Δλ can be expressed as
Fig. 3. Electric field amplitude distribution of WGM within different PDMS thickness-clad MBR cavities at 1550 nm: (a) 5.5 µm, (b) 11 µm, (c) 15 µm, (d) 71.45 µm.
4. Experimental details and results
4.1 MNPs’ agglomeration
For the perpendicular configuration case, the chain clusters along the magnetic field direction may lead to the uneven density distribution of MNPs along the periphery of the capillary. Therefore, the local ERI is influenced by the magnetic field's intensity and direction. To verify this, we simulated the magnetic nanochain distribution within the capillary tube. The results are shown in Figs. 4(a) and 4(b) (refer to Visualization 1 for the typically dynamic evolution based on calculation). The magnetic chains are arranged along the capillary axis when the magnetic field direction is parallel to the capillary axis, as shown in Fig. 4(a). However, when the magnetic field direction is perpendicular to the capillary axis, many MNPs agglomerate near Areas I and II, as shown in Fig. 4(b). Contrarily, few MNPs gather near Area III and IV. This phenomenon illustrates that the local MNP concentration depends on the direction of the magnetic field.
Fig. 4. Simulation and microscope images of the magnetic nanoparticle distributions under different magnetic field directions: (a), (c) parallel to the capillary axis, (b), (d) perpendicular to the capillary axis (Multimedia view).
As the MNPs are too small (∼10 nm in diameter) to be observed by optical microscopy, we mix MF with non-magnetic carbon nanotubes (8-15 nm in diameter, 3-12 µm in length) for better illustration and imaging purposes. Figures 4(c) and 4(d) show the magnetic nanochain distribution in the capillary tube observed with the microscope (refer to Visualization 2 for the typically dynamic evolution observed with the microscope). The observations agree well with the simulation results. Therefore, simulation and imaging results confirm the asymmetric distribution of MNPs along the periphery of the microcavity for the perpendicular configuration.
4.2 Bidirectional magnetic field measurement
Figure 5 shows the schematic diagram of the experimental setup. A highly stable light source with emitting light covering the wavelength range of 1450-1650 nm was employed. The output power of the light source is 12 mW. The whole sensing structure was placed in the temperature-controllable oven for temperature sensing. A permanent magnet was set above the sensor. The magnetic field strength was adjusted by changing the distance between the magnet and the oven, which was monitored simultaneously by a Gauss meter with an accuracy of 0.1 mT. The transmission spectra were recorded by the optical spectrum analyzer (OSA) with 0.02 nm resolution.
The coupling distance between the capillary and the microfiber is accurately controlled by two three-axis translation stages. The detailed process is as follows: first, the lead-in ends of the two tapered microfibers are connected to the light source by a 1 × 2 optical splitter, and the other two lead-out ends are connected to the OSA. Then, the ends of the tapered sections are fixed on the glass slide with UV glue and try to keep the tapered region partially suspended. Next, the MCR and MBR cavities are fixed on the three-dimensional translation platforms. Through adjusting, the MCR and MBR cavities can be close to the two tapered microfibers for effective coupling. This process is synchronously observed by a CCD camera connected to the computer.
For CH1, the sensor's response to magnetic field intensity and direction is studied. As the MCR cavity is formed naturally with a capillary tube, WGMs can be effectively excited in the HF-etched tube. The dip of the response spectrum near the 1585 nm wavelength is selected for monitoring and analysis, and the corresponding Q-factor and FSR are 7.2 × 104 and 0.6 nm, respectively. Figures 6(a) and 6(b) show the transmission spectra for CH1 under different magnetic field strengths for perpendicular and parallel orientations, respectively. For perpendicular configuration, the resonant wavelength changes greatly with the magnetic field intensity ranging from 0 to 13 mT [see Fig. 6(a)]. However, the blueshift of the spectra is relatively slight for parallel configuration [see Fig. 6(b)].
Fig. 6. Response of transmission spectra to magnetic field intensity at different magnetic field directions: (a) perpendicular to the capillary axis, (b) parallel to the capillary axis, (c) resonance wavelength as a function of magnetic field intensity at perpendicular and parallel directions.
Figure 6(c) explicitly shows the corresponding resonant wavelength as a function of magnetic field intensity in perpendicular and parallel directions. As the magnetic field ranges from 0 to 13 mT, the linear responsivities of the sensing structures are 46 and -3 pm/mT, respectively.
It should be noted that MFs can exhibit a phenomenon known as the magneto-optical effect in the presence of a magnetic field. This effect causes a change in the polarization state of light passing through the MFs [42]. For magnetic field applied parallel or perpendicular to the light path (magnetic field perpendicular or parallel to the capillary axis), the MFs’ anisotropy caused by the magneto-optical effect can undergo changes, which may lead to different variations in the refractive index and scattering properties of light. Therefore, it leads to the results of varying spectral shift directions and degrees under different magnetic field directions. This provides the fundamentals for bidirectional magnetic field measurement.
4.3 Temperature measurement
For CH2, the temperature measurement was carried out. Utilizing the zoom function on the spectrometer, we magnified the spectral region around 1547 nm for closer observation. The process of PDMS expansion is relatively slow and takes a certain amount of time to reach stability. In order to further ensure the reading accuracy, the data was recorded 5 minutes after the temperature changed, when the spectrum no longer drifts. Figure 7(a) shows the transmission spectra of the MBR cavity at different temperatures, which have been vertically stacked with +1–7 dB offset. The transmission spectra present a redshift. The corresponding Q-factor and FSR are 1.5 × 104 and 1.3 nm, respectively. When the temperature rises, the MBR’s cavity will expand due to heating and get closer to the tapered fiber. The coupling distance between the cavity and the tapered fiber changes accordingly. At the same time, the increase of loss energy results in a decrease in the valley contrast (relative depth) of the outgoing spectrum and the radial modes broadening. The linear responsivity is 79.7 pm/°C, as shown in Fig. 7(b). Repeated experiments employing MBR structures with different sizes indicate the reliability and reproducibility of the sensing structure, as shown in Fig. 7(c).
Fig. 7. Transmission spectra corresponding to the variation of temperature: (a) temperature increases from 25 to 65 °C, (b) resonance wavelength as a function of temperature, (c) standard deviation of temperature sensing.
For comparison, Table 1 lists the sensing structures, fabrication methods, and sensing performance of the related optical fiber sensors based on WGM [43,49–56]. The previous magnetic field sensors based on MCR and MBR structures have the advantage of high sensitivity but require complex manufacturing technology [50,51]. Temperature sensors based on spindle-shaped and PMMA-microbubble structures have the limitations of low sensitivity and complex manufacturing processes [53,55]. All the reported works are merely concerned with single parameter measurement. Yu et al. proposed a microcapillary resonator to measure temperature-compensated DC magnetic field [56], but the sensitivities (-0.3 pm/mT, 18.381 pm/°C) still need to be improved. By contrast, the dual-channel WGM-based sensor proposed in this work not only has high sensitivities (46 pm/mT, 79.7 pm/°C) but also has a significant advantage in high Q-factor, small size, compact structure, and simple fabrication, which can be applied in the field of simultaneous temperature and magnetic field high-precision measurement. Finally, we would like to point out that the designed sensor has some limitations as well. It requires a high level of environmental stability. It can't be measured accurately in unstable or vibrating environments. We can attempt to design a stable and shockproof packaging scheme to enhance the stability of the sensor further.
Table 1. Sensing performance of various magnetic field sensors based on WGM
5. Conclusions
In summary, using MF and PDMS as key sensitive materials, a novel bidirectional magnetic field and temperature dual-parameter sensor is proposed. The visualization of MNPs’ distribution within MF is simulated and experimentally observed. The maximum magnetic field sensitivities under perpendicular and parallel directions are 46 pm/mT and -3 pm/mT, respectively. The maximum temperature sensitivity is 79.7 pm/°C. Compared with other related optical fiber WGM structures, this sensor has two kinds of microcavities successively integrated into the single capillary tube. Therefore, it possesses special characteristics like small size, compact structure, and simple fabrication. In addition, dual-parameter measurement based on the two-cavity structure can be simultaneously obtained with this configuration. Thus, it is expected to be used in field such as vector magnetic field and temperature dual-parameter sensing.
Funding
National Natural Science Foundation of China (Grant No. 62075130); Science Foundation of Shanghai (23ZR1443300); Program of Shanghai Academic Research Leader (Grant No. 23XD1402200).
Disclosures
The authors declare no conflict 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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