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Abstract
A kind of temperature and magnetic field sensor using Fabry-Perot interferometers (FPIs) and Vernier effect to enhance sensitivity is proposed. The sensor structure involves filling the FP air cavities with polydimethylsiloxane (PDMS) and magnetic fluid (MF) to create the PDMS and MF cavities for temperature and magnetic field detection, respectively. The two cavities are reflective structures, which are interconnected in series through a fiber-optic circulator. Experimental data demonstrates that the Vernier effect effectively enhances the sensor sensitivity. The average temperature sensitivity of the sensor is 26765 pm/°C within the range of 35∼39.5°C. The magnetic field intensity sensitivity is obtained to be -2245 pm/mT within the range of 3∼11 mT. The sensitivities of the temperature and magnetic field using the Vernier effect are about five times larger than those of the corresponding single FP cavity counterparts.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, different types of fiber-optic temperature and magnetic field sensor structures have emerged and been applied in various aspects of the industrial sector and daily life [1–4]. For example, in daily life, optical fiber sensors can be used to monitor the internal temperature of air conditioners due to their small size and stability [4]. They are mainly divided into two categories, that is those based on the fiber grating and those based on the interferometer. Fiber Bragg gratings are compact and lightweight, but they have the disadvantages of low sensitivity and cross-sensitivity. In addition, the equipment used to manufacture fiber grating is expensive. Michelson interferometer [5,6], Sagnac interferometer [7,8], Mach-Zehnder interferometer (MZI) [9–11], and Fabry-Perot interferometer (FPI) [12,13] are four kinds of typical fiber-optic interferometric configurations. Compared to fiber Bragg gratings, interferometer-based fiber-optic sensors can offer higher sensitivity and have the potential to address the issue of crosstalk. In addition, the well-known optical Vernier effect can be exploited in interferometer-based fiber-optic sensors to further improve the sensitivity, which has become the research hotspot recently. A typical structure consisting of two interferometers, called reference interferometer and sensing interferometer, can produce spectra with two different free spectral ranges (FSRs) to simulate a pair of Vernier scales. The two interference spectra from the different interferometers are superimposed together to form a Vernier spectrum, which results in a Vernier envelope with a much wider FSR than that of a single interferometer. Accordingly, the response of envelope shift to ambient change will be much more significant, which reflects the sensitivity amplification effect.
In 2012, R. Xu et al. first proposed the application of optical Vernier effect in optical fiber sensors [14]. Subsequently, some temperature sensors based on Vernier effect have been proposed. In 2015, L. Shao et al. used the cascaded fiber-optic Sagnac interferometers based on Vernier effect to enhance the sensitivity of temperature sensing [15]. In 2020, L. Xie et al. proposed a concatenated tapered two-mode fiber-sensitized temperature sensor based on Vernier effect and conducted experimental verification [16]. Both theory and experiment show that the series structure has a higher extinction ratio than that of the parallel counterpart. In 2021, M. G. Sigifredo et al. proposed a highly sensitive temperature sensor based on two cascaded MZIs using the Vernier effect [17]. The all-fiber MZIs were assembled by splicing a segment of hollow fiber between two sections of multimode fibers. In 2022, R. Pan et al. proposed and demonstrated a novel high-sensitive temperature sensor with parallel polydimethylsiloxane (PDMS)-filled FPIs based on the dual Vernier effect [18]. The sensitivity of temperature sensing is greatly improved by using temperature-sensitive materials combined with the Vernier effect.
Magnetic field sensors have been widely used in many scientific and industrial application scenarios, including biomedical detection, aviation industry, space, and geophysical research. MF is a kind of stable colloidal solution, which is composed of nanometer magnetic solid particles, carrier solution, and surfactant. It not only has the fluidity of liquid but also has the magnetic properties of solid magnetic materials. Due to its magneto-induced refractive index (RI) modulation, magnetic fluid (MF) has been widely used as magnetic field indicator in all-fiber-optic magnetic field sensing field. It is widely used for designing various new-fashioned fiber-optic magnetic field sensors [19–22]. Fiber-optic FPIs based on MF have attracted a lot of interest due to their simple and compact structure, and easy fabrication among optical fiber magnetic field sensors. In 2013, S. Dong et al. studied magnetic field sensing based on the change of MF’s volume using the air-gap FPI [23]. The highest sensitivity of magnetic field sensing can reach 117.3 pm/mT when the sensing head is set at 45° azimuthal angle (with respect to the magnetic field direction). In 2014, Y. Zhao et al. proposed to use fiber Bragg grating to compensate for the temperature effect of the fiber-optic FP magnetic field sensor [24]. The maximum measured magnetic field intensity is up to 600 Gs with a sensitivity of 40 pm/Gs and the measurement resolution is 0.5 Gs. In 2014, P. Zhang et al. proposed an FP magnetic field sensor using the Vernier effect, which used a sensor embedded with metal wire to perform the measurement [25]. The sensitivity was significantly higher than that of a corresponding single FPI. In 2018, T. Yao et al. made a MF-filled fiber-optic FPI and studied the optical force acting on the magnetic nanoparticles [26]. The relative relationship between the interference spectral drift and the refractive index of MF was obtained.
In this work, an optical fiber structure designed for temperature and magnetic field sensing is proposed and optimized using the optical Vernier effect to achieve high sensing performance. Two sensing probes are fabricated with single-mode fiber (SMF) FP cavities. One of the sensing probes is filled with temperature-sensitive PDMS material to improve the temperature sensitivity of the structure, while the other sensing probe is filled with MF for magnetic field detection. Two sets of interferometric spectra with similar, yet distinct, FSRs are designed to generate the Vernier effect. To enhance the reflected light intensity, a gold film is deposited on the end face of the fiber. The interconnected reflective structures and sequential light passage through the cavities effectively avoid interference, which ensure accurate and reliable measurements. Experimental results show that the average temperature sensitivity of 26765 pm/°C is obtained in the range of 35 to 39.5°C and the maximum magnetic field sensitivity of -2245 pm/mT is obtained in the range of 3 to 11 mT, both of which are about five times larger than those of the corresponding single FP cavity counterparts.
2. Sensing principle
The structure of the sensor is schematically shown in Fig. 1. It primarily consists of two FP cavities: one is filled with PDMS for temperature sensing (referred as FP-PDMS) [Figs. 1(a) and 1(c)], and the other incorporates a filled MF for magnetic field sensing (referred as FP-MF) [Figs. 1(b) and 1(d)]. By adjusting the lengths of the two FP cavities, the FSRs of the two cavities can be very close to each other, which will result in the Vernier effect assigned to the spectral superposition and then increase the sensitivity of the sensor.
Fig. 1. Schematic diagram of the sensor structure (a) and (b), and the corresponding photographs of the as-fabricated sensing probes (c) and (d).
The reflected light intensity of a single FPI can be expressed as
The FSR of the two FPIs can be expressed as [27,28]
An important characteristic of the Vernier effect is the magnification factor (M), which describes how large the FSR of the envelope is when compared with that of the individual sensing FPI and is defined as [29]
where $FS{R_S}$ is the FSR of the sensing cavity, $FS{R_R}$ is the FSR of the reference cavity. In temperature measurement, FP-PDMS serves as the sensing cavity and FP-MF acts as its reference cavity. Whereas in magnetic field measurement, FP-MF functions as the sensing cavity and FP-PDMS becomes the reference cavity. When there are any changes in external temperature or magnetic field, the length of the FP-PDMS and the refractive index of the FP-MF (viz. MF) will change correspondingly. The cascaded double cavity structure will show improved sensitivity in both temperature and magnetic field measurements. The sensitivities are M times larger than those of their single-sensing cavity counterparts.For the FP-PDMS sensing probe, the employed PDMS has relatively large thermo-optic coefficient (TOC) and thermal expansion coefficient (TEC). The TEC is much larger than the TOC ($TOC ={-} 4.5 \times {10^{ - 4}}/^\circ C$, $TEC = 9.6 \times {10^{ - 4}}/^\circ C$ [30]). During the experimental process, it was observed that the dominant influence on PDMS is primarily attributed to its thermal expansion behavior. PDMS can only expand in the axial direction due to constraint in the radial direction. Consequently, as the temperature increases, the cavity length (L) expands, which causes a redshift in the reflective spectrum.
Based on Fresnel’s law, the reflectivity of light on the SMF end-face can be expressed as $R = {[({n_{Si{O_2}}} - {n_{PDMS}})/({n_{Si{O_2}}} + {n_{PDMS}})]^2}$, where ${n_{PDMS}}$ and ${n_{Si{O_2}}}$ are the refractive indices of the PDMS and the fiber core, respectively. Considering ${n_{PDMS}} = 1.3804$ and ${n_{Si{O_2}}} = 1.467$, when the light reaches the first reflecting interface (M1), the reflectance R at the PDMS-fiber interface is 3.04%, which is lower than the reflectance at the air-fiber interface (R = 18.93%, unfilled cavity, i.e. air cavity). Figure 2 plots the simulated reflection spectra for the cavity with different fillers, which indicates that the reflection spectra of the air cavity change remarkably when the cavity is filled with PDMS. After coating the cavity with gold film, the reflected light intensity can be increased remarkably and a good interference effect can be obtained. Therefore, the two reflecting interfaces are coated with gold film in our experiments.
For the FP-MF sensing probe, the magnetic moment of magnetic nanoparticles (MNPs) within MF will change with the applied magnetic field. As shown in Fig. 3, in the absence of an external magnetic field, H = 0 Oe, MNPs are irregularly distributed in the carrier fluid assigned to the never-ending Brownian motion, which shows a relatively stable state as a whole. When the applied magnetic field intensity is less than the initial critical intensity (H0), the polarization direction of the magnetic MNPs is along the magnetic field direction to a certain extent and only few particles form the chain structure, as shown in Fig. 3(b) for 0 < H ≤ H0. When the applied magnetic field is greater than H0 and less than the saturation magnetization (Hc), almost all the MNPs will produce magnetic chain structures along the direction of the magnetic field [see Fig. 3(c)]. As the strength of the magnetic field increases further, more and more MNPs come together to create magnetic chains. When the magnetic field intensity increases beyond Hc, as shown in Fig. 3(d) for H ≥ Hc, all particles are bound in the chain and reach the saturation state, so the refractive index of MF no longer changes. Therefore, the refractive index of MF will gradually change with the magnetic field until it reaches saturation.
The explicit relationship between refractive index of MF (${n_{MF}}$) and magnetic field intensity (H) can be expressed by the Langevin-like function [31]
3. Experimental details and discussion
For fabricating the FP-MF cavity for magnetic field sensing, a kind of water-based MF (Initial Susceptibility: 0.55, Density: 1.18 gm/ml, Nature of Surfactant: cationic) is used. The detailed production process is as follows: initially, a 20 mm section of SMF is inserted into the magnetron sputtering system (ETD-900 M) for 240 s at a working current of 15 A. The gold film is then coated onto the end-face of the SMF to enhance its reflectivity, which functions as a reflective mirror. Then, the gold-coated SMF is placed into a capillary tube and secured with UV adhesive. The inner diameter of the capillary glass tube is 126 µm, which is slightly larger than the inner diameter of the SMF (125 µm). Next, the MF is slowly injected into the capillary tube using a syringe. Then, an uncoated 100 mm segment of SMF is inserted from the other end of the capillary tube using a three-dimensional displacement platform. Finally, the capillary tube is sealed with UV adhesive to prevent leakage of MF. The distance between the two fiber segments in the capillary tube is measured with the help of a microscope. The obtained length of the as-fabricated FP-MF cavity is L1 = 214.98 µm.
The thermal-sensitive material PDMS is selected to fill with FP cavity for temperature sensing. The production process is similar to that of the FP-MF. The thermal-sensitive material PDMS solution is first prepared by mixing the elastic polymer (Sylgard 184-A) and the curing agent (Sylgard 184-B) with a ratio of 10:1. Then, air bubbles are removed from the mixture using a centrifuge. A notch is made on one side of the capillary glass tube to facilitate the insertion of PDMS and prevent the formation of bubbles during the curing process. The prepared PDMS mixture solution is carefully dropped into the open hole and left to cure at room temperature for 24 hours. Similar to the FP-MF cavity, but the end-face of the optical fiber is coated with a gold film (deposition with 15 A current for 15 s) to enhance the reflectivity and improve the interference intensity. The length of the as-fabricated FP-PDMS cavity is measured to be L2 = 261.68 µm.
The schematic of the experimental setup for the temperature and magnetic field measurements is shown in Fig. 4. The light from the ASE source (wavelength range: 1525-1610 nm, power: 10 mW) is injected into Coupler 1 through Port 1 and then is transmitted through the FP-MF sensing probe. A stable magnetic field is generated with a set of coils, which is powered by a programmable DC supply. A Gauss meter is used to calibrate the magnetic field. The direction of the magnetic field is oriented to be perpendicular to the optical path. When the external magnetic field changes, the refractive index of MF will change, which will modulate the optical signal. The reflected light reaches Port 3 through Port 2 and enters Coupler 2 through Port 4. This transmitted light will enter the FP-PDMS sensing probe for temperature measurement. Using a temperature-controlled column oven (LCO 102, ECOM, with a resolution of 0.1 °C), the ambient temperature near the FP-PDMS sensing probe can be manipulated. As the PDMS is heated, it will expand, which will result in the variation of cavity length and then modulate the optical signal. The reflected light travels from Port 5 to Port 6 and is detected by an optical spectrum analyzer (OSA, AQ6370, YOKOGAWA, Tokyo, Japan, with a wavelength resolution of 0.02 nm). This system enables the independent detection of temperature and magnetic field, without any mutual interference.
For comparison, the experimental results for temperature measurement using a single FP-PDMS cavity are shown in Fig. 5. Spectra are recorded every 0.5 °C interval. As the temperature increases from 35 to 39.5 °C, a significant redshift is observed in the spectra. This is because the increase in temperature triggers the thermo-optical effect and thermal expansion effect of PDMS, which increases the length of PDMS. The corresponding relationship between dip wavelength shift and temperature at around 1532 nm is shown in Fig. 5(c). The process of PDMS expansion is relatively slow. In order to ensure the accuracy, the data was recorded 10 minutes after then temperature changing. At time, the spectrum no longer drifts. Within the detection range, the sensor exhibits a temperature sensitivity of 5880 pm/°C and excellent linearity.
Fig. 5. Reflective spectra of single FP-PDMS cavity with the temperature range of 35-37 °C (a) and 37.5-39.5 °C (b), and the corresponding dip wavelength shift with temperature (c).
Similarly, the magnetic field sensing using a single FP-MF cavity is measured and the typical experimental results are shown in Fig. 6(a). As the magnetic field increases from 3 to 9 mT, the obtained spectrum demonstrates a linear redshift. The observed redshift in the spectrum can be attributed to the increase in the refractive index of MF with increase of magnetic field. Figure 6(b) presents the relationship between the peak wavelength shift and magnetic field. When the magnetic field intensity is beyond 12 mT, the spectral drift is unobvious. It indicates that the MF gradually tends to magnetization saturation. Within the detection range, the linear fitting analysis yielded a magnetic field sensitivity of 509 pm/mT. The increased light absorption and then reduced reflection observed within the detection range can be attributed to the generation of more magnetic chains when escalating the magnetic field. Consequently, this leads to a decrease in interference contrast as the magnetic field intensifies.
Fig. 6. Typical reflective spectra of single FP-MF cavity with the magnetic field range of 3-9 mT (a) and the corresponding dip wavelength shift with the magnetic field (b).
To improve the sensitivity of temperature and magnetic field, the FP-PDMS and FP-MF cavities with slight difference in FSR are interconnected to generate the Vernier effect. Figure 7(a) plots the typical reflection spectrum of the cascaded structure. The upper envelope is extracted from the experimental data using the curve fitting method. Figure 7(b) is the FFT spectrum of the device. It can be seen from Fig. 7(b) that the sensor has two main frequency peaks, which are labeled as Peak 1 (0.21) and Peak 2 (0.27). They correspond exactly to the spatial frequency values of FP-MF and FP-PDMS cavities. Therefore, the spectrum can be considered to being stemmed from those of two FPIs. We can use bandpass filtering and inverse FFT to separate and extract the reflection spectra of FP-MF and FP-PDMS cavities from the sensor spectrum. The FSRs of FP-PDMS and FP-MF cavities are 3.1 and 3.8 nm, respectively, which correspond to a cavity length of 291.68 and 223.91 nm, respectively. Within the tolerance of error, the two cavity lengths are consistent with the measured ones. Substituting the values of FSRs into Eq. (6), the amplification factor of Vernier effect is calculated to be around 5.0.
Fig. 7. Reflection spectrum (a) and corresponding FFT spectrum of the sensor (b), reflection spectrum of FP-PDMS (c) and FP-MF cavities (d) extracted from the sensor spectrum.
The wavelength shift direction of the envelope spectrum depends on the optical path difference between the reference and sensing FP cavities. In this study, the FP-PDMS cavity possesses a larger optical path compared to that of the PF-MF cavity. This results in the smaller FSR of the FP-PDMS cavity (FSRPDMS) compared with that of the FP-MF cavity (FSRMF). Consequently, when conducting temperature detection, the direction of wavelength shift in the envelope spectrum is similar to that of a single FP-PDMS cavity. Figures 8(a) and 8(b) display a redshift of the envelope spectra with increasing temperature at a constant magnetic field. The spectral shift direction is the same as that of a single FP-PDMS cavity. The linear fitting of the relationship between the spectral envelope shift and the temperature is shown in Fig. 8(c). In the temperature range of 35-37 °C, the sensitivity of the Vernier envelope reaches 27540 pm/°C. Within the temperature range of 37.5-39.5 °C, the sensitivity of the Vernier envelope is 25990 pm/°C. The average temperature within 35-39.5 °C is about 26765 pm/°C, which is around five times larger than that of the corresponding single FP-PDMS cavity. A re-peak finding method is utilized to enable cyclic positioning and then extend the detection range.
Fig. 8. Reflective spectra shift of the sensor with temperature in the range of 35 to 37 °C (a) and 37.5 to 39.5 °C (b), and the corresponding spectral envelope shift with temperature (c).
When conducting magnetic field detection, the FP-MF cavity serves as the sensing cavity. At constant temperature, the Vernier envelope shown in Fig. 9(a) experiences a blueshift with the magnetic field, which is opposite to the spectral shift direction observed in the FP-PDMS sensing probe with temperature. For clarity of presentation, the curves in Fig. 9(a) are offset vertically. The linear fitting of the experimental data shown in Fig. 9(b) gives a sensitivity of -2245 pm/mT. The Vernier envelope significantly enhances the measurement sensitivity by nearly five times compared to that of the corresponding single FP-MF cavity. Therefore, the sensitivity of temperature and magnetic field measurements is substantially amplified by utilizing the Vernier effect.
Fig. 9. Reflective spectra of the sensor at different magnetic field strengths (a) and the corresponding spectral envelope shift with magnetic field strength (b).
Table 1 lists the sensing performance of various temperature and magnetic field measurement structures. Obviously, the utilization of Vernier effect in this work results in a significant improvement in both temperature and magnetic field sensitivity. In addition, owing to its simple manufacturing process and compact size, this sensor holds immense potential for extensive applications in the field of high-precision measurement of temperature and magnetic fields.
Table 1. Sensing performance of various temperature and magnetic field measurement structures
4. Conclusion and perspective
In summary, this study proposes a highly sensitive sensor for temperature and magnetic field based on the interconnection of two FP cavities, which are filled with PDMS and MF, respectively. The two sets of interference spectrums have very similar FSRs, which allows for enhanced sensitivity through the utilization of the Vernier effect. The temperature and magnetic field sensitivities are 26765 pm/°C and -2245 pm/mT, respectively. Both of which are approximately five times higher than those of their single FP cavity counterparts.
However, the sensor has some limitations. For one thing, it can't measure magnetic field and temperature at the same time. Second, it has slow response to temperature. Despite these limitations, the sensor is still widely used in various industries due to its high sensitivity and reliability.
The combination of the Vernier effect and fiber interferometer is an innovation in the field of sensing. According to the physical mechanism of on the optical Vernier effect, we can try to find materials with opposite temperature responses to further improve the sensitivity. Thus, the designed sensor remains a valuable tool for many applications in the future.
Funding
National Natural Science Foundation of China (62075130, 61675132); Natural Science Foundation of Shanghai (23ZR1443300); Program of Shanghai Academic Research Leader (23XD1402200); Shanghai Shuguang Program (16SG40).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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