1. Introduction

Optical fiber is a waveguide made of glass or plastic [1–3]. With the continuous development of micro/nano optical fiber sensing technology, the demand of high-precision synchronous detection of magnetic field and temperature becomes more and more for the various fields, such as magnetic resonance imaging, marine resource exploration, thermomagnetic material processing [4]. Common optical fiber temperature sensors are mainly based on thermo-sensitive mediums [5–7], while the intrinsic optical fiber magnetic field sensors are predominantly utilizing the Faraday rotation effect or the magnetostrictive effect [8–10]. The Faraday rotation effect refers to the varying external magnetic field causing different degrees of rotation of linearly polarized light in the magneto-optical medium. Although fiber optic sensors doped with magneto-optical materials can achieve initial magnetic field detection, there are issues such as complex operation, difficult signal demodulation, low sensitivity, and limited practicality [9]. Magnetostrictive fiber sensors mainly rely on the deformation of materials under different magnetic fields for sensing. Although they are easy to fabricate, the sensing characteristics are greatly constrained by the elastic limit of the material, resulting in a narrow range of magnetic field detection [10]. In addition, these single-parameter sensors could be incompetent for synchronous detection of magnetic field and temperature. Magnetic fluid (MF) is a special material with a magnetically controllable refractive index. By combining MF with appropriate functional optical fiber devices, the magnetic field characteristics can be detected. Most importantly, the refractive index of MF is simultaneously modulated by both the magnetic field intensity and the temperature. As long as the cross-sensitivity between magnetic field and temperature can be overcome, it is possible to achieve synchronous detection of magnetic field and temperature.

The initial optical fiber magnetic field sensor is mainly based on single mode fiber (SMF), but it does not have separate channels to fill the magnetic sensitive medium and thermo-sensitive medium respectively, which is not conducive to the dual-parameter detection of magnetic field and temperature. With the increasing demand for synchronous detection of magnetic field and temperature, researchers gradually turn their vision to the photonic crystal fiber (PCF) [11–16] for highly flexible structure and the existence of air holes in the PCFs provides a natural pathway for filling MF and thermo-sensitive medium. Additionally, if metals are appropriately modified at specific positions in the PCF, surface plasmon resonance (SPR) can be excited [17–19], and the surface plasmon polaritons (SPPs) on the metal surface exhibit high sensitivity to micro changes in the refractive index of the surrounding medium. When the metal is added near the MF and thermo-sensitive medium respectively, the fundamental mode (FM) could couple with the SPP modes by using SPR effect, enabling synchronous detection of magnetic field and temperature. In 2017, H. Liu et al. firstly proposed a PCF sensor which can simultaneously detect temperature and magnetic fields [20]. The optimum temperature sensitivity and magnetic field sensitivity are 0.512 nm/°C and 1927 pm/mT, respectively. However, it is relatively difficult to construct this sensor by accurately filling MF into the certain small air hole with the diameter of only 0.7 µm. In 2019, Y. Ying et al. reported a D-shaped PCF sensor which deposited MF on the side-polished plane for detecting magnetic field and temperature [21]. Although this sensor can reduce the fabrication difficulty to a certain extent, the magnetic field sensitivity and temperature sensitivity are only 0.21 nm/Oe (2100 pm/mT) and 1.25 nm/°C. In 2022, D. Wang et al. designed a dual-elliptical-channel PCF sensor coated with gold film, and the two channels filled with MF and polydimethylsiloxane (PDMS) respectively [22]. The sensor could simultaneously detect magnetic fields ranging from 50 Oe to 130 Oe and the temperatures of 17.5 °C to 27.5 °C. The maximum magnetic field sensitivity and temperature sensitivity are 650 pm/mT and 2360 pm/°C, respectively. In the same year, they proposed a dual-side-polished open-ring PCF-SPR sensor [23]. The left channel was coated with a gold film and filled with MF, while the right channel was deposited with a silver film and filled with PDMS. This model achieved the dual-parameter sensing of magnetic field and temperature with maximum temperature sensitivity and magnetic field sensitivity of 3083 pm/mT and 6520 pm/°C, respectively. However, the current optical fiber SPR dual-parameter sensors commonly face enormous challenges in filling the target analyte to the desired location accurately. Moreover, the magnetic field sensitivity and temperature sensitivity of the sensor are still at a relatively low level, making it difficult to adapt the growing detection demands. Consequently, it is still an urgent issue to design a sensor that can appreciably improve the synchronous detection of magnetic field and temperature with high sensitivity.

In this paper, an ultra-high sensitive dual-parameter sensor based on double-hole fiber (DHF) for simultaneously detection of magnetic field and temperature is proposed and systematically analyzed for the first time. In order to reduce the difficulty of filling sensing medium, two large air holes are arranged symmetrically at two sides of the Ge-doped core of DHF. To enhance the sensitivity to both magnetic field and temperature, Al wires with different diameters are embedded on the inner walls of the air holes in the DHF, creating a magnetic field sensing channel filled with the MF and a temperature sensing channel filled with thermo-sensitive liquid. The two air holes are large enough to significantly reduce the filling difficulty of sensing media in comparison to previous researches [11,16,20–23]. In order to achieve the high performance of the sensor, finite element method (FEM) is employed to systematically optimizing the structure parameters and metal materials of the sensor. Numerical results demonstrate that the dual-parameter sensor based on DHF can simultaneously detect magnetic field in the range from 40 Oe to 130 Oe and temperature from 24.3 °C to 49.3 °C. The maximum magnetic field sensitivity and the maximum temperature sensitivity are as high as 64000 pm/mT and 44.6 nm/°C respectively, which are increased by more than one order of magnitude compared to all the current reports about dual-parameter optical fiber sensors for simultaneous detection of magnetic field and temperature. Additionally, a detailed analysis of the fabrication tolerance of the structural parameters that significantly affect the sensor performance is conducted. The overview of this paper are as follows: the structure of sensor based the DHF is introduced and sensor principle is illustrated in Section 2; the FM polarization direction and structure parameters of the sensor are optimized in Section 3; the experimental setup, magnetic field sensing characteristics, temperature sensing characteristics and dual-parameter sensing matrix of the proposed sensor are analyzed in Section 4; the manufacture feasibility, fabrication tolerances, and performance comparison with recent relative research progress are discussed in Section 5, and the Section 6 is the conclusion. The proposed DHF-based dual-parameter sensor has simple structure, high sensitivity and low fabrication difficulty, which has crucial potential applications in thermal-magnetic material property study, geological environmental monitoring, and other fields.

2. Sensor structure and principle

In order to simplify the structure of the optical fiber sensor and greatly enhance the magnetic field and temperature sensitivity, a DHF-based dual-parameter sensor for simultaneous detection of magnetic field and temperature is proposed, as shown in Fig. 1. The DHF contains two large air holes with the diameter of dc₁ and dc₂ arranged symmetrically at two sides of the Ge-doped core with the diameter of d₀. To enhance the sensitivity to both magnetic field and temperature, two metal wires with the diameter of dm₁ and dm₂ are embedded on the inner walls of the air holes in the DHF, creating a magnetic field sensing channel (gray region) filled with the MF and a temperature sensing channel (pink region) filled with thermo-sensitive liquid. The distances between two metal wires to the edge of core are denoted by L₁ and L₂. The center of the air holes, metal wires and fiber core are arranged on the same horizontal line. The two air holes are designed to be large enough to significantly reduce the difficulty of filling sensing media. It is worth mentioning that it is the first time to propose this kind of DHF with simple structure, which can significantly reduce the filling difficulty of sensing media due to the design of dual large air holes in the fiber.

 

Fig. 1. Cross-section of the proposed dual-parameter sensor based on the DHF.

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The material of cladding in the DHF is pure silica whose refractive index n_cladding can be determined by Sellmeier equation [24]. The fiber core adopts Ge-doped silica whose refractive index n_core is slightly higher than that of the cladding. Thus the relative refractive index difference △ between the core and cladding can be expressed as [25]

Two metal wire are used to excite the SPR effect and the corresponding dielectric constant ε_m can be obtained with Eq. (2) [26]:

The hydrated Fe₃O₄ MF with a concentration of 0.68 emu/g is filled into one air hole of the DHF as magnetic field sensing channel, named channel 1 (Ch1). The refractive index of MF n_MF is related to both magnetic field and temperature, which can be expressed as [27]

The thermo-sensitive liquid is filled into another air hole of the DHF as temperature sensing channel, named as Ch2. Here, the main component of the thermo-sensitive liquid in the dual-parameter sensor is chloroform, whose refractive index n_Chl can be determined by Eq. (4) [29]. It should be noted that for avoiding the interaction between chloroform and oxygen in the air to form phosgene, 0.6% ethanol should also be added into chloroform to maintain the liquid phase. The refractive index of ethanol n_Eth can be obtained with Eq. (5) [30].

The principle of the sensor is based on the SPR effect that is a common physical optical phenomenon [33]. Due to n_core> n_cladding, when the beam is incident from the core to the cladding, an evanescent wave is generated at the interface of the Ge-doped silica and SiO₂ [34]. At the same time, under the influence of the incident light, the free electrons on the surface of the metal wire in Ch1 and Ch2 undergo collective oscillation, manifesting as surface plasmon waves (SPW). When the propagation constant of the evanescent wave and the SPW is identical and the phase matching condition is satisfied, as described in Eq. (9) [35], the real part of the effective refractive index of FM and SPP mode are equal and thus the SPR is excited.

The FEM is employed to model the characteristics of the sensor. Under the initial parameters of d₀ = 14.0 µm, dm₁ = 1.0 µm, dm₂ = 1.6 µm, L₁= 0.5 µm, L₂= 0.5 µm, △ = 1.0%, dc₁ = 32.0 µm, dc₂ = 32.0 µm and initial metal of Al, Fig. 2(a) show the effective refractive indexes of FM (red solid-line) and SPP mode (blue solid-line), and the loss of FM (black solid-line) at the fixed H = 50 Oe and T = 24.3°C. As the wavelength increases, both the FM and SPP mode exhibit a decreasing trend in refractive index, and two high-loss peaks, named Peak 1 and Peak 2, appear in the FM loss spectrum. It should be noted that as the wavelength increases, the accelerated SPW reacts with the electron beam, forming an “S-shaped” dispersion curve [37]. Furthermore, the wavelength corresponding to the maximum loss of the FM is identical to the Resonant Wavelength (RW) of 757 nm at which the dispersion curves of the FM and SPP modes intersect. When λ < 757 nm, the SPP mode has higher effective refractive index than the FM does, and thus the photon energy continuously couples from the fiber core to the surface of the metal wire because of the SPR effect, leading to an rapid increase in loss of the FM. When λ > 757 nm, the effective refractive index of the FM is larger than that of the SPP mode, and thus the energy begins to return back to the fiber core, resulting in a rapid decrease in the loss of FM. Therefore, a loss peak (Peak 1) appears in the loss curve of the FM at the RW of 757 nm. The energy exchange between the FM and SPP mode can be clearly observed from the change of modal field in the inset of Fig. 2(a). So does the same reason for a loss peak (Peak 2) in the loss curve of the FM at the RW of 1185 nm. Figures 2(b)-(c) respectively describe the loss spectra of the FM when the magnetic field and temperature alter within a certain range. It can be found that Peak 1 shift towards the longer wavelength and Peak 2 keep near constant with the increase of magnetic field intensity at a constant T = 24.3°C in Fig. 2(b). With the increase of the temperature at a constant H = 50 Oe, Peak 1 and Peak 2 both shift towards the shorter wavelength, but the shift magnitude of Peak 2 is more than that of Peak 1, as shown in Fig. 2(c). And for that, Peak 1 is more sensitive to the magnetic field than the temperature and Peak 2 is more sensitive to the temperature than the magnetic field. When the magnetic field changes, the wavelength corresponding to the highest loss of Peak 1 is defined as RW₁H and the wavelength corresponding to the maximum loss of Peak 2 is defined as RW₂H. When the T varies, the wavelength corresponding to the highest loss of Peak 1 is defined as RW₁T and the wavelength corresponding to the maximum loss of Peak 2 is defined as RW₂T. In addition, the refractive indices of the MF and the thermo-sensitive liquid also varies when the magnetic field and temperature changes, resulting in shifts of RW₁H, RW₂H, RW₁T, and RW₂T. In a word, since Peak 1 and Peak 2 exhibit different response to the change of magnetic field intensity and temperature, those result in different shifts of the four resonance wavelengths, which offer the possibility of simultaneous detection of magnetic field and temperature by monitoring the shifts of RW₁H, and RW₂H with the magnetic field and the shifts of RW₁T and RW₂T with the temperature. Besides, the sensing coefficient matrix of magnetic field sensitivities and temperature sensitivities are obtained by the shift of the corresponding RWs:

 

Fig. 2. (a) The effective indexes of the FM (red solid-line) and SPP mode (blue solid-line), and the loss spectrum of FM (black solid line). The inset shows the field distributions when H = 50 Oe and T = 24.3°C; (b) loss peaks at different magnetic field intensity and a constant temperature of 24.3°C; (c) loss peaks at different temperature and a constant magnetic field intensity of 50 Oe.

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3. Sensor optimization

In order to realize the higher sensitivity, lower FM loss and sharper peak of the sensor, structural parameter optimization is necessary. The principle of the SPR effect is the energy exchange between the FM in core and the SPP mode near the metal. Therefore, the structural parameters that influence the coupling characteristics of FM and SPP modes should be optimized, which including the diameter of the fiber core and metal wires, distances between the core and air holes, relative refractive index difference between the core and cladding, diameter of the left air hole and right air hole, and metal material of the DHF-based dual-parameter sensor. It is worth mentioning that the optimization cost is lower because the DHF-based dual-parameter sensor has very simple structure. It is worth noting that the reason for using the magnetic field sensitivity corresponding to Peak 1 at 50 Oe and the temperature sensitivity corresponding to Peak 2 at 24.3 °C as the primary optimization criterion is that Peak 1 is mainly used for magnetic field detection, while Peak 2 is primarily for temperature, which is the most critical performance of the sensor. In addition, the peak loss and full width at half maximum (FWHM) of the FM loss spectrum can also be utilized as the secondary optimization criterion, since they affect the spectral response of the sensor during actual measurements. The initial structural parameters of the DHF-based dual-parameter sensor are d₀ = 14.0 µm, dm₁ = 1.0 µm, dm₂ = 1.6 µm, L₁= 0.5 µm, L₂= 0.5 µm, dc₁ = dc₂ = 32.0 µm, △ = 1.0%, and Al is selected to excite the SPR effect.

3.1 Polarization direction

Due to the lack of rotational symmetry in DHF, x-polarization (x-pol) FM and y-polarization (y-pol) FM is non-degenerate, which could couple with SPP modes. Figure 3 compares the loss curves and 2D mode field distributions of x-pol and y-pol FM. It is evident that x-pol FM exhibits two distinct loss peaks with the change in magnetic field and temperature. In contrast, the loss of y-pol FM keep near constant and there is a slight change in the loss spectrum of y-pol FM with the change of magnetic field and temperature, making it impossible for magnetic field or temperature detection. This can be explained with the mode field distribution in Fig. 3(a). The x-pol FM can simultaneously couple with SPP modes on both sides of the core, resulting in obvious energy distribution near the core and the two metal wires. On the contrary, the y-pol FM does not exchange energy with either side of the wires. In addition, the 3D mode field distribution model [38] of x-pol and y-pol FM in Fig. 3(b) further proves this point. Consequently, x-pol FM is more suitable for magnetic field and temperature sensing.

 

Fig. 3. (a) Loss spectrum and 2D mode field distribution of x-pol FM and y-pol FM; (b) the 3D mode field distribution model of x-pol and y-pol FM.

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3.2 Structural parameter optimization of the sensor

The aim of the DHF-based dual parameter sensor is to implement simultaneous detection of magnetic field and temperature by using SPR effect. The strength of SPR effect is mainly determined by the mode coupling between the core FM and SPP mode, which is closely related to the diameters of the fiber core and the metal wire, as well as their spacing. So we begin to optimize the size of fiber core and the metal wire, as well as their spacing first.

Firstly, the diameter of the fiber core is optimized as shown in Fig. 4(a)-(f). When d₀> 18 µm, the coupling strength of FM and SPP mode is too low. When d₀< 10 µm, the full width at half maximum (FWHM) of Peak 2 becomes too wide to measure the RW accurately. Therefore, the varied range of d₀ is set as 10 µm < d₀< 18 µm. As d₀ decreases, S₁(H) remains constant at 8000 pm/mT, while S₂(T) continues to increase and reaches the maximum of 16.4 nm/°C at d₀= 10 µm. However, it is worth noting that when d₀ = 10 µm, the peak loss of Peak 1 increases sharply and is 2.44 times greater than that at d₀ = 12 µm. So d₀ is set as 12 µm to trade off the peak loss and temperature sensitivity. At this point, S₁(H) = 8000 pm/mT and S₂(T) = 13.4 nm/°C. Additionally, as the fiber core diameter increases, both RW₁H and RW₂T shift towards shorter wavelength, which is because the higher the energy in the fiber core, the higher the refractive index of the FM. This makes phase velocity decreased, causing RW₁H and RW₂T blue-shift, which can be proved in Fig. 4(g).

 

Fig. 4. The curves of the FM loss (a)-(e), S₁(H) and S₂(T) (f), and the effective refractive index of the FM and SPP modes (g) for the sensor with different d₀.

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Then, we turn to optimize the diameters of the metal wires, dm₁ and dm₂. It should be emphasized that when dm₁ and dm₂ are altered, the distance between the two metal wires and the core remains constant, which ensures that the sensor performance is only affected by the metal wires. When dm₁ > 1.0 µm, there is an obvious decrease in S₁(H); when dm₁ < 0.2 µm, the FM loss increases significantly, which is detrimental to optical signal transmission. Therefore, the range of dm₁ is optimized from 0.2 µm and 1.0 µm. Figure 5(a) shows the change of RWs of Peak 1 and Peak 2 with the left metal wire within the diameter range from 0.2 µm to 1.0 µm. As dm₁ increases, RW₁H shifts towards shorter wavelength and RW₂T keep constant. For the metal wire with relatively large dm₁, the evanescent field cannot penetrate the metal wire, so the FM can only couple energy with the part of the metal wire close to the fiber core, resulting in the weak SPR effect. As dm₁ decreases, the FM can exchange energy with more free electrons on the surface of the metal wire, enhancing the SPR effect. Therefore, as dm₁ decreases, S₁(H) raises continuously. When dm₁ = 0.4 µm, S₁(H) reaches the maximum of 19000 pm/mT. Hence, dm₁ is set to 0.4 µm. It is worth noting that since dm₁ is only sensitive to the magnetic field intensity and has a slight effect on RW₂T, so S₂(T) remains constant at 13.4 nm/°C.

 

Fig. 5. The variation of RW₁H (red line) and RW₂T (blue line) with (a) dm₁ and (b) dm₂.

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After determining d₀ = 12 µm and dm₁ = 0.4 µm, the diameter of the right metal wire dm₂ is further optimized. The initial parameter for dm₂ is 1.6 µm, and S₂(T) is 13.4 nm/°C. If dm₂ is increased, S₂(T) will decrease. Therefore, to improve the S₂(T), dm₂ needs to be reduced. However, when dm₂ < 1.4 µm, the peak loss of FM increases significantly. So, dm₂ will be adjusted in the range of 1.4 µm to 1.7 µm. Figure 5(b) depicts the change of the corresponding resonance wavelength with dm₂. As dm₂ increases, the refractive index of the FM rises and thus RW₂T shifts blue. The linear fitting results in Fig. 5(b) indicate that the R² is 99.09% and 98.82% when the temperature is 24.3°C and 29.3°C, respectively, which means that RW₂T exhibits a good linearity with dm₂. At the same time, S₂(T) reduces continuously for the same reason as dm₁. Additionally, when dm₂ = 1.4 µm, S₂(T) reaches the highest value of 20.4 nm/°C. So, dm₂ is set to 1.4 µm. Furthermore, since dm₂ is only sensitive to temperature and has a slight effect on RW₁H, thus S₁(H) remains constant at 19000 pm/mT.

In addition to d₀, dm₁ and dm₂, the distance between the metal wire and the core also affects the characteristics of the DHF-based dual-parameter sensor due to the limited penetration depth of the evanescent wave. When L₁ and L₂ change, the other structural parameters keep constant. Figure 6 optimizes the distance L₁ between the left metal wire and the fiber core. Since L₁ mainly controls the distance between Ch1 and the core, S₂(T) is not significantly affected by L₁ and maintains at 20.4 nm/°C. When L₁ increases, S₁(H) is invariant, indicating that L₁ needs to be shortened. When L₁ is reduced to 0.35 µm, S₁(H) is 1.105 times the original of 19000 pm/mT, but the peak loss of the FM is 1.976 times the initial of 58.35 dB/cm. Additionally, when L₁ is 0.45 µm or 0.5 µm, S₁(H) is both 20000 pm/mT, but the peak loss of the FM is smaller if L₁ = 0.45 µm. Therefore, L₁ should be determined as 0.45 µm. It should also be noted that as L₁ increases, RW₂T shifts towards shorter wavelength. This is because as the distance increases, fewer energy coupled to the surface of metal, and most photons remain in the core, raising the refractive index of the FM.

 

Fig. 6. The relationship between FM loss and wavelength at different L₁.

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When d₀ = 12.0 µm, dm₁ = 0.4 µm, dm₂ = 1.4 µm, L₁ = 0.45 µm, further optimization of L₂ can be performed. Due to high loss of FM when L₂< 0.4 µm, so we investigate the change of magnetic sensitivity and temperature for the case of L₂ > 0.4 µm shown in Fig. 7. When L₂> 0.6 µm, the coupling strength between the FM and SPP mode becomes weaker. Therefore, the optimized range for the structural parameter of L₂ is 0.4 µm < L₂< 0.6 µm. Obviously, since L₂ mainly affects the temperature sensing characteristics of Ch2, there is almost no change in S₁(H). In addition, as L₂ decreases, S₂(T) is constantly improved. Additionally, it is worth mentioning that when L₂ = 0.4 µm, S₂(T) reaches the maximum of 35.8 nm/°C, which is 1.755 times the initial parameter of L₂ = 0.5 µm. So, L₂ is set to 0.4 µm.

 

Fig. 7. The change of S₁(H) and S₂(T) with L₂.

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Next, the diameters of the two air holes need to be determined. It should be noted that the optimization of the two air holes will not affect L₁ and L₂ since the intersection point of air hole and the metal wire is always fixed. With the increase of the air hole diameter, S₁(H) and S₂(T) remain almost unchanged. This can be explained that the contact areas between the metal wires and the MF and thermo-sensitive liquid are not influenced by dc₁ and dc₂. Additionally, increasing both dc₁ and dc₂ to 41 µm not only ensure better fusion splicing between DHF and SMF but reduce the filling difficulty of the MF and thermo-sensitive liquid.

3.3 Relative refractive index difference of core and cladding

Equation (1) illustrates that △ is related to the refractive index of the fiber core and directly affects the coupling between the FM and SPP mode at the metal surface. The initial △ is 1.0%, corresponding to S₁(H) and S₂(T) of 20000 pm/mT and 35.8 nm/°C, respectively. When △ < 0.98%, there is no significant change in S₁(H), as a result △ should be increased. When △ > 1.02%, both S₁(H) and S₂(T) will decrease a lot. Therefore, the adjustment range for △ is chosen to be 0.98% - 1.02%. Table 1 reveals that as △ increases, RW₁H and RW₂T blue-shift and both S₁(H) and S₂(T) decrease simultaneously. This can be explained that the confinement ability to the FM can be strengthened with the increase in △. As a result, the effective refractive index of the FM increases and thus there is a blue-shift in the RW. It should be noted that although △ affects both the shift of RW₁H and RW₂T, it is more sensitive to RW₂T. This is because the metal wire in Ch2 has relatively large diameter and stronger coupling with the evanescent wave. Moreover, when the △ is 0.98%, the DHF-based dual-parameter sensor has the highest S₁(H) and S₂(T) of 20000 pm/mT and 44.6 nm/°C. Consequently, △ = 0.98% is selected.

Table 1. The variation of RW₁H, S₁(H), RW₂T and S₂(T) with △.

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3.4 Optimization of the metals

Once the structural parameters and △ of the DHF are determined, we turn to investigate the effect of metal. Currently, metals such as Au, Ag, Cu, and Al are commonly utilized to stimulate the SPR effect. It is because these metals can be modified in the fiber by filling the wire, coating, replacement reaction, and so on. The SPR sensing characteristics of the four metals is compared in Fig. 8, and Table 2 provides the values of λ_c and λ_p in Eq. (2) for these metals.

 

Fig. 8. (a) Loss curves of the DHF-based dual-parameter sensor with different metals and (b) the real part of the dielectric constants as a function of the wavelength for Al and Cu.

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Table 2. λ_c and λ_p of the four metals.

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For Au and Ag, only one resonance peak exists within the desired wavelength range, making it unsuitable to achieve dual-parameter detection of magnetic field and temperature. For Cu, although there are two resonance peaks, the magnetic field sensitivity at 50 Oe is much lower than that of Al. This is because Al has a larger real part of the relative dielectric constant shown in Fig. 8(b), resulting in a higher surface refractive index and energy exchange between the fiber core and the surface of the Al wire enhanced. Therefore, Al is determined as the metal material for exciting SPR effect.

In summary, the optimal structure parameter of the proposed DHF-based dual-parameter sensor are d₀ = 12.0 µm, dm₁ = 0.4 µm, dm₂ = 1.4 µm, L₁= 0.45 µm, L₂= 0.4 µm, △ = 0.98%, dc₁= dc₂= 41.0 µm, and Al is selected to excite SPR effect. After the structural parameter optimization, S₁(H) = 20000 pm/mT and S₂(T) = 44.6 nm/°C, which are 2.50 times and 3.72 times before optimization.

4. Magnetic field and temperature sensing

The DHF-based dual-parameter sensor can simultaneously detect magnetic field and temperature by using the experimental setup in Fig. 9. Two single mode fibers are fused to the sides of the DHF, one end connected to a broadband light source and the other to the optical spectrum analyzer (OSA). It should be noted that the DHF has the similar core diameter with SMF, but the outer diameter of the DHF (98.9 µm) is smaller than that of the SMF (125 µm). The operation mode of core alignment can be adopted to splice the DHF and SMF by using the fusion splicer. Since the outer diameter of the SMF is greater than that of the DHF, the SMF can completely cover both Ch1 and Ch2 after spliced, which can effectively seal the filling liquid channel and prevent leakage of the MF and the thermo-sensitive liquid. Then, a magnetic field generator and a temperature control platform are used to apply a magnetic field and temperature to the sensor, respectively. At this point, the light source is turned on and adjusted to the appropriate wavelength, the corresponding loss spectrum will be observed and recorded on the OSA. The corresponding curves will be input into the PC for analysis, thereby realizing the simultaneous detection of magnetic field and temperature.

 

Fig. 9. Experimental setup for the detection of magnetic field and temperature.

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When the temperature is constant at 24.3°C, the FM loss spectrum at different magnetic field intensities and the change of S₁(H) and S₂(H) with the magnetic field are shown in Fig. 10(a) and (b) respectively. Figure 10(a) shows that as the H increases, RW₁H redshifts, and the variation of RW₂H is not obvious. Figure 10(b) indicates that the magnetic field sensitivity is inversely proportional to the magnetic field intensity. This is because as H increases, the refractive index of MF becomes larger, and the significant amount of energy is transferred from the core to the surface of the Al wire. In addition, it is worth mentioning that the S₁(H) at any magnetic field intensity is above 1000 pm/mT, and the maximum is 64000 pm/mT (H = 40 Oe), which is the highest in current reports [20–23,39,40]. It should be noted that the thermo-sensitive liquid is not sensitive to the variation of magnetic field, so the change in S₂(H) is much less than S₁(H). Figure 10(c)-(d) fit the RW₁H and H, RW₂H and H, respectively. The expressions are provided in the figure and all the R² are greater than 91.2%. Simultaneously, Fig. 10(c)-(d) also manifests that the DHF-based dual-parameter sensor can detect the magnetic field intensity at the range of 40 Oe to 130 Oe. Besides, taking the first derivative of each expression yields the corresponding average magnetic field sensitivity. When 40 Oe < H< 60 Oe, the average magnetic field sensitivities are 34000 pm/mT and 8800 pm/mT; when 70 Oe < H< 130 Oe, the average magnetic field sensitivities are 3200 pm/mT and 960 pm/mT, respectively.

 

Fig. 10. (a) The FM loss spectrum at different magnetic field intensities; (b) the relationship between S₁(H) and S₂(H) with the magnetic field intensity; linear fitting of (c) RW₁H and magnetic field intensity, (d) RW₂H and magnetic field intensity.

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Similarly, when the H is constant at 50 Oe, the FM loss curves at different temperatures and the change of S₁(T) and S₂(T) with the temperature are shown in Fig. 11(a) and (b) respectively. As the temperature increases, Fig. 11(a) indicates that both RW₁T and RW₂T shift blue. Figure 11(b) shows that the refractive indices of the thermo-sensitive liquid and MF both decrease when the T is rising, causing more photon energy to be confined in the core and resulting in a diminishment of S₁(T) and S₂(T). In addition, For S₁(T), all the temperature sensitivities are greater than 6.2 nm/°C, and the highest temperature sensitivity is 17 nm/°C when T = 24.3 °C. For S₂(T), the maximum temperature sensitivity is 44.6 nm/°C at 24.3 °C, which is 1∼2 orders of magnitude higher than that of current dual-parameter SPR sensors [20–23,39,40]. Figure 11(c)-(d) also show the linear fitting of the RW₁T and T, and RW₂T and T, with the expressions provided in the figure and all the R² are greater than 90.5%. At the same time, Fig. 11(c)-(d) also shows that the DHF-based dual-parameter sensor can detect the temperature in the range of 24.3 °C to 49.3 °C. Moreover, the average temperature sensitivities can be obtained by the identical method as the average magnetic field sensitivity, which are 10.2 nm/°C and 18.8 nm/°C, respectively.

 

Fig. 11. (a) The FM loss curves at different temperatures; (b) the relationship between S₁(T) and S₂(T) with the temperature; linear fitting of (c) RW₁T and temperature, (d) RW₂T and temperature.

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It should be illustrated that the average sensitivity of Peak 1 to the magnetic field and temperature is different, and the average sensitivity of Peak 2 to the magnetic field and temperature is also different. Meanwhile, RW₁H and RW₂H both reveal linear relationships with the magnetic field intensity, and RW₁T and RW₂T also show linear relationships with the temperature. Therefore, by introducing the measurement matrix expressed in Eq. (12) [29], it is possible to simultaneously detect the magnetic field and temperature.

Substituting the average magnetic field sensitivity and average temperature sensitivity of Peak 1 and Peak 2 into Eq. (13) could obtain the dual-parameter sensing matrix shown in Eq. (14). By measuring the wavelength deviation of the Peak 1 and Peak 2, it is possible to demodulate the magnetic field and temperature separately, which addresses the issue of cross-sensitivity caused by temperature variations.

In addition, Fig. 12 expresses the FM loss spectrum when the magnetic field and temperature alter simultaneously. Obviously, with the simultaneous increase of magnetic field and temperature, both Peak 1 and Peak 2 exhibit a blue shift. It should be noted that the matrix is tenable when substituting the variations of magnetic field and temperature, as well as the displacement of the two resonant peaks into the dual-parameter sensing matrix, which indicates that the proposed DHF-based dual-parameter sensor can effectively overcome cross-sensitivity.

 

Fig. 12. FM loss spectrum when the magnetic field and temperature alter simultaneously.

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5. Discussion

5.1 Manufacture feasibility

As displayed in Fig. 13, the manufacture feasibility of DHF-based dual-parameter sensor is analyzed. Firstly, prepare the optical fiber preform by Modified Chemical Vapor Deposition (MCVD) technique and adjust the relative refractive index difference between the core and cladding to 0.98% with Ge-doped core. Secondly, place the preform in an ultrasonic drill device and manufacture two symmetric air holes about Ge-doped core in the preform. The drill technology with ultrasonic wave has been commonly used to manufacture the preform of Panda polarization-maintaining fiber. Thirdly, draw the cleaned preform into DHF in fiber draw tower and ensure that the size and uniformity meet the requirements. Fourthly, place the Al wire with a relatively large diameter through one of the air holes in the DHF by the aid of the microscope and adjust the Al wire to the closest position to the core, then fix the wire with a small amount of cured glue at the end of the DHF. Fifthly, repeat last step and suspend another Al wire with the relatively small diameter in the other air hole, and the two Al wires are on the same horizontal line. Sixthly, seal the end of Ch2 with cured glue and insert the sealed end into a container filled with MF. When Ch1 is full of MF, remove the DHF and cut off the part with curing glue. Finally, seal the end of Ch1 in the same way and insert the sealed end into a container filled with thermo-sensitive liquid. When Ch2 is full of the thermo-sensitive liquid, remove the DHF again and cut off the part with curing glue, and the proposed DHF-based dual-parameter sensor is prepared.

 

Fig. 13. Manufacture process of the proposed DHF-based dual-parameter sensor.

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5.2 Fabrication tolerance

The fabrication tolerance of the sensor can characterize the effect of small structural variations during the fabrication process on its performance, which is commonly used to evaluate the stability of the sensor. In terms of the structural parameter optimization of the proposed DHF-based dual-parameter sensor, the S₁(H) is more sensitive with the parameters of dm₁ and L₁ and the S₂(T) is more sensitive to the parameters of d₀, dm₂ and L₂. So we focus on discussing the fabrication tolerance of these parameters. Table 3 gives the variation of S₁(H) at 50 Oe and S₂(T) at 24.3°C when the above structural parameters change within ±1%. There is only about 1 nm/mT change in S₁(H) for ±1% fluctuation of dm₁ and L₁, and below 5.2 nm/°C alternation in S₂(T) for ±1% fluctuation of d₀, dm₂ and L₂. Furthermore, for the worst situation that ±1% fluctuation simultaneously appears for all structural parameters of the DHF-based dual-parameter sensor, S₁(H) nearly keep constant and the maximum variation of S₂(T) is only 5.1 nm/°C, as shown in Fig. 14. Consequently, the proposed DHF-based dual-parameter sensor has the fabrication feasibility due to its strong capability resistant to the fluctuation of structure parameters of the sensor.

 

Fig. 14. S₁(H) and S₂(T) when the whole structure changes with ±1% fluctuation.

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Table 3. S₁(H) or S₂(T) when dm₁, L₁, d₀, dm₂ and L₂ vary within the range of ±1%.

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5.3 Performance comparison

To emphasize the advantages of the proposed DHF-based dual-parameter sensor, Table 4 lists the performance comparison with that of other sensors reported in recent years, including fiber type, maximum magnetic field sensitivity, and maximum temperature sensitivity. It can be found that the currently reported SPR dual-parameter fiber sensors for magnetic field and temperature sensing are primarily based on complex PCF structures. Due to the small size of air holes in PCF, it is difficult in injecting the mediums into such small air holes. In contrast, the designed DHF-based dual-parameter sensor has a simpler structure and easy to fill the MF and thermo-sensitive liquid by capillary effect. In addition, compared to Ref. [20–23,19–40], both the maximum magnetic field sensitivity and the maximum temperature sensitivity have been improved by 1∼2 orders of magnitude.

Table 4. Comparison of different dual-parameter sensors for magnetic field and temperature sensing.

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6. Conclusion

A DHF-based dual-parameter sensor for simultaneous detection of magnetic field and temperature is proposed and analyzed. The sensor utilizes the DHF containing a Ge-doped core with two large air holes symmetrically arranged at its two sides. To enhance the sensitivity to both magnetic field and temperature, Al wires with different diameters are embedded on the inner walls of the air holes in the DHF, creating a magnetic field sensing channel filled with the MF and a temperature sensing channel filled with thermo-sensitive liquid. The structural parameters of the proposed DHF-based dual-parameter sensor are systematically and comprehensively optimized based on the S₁(H) and S₂(T). The optimal parameters are d₀ = 12.0 µm, dm₁ = 0.4 µm, dm₂ = 1.4 µm, L₁= 0.45 µm, L₂= 0.4 µm, dc₁= dc₂= 41.0 µm and △ = 0.98%. The influence of different metals is discussed, and Al is selected to excite the SPR effect for higher magnetic field sensitivity and temperature sensitivity. Numerical results indicate that the proposed DHF-based dual-parameter sensor can simultaneously detect the magnetic field ranging from 40 Oe to 130 Oe and the temperature ranging from 24.3 °C to 49.3 °C. The maximum magnetic field sensitivity reaches up to 64000 pm/mT, while the maximum temperature sensitivity is approximately 44.6 nm/°C, both exceeding current reports by more than one order of magnitude for simultaneous detection of magnetic field and temperature. In addition, the dual-parameter sensing matrix is constructed for simultaneous measurement of the magnetic field and temperature. Analysis of fabrication tolerances illustrates that the performance of the proposed sensor remains stable when the structural parameters vary within ±1% fluctuation. The proposed DHF-based dual-parameter sensor is simple to fabricate, easy to fill sensing medium, and features extremely high magnetic field and temperature sensitivity, which offering enormous potential applications in material characterization analysis, geological environmental monitoring and aeronautical engineering.