Dual-Parameter Surface Plasmon Resonance Photonic Crystal Fiber Sensor for Simultaneous Magnetic Field and Temperature Detection with Potential SERS Applications

Abstract

A high-sensitivity surface plasmon resonance (SPR) dual-parameter sensor based on photonic crystal fiber (PCF) is proposed for simultaneous measurement of magnetic field and temperature. The grooves on the right and upper sides of the PCF, serving as distinct detection channels, are filled with magnetic fluid and polydimethylsiloxane, respectively, enabling high-sensitivity detection of magnetic field and temperature. The structure parameters and sensing characteristics of the proposed sensor are investigated based on the finite element method. Numerical results indicate, within the wavelength range of 850–1050 nm, that the sensor achieves a high magnetic field sensitivity of 86 pm/Gs under x-polarization in the range of 100–600 Gs, and exhibits a temperature sensitivity of −2.63 nm/°C under y-polarization within the temperature range of 20–40 °C. Furthermore, the detection precision and applicability of the sensor in actual measurement applications could be further enhanced in the future by introducing surface-enhanced Raman scattering technology.

1. Introduction

Magnetic field, a fundamental physical property of matter, plays a crucial role in various applications, including industrial production, environmental monitoring, medical diagnostics, resource exploration, aerospace, and other fields [1,2,3]. Compared to traditional magnetic field sensors, which often feature large sizes and complex structures, fiber-optic magnetic field sensors have attracted considerable interest owing to their high sensitivity, anti-electromagnetic interference, excellent remote sensing capabilities, compact design, and multiplexing ability [4]. Magnetic field sensors utilizing optical fiber provide stable and reliable monitoring under diverse and challenging conditions, including marine underwater detection, geological exploration, and smart grids [5]. Based on different sensing mechanisms, fiber-optic magnetic field sensors are mainly classified based on three effects: the Faraday rotation effect, magnetostrictive effect, and magneto-refractive (MR) effect [6,7]. In recent years, fiber-optic sensors utilizing the MR effect have attracted progressive attention due to their advantages, such as ease of fabrication and high sensitivity.

Magnetic fluid (MF), a type of magnetic colloidal fluid, possesses remarkable magneto-optical properties, including a tunable refractive index (RI), magneto-optical effects, and nonlinear optical effects [8]. As a result, MF is widely utilized in various fiber-optic sensors as an ideal magnetic-field-sensitive material for accurate magnetic field measurements [9,10,11]. Gu et al. designed an inline Mach–Zehnder interferometer (MZI) with a tapered structure and MF coating for detecting magnetic fields [9]. The presented sensor demonstrated the average sensitivities of −5.148 nm/mT and −5.782 nm/mT around the wavelength of 1500 nm. Tian et al. proposed a vector magnetic field sensor based on a coreless D-shaped fiber encapsulated with MF [10]. Experimental results indicated that the sensor attained magnetic field sensitivities of −0.231 nm/mT and −0.483 dB/mT. Zhang et al. presented a magnetic field sensor that employs an asymmetric four-hole fiber filled with MF [11]. By combining the Sagnac effect, the sensor exhibits an excellent sensitivity of 226.2 pm/Gs with a detection precision of 0.221 Gs.

Recently, surface plasmon resonance (SPR)-based fiber-optic sensors have been widely applied across diverse fields, such as electrochemical testing, Raman signal enhancement, and magnetic field monitoring, owing to their label-free, high sensitivity, in situ functionality, and real-time detection capabilities [12]. Especially, the localized surface plasmon resonance (LSPR) phenomenon induced by gold nanoparticles (Au NPs) can significantly enhance Raman signals, enabling ultrasensitive molecular detection [13]. Recently, SPR sensors combined with photonic crystal fibers (PCFs) have attracted significant attention in magnetic field sensing due to their highly flexible structural design and diverse functionalities [14,15,16]. Yao et al. developed a PCF-SPR-based magnetic field sensor with MF filled in the central air hole of the fiber, achieving a magnetic field sensitivity of 590 pm/Oe [14]. Wang et al. proposed a D-shaped PCF-SPR sensor based on MR effect, with a special hole filled with MF, exhibiting a high magnetic field sensitivity of 21,750 pm/mT [15]. Yao et al. designed a D-shaped MR-PCF based on SPR utilizing the erbium-doped materials [16]. The optimized sensor demonstrates a magnetic field sensitivity of 53 pm/mT. These studies have made valuable contributions to novel sensor structural designs and improvements in magnetic field sensitivity. In practice, measuring a single physical parameter is often complicated by temperature cross-sensitivity, particularly for MF, whose RI is sensitive to temperature variations.

To address these issues, many researchers have made remarkable progress in advancing dual-parameter sensing [17,18,19]. Fan et al. designed a D-shape SPR-PCF filled with two types of liquid crystals [17]. The temperature sensitivity of this sensor is 3.2 nm/°C, while its RI sensitivity is 2567 nm/RIU. Danlard et al. proposed a quasi-D-shaped plasmonic PCF microsensor capable of simultaneously measuring RI and temperature [18]. The sensor demonstrated a wavelength sensitivity of 5000 nm/RIU for RI detection and 3.0 nm/°C for temperature sensing. Wang et al. proposed an SPR-PCF sensor with two open ring channels, enabling the simultaneous sensing of magnetic field and temperature [19]. The sensor achieved sensitivities of 308.3 pm/Oe for magnetic field detection and 6520 pm/°C for temperature measurement. Although significant progress has been made in achieving dual-parameter sensing of RI and temperature, studies focused on the simultaneous detection of magnetic field and temperature are still comparatively scarce. In particular, existing studies on magnetic field and temperature dual-parameter sensing primarily focus on analyzing sensor performance under a single polarization mode. To enhance the multifunctionality and reusability of fiber sensors, it is crucial to fully exploit the sensor’s performance under different polarization modes.

As testing environment becomes increasingly complex, fiber-optic sensors capable of detecting multiple parameters simultaneously are becoming increasingly significant. Multi-parameter sensors can provide more comprehensive detection information, thereby improving the detection efficiency and accuracy of measurements. These sensors not only offer cost-effective detection capabilities but also promote the miniaturization and integration of sensing devices [20]. Herein, we propose a highly sensitive dual-parameter SPR-based PCF sensor capable of simultaneously detecting magnetic field and temperature. To enable dual-parameter measurements, the proposed sensor is designed with groove structures on the upper and right sides of the PCF, enabling the simultaneous detection of different physical quantities. Numerical simulation results indicate that the magnetic field sensitivity based on the x-polarization reaches 86 pm/Gs within the range of 100–600 Gs, while the temperature sensitivity based on y-polarization is −2.628 nm/°C within the range of 15 °C to 50 °C. Furthermore, the use of Au NPs as surface plasmon materials for achieving dual-parameter simultaneous measurement of magnetic field intensity and temperature is investigated, which not only further validates the effectiveness of the proposed dual-polarization strategy but also establishes a foundation for the realization of Raman signal enhancement. Therefore, the proposed SPR-PCF sensor, employing a polarization separation strategy, effectively enhances its multiplexing capability and overall performance.

2. Structure Design and Theoretical Analysis

2.1. Structure Design

Figure 1 depicts the designed SPR-PCF sensor structure featuring dual channels for simultaneous detection of magnetic field and temperature. The structure comprises two layers of air holes with a diameter of d = 2.2 μm, and the lattice spacing between the outermost air holes is Λ_out = 3.1 μm. Two distinct grooves are designed on the upper and right sides of the PCF to form separate sensing channels. Gold films, selected as the plasmonic material, are deposited in the grooves to effectively excite the SPR effect, with a gold film thickness of t_Au = 35 nm. To flexibly control the resonance wavelength (RW) and strengthen the interaction between the evanescent wave and the target analyte, TiO₂ films with thicknesses of t_up-TiO2 = 30 nm and t_right-TiO2 = 80 nm are deposited on the gold film of the upper and right grooves, respectively. The lattice spacing between the innermost air holes (Λ_in) is 4.4 μm, the groove width (W) is 2 μm, and the depths of the upper channel (h-up) and right channel (h-right) are both 4 μm.

To achieve simultaneous dual-parameter sensing of magnetic field intensity and temperature, the sensor can be packaged according to the following steps: First, temperature-sensitive material polydimethylsiloxane (PDMS) and curing agent are mixed uniformly at a mass ratio of 10:1, vacuum-degassed, and selectively filled into the upper channel of the PCF, then cured by heating for 2 h to realize temperature sensing. Next, a glass capillary tube is placed around the PCF, and MF is filled into it by capillary action. MF, composed of magnetic nanoparticles, is sensitive to magnetic fields, and its behavior depends on the external magnetic field and temperature [21,22], thus enabling effective magnetic field sensing. Finally, both ends of the capillary tube are sealed with UV adhesive to prevent leakage of the MF. As a polymer material with a high thermo-optic coefficient, the relationship between the RI of PDMS (n_PDMS) and temperature (T) can be described by the following equation [23]:

$$n_{PDMS}(T)=-4.5\times {10}^{-4}\cdot T+1.4176$$

(1)

The RI of the air holes is set to 1, and the substrate material of the PCF is fused silica. The dispersion relation corresponding to temperature for fused silica can be derived using Sellmeier’s equation [24]:

$$n^2(\lambda ,T)=(n_1+n_{2}T)+{\displaystyle \frac{(n_3+n_{4}T){\lambda }^2}{{\lambda }^2-(n_5+n_{6}T)}}+{\displaystyle \frac{(n_7+n_{8}T){\lambda }^2}{{\lambda }^2-n_9}}$$

(2)

where λ denotes the wavelength of the incident light in micrometers, and n₁ to n₉ denote constants. TiO₂, with its high RI and excellent optical properties, can effectively modulate the sensing characteristics of the SPR-PCF sensor. Its RI can be determined using the following equation [25]:

$$n^2=5.913+{\displaystyle \frac{2.441\times {10}^7}{({\lambda }^2-0.803\times {10}^7)}}$$

(3)

Moreover, the dielectric constant of gold (ε_Au) can be described by the Drude–Lorentz model, as shown in the following equation [26]:

$${\epsilon }_{Au}(\omega )={\epsilon }_{\infty }-{\omega }_p^2/\omega (\omega +i{\omega }_{\tau })$$

(4)

where ω_p = 1.36 × 10¹⁶ and ω_τ = 1.45 × 10¹⁴ represent the plasma frequency and the electron scattering frequency of gold, respectively. Additionally, ε_∞ = 9.75 denotes the dielectric constant of gold at high frequencies. The angular frequency of the incident light is represented by ω. Moreover, the thermal expansion effect of the gold film influences its dielectric constant, which changes with temperature [27]. To account for temperature effects, the thickness d of the gold film is typically described by incorporating a modified thermal expansion coefficient α’L as d = d₀[1 + α’L(T − T₀)], where d₀ is the thickness of the gold film at T₀ = 25 °C. Since the temperature sensitivity of the MF and PDMS is much higher than that of the gold film, the temperature effect on the gold film is neglected [28].

The proposed PCF sensor structure can be fabricated using a mature stack-and-draw technique. In the manufacturing process, high-purity solid silica rods and capillary tubes are carefully stacked according to predetermined structural parameters to form a precise fiber preform. Meanwhile, the drawing speed and temperature in the drawing tower must be carefully controlled to achieve a PCF structure that meets the design requirements [29,30]. Subsequently, femtosecond laser micromachining technology is employed to precisely machine two grooves on the side surface of the PCF. This advanced laser technology allows accurate control of groove dimensions and positions without causing significant thermal damage or structural deformation to the PCF, thereby ensuring high structural integrity and optical performance [31]. Finally, magnetron sputtering deposition technology is utilized to uniformly deposit a gold film with precisely controlled thickness onto the surfaces of the grooves in the PCF [32].

2.2. Theoretical Analysis

The proposed sensor structure and its sensing properties are simulated and investigated using Comsol Multiphysics v5.5 which utilizes the finite element method (FEM). To obtain accurate simulation results, a perfectly matched layer (PML) is added around the simulation structure to absorb scattered light [33]. The sensing performance of the dual-parameter SPR-PCF sensor is evaluated by calculating and analyzing the confinement loss (a_CL), as given by the following equation [34]:

$${\alpha }_{CL}(dB/cm)=8.686\times 2\pi /\lambda \times \mathrm{Im}(n_{eff})\times {10}^4$$

(5)

In this equation, Im(n_eff) denotes the imaginary component of the effective RI. The dispersion relationships of the fundamental modes (x-pol and y-pol) and the surface plasmon polariton (SPP) mode are illustrated in Figure 2. The black and yellow dashed lines represent the core modes and the SPP mode, respectively, while the blue and red curves correspond to the confinement loss (CL) of the x-pol and y-pol. Different polarization directions of the incident light (x-pol and y-pol) correspond to electric field components oriented along different directions in the cross-section of the PCF. As observed in Figure 2, the real part of the effective RI decreases for both the core modes (x-pol and y-pol) and the SPP mode as the operating wavelength increases from 850 nm to 1050 nm. When the effective RI curve of the core mode intersects with that of the SPP mode, the phase-matching condition is satisfied. In this case, part of the energy from the core mode is transferred to the SPP mode, resulting in a peak in the CL spectrum of the core mode, as explained by coupled-mode theory [35]. The wavelength corresponding to this peak is referred to as the RW. It should be noted that the proposed dual-parameter sensor can generate resonance peaks based on different polarization modes within the same wavelength range, effectively enhancing the sensor’s wavelength multiplexing capability. The inset illustrates the optical field distribution at the coupling between the core mode and the SPP mode. Because of the high sensitivity of SPR to the RI of the surrounding environment, the performance of the SPR-PCF sensor can be evaluated by examining the RW shift observed in the SPR spectrum. Sensitivity and resolution are crucial for evaluating the sensing performance of the proposed sensor. The wavelength interrogation method can be used to calculate these two parameters [33]:

$$S={\displaystyle \frac{\Delta {\lambda }_{peak}}{\Delta n}}nm/RIU$$

(6)

$$R={\displaystyle \frac{\Delta n\times \Delta {\lambda }_{\min }}{\Delta {\lambda }_{peak}}}RIU$$

(7)

where Δλ_peak and Δn represent the shift in RW and the change in the RI of the analyte, respectively, and Δλ_min denotes the minimum resolution of the optical spectrum analyzer (OSA), which is set to 0.1 nm. To assess the detection accuracy of the sensor, the figure of merit (FOM) is determined to quantify this performance:

$$FOM={\displaystyle \frac{Sensitivity(nm/RIU)}{FWHM(nm)}}$$

(8)

where FWHM refers to the full-width at half-maximum of the resonance peak. A larger FOM value represents better detection precision.

2.3. Single-Parameter Magnetic Field Sensing of the SPR-PCF Sensor

To demonstrate the practicality of the designed magnetic field and temperature dual-parameter PCF-SPR sensor, as shown in Figure 3a, the single-parameter magnetic field sensing is first investigated. Figure 3b reveals that the SPR CL spectrum exhibits a single RW based on the x-pol core mode, which appears at 923 nm with a magnetic field strength of 100 Gs. Furthermore, the inset demonstrates that compared to the y-pol core mode, the SPR effect induced by the x-pol core mode significantly enhances the electric field intensity at the surface of the gold film, which contributes to the amplification of Raman signal intensity and improved detection sensitivity. Figure 3c demonstrates that as the magnetic field strength increases, the RW undergoes a red shift. Figure 3d illustrates how the RW varies with magnetic field intensity. The single-parameter PCF-SPR sensor based on the x-pol core mode achieves a magnetic field sensitivity of 86 pm/Gs with a good linearity (R² = 0.99).

2.4. Single-Parameter Temperature Sensing of the SPR-PCF Sensor

Similarly, Figure 4a shows the cross-sectional view of the single-channel temperature sensing PCF-SPR sensor, which includes an upper groove. From Figure 4b, it can be observed that at a temperature of 25 °C, the SPR CL spectrum exhibits another RW at 998 nm, which is based on the y-pol core mode. The corresponding inset also illustrates the enhancement of the electric field strength on the gold film surface due to the SPR effect triggered by the y-polarized core mode. Figure 4c shows that as the temperature increases from 25 °C to 65 °C, the RW has a significant blue shift. Figure 4d indicates the variation of RW with temperature. It can be seen that the single-parameter PCF-SPR sensor based on the y-pol core mode achieves a temperature sensitivity of −2.64 nm/°C with excellent linearity (R² = 0.99). These above simulation results indicate that the proposed dual-channel sensor provides a feasible strategy for concurrently detecting magnetic field and temperature, leveraging the distinct polarization characteristics of the core mode.

3. Results

Figure 5 presents a schematic illustration of the experimental configuration used for detecting magnetic field intensity and temperature. The incident light emitted from the broadband light source is coupled into the sensing fiber with MF encapsulated through a polarization controller. An electromagnet is positioned in the sensing region, and its current is adjusted to generate magnetic fields of varying intensities. Additionally, a heating stage with a thermal insulation cover ensures a stable and adjustable temperature. An OSA is employed to monitor and analyze the changes in the RWs of the output spectrum, enabling the simultaneous demodulation of magnetic field and temperature variations.

3.1. Effect of TiO₂ and Au Film Thicknesses on Sensing Performance

To achieve excellent sensing performance of temperature and magnetic field, the thickness of TiO₂ film in the right groove (t_right-TiO2) is first optimized, with the corresponding results presented in Figure 6. It is found that as the t_right-TiO2 thickness increases, the loss peak of the x-pol mode shifts to longer wavelengths, and the loss depth increases, while the loss characteristics of the y-pol mode remain unchanged. Specifically, when the t_right-TiO2 thickness varies from 70 nm to 90 nm, the sensor’s magnetic field sensitivity is 88 pm/Gs, 86 pm/Gs, and 84 pm/Gs, respectively. Considering both magnetic field sensitivity and loss depth, an optimized t_right-TiO thickness of 80 nm is chosen.

Similarly, Figure 7 illustrates the effect of the TiO₂ film thickness in the upper groove (t_up-TiO2). It can be observed that variations in t_up-TiO2 thickness affect only the loss characteristics in the y-pol direction, with no impact on its magnetic field sensing properties. As illustrated in Figure 7d, with the increase in the film thickness from 20 nm to 40 nm, the sensor’s temperature sensitivity is −2.33 nm/°C, −2.63 nm/°C, and −2.63 nm/°C, respectively. Ultimately, a t_up-TiO2 thickness of 30 nm is selected.

The Au film thickness strongly influences the performance of the sensor, and its optimization results are shown in Figure 8. As the thickness of the t_Au increases, the loss peak for both x-pol and y-pol has a significant blue shift, while the resonance depth decreases. This phenomenon arises from the effective shielding of the core mode by the surface plasmon as the thickness of the Au film increases. From Figure 8d, it is clear that although the temperature sensitivity improves as the Au film thickness grows from 35 nm to 45 nm, the change is relatively small. However, the resonance peak intensity sharply decreases from 280.1 dB/cm at t_Au = 35 nm to 53.0 dB/cm at t_Au = 45 nm. A stronger loss peak intensity is beneficial for enhancing the detection capability of the sensor and achieving higher detection sensitivity. The optimized Au film thickness is to be t_Au = 35 nm.

3.2. Effect of Variation of Structural Parameters on the Spectral Response

Under a magnetic field of 100 Gs and a temperature of 25 °C, the influence of structural parameter variations on the spectral response is investigated, as shown in Figure 9a₁,a₂–f₁,f₂. As Λ_out increases from 3 μm to 3.2 μm (Figure 9a₁,a₂), the resonance peaks of both x- and y-polarization exhibit minor changes. In contrast, an increase in Λin from 4.2 μm to 4.6 μm results in a blue shift of the resonance peaks for both x- and y-polarization (Figure 9b₁,b₂). When ddd increases from 3 μm to 3.2 μm (Figure 9c₁,c₂), the resonance intensity of both x- and y-polarization decreases. As h-up increases from 5.5 μm to 6.5 μm (Figure 9d₁,d₂), a significant red shift is observed only in the y-polarized resonance peak, while the x-polarized resonance peak remains nearly unchanged. Conversely, when h-right increases from 3.5 μm to 4.5 μm (Figure 9e₁,e₂), a noticeable red shift occurs exclusively in the x-polarized resonance peak, accompanied by a significant decrease in intensity, whereas the y-polarized resonance remains unaffected. Furthermore, as W increases from 1.9 μm to 2.1 μm (Figure 9f₁,f₂), both x- and y-polarized resonance peaks exhibit a slight red shift. Based on the above results, it is evident that the proposed SPR spectrum can be flexibly tuned by adjusting the structural parameters, greatly enhancing the design flexibility and multifunctionality of the sensor.

3.3. Dual-Parameter Sensing of Magnetic Field and Temperature

Based on the optimized structural parameters, the CL characteristics of the core mode under varying magnetic field strengths (ranging from 100 Gs to 600 Gs) are investigated at a constant temperature of 25 °C, with the results shown in Figure 10. As observed in Figure 10a,b, as the magnetic field strength increases, the RW based on the x-pol mode shifts to a longer wavelength, while the RW based on the y-pol mode remains unchanged. The relationship between the RWs and magnetic field strength is depicted in Figure 10c. The results show that the magnetic field sensitivity of the x-pol core mode is 86 pm/Gs, with a corresponding resolution of 1.2 Gs. Figure 10d illustrates the corresponding FWHM and figure of FOM of the designed sensor as the magnetic field strength varies. It is evident that the trends of the FWHM and FOM are opposite: when the magnetic field strength reaches 600 Gs, the sensor achieves the minimum FWHM and the maximum FOM.

Similarly, Figure 11 illustrates the temperature sensing performance of the designed dual-parameter sensor within the range of 25 °C to 65 °C, with the magnetic field strength held constant at 100 Gs. As shown in Figure 10a,b, the RWs for both x-polarized and y-polarized modes show a blue shift. However, the shift in the RW for x-pol is smaller compared to that for y-pol. This difference occurs because PDMS, as a temperature-sensitive material characterized by a high thermo-optic coefficient, has an RI that is much more affected by temperature changes than that of MF. Figure 11c depicts the relationship between the RWs and temperature. The RW based on x-polarization exhibits a temperature sensitivity of −0.15 nm/°C, with a resolution of 0.67 °C. In contrast, the RW based on y-polarization demonstrates a higher sensitivity of −2.63 nm/°C and a resolution of 0.038 °C. The corresponding FWHM and FOM of the designed dual-parameter sensor as a function of temperature are shown in Figure 11d. Compared to the x-polarization, the RW based on the y-polarization exhibits a smaller FWHM and a higher FOM. This is due to the higher RI of PDMS, which strengthens the coupling between the x-polarized core mode and the SPP mode.

To further verify the applicability of the designed dual-polarization sensor and explore its potential for improving sensitivity, the use of Au NPs instead of gold films to enable the simultaneous sensing of magnetic field and temperature is also investigated and the cross-sectional diagram is depicted in Figure 12a. The inset of Figure 12a illustrates the LSPR effect generated by the integrated Au NPs. Compared to the conventional SPR effect, the localized electromagnetic field excited at the surface of the gold nanoparticles significantly enhances the signal, facilitating signal amplification. This effect is particularly pronounced in surface-enhanced Raman scattering (SERS) applications. Specifically, the strong localized electromagnetic field around the Au NPs significantly enhances the Raman signals of molecules adsorbed on or near the particle surface, thereby significantly improving the sensitivity of the sensor. Figure 12b,c shows the CL spectra for x-pol and y-pol at different magnetic field strengths, while Figure 12d,e displays the CL spectra for both polarizations at varying temperatures. From these results, it can be seen that the proposed dual-polarization strategy enables the dual-parameter sensor based on PCF and integrated Au NPs to effectively achieve simultaneous magnetic field and temperature sensing, demonstrating the wide applicability of this strategy. The sensitivities for both magnetic field and temperature are displayed in Figure 12f. The magnetic field sensitivity based on the x-pol resonance peak reaches a maximum of 60 pm/Gs when the magnetic field increases from 100 Gs to 600 Gs, while the position of the y-pol resonance peak remains unchanged. Conversely, when the temperature rises from 25 °C to 65 °C, the temperature sensitivity based on the x-pol resonance peak is −0.13 nm/°C, whereas the sensitivity based on the y-pol resonance peak is significantly higher at −2.12 nm/°C. According to these experimental results, simultaneous dual-parameter sensing of magnetic field and temperature can be achieved using a sensitivity matrix, which is defined as follows:

$$\left[\begin{array}{l}\Delta {\lambda }_x\\ \Delta {\lambda }_y\end{array}\right]=\left[\begin{array}{cc}60& -0.13\\ 0& -2.12\end{array}\right]\left[\begin{array}{l}\Delta MF\\ \Delta T\end{array}\right]$$

(9)

where ΔMF and ΔT denote the variations in magnetic field intensity and temperature, respectively, while Δλ_x and Δλ_y correspond to the wavelength shifts of the x- and y-polarized resonance peaks (λ_x and λ_y). Therefore, changes in magnetic field and temperature can be accurately determined using the following equations:

$$\left[\begin{array}{l}\Delta MF\\ \Delta T\end{array}\right]={\left[\begin{array}{cc}60& -0.13\\ 0& -2.12\end{array}\right]}^{-1}\left[\begin{array}{l}\Delta {\lambda }_x\\ \Delta {\lambda }_y\end{array}\right]$$

(10)

The LSPR effect generated by Au NPs is advantageous for signal enhancement. In particular, the strong electromagnetic field enhancement induced by Au NPs can be utilized to amplify Raman signals, providing a potential platform for SERS. In future research, the integration of SERS technology with sensors is expected to further enhance their detection sensitivity and accuracy [36]. In addition, the sensitivity of the proposed dual-parameter sensor can be further improved by employing long-range SPR (LRSPR) [37,38]. LRSPR effectively reduces mode propagation loss and enhances electric field penetration depth, enabling sensors based on LRSPR to achieve higher sensitivity and detection accuracy, thereby expanding the application potential of the proposed dual-polarization PCF sensor.

Table 1. Comparison of various fiber-optic sensors developed to date.

Ref.	Structure	Magnetic Field Sensitivity (pm/Oe)	Temperature Sensitivity (pm/°C)	Number of Simultaneously Detectable Parameters	Result Type
[14]	D-shaped PCF	190	−29.7	1	Simulation
[15]	D-shaped PCF	2175			Simulation
[16]	D-shaped PCF	5	0	1	Simulation
[19]	Two opening ring PCF	308	−6520	2	Simulation
[39]	D-shaped PCF	143	−229	2	Simulation
[40]	Symmetrically side-polished PCF	467	0	1	Simulation
Our work	Multi-channel PCF	860	−2628	2	Simulation

provides a performance comparison of the recently reported SPR-based magnetic field sensor and the proposed sensor. It can be observed that the proposed sensor not only achieves high sensitivity for simultaneous magnetic field and temperature measurement, but also exhibits exceptional sensing performance. Furthermore, the sensing technology utilizing the different polarization characteristics of the core mode significantly improves the multifunctionality and the detection efficiency of the sensor, demonstrating their potential for use in magnetic field sensing and other applications requiring multi-parameter sensing.

4. Discussion

In summary, a dual-parameter PCF sensor based on the SPR effect, utilizing different polarization characteristics, has been proposed. The sensor design includes two independent grooves located at the upper and right sides of the PCF, serving as separate sensing channels. MF and PDMS are incorporated into these channels to enable the detection of magnetic field strength and temperature. Additionally, Au and TiO₂ layers are deposited onto the grooves to effectively excite the SPR effect and provide flexibility in adjusting the RWs. The results exhibit that the proposed sensor achieves a magnetic field sensitivity of 86 pm/Gs and a temperature sensitivity of −2.63 nm/°C. The excellent sensing performance highlights the multiple significant advantages of the polarization-separated SPR-PCF sensor, especially the realization of dual-parameter sensing based on Au NPs, which provides a potential opportunity for the implementation of Raman technology.