Introduction

Photonic crystal fiber (PCF), with their periodically aligned pore structure, is an excellent platform for developing sensors with many sensing advantages. Recently, researchers have combined the surface plasmon resonance (SPR) effect with PCF sensing technology to construct PCF sensors that can excite the SPR effect. This type of sensor has good sensing characteristics, which makes it suitable for sensor development [1]. SPR technology is based on the principle of total reflection. When the incident light on the surface of the fiber undergoes total reflection, part of the light will return to the fiber. The other part will propagate along the surface of the fiber in the form of a swift wave, which is interfered with by the photons and undergoes a collective oscillation to form a plasma wave, and the resonance of the surface plasma wave (SPW) with the evanescent wave occurs under a certain incident angle and wavelength to produce the SPR effect, which results in a corresponding Resonance Absorption Peak [1]. At present, SPR technology has been used in the fields of biomonitoring analysis [2,3,4]. PCF sensors based on the SPR effect are characterized by high sensitivity and flexible design [5, 6].

The optical phenomenon of SPR allows it to track the interactions between biomolecules in their natural state in real-time. In 2006, Hassani et al. designed a PCF based SPR sensor by combining SPR sensing with PCF for the first time [7]. This sensor has a stable structure and good sensing characteristics. However, fabricating is more difficult because its metal film and measurement channels are located in the air holes. In 2012, Ming Tian et al. proposed a D-type PCF [8]. In this structure, a meta film and a liquid are applied to the exterior of the cladding, making it easy to prepare. The above sensors can only measure one parameter, and the study of multi-parameter measurement is conducive to improving optical fiber integration. In 2021, Xiao et al. designed a PCF-SPR sensor that can perform simultaneous three-parameter measurements. The air holes next to the fiber core are filled with temperature-sensitive materials and magnetic fluids, respectively, and graphene and metal films are coated on the side-throw surface of the fiber, enabling simultaneous measurement of temperature, refractive index, and magnetic field [9]. In 2022, Yin et al. designed a D-type dual-core PCF-SPR sensor. The upper throw surface is coated with temperature-sensitive material and a metal film for temperature measurement, and the lower throw surface is coated with a metal film for refractive index measurement [10]. The reported SPR-PCF sensors achieve multifunctional detection but still have the disadvantages of complex preparation and low integration and do not meet the trend of device miniaturization and integration.

This paper proposes a three-parameter dual-core PCF-SPR sensor based on the above research background. Temperature and refractive index measurements are realized by applying a metal film and temperature-sensitive material to the upper polished surface and a gold film to the lower polished surface. Air holes next to the refractive index channel cores are filled with magnetic fluid for magnetic field measurements. This makes the three-parameter sensor easier to fabricate. The detection ranges chosen for this study were temperature 0–50 °C, refractive index 1.36–1.42, and magnetic field strength 20–550 Oe. The results showed that the refractive index showed a maximum sensitivity of 20,000 nm/RIU, the linear sensitivity for temperature was 5.3 nm/°C, and the linear sensitivity for the magnetic field was 116 pm/Oe.

Theoretical Foundations and Sensing Structures

The cross-section of the sensor is shown in Fig. 1, from which it can be seen that the two sides are polished to different depths, with the upper polished depth being d1 and the lower polished depth being d2. The radius of the air holes is r1, the radius of the magnetic field channel is r2, and the spacing between the nearest neighboring air holes is c. Polydimethylsiloxane (PDMS) was coated immediately adjacent to the gold film for temperature measurements. A layer of gold film with a thickness of t2 on the lower polished surface is coated with gold for detecting the RI of the liquid, and one end of the fiber core of the lower polished surface is filled with a magnetic fluid. A gold film of thickness t2 was coated on the lower polished surface to detect the RI of the fluid, and the air holes at one end of the fiber core on the lower polished surface were filled with magnetic fluid. The air holes were coated with a gold film to detect the magnetic field. The PDMS will be easily connected to other materials after heating. Based on the properties of PDMS as well as Si, temperature measurements can be realized [11]. Selection of Fe3O4 as a magnetic fluid to enable the detection of magnetic fields [12].

Fig. 1
figure 1

Cross-section of a multi-parameter PCF

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The following process can prepare the sensor: first, PCF preforms are obtained by ultrasonic drilling [11, 12], sol-gel [13], beam stacking [14], or extrusion [15, 16]. After that, it is processed into PCF semi-finished products [17]. Double-sided polished photonic crystal fiber can be obtained by polishing [18, 19]. Then, a gold film is applied to the two polishing planes and the surface of the air holes at one end of the fiber core (2) by magnetron sputtering. [20, 21]. Then, PDMS [22] is applied to the gold film on the upper surface. Finally, Fe3O4 was injected into the air holes coated with gold film using a micro syringe and plasticized. At this point, the fabrication of the sensor designed in this paper is complete, as shown in Fig. 2.

Fig. 2
figure 2

Three-dimensional modeling of the PCF-SPR sensor

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Silicon dioxide is commonly used as a material for making optical fiber, and the equation for calculating its material dispersion is as follows [23]:

$${n}^{2}\left(\lambda \right)=1+\sum\nolimits_{i=1}^{3}\frac{{a}_{i}{\lambda }^{2}}{{\lambda }^{2}-{b}_{i}^{2}}$$
(1)

The dielectric constant of the gold film can be expressed in terms of the Lorentz-Drude model as follows [24]:

$${\varepsilon }_{r}\left(\omega \right)=1-\frac{{\Omega }_{p}^{2}}{\omega \left(\omega -i{\tau }_{0}\right)}+\sum\nolimits_{j=1}^{k}\frac{{f}_{j}{\omega }_{p}^{2}}{\left({\omega }_{j}^{2}-{\omega }^{2}\right)+i\omega {\tau }_{j}}$$
(2)

We can also use expressions to characterize the refractive index of the PDMS used for detecting temperature as a function of temperature [25].

$${n}_{PDMS}=-4.5\times {10}^{-4}\cdot T+1.4176$$
(3)

A magnetofluid is a colloidal solution. The Langevin function expresses its dependence on temperature and magnetic field strength [26,27,28,29]. The magnetic fluid used in this simulation is Fe3 O4. The following expression can represent its material detection expression [30].

$${n}_{MF}=1.3592-2.4\times {10}^{-4}\cdot T+4.98\times {10}^{-5}\cdot H$$
(4)

Sensitivity is an essential index for evaluating the performance of photonic crystal fiber optic sensors, and it can be represented by the following expression [31].

$$S\left(\lambda \right)=\frac{\Delta {\lambda }_{\mathrm{peak}}}{\Delta {n}_{s}}(\frac{\mathrm{nm}}{\mathrm{RIU}})$$
(5)

The full width at half maxima (FWHM) of the resonance peak affects the sensor’s resolution, and too much sensor sensitivity leads to too much FWMH, which results in lower sensor resolution [32]. For this, we choose the quality factor figure of merit (FOM) to judge the transmission characteristics [10]:

$$\mathrm{FOM}=\frac{S(\lambda )}{\mathrm{FWHM}}$$
(6)

According to the above formula, the material’s refractive index changes when the magnetic field and temperature change, leading to a shift in the resonance wavelength. By observing the shift, we can calculate its sensitivity. The expression for calculating the sensitivity of the two is as follows [10]:

$$\begin{array}{c}K_{ch}\left(T\right)=\Delta\lambda_{ch}/\Delta T\\K_{ch}\left(H\right)=\Delta\lambda_{ch}/\Delta H\end{array}$$
(7)

We can derive the sensitivity matrices for the temperature and magnetic field channels using the following matrices:

$$\begin{pmatrix}\Delta\lambda_1\\\Delta\lambda_2\end{pmatrix}=\begin{pmatrix}\frac{\lambda_{1T}}{\Delta T}&\frac{\lambda_{1H}}{\Delta H}\\\frac{\lambda_{2T}}{\Delta T}&\frac{\lambda_{2H}}{\Delta H}\end{pmatrix}\begin{pmatrix}\Delta T\\\Delta B\end{pmatrix}=\begin{pmatrix}K_{ch1}\left(T\right)&K_{ch1}\left(H\right)\\K_{ch2}\left(T\right)&K_{ch2}\left(H\right)\end{pmatrix}\begin{pmatrix}\Delta T\\\Delta H\end{pmatrix}$$
(8)

where ∆λij denotes the shift of the resonance wavelengths of the temperature and magnetic field channels for temperature or magnetic field changes, ∆Tand ∆H denote the changes in temperature and magnetic field, respectively, and Kchi(J) denotes the sensitivity of the two channels to changes in temperature and magnetic field.

We can get the temperature and magnetic field sensitivity matrices by solving the inverse matrix of the above matrices [10]:

$$\begin{pmatrix}\Delta T\\\Delta H\end{pmatrix}=\begin{pmatrix}K_{ch1}\left(T\right)&K_{ch1}\left(H\right)\\K_{ch2}\left(T\right)&K_{ch2}\left(H\right)\end{pmatrix}^{-1}\begin{pmatrix}\Delta\lambda_1\\\Delta\lambda_2\end{pmatrix}$$
(9)

In this simulation, we use the finite element method in Comsol to perform the analysis. The perfectly matched layer (PML) first absorbs the radiant energy of other light and allows for a stable transmission of energy in the core.

Figure 3 shows the electric field distribution. For the parameters, we chose the radius of the air holes as r1 = 1.5 um, the radius of the air holes injected into the magnetic fluid as r2 = 1.5um, the thickness of the gold film covering it as t3 = 0.4 μm, and the depth of the upper polishing depth and the depth of the lower polishing depth as d1 = 8.5 μm and d2 = 3.0 μm, respectively. The upper and lower polishing surfaces were coated with a 0.5 μm gold film (t1 = 0.5 μm, t2 = 0.5 μm). The spacing of adjacent air holes is c = 6.3 μm. Data analysis shows light can propagate independently in both cores, thus completing the detection.

Fig. 3
figure 3

Electric field distributions of the core 1: a Core mode in the direction of Y polarization at 800 nm; b core mode in the direction of X polarization at 800 nm; c resonance modes in the direction of Y polarization at 892 nm; d SPP modes in the direction of Y polarization at 890 nm; Electric field distributions of the core 2: e core mode in the direction of Y polarization at 800 nm; f resonance modes in the direction of X polarization at 700 nm; g SPP modes in the direction of Y polarization at 970 nm; h resonance modes in the direction of Y polarization at 970 nm. Arrows indicate polarized direction of electric fields

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We give plots of the dispersion relations of core (1) and core (2) in the X and Y directions, respectively, along with their loss spectra. As shown in Fig. 4, observation of Fig. 4a reveals a clear loss peak in the Y-pol direction and the core mode intersects with the SPP mode out of the resonance wavelength, and there is no loss peak in the X-pol direction. Thus, for the fiber core (1), we mainly study his Y-pol direction. Observing Fig. 4b, c, we can find that the core mode and SPP mode in the X-pol and Y-pol directions are intersected at the resonance wavelength, and there are obvious loss peaks in both directions, so for the core (2), we mainly study his X-pol and Y-pol directions.

Fig. 4
figure 4

a The dispersion relationship between core mode and SPP mode of core 1, together with the loss spectrum of X-pol and Y-pol.; b core 2 Dispersion relation between core mode and SPP modes in Y-pol direction; c core 2 Dispersion relation between core mode and SPP modes in X-pol direction

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Results and Discussion

PML and scattering boundary conditions were introduced in the calculations to improve the accuracy of the results. The designed PCF-SPR sensor was analyzed using the control variable method and the resonance wavelength shift was measured using the wavelength modulation method, which enabled multiparameter measurements. Finally, the sensitivity of the measured parameters is calculated and discussed by data processing.

Refractive Index Sensitivity

Figure 5b shows the fitted curve between the liquid resonance wavelength and RI. The fitting equation in the figure, as well as the data, shows that the fit is good. According to the calculation, the refractive index’s sensitivity is up to 20,000 nm/RIU.

Fig. 5
figure 5

a Variation of the loss spectrum with the refractive index of the liquid and b the results of the numerical fitting of the resonance wavelength as a function of the refractive index of the liquid

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Temperature Sensitivity and Magnetic Field Sensitivity

Figure 6b shows the fitted curve between resonance wavelength and temperature. Based on the fitted curve equations as well as the data, it can be seen that the fit is good. The linear sensitivity is calculated to be 5.3 nm/°C because it is needed to derive the linear sensitivity in the subsequent matrix. In addition, the increase in the refractive index leads to the red shift of the phase matching point between the SPW and the core fundamental mode, so the resonance wavelength is red-shifted.

Fig. 6
figure 6

a Variation of loss spectrum with temperature and b results of numerical fitting of resonant wavelength as a function of temperature

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Figures 6 and 7 show that the resonance wavelengths of the magnetic field channel and the temperature channel are blue shifted when the temperature varies. This is due to the negative temperature coefficients of the MF and PDMS for both the magnetic field channel and the temperature channel. After linear fitting, the linear sensitivity of the temperature channel was 5300 pm/°C; maximum sensitivity to temperature up to 9200 pm/°C; the sensitivity of the magnetic field channel to temperature was 425.71 pm/°C.

Fig. 7
figure 7

a Loss spectrum of the magnetic field channel as a function of liquid temperature and b numerical fitting results of the resonance wavelength as a function of liquid temperature

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Figure 8 shows that the magnetic field channel resonance wavelengths are red-shifted when the magnetic field strength is varied between 20 and 550 Oe. According to Eq. (4), it can be seen that the magnetic field strength is positively correlated with the MF when the temperature is determined. Therefore, the resonance wavelength is red-shifted, and the linear sensitivity of the magnetic field channel to magnetic field variations is 116 pm/Oe with an R-squared of 0.99214. Moreover, the sensitivity of the temperature channel to magnetic field variations is found to be 0 pm/°C by using Eq. (3).

Fig. 8
figure 8

a Variation of loss spectrum with external magnetic field and b numerical fitting results of resonant wavelength as a function of magnetic field

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The linear sensitivity of the temperature channel for temperature and magnetic field changes is 5300 pm/°C and 0 p/°C, respectively. The linear sensitivity of the magnetic field channel for temperature and magnetic field changes is 425.71 pm/Oe and 116 pm/Oe, respectively. According to Eqs. (9) and (10), the temperature and magnetic field sensitivity matrix is as follows:

$$\begin{pmatrix}\Delta T\\\Delta H\end{pmatrix}=\begin{pmatrix}-0.426&0.116\\-5.3&0\end{pmatrix}^{-1}\begin{pmatrix}\Delta\lambda_1\\\Delta\lambda_2\end{pmatrix}=\begin{pmatrix}0&-0.189\\8.62&-0.693\end{pmatrix}\begin{pmatrix}\Delta\lambda_1\\\Delta\lambda_2\end{pmatrix}$$
(10)

Since few multi-parameter measurement structures are available, we compare them with some of the two-parameter structures, as shown in Table 1. The table shows that the present design is better than some of the current designs of two-parameter structures in terms of temperature and refractive index. The sensitivity of the magnetic field of the present work is also approximately equal to or better than that of other designs.

Table 1 Comparison of refractive index, temperature, and magnetic field sensitivity with other SPR-based sensor structures
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Influence of Structural Parameters on Sensor Stability

The stability of the designed sensor has a significant impact on its performance. Different structural parameters may have different effects on the sensor performance. In this simulation, different radii of air holes, inter-hole distances and polishing depths are observed to determine whether the sensor is stable. Observations in Fig. 9a–i show that the resonance peaks increase with the increase of the aperture radius under the same environmental conditions. When the aperture radius increases, the fiber core is squeezed horizontally, and more energy leaks into the metal interface, resulting in increased energy loss and an enhanced SPR effect.

Fig. 9
figure 9

Loss spectra of the three channels for different values of r1, r2, c, d1 and d2. a–c Loss spectrum of core 1 and core 2 with different values of stomatal radius; d–f loss spectrum of core1 and core2 with different values of stomatal spacing; g–i loss spectrum of core 1 and core 2 with different values of depths

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Under the same analytical method, an increase in the air hole spacing or polishing depth squeezes the fiber core to some extent, increasing the energy loss and strengthening the SPR effect. However, the resonance wavelength was almost constant, indicating that the sensors involved are relatively stable.

Effect of Gold Film Thickness on Sensing Characteristics

Since the metal film affects the excitation of SPR, we investigated the effect of different polished surface gold films and the thickness of the gold film in the magnetic field channel on the sensor's performance. Figure 10 shows the simulation results. The figure shows that the resonance wavelength position is red-shifted, and the energy loss is gradually reduced with the increase in the thickness of the gold film. This is because less energy can be coupled to the SPW mode with the increase in thickness, resulting in lower losses. The refractive index of the SPW increases as the thickness of the gold film increases. However, the refractive index of the core remains constant, so the matching point between the SPW and the core is red-shifted, and the resonance wavelength position is also red-shifted.

Fig. 10
figure 10

Loss spectra of temperature channel, refractive index channel and magnetic field channel for different values of t1, t2, and t3. (1) Loss spectra for different gold film thicknesses in the temperature channel; (2) loss spectra corresponding to different gold film thicknesses for the refractive index channel; (3) loss spectra corresponding to different gold film thicknesses for magnetic field channels

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However, when the thickness is chosen, the level of loss and the width of the spectrum will also affect the sensor performance detection. Therefore, by observing the images of temperature and refractive index channels, it was found that the loss was too high for detection at a gold film thickness of 40 nm. In addition, when the gold film thickness is 60 nm, the signal-to-noise ratio is low, which may result in false-positive responses [37, 38]. Finally, the gold film thickness was determined to be 50 nm for the temperature channel. Similarly, using the same analytical method, the gold film thickness was chosen to be 50 nm for the refractive index channel and 45 nm for the magnetic field channel because either the loss was too significant or the spectra were too broad for detection.

Conclusion

This study presents an SPR-PCF sensor that simultaneously measures refractive index, temperature, and ambient magnetic field. Using dual-polished and single-channel filled magnetic fluids makes the deposition of metal films and temperature-sensitive materials easier, thus reducing the difficulty of fabricating the sensor. The relative stability of the designed sensors also reduces their fabrication accuracy. The maximum sensitivity of the RI measurement is 20,000 nm/RIU when the RI of the fluid is 1.36 to 1.42. The sensing matrix is also given when the temperature detection range is 0 °C to 50 °C, and the magnetic field detection range is 20 to 550 Oe. Moreover, calculating the resolution of the refractive index is 4.5 × 10−6, the resolution of temperature is 2.9 × 10−2, and the resolution of magnetic field strength is 0.63. The sensor is highly integrated and more miniaturized, providing a new solution for sensor fabrication.