Numerical Analysis of Multifunctional Biosensor with Dual-Channel Photonic Crystal Fibers Based on Localized Surface Plasmon Resonance

A multifunctional biosensor composed of a dual-channel photonic crystal fiber (PCF) based on localized surface plasmon resonance (LSPR) is presented to measure dynamic changes in the magnetic field, temperature, and analyte refractive index at mid-infrared wavelengths. The finite-element method (FEM) is used to model and determine the sensing properties of the sensor. The flat dual-channel surface is coated with a gold film, and two nanowires are put on the fanshaped openings to create directional resonance coupling to detect the analyte refractive index and temperature. By utilizing that the refractive index (RI) of the filled magnetic fluid (MF) is sensitive to the external magnetic field and temperature, a sensor with multi-physical detection functions is obtained. For refractive indexes ranging from 1.47 to 1.52, the maximum sensitivity is as high as 31,000 nm/RIU, with a resolution of 3.22 × 10−6 RIU. The maximum sensitivities for the magnetic field and temperature are 1970 pm/Oe and −5500 pm/◦C, respectively.


Introduction
Biosensing is a topic of extensive investigation, suggesting a broad range of possible applications, such as molecular biology, biomedicine, and drug discovery [1][2][3]. Recent decades have witnessed a growing research interest in the study of optical fiber based on multifunctional biosensors [4][5][6]. In recent years, sensors comprising photonic crystal fibers based on surface plasmon resonance (PCF-SPR) have attracted considerable attention due to their small volume, rapid detection, high sensitivity, anti-electromagnetic interference, label-free detection, and in situ monitoring of biomolecular interactions. PCF-SPR is mainly based on the coupling of a core-guided mode to the plasmonic mode along with a metalized micro-structure fiber [7,8]. In 2006, A. Hassani and M. Skorobogatiy presented the concept of the PCF-SPR sensor with optimized microfluidics and illustrated that the phase matching and packaging issues could be facilitated with PCF operated in the single-mode regime [9]. Shuai et al., designed a closed-form multi-core holey fiber-based plasmonic sensor in a large dynamic RI range from 1.33 to 1.53 with high sensitivity and linearity [10]. In 2010,

Model and Method
The structure of the biosensor is shown in Figure 1a,b displays the cross-sectional FEM mesh of the sensor. The perfectly matched layer (PML) is set as a boundary condition to absorb radiation from the outer surface and to evaluate the SPR properties. The sensor is composed of three layers of air holes arranged in a hexagonal lattice to restrict energy from transmitting into the fiber core. The diameter of the air holes is d 1 = 0.5 µm and n a = 1.0 is the refractive index (RI) of air. The pitch size of the hexagonal lattice is Λ = 2 µm and the refractive index (n c ) of the analyte flowing through the channel ranges from 1.47 to 1.52. The refractive index of the biologic fluid, such as the hemoglobin concentration changes from 160 to 260 (g/L), leading to the refractive index of the analyte changing from 1.4 to 1.58 [18]. The fiber is side-polished to form flat planes with two fan-shaped openings where a 50 nm thick gold layer is coated and two silver nanowires with a diameter of 50 nm are filled at the tip end of the fan-shaped openings. One advantage of such silver nanowires compared with other plasmonic nanoparticles, for example, spheres or cubes, is because of their relatively easy fabrication and controllable structural parameter changes. Gold layer can be produced by chemical vapor deposition (CVD) and silver nanowires can be fabricated by combining nanoimprint lithography and lit-off process [19,20]. For the fabrication of metal nanoparticles-based Au layer PCF sensors, the PCF sensor sputtered with metal layer can be immersed into metal nanoparticle solution in order to form the sensing structure [21]. An SEM image showing the intersecting surface of the as-fabricated metal nanoparticles-based Au layer PCF sensor is shown in Figure S1 for reference [22]. In the magnetic sensing operation, a magnetic fluid (MF) is filled in the big hole at the center of the PCF and the diameter of the central small air hole is d 2 = 1 µm. The MF is water-based Fe 3 O 4 synthesized by chemical co-precipitation [23] and the concentration is 0.85 emu/g. The phase-matching wavelength between the core-guided mode and plasmonic mode varies when the refractive indexes of the PCF biosensor elements (fused silica of the cladding material, gold layer, silver nanowires, and MF) change with temperature [24]. the refractive index (nc) of the analyte flowing through the channel ranges from 1.47 to 1.52. The refractive index of the biologic fluid, such as the hemoglobin concentration changes from 160 to 260 (g/L), leading to the refractive index of the analyte changing from 1.4 to 1.58 [18]. The fiber is side-polished to form flat planes with two fan-shaped openings where a 50 nm thick gold layer is coated and two silver nanowires with a diameter of 50 nm are filled at the tip end of the fan-shaped openings. One advantage of such silver nanowires compared with other plasmonic nanoparticles, for example, spheres or cubes, is because of their relatively easy fabrication and controllable structural parameter changes. Gold layer can be produced by chemical vapor deposition (CVD) and silver nanowires can be fabricated by combining nanoimprint lithography and lit-off process [19,20]. For the fabrication of metal nanoparticles-based Au layer PCF sensors, the PCF sensor sputtered with metal layer can be immersed into metal nanoparticle solution in order to form the sensing structure [21]. An SEM image showing the intersecting surface of the as-fabricated metal nanoparticles-based Au layer PCF sensor is shown in Suppl. 1 for reference [22]. In the magnetic sensing operation, a magnetic fluid (MF) is filled in the big hole at the center of the PCF and the diameter of the central small air hole is d2 = 1 μm. The MF is water-based Fe3O4 synthesized by chemical co-precipitation [23] and the concentration is 0.85 emu/g. The phase-matching wavelength between the core-guided mode and plasmonic mode varies when the refractive indexes of the PCF biosensor elements (fused silica of the cladding material, gold layer, silver nanowires, and MF) change with temperature [24]. The PCF is composed of fused silica and the Ghosh model is used to define the dispersion equation of the fused silica as follows: where λ is the wavelength in nm and T is the temperature in Celsius. The coefficients are given in the following [25]: The PCF is composed of fused silica and the Ghosh model is used to define the dispersion equation of the fused silica as follows: where λ is the wavelength in nm and T is the temperature in Celsius. The coefficients are given in the following [25]: The following Drude model is used to define the dielectric property of the metal [26]: The plasma frequency ω p is expressed as follows [27]: where ω p0 is the plasma frequency of the metal at T 0 = 298.15 K and α V is the volumetric thermal expansion coefficient of metal. The scattering frequency ω c is given by the following [28]: The following Lawrence's electron-electron scattering model is used to express the phonon-electron scattering ω ce (T) [29]: ω cp is obtained by the following Holstein's phonon-electron scattering model [30]: Here, ω 0 can be calculated from Equations (4)-(6) at 298.15 K and T D is the Debye temperature [31]. The parameters of gold and silver are given in Table 1 [32]. Based on the magneto-optical effect of MF, the refractive index is closely related to the magnetic particles in magnetic fluid. The dispersion equation of MF is given by the following Langevin-function [33]: here n 0 is 1.4620, H c,n is associated with the concentration of the magnetic fluid, n s represents the saturated value of the refractive index of the MF, H is the field strength in Oe, and α is the fitting parameters. The spectral characteristics can be analyzed by the propagation loss α loss and it is expressed as follows [34]: Im(n eff ) × 10 6 (dB/m) ≈ 8.686Im(n eff )2π/λ (8) where λ is the wavelength in nm and the effective refractive index is a complex number, which is divided into the real part Re n eff and the imaginary part Im n eff . In the wavelength interrogation mode, the peak sensitivity S is described as the shift in the resonance wavelength corresponding to the variation in the magnetic field intensity, temperature, and RI of the analyte and S is expressed as follows [30]: where ∆λ peak is the shift in the peak wavelength, ∆H is the magnetic field intensity variation, ∆T is the temperature variation, and ∆n is the RI of analyte variation. The resolution of the sensor is defined as follows [31]: The wavelength resolution of the detector is set to be ∆λ min = 0.1 nm. The Gaussian-like (HE 11 −like) modes are used as the core-guided modes, which can be divided into the HE 11x (the predominantly x−polarized) mode and the HE 11y (the predominantly y−polarized) mode. Figure 2 shows that the resonance intensity is higher, and the energy on the surface of the gold layer and silver nanowires in the x−polarized direction is greater than that in the y−polarized direction. Therefore, we analyze the biosensor in the x−polarized direction. . In the wave length interrogation mode, the peak sensitivity S is described as the shift in the resonanc wavelength corresponding to the variation in the magnetic field intensity, temperature and RI of the analyte and S is expressed as follows [30]:

Results and Discussion
is the shift in the peak wavelength, H Δ is the magnetic field intensity var iation, T Δ is the temperature variation, and n Δ is the RI of analyte variation. The res olution of the sensor is defined as follows [31]: The wavelength resolution of the detector is set to be nm Figure 2 presents the propagation losses of the core-guided mode in the x−polarized and y−polarized directions. The structural parameters are Λ = 2 μm, d1 = 0.5 μm, d2 = 1. μm, dsilver = 50 nm, tAu = 50 nm, na = 1.0, nc = 1.48, nMF = 1.4620 (H = 0 Oe). The Gaussian-lik (HE11−like) modes are used as the core-guided modes, which can be divided into the HE11 (the predominantly x−polarized) mode and the HE11y (the predominantly y−polarized mode. Figure 2 shows that the resonance intensity is higher, and the energy on the surfac of the gold layer and silver nanowires in the x−polarized direction is greater than that i the y−polarized direction. Therefore, we analyze the biosensor in the x−polarized direc tion. The dual-channel PCF-SPR biosensor is based on SPR between plasmonic mode generated by the interaction between the metal of the inner air holes and the analyte and the core-guided mode. Figure 3 presents the loss spectrum for the core-guided mode and The dual-channel PCF-SPR biosensor is based on SPR between plasmonic modes generated by the interaction between the metal of the inner air holes and the analyte and the core-guided mode. Figure 3 presents the loss spectrum for the core-guided mode and the real part of n eff of the core-guided mode and plasmonic mode. The structural parameters are the following: Λ = 2 µm, d 1 = 0.5 µm, d 2 = 1.0 µm, d silver = 50 nm, t Au = 50 nm, n a = 1.0, n c = 1.48, and n MF = 1.4620 (H = 0 Oe). The propagation loss of the core-guided mode is presented by the blue line, and Re (n eff )) of the core-guided and plasmonic modes are shown by the black and pink lines, respectively. It can be seen from point (m) in Figure 3 that the real part of n eff of the core-guided mode (black) and plasmonic mode (pink) shows an overlap at the resonance wavelength of 1550 nm, where a sharp loss occurs. The peak in the loss spectrum indicates that the maximum energy of the core-guided mode is coupled to the plasmonic mode. Insets A and B exhibit that the near-field energy is mainly concentrated in the fiber core, and the energy is transferred to the surface of the metal outside the resonance wavelength. Inset (C) illustrates the electric field distribution of the core-guided mode in the x-polarized direction at the phase-matching wavelength of 1550 nm. There is a noticeable loss at the phase-matching wavelength, resulting in a significant signal for analyte monitoring. Therefore, the sensor is sensitive to slight changes in the refractive index in the external environment. The loss spectrum is then evaluated to determine the sensor's performance.

Results and Discussion
presented by the blue line, and Re (neff)) of the core-guided and plasmonic modes ar shown by the black and pink lines, respectively. It can be seen from point (m) in Figure that the real part of neff of the core-guided mode (black) and plasmonic mode (pink) show an overlap at the resonance wavelength of 1550 nm, where a sharp loss occurs. The peak in the loss spectrum indicates that the maximum energy of the core-guided mode is cou pled to the plasmonic mode. Insets A and B exhibit that the near-field energy is mainly concentrated in the fiber core, and the energy is transferred to the surface of the meta outside the resonance wavelength. Inset (C) illustrates the electric field distribution of th core-guided mode in the x-polarized direction at the phase-matching wavelength of 155 nm. There is a noticeable loss at the phase-matching wavelength, resulting in a significan signal for analyte monitoring. Therefore, the sensor is sensitive to slight changes in th refractive index in the external environment. The loss spectrum is then evaluated to de termine the sensor's performance.  Figure 4 displays the loss curves of the core-guided mode for different MF hole di ameters. The resonance wavelength shifts from 1600 to 1530 nm when the MF hole diam eter d2 changes from 0.6 to 1.2 μm. The core-guided mode loss decreases for refractiv index nMF = 1.4620 when the surrounding magnetic field intensity is zero. It can be ex plained by the fact that a smaller hole in the center effectively reduces the neff of the core guided mode while matching the neff of the plasmonic mode [35]. As a result, a smaller MF hole in the center improves the coupling of the core-guided mode and plasmonic mode.  Figure 4 displays the loss curves of the core-guided mode for different MF hole diameters. The resonance wavelength shifts from 1600 to 1530 nm when the MF hole diameter d 2 changes from 0.6 to 1.2 µm. The core-guided mode loss decreases for refractive index n MF = 1.4620 when the surrounding magnetic field intensity is zero. It can be explained by the fact that a smaller hole in the center effectively reduces the n eff of the core-guided mode while matching the n eff of the plasmonic mode [35]. As a result, a smaller MF hole in the center improves the coupling of the core-guided mode and plasmonic mode.   Figure 5 presents the variance in the core−guided mode for different filling states a the same wavelength, and the loss depth is bigger with the two silver nanowires. Th structure parameters are the following: Λ = 2 μm, d1 = 0.5 μm, d2 = 0.6 μm, dsilver = 50 nm tAu = 50 nm, na = 1.0, nc = 1.50, and nMF = 1.4620 (H = 0 Oe). When SPR occurs at a particula wavelength, the plasmonic modes occur on the metal surface [36]. The LSPR is stronge and sharper on the silver nanowires than without them, and hence, the silver nanowire   structure parameters are the following: Λ = 2 µm, d 1 = 0.5 µm, d 2 = 0.6 µm, d silver = 50 nm, t Au = 50 nm, n a = 1.0, n c = 1.50, and n MF = 1.4620 (H = 0 Oe). When SPR occurs at a particular wavelength, the plasmonic modes occur on the metal surface [36]. The LSPR is stronger and sharper on the silver nanowires than without them, and hence, the silver nanowires have a large influence on the total resonance of the biosensor [37,38].  Figure 5 presents the variance in the core−guided mode for different filling states at the same wavelength, and the loss depth is bigger with the two silver nanowires. The structure parameters are the following: Λ = 2 μm, d1 = 0.5 μm, d2 = 0.6 μm, dsilver = 50 nm tAu = 50 nm, na = 1.0, nc = 1.50, and nMF = 1.4620 (H = 0 Oe). When SPR occurs at a particular wavelength, the plasmonic modes occur on the metal surface [36]. The LSPR is stronger and sharper on the silver nanowires than without them, and hence, the silver nanowires have a large influence on the total resonance of the biosensor [37,38]. The loss response to different magnetic fields is presented in Figure 6a, where na, nc, and T are 1.0, 1.48, and 298.15 K, respectively, and the other parameters are the same. The sensing properties of the PCF-SPR magnetic field sensor are investigated under an applied magnetic field of between 0 and 271 Oe. Figure 6a shows the red-shifted wavelength and larger peak intensity in the presence of the magnetic field. As the external magnetic field gets stronger, more energy is transported from the core guided mode to the plasmonic mode, resulting in higher coupling efficiency. The resonance wavelength and loss for different magnetic fields are plotted in Figure 6b, which shows the maximum peak shift 60 nm Here, the maximum peak magnetic field intensity sensitivity is as large as 1.97 nm/Oe and the resolution of magnetic field detection is 0.05 Oe. The loss response to different magnetic fields is presented in Figure 6a, where n a , n c , and T are 1.0, 1.48, and 298.15 K, respectively, and the other parameters are the same. The sensing properties of the PCF-SPR magnetic field sensor are investigated under an applied magnetic field of between 0 and 271 Oe. Figure 6a shows the red-shifted wavelength and larger peak intensity in the presence of the magnetic field. As the external magnetic field gets stronger, more energy is transported from the core guided mode to the plasmonic mode, resulting in higher coupling efficiency. The resonance wavelength and loss for different magnetic fields are plotted in Figure 6b, which shows the maximum peak shift ∆λ peak = 60 nm. Here, the maximum peak magnetic field intensity sensitivity is as large as 1.97 nm/Oe and the resolution of magnetic field detection is 0.05 Oe.  Figure 7a shows the loss curves of the sensor at different temperatures between 10 and 60 °C. The refractive index of the analyte is 1.0, and the surrounding magnetic field intensity is 150 Oe. The resonance peaks corresponding to 10, 20, 30, 40, 50, and 60 °C are 1320, 1300, 1280, 1250, 1210, and 1165 nm, respectively, as shown in Figure 7b. The resonance wavelength shifts from 1320 to 1165 nm when the temperature varies from 10 to 60   Figure 7a shows the loss curves of the sensor at different temperatures between 10 and 60 • C. The refractive index of the analyte is 1.0, and the surrounding magnetic field intensity is 150 Oe. The resonance peaks corresponding to 10,20,30,40,50, and 60 • C are 1320, 1300, 1280, 1250, 1210, and 1165 nm, respectively, as shown in Figure 7b. The resonance wavelength shifts from 1320 to 1165 nm when the temperature varies from 10 to 60 • C. Since the effective refractive index of the MF decreases with temperature increases, less energy is transported from the core guided mode to the surface plasmon mode. The core-guided mode loss increases for refractive index n MF = 1.4620 when the surrounding magnetic field intensity is zero. The absorption loss of the gold layer and silver nanowires increases in the short wavelength direction. According to Figure 7b, the maximum temperature sensitivity is −5.5 nm/ • C, and the resolution is 0.018 • C.  Figure 7a shows the loss curves of the sensor at different temperatures between 10 and 60 °C. The refractive index of the analyte is 1.0, and the surrounding magnetic field intensity is 150 Oe. The resonance peaks corresponding to 10,20,30,40,50, and 60 °C are 1320, 1300, 1280, 1250, 1210, and 1165 nm, respectively, as shown in Figure 7b. The resonance wavelength shifts from 1320 to 1165 nm when the temperature varies from 10 to 60 °C. Since the effective refractive index of the MF decreases with temperature increases, less energy is transported from the core guided mode to the surface plasmon mode. The core-guided mode loss increases for refractive index nMF = 1.4620 when the surrounding magnetic field intensity is zero. The absorption loss of the gold layer and silver nanowires increases in the short wavelength direction. According to Figure 7b, the maximum temperature sensitivity is −5.5 nm/°C, and the resolution is 0.018 °C.    Figure 8b. The resonance wavelength increases with increasing analyte refractive index. The resonance intensity increases distinctly as n c changes from 1.47 to 1.49, and the resonance intensity decreases between 1.50 and 1.52. Figure 8b reveals that the maximum peak shift is ∆λ peak = 310 nm. Therefore, the maximum spectral sensitivity is 31,000 nm/RIU, and the resolution is 3.22 × 10 −6 RIU in the sensing range between 1.47 and 1.52. Silver nanowirebased PCF biosensor exhibits maximized sensitivity over some related research studies of nanospheres, nanorods, and other nanoparticles-based PCF sensors [39][40][41]. The refractive index sensitivity of the multifunctional biosensor with a dual-channel PCF-SPR structure has obvious advantages in its detection range, which is mainly because of its increased region of the plasmonic modes excited by the fan-shaped biosensor and more sensitive to the change of refractive index of the solution [39]. Besides the sensitivity, the sensor's dynamic operation range, linearity, and resolution, as well as the full width at half-maxima (FWHM), are all significant criteria. The minimum FWHM is 49.61 nm for n a = 1.47, as shown in Figure 6a. SPR structure has obvious advantages in its detection range, which is mainly because of its increased region of the plasmonic modes excited by the fan-shaped biosensor and more sensitive to the change of refractive index of the solution [39]. Besides the sensitivity, the sensor's dynamic operation range, linearity, and resolution, as well as the full width at half-maxima (FWHM), are all significant criteria. The minimum FWHM is 49.61 nm for na = 1.47, as shown in Figure 6a.

Conclusions
A dual-channel LSPR sensor based on the MF-filled PCF is described, and mode coupling is numerically analyzed by FEM. The reflectance spectra of the MF-filled sensor are sensitive to the magnetic field and temperature. The sensor not only measures the liquid in the external environment but also determines the intensity of the magnetic field and temperature. A maximum spectral sensitivity of 31,000 nm/RIU and a resolution of 3.22 × 10 −6 RIU are achieved for the sensing range between 1.47 and 1.52. The maximum sensitivities for the magnetic field and temperature are 1970 pm/Oe and −5500 pm/°C, respectively. The minimum FWHM is 49.61 nm for na = 1.47. This multifunctional PCF-SPR biosensor boasting high sensitivity and resolution has great potential in biological analysis and medical monitoring.

Conclusions
A dual-channel LSPR sensor based on the MF-filled PCF is described, and mode coupling is numerically analyzed by FEM. The reflectance spectra of the MF-filled sensor are sensitive to the magnetic field and temperature. The sensor not only measures the liquid in the external environment but also determines the intensity of the magnetic field and temperature. A maximum spectral sensitivity of 31,000 nm/RIU and a resolution of 3.22 × 10 −6 RIU are achieved for the sensing range between 1.47 and 1.52. The maximum sensitivities for the magnetic field and temperature are 1970 pm/Oe and −5500 pm/ • C, respectively. The minimum FWHM is 49.61 nm for n a = 1.47. This multifunctional PCF-SPR biosensor boasting high sensitivity and resolution has great potential in biological analysis and medical monitoring.

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Data Availability Statement:
The authors confirm that the data supporting the findings of this study are available within the article.

Conflicts of Interest:
The authors declare no conflict of interest.