Surface Plasmon Resonance Sensor Based on Dual-Side Polished Microstructured Optical Fiber with Dual-Core

A surface plasmon resonance (SPR) sensor based on a dual-side polished microstructured optical fiber (MOF) with a dual core is proposed for a large analyte refractive index (RI; na) detection range. Gold is used as a plasmonic material coated on the polished surface, and analytes can be directly contacted with the gold film. The special structure not only facilitates the fabrication of the sensor, but also can work in the na range of 1.42–1.46 when the background material RI is 1.45, which is beyond the reach of other traditional MOF-SPR sensors. The sensing performance of the sensor was investigated by the wavelength and amplitude interrogation methods. The detailed numerical results showed that the proposed sensor can work effectively in the na range of 1.35–1.47 and exhibits higher sensitivity in the na range of 1.42–1.43.

To effectively overcome the limitations of prism-based SPR sensors, optical fiber-based SPR sensors have been developed, in which the fiber acts as a prism, coupling incident light with plasmons. Compared with prism-based devices, the optical fiber design is simpler and more flexible, which can reduce the size of the sensor to a large extent. In addition, the advantages of electromagnetic immunity, high degree of integration, mechanical stability, and in situ monitoring have made optical fiber design more and more attractive [1][2][3][4][5][6][7][8][9][10][11]15,16]. However, the phase-matching condition between the core mode and the surface plasmon polariton (SPP) mode of optical fiber-based SPR sensors is difficult to meet.

Structure Design and Principle
The schematic diagram of the proposed SPR sensor based on a dual-side polished MOF with a dual core is depicted in Figure 1. This structure can be obtained by a wheel-polishing setup with a 3D mechanical platform, which can move along the X, Y, and Z directions [47]. By employing a light source and an optical spectrum analyzer to online monitor the transmission spectrum during the polishing process, the polishing position, length, and depth could be easy to set up and operate accurately via a computer program [46,47]. Gold was used as a plasmonic material to coat the polished surface, which is not as difficult as coating a gold film on the inner surface of small air holes. Here, the center-to-center distance between two adjacent air holes (Λ) was 3 µm, and the diameter of air holes (d) was 0.5Λ. The thickness of the gold film (m) was 40 nm, and the polishing depth from the fiber center to the polished surface (h) was 2.1Λ. The mode characteristics and the sensing performance of the proposed sensor were simulated through commercially available software COMSOL. A perfectly matched layer (PML) was added to the outer computational region, which was applied to absorb scattered light [9,10,15,16,18,19,[25][26][27][28][29]31,[36][37][38].
In this sensor, we used fused silica as a background material and set its RI at 1.45 [17,20,24,25,27,29,41] to detect a range of n a , which the other MOF-based SPR sensors cannot realize. The RI of the air was set to 1. To achieve the dielectric constant of gold (ε(ω)), we used the Drude-Lorentz model, of which the equation can be written as follows [48]: where ε ∞ is the permittivity at high frequencies, ω can be interpreted as the angular frequency, ω D and γ D indicate the plasma frequency and the damping frequency, respectively, ∆ε is the weighting Sensors 2020, 20, 3911 3 of 10 factor, and Γ L and Ω L are the spectral width and the oscillator strength of the Lorentz oscillators, respectively [10,34,36,48].

Coupling Properties
Like other dual-core MOFs [37][38][39], the proposed sensor can support four supermodes in fundamental modes. Figure 2 shows the electric field distributions of the four supermodes at 1100 nm for na =1.44. Insets A and B of Figure 2 represent the even mode and the odd mode in the x polarized direction (x-even mode and x-odd mode), respectively. Insets C and D of Figure 2 represent the even mode and the odd mode in the y polarized direction (y-even mode and y-odd mode), respectively. Here, we only investigated the coupling properties of the x-polarized core mode, because the y-polarized core mode with the electric field was parallel to the gold film surface and was not easily coupled with SPP modes [39][40][41]. In theory, when the real parts of neff (Re(neff)) of the core mode and the SPP mode are equal, the phase-matching condition between them are satisfied. Then, the two modes will be coupled with each other, and the maximum energy transfer from the core mode to the SPP mode can be achieved [5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]37]. Figure 3 shows the Re(neff) curves of the x-even core modes and x-even SPP modes, the loss spectra of the x-even core modes, and the electric field distributions of the relevant modes for na = 1.44, 1.45, and 1.46. The black solid line represents the Re(neff) of the x-even core mode, while the red solid, dashed, and dotted lines represent the Re(neff) of the x-even SPP modes at na = 1.44, 1.45, and 1.46, respectively, as shown in Figure 3a. The blue solid, dashed, and dotted lines stand for the losses of the x-even core modes at na = 1.44, 1.45, and 1.46, respectively ( Figure 3b). Take na equal to 1.44 as an example. The x-even core mode (inset A of Figure 3c) and the x-even SPP mode (inset B of Figure 3c) were coupled with each other (inset C of Figure 3c) at a wavelength of 1518 nm (point C in Figure 3a,b). At this wavelength (also called resonance wavelength), a significant loss peak appeared (see the blue solid curve in Figure 3b), which indicated the maximum energy transfer from the x-even core mode to the x-even SPP mode. The insets D, E, F, and G of Figure 3c represent the

Coupling Properties
Like other dual-core MOFs [37][38][39], the proposed sensor can support four supermodes in fundamental modes. Figure 2 shows the electric field distributions of the four supermodes at 1100 nm for n a =1. 44. Insets A and B of Figure 2 represent the even mode and the odd mode in the x polarized direction (x-even mode and x-odd mode), respectively. Insets C and D of Figure 2 represent the even mode and the odd mode in the y polarized direction (y-even mode and y-odd mode), respectively. Here, we only investigated the coupling properties of the x-polarized core mode, because the y-polarized core mode with the electric field was parallel to the gold film surface and was not easily coupled with SPP modes [39][40][41].

Coupling Properties
Like other dual-core MOFs [37][38][39], the proposed sensor can support four supermodes in fundamental modes. Figure 2 shows the electric field distributions of the four supermodes at 1100 nm for na =1.44. Insets A and B of Figure 2 represent the even mode and the odd mode in the x polarized direction (x-even mode and x-odd mode), respectively. Insets C and D of Figure 2 represent the even mode and the odd mode in the y polarized direction (y-even mode and y-odd mode), respectively. Here, we only investigated the coupling properties of the x-polarized core mode, because the y-polarized core mode with the electric field was parallel to the gold film surface and was not easily coupled with SPP modes [39][40][41]. In theory, when the real parts of neff (Re(neff)) of the core mode and the SPP mode are equal, the phase-matching condition between them are satisfied. Then, the two modes will be coupled with each other, and the maximum energy transfer from the core mode to the SPP mode can be achieved [5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]37]. Figure 3 shows the Re(neff) curves of the x-even core modes and x-even SPP modes, the loss spectra of the x-even core modes, and the electric field distributions of the relevant modes for na = 1.44, 1.45, and 1.46. The black solid line represents the Re(neff) of the x-even core mode, while the red solid, dashed, and dotted lines represent the Re(neff) of the x-even SPP modes at na = 1.44, 1.45, and 1.46, respectively, as shown in Figure 3a. The blue solid, dashed, and dotted lines stand for the losses of the x-even core modes at na = 1.44, 1.45, and 1.46, respectively ( Figure 3b). Take na equal to 1.44 as an example. The x-even core mode (inset A of Figure 3c) and the x-even SPP mode (inset B of Figure 3c) were coupled with each other (inset C of Figure 3c) at a wavelength of 1518 nm (point C in Figure 3a,b). At this wavelength (also called resonance wavelength), a significant loss peak appeared (see the blue solid curve in Figure 3b), which indicated the maximum energy transfer from the x-even core mode to the x-even SPP mode. The insets D, E, F, and G of Figure 3c represent the In theory, when the real parts of n eff (Re(n eff )) of the core mode and the SPP mode are equal, the phase-matching condition between them are satisfied. Then, the two modes will be coupled with each other, and the maximum energy transfer from the core mode to the SPP mode can be achieved [5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]37]. Figure 3 shows the Re(n eff ) curves of the x-even core modes and x-even SPP modes, the loss spectra of the x-even core modes, and the electric field distributions of the relevant modes for n a = 1.44, 1.45, and 1.46. The black solid line represents the Re(n eff ) of the x-even core mode, while the red solid, dashed, and dotted lines represent the Re(n eff ) of the x-even SPP modes at n a = 1.44, 1.45, and 1.46, respectively, as shown in Figure 3a. The blue solid, dashed, and dotted lines stand for the losses of the x-even core modes at n a = 1.44, 1.45, and 1.46, respectively (Figure 3b). Take n a equal to 1.44 as an example. The x-even core mode (inset A of Figure 3c) and the x-even SPP mode (inset B of Figure 3c) were coupled with each other (inset C of Figure 3c) at a wavelength of 1518 nm (point C in Figure 3a,b). At this wavelength (also called resonance wavelength), a significant loss peak appeared (see the blue solid curve in Figure 3b), which indicated the maximum energy transfer from the x-even core mode to the x-even SPP mode. The insets D, E, F, and G of Figure 3c represent the electric field distributions at points D, E, F, and G, respectively (Figure 3a,b), and they can also show the energy transfer from the x-even core mode to the x-even SPP mode at n a = 1.45 and 1.46, respectively. As shown in Figure 3, the values of resonance wavelengths were shifted from 1518 to 1533 nm and from 1533 to 1556 nm due to the variations of n a from 1.44 to 1.45 and from 1.45 to 1.46, respectively. We can observe that a tiny change of n a can lead to a significant shift of resonance wavelength. This capability can be utilized to detect the changes of the analyte RI [19,[24][25][26]37,38].
Sensors 2020, 20, x FOR PEER REVIEW 4 of 10 electric field distributions at points D, E, F, and G, respectively (Figure 3a,b), and they can also show the energy transfer from the x-even core mode to the x-even SPP mode at na = 1.45 and 1.46, respectively. As shown in Figure 3, the values of resonance wavelengths were shifted from 1518 to 1533 nm and from 1533 to 1556 nm due to the variations of na from 1.44 to 1.45 and from 1.45 to 1.46, respectively. We can observe that a tiny change of na can lead to a significant shift of resonance wavelength. This capability can be utilized to detect the changes of the analyte RI [19,[24][25][26]37,38]. When varying the na from 1.44 to 1.46, the Re(neff) curves of the x-odd core modes (black solid lines) and the x-odd SPP modes (red solid, dashed, and dotted lines) and the loss spectra (blue solid, dashed, and dotted lines) of the x-odd core modes, as well as the electric field distributions of the relevant modes are shown in Figure 4. Similar to the coupling properties of the x-even core modes, the phase-matching conditions between the x-odd core mode and x-odd SPP modes were satisfied at the wavelength of 1518 nm (point C in Figure 4a,b) for na = 1.44, at the wavelength of 1533 nm (point E in Figure 4a,b) for na = 1.45, and at 1556 nm (point G in Figure 4a,b) for na = 1.46. At the resonance wavelengths, the corresponding electric field distributions are shown in insets C, E, and G of Figure  4c, when the na values were 1.44, 1.45, and 1.46, respectively. Compared with Figure 3a,b, we found that, unlike the resonance wavelength of the x-even core mode shifting to longer wavelengths with na increasing from 1.44 to 1.46, the resonance wavelength of the x-odd core mode moved to a shorter wavelength as na varied from 1.44 to 1.45, whereas the resonance wavelength moved towards longer wavelengths as na increased from 1.45 to 1.46. This unexpected peak behavior disturbs the regularity of the SPR sensor and therefore cannot be utilized to detect the changes of the analyte RI.
From Figures 3 and 4, we can see that the resonance wavelengths of the x-even core modes move toward longer wavelengths with increasing na, but the behavior of the resonance wavelengths of the x-odd core modes is not regular and cannot be used to detect the variations of the analyte RI. In the following discussion, we only consider the sensing performance of the x-even core modes. represented by the blue solid, dashed, and dotted lines, respectively; (c) electric field distributions of the x-even core mode A at 1100 nm, x-even SPP mode B at 1340 nm, and x-even core mode C at 1518 nm for n a = 1.44, electric field distributions of x-even SPP mode D at 1350 nm and x-even core mode E at 1533 nm for n a = 1.45, and electric field distributions of x-even SPP mode F at 1430 nm and x-even core mode G at 1556 nm for n a = 1.46.
When varying the n a from 1.44 to 1.46, the Re(n eff ) curves of the x-odd core modes (black solid lines) and the x-odd SPP modes (red solid, dashed, and dotted lines) and the loss spectra (blue solid, dashed, and dotted lines) of the x-odd core modes, as well as the electric field distributions of the relevant modes are shown in Figure 4. Similar to the coupling properties of the x-even core modes, the phase-matching conditions between the x-odd core mode and x-odd SPP modes were satisfied at the wavelength of 1518 nm (point C in Figure 4a,b) for n a = 1.44, at the wavelength of 1533 nm (point E in Figure 4a,b) for n a = 1.45, and at 1556 nm (point G in Figure 4a,b) for n a = 1.46. At the resonance wavelengths, the corresponding electric field distributions are shown in insets C, E, and G of Figure 4c, when the n a values were 1.44, 1.45, and 1.46, respectively. Compared with Figure 3a,b, we found that, unlike the resonance wavelength of the x-even core mode shifting to longer wavelengths with n a increasing from 1.44 to 1.46, the resonance wavelength of the x-odd core mode moved to a shorter wavelength as n a varied from 1.44 to 1.45, whereas the resonance wavelength moved towards longer wavelengths as n a increased from 1.45 to 1.46. This unexpected peak behavior disturbs the regularity of the SPR sensor and therefore cannot be utilized to detect the changes of the analyte RI.
From Figures 3 and 4, we can see that the resonance wavelengths of the x-even core modes move toward longer wavelengths with increasing n a , but the behavior of the resonance wavelengths of the x-odd core modes is not regular and cannot be used to detect the variations of the analyte RI. In the following discussion, we only consider the sensing performance of the x-even core modes.

Sensing Performance
The sensing performance of the sensor can be evaluated by wavelength sensitivity (wavelength interrogation) and amplitude sensitivity (amplitude interrogation) [5,10,15,18,26]. The wavelength sensitivity can be calculated from the following equation [5,[10][11][12][13][14][15][17][18][19][20]26,37,38]: where Δλpeak is the shift of the resonance wavelength and Δna is the variation of na. As shown by the blue solid and dashed lines in Figure 3b, we observed Δλpeak of 15 nm when na was varied from 1.44 to 1.45. According to Equation (2), the corresponding wavelength sensitivity in terms of refractive index units (RIU) was 1500 nm/RIU. The amplitude sensitivity can be calculated at a particular wavelength. Assuming a reasonable length of the sensor was L = 1/α(λ, na), the amplitude sensitivity was expressed as [5,10,17,18,26,29,38]: a a a n S RIU n n α λ α λ where α (λ, na) is the overall loss for a particular wavelength, ∂α(λ, na) is the difference between two adjacent loss spectra due to a small change in na, and ∂na is the change of na. According to Equation (3), we plotted the amplitude sensitivity curves in Figure 5. As is shown by the blue solid curve, the maximum amplitude sensitivity of the x-even core mode was 72.18 RIU -1 at 1534 nm for m = 40 nm.

Sensing Performance
The sensing performance of the sensor can be evaluated by wavelength sensitivity (wavelength interrogation) and amplitude sensitivity (amplitude interrogation) [5,10,15,18,26]. The wavelength sensitivity can be calculated from the following equation [5,[10][11][12][13][14][15][17][18][19][20]26,37,38]: where ∆λ peak is the shift of the resonance wavelength and ∆n a is the variation of n a . As shown by the blue solid and dashed lines in Figure 3b, we observed ∆λ peak of 15 nm when n a was varied from 1.44 to 1.45. According to Equation (2), the corresponding wavelength sensitivity in terms of refractive index units (RIU) was 1500 nm/RIU. The amplitude sensitivity can be calculated at a particular wavelength. Assuming a reasonable length of the sensor was L = 1/α(λ, n a ), the amplitude sensitivity was expressed as [5,10,17,18,26,29,38]: where α (λ, n a ) is the overall loss for a particular wavelength, ∂α(λ, n a ) is the difference between two adjacent loss spectra due to a small change in n a , and ∂n a is the change of n a . According to Equation (3), we plotted the amplitude sensitivity curves in Figure 5. As is shown by the blue solid Sensors 2020, 20, 3911 6 of 10 curve, the maximum amplitude sensitivity of the x-even core mode was 72.18 RIU -1 at 1534 nm for m = 40 nm.
core modes by varying m for na = 1.44 and 1.45. Comparing Figures 3b and 6, it can be evident that the resonance wavelength moved to a shorter wavelength by increasing m from 30 to 50 nm in the case of na = 1.44 and 1.45. According to Equation (2), the values of the wavelength sensitivities were 300 and 1700 nm nm/RIU for m of 30 and 50 nm, respectively. The peak losses and the wavelengths influenced by varying m also affected the amplitude sensitivities. Figure 5 shows the amplitude sensitivities of x-even core modes as m varied from 30 to 50 nm. It can be found that the maximum amplitude sensitivities of 21.35 and 55.3 RIU -1 were achieved at 1486 and 1518 nm for m of 30 and 50 nm, respectively.  To further evaluate the performance of the designed sensor, Table 1 shows the summary of several sensing parameters including the peak wavelength, the peak loss, the wavelength sensitivity, the maximum amplitude sensitivity, and the wavelength for the maximum amplitude sensitivity of different m at an na range of 1.35-1.47. By means of a detailed investigation of theses parameters, it was found that m can affect the peak wavelength and the peak loss and therefore affect the wavelength sensitivity, the maximum amplitude sensitivity, and the wavelength for the maximum amplitude sensitivity. It is worth noting that the trend of the wavelength for the maximum amplitude sensitivity was roughly the same as that of the peak wavelength, because according to Equation (3), the maximum amplitude sensitivity is related to the maximum ∂α (λ, na), which generally occurs in the vicinity of the resonance peak. The change of m has a slight impact on

Gold Film Thickness
The thickness of a gold film is the most important factor that affects the SPR spectra and thus the sensing performance [8][9][10]12,13,15,16,18,24,[33][34][35][36]. Figure 6 shows the loss spectra of the x-even core modes by varying m for n a = 1.44 and 1.45. Comparing Figures 3b and 6, it can be evident that the resonance wavelength moved to a shorter wavelength by increasing m from 30 to 50 nm in the case of n a = 1.44 and 1.45. According to Equation (2), the values of the wavelength sensitivities were 300 and 1700 nm nm/RIU for m of 30 and 50 nm, respectively. The peak losses and the wavelengths influenced by varying m also affected the amplitude sensitivities. Figure 5 shows the amplitude sensitivities of x-even core modes as m varied from 30 to 50 nm. It can be found that the maximum amplitude sensitivities of 21. 35 (2), the values of the wavelength sensitivities were 300 and 1700 nm nm/RIU for m of 30 and 50 nm, respectively. The peak losses and the wavelengths influenced by varying m also affected the amplitude sensitivities. Figure 5 shows the amplitude sensitivities of x-even core modes as m varied from 30 to 50 nm. It can be found that the maximum amplitude sensitivities of 21.35 and 55.3 RIU -1 were achieved at 1486 and 1518 nm for m of 30 and 50 nm, respectively.  To further evaluate the performance of the designed sensor, Table 1 shows the summary of several sensing parameters including the peak wavelength, the peak loss, the wavelength sensitivity, the maximum amplitude sensitivity, and the wavelength for the maximum amplitude sensitivity of different m at an na range of 1.35-1.47. By means of a detailed investigation of theses parameters, it was found that m can affect the peak wavelength and the peak loss and therefore affect the wavelength sensitivity, the maximum amplitude sensitivity, and the wavelength for the maximum amplitude sensitivity. It is worth noting that the trend of the wavelength for the maximum amplitude sensitivity was roughly the same as that of the peak wavelength, because To further evaluate the performance of the designed sensor, Table 1 shows the summary of several sensing parameters including the peak wavelength, the peak loss, the wavelength sensitivity, the maximum amplitude sensitivity, and the wavelength for the maximum amplitude sensitivity of In general, the ability of detecting large RI ranges makes the designed sensor more competitive than D-shaped MOF-SPR sensors [17,[21][22][23][32][33][34]38]. Compared with single-core dual-side polished MOF-SPR sensors [18,42], the designed dual-core structure can detect n a higher than the RI of the background material of the MOF. Although other structures such as inner-coated or grooved MOF-SPR sensors can detect a wide RI range [19,39,[43][44][45], the designed dual-side polished structure has advantages that it can be readily coated with the gold films and has outside sensing channels, making it ideal for use as a real-time sensor.

Conclusions
We have proposed and numerically investigated an SPR sensor based on a dual-side polished MOF with a dual core to realize a large range of n a detection. The gold and the analyte layers were placed outside the MOF structure, which can be expected to simplify the manufacturing process. The coupling characteristics, sensing performance, and the influence of the gold film thickness of the sensor were investigated by the finite element method in the wavelength and amplitude interrogation. Since the peak behavior of the x-odd mode disturbed the regularity of the SPR sensor, the x-even mode was determined to analyze the sensing performance. The simulation results showed that the sensor could detect a large n a range covering from 1.35 to 1.47 and had higher wavelength sensitivity and amplitude sensitivity in the n a range of 1.42-1.43 when the background material RI was 1.45. The proposed sensor can overcome the defect that other traditional MOF-SPR sensors cannot work in the n a range of 1.42-1.46, which makes it exhibit great potential in biological and chemical sensing fields.