A Large Detection-Range Plasmonic Sensor Based on An H-Shaped Photonic Crystal Fiber

An H-shaped photonic crystal fiber (PCF)-based surface plasmon resonance (SPR) sensor is proposed for detecting large refractive index (RI) range which can either be higher or lower than the RI of the fiber material used. The grooves of the H-shaped PCF as the sensing channels are coated with gold film and then brought into direct contact with the analyte, which not only reduces the complexity of the fabrication but also provides reusable capacity compared with other designs. The sensing performance of the proposed sensor is investigated by using the finite element method. Numerical results show that the sensor can work normally in the large analyte RI (na) range from 1.33 to 1.49, and reach the maximum sensitivity of 25,900 nm/RIU (RI units) at the na range 1.47–1.48. Moreover, the sensor shows good stability in the tolerances of ±10% of the gold-film thickness.

In this paper, we propose an open structure PCF-SPR sensor design that not only solves the problem of sensor fabrication but also can detect the RI over a larger range, either higher or lower than that of the fiber materials. The basic geometry of the PCF follows the H-shaped structure as shown in Figure 1. This open structure avoids coating in the holes with metal film and can be in direct contact with the analyte, thus reducing the manufacturing complexity and offering reusable capability. We use the finite element method based commercial COMSOL software to analysis the electromagnetic modes and the sensing performance of the sensor.
In this paper, we propose an open structure PCF-SPR sensor design that not only solves the problem of sensor fabrication but also can detect the RI over a larger range, either higher or lower than that of the fiber materials. The basic geometry of the PCF follows the H-shaped structure as shown in Figure 1. This open structure avoids coating in the holes with metal film and can be in direct contact with the analyte, thus reducing the manufacturing complexity and offering reusable capability. We use the finite element method based commercial COMSOL software to analysis the electromagnetic modes and the sensing performance of the sensor.

Structure Design and Principle
The schematic diagram of the proposed H-shaped PCF-SPR sensor is shown in Figure 1. The three layers of air holes are arranged in a hexagonal geometry, forming an H-shaped structure with symmetrical grooves. The gold film as a plasmonic material is placed on the internal surface of the grooves. These grooves are particularly advantageous for metal coating, and have the characteristics of good accessibility and easy replacement of analyte. The special structure can be made by femtosecond laser micromachining [25], focused ion-beam milling [26,27], or chemical etching of the original side-hole PCF [28,29]. In our simulation, the distance between the holes is Λ = 8 μm and the diameters of the cladding holes is 0.5Λ, respectively. The opening depth is set to h = 3Λ, the widths of the two grooves are both 0.5Λ, and the thickness of gold film is m1 = m2 = 40 nm. The RI of air is 1, and the RI of the fiber materials is fixed at 1.45 in order to clearly show that the RI of the analyte can either be higher or lower than that of the fiber materials. In addition, the complex dielectric constant (Ɛ(ω)) of gold is defined by using the Drude-Lorentz model [30]:

Structure Design and Principle
The schematic diagram of the proposed H-shaped PCF-SPR sensor is shown in Figure 1. The three layers of air holes are arranged in a hexagonal geometry, forming an H-shaped structure with symmetrical grooves. The gold film as a plasmonic material is placed on the internal surface of the grooves. These grooves are particularly advantageous for metal coating, and have the characteristics of good accessibility and easy replacement of analyte. The special structure can be made by femtosecond laser micromachining [25], focused ion-beam milling [26,27], or chemical etching of the original side-hole PCF [28,29].
In our simulation, the distance between the holes is Λ = 8 µm and the diameters of the cladding holes is 0.5Λ, respectively. The opening depth is set to h = 3Λ, the widths of the two grooves are both 0.5Λ, and the thickness of gold film is m 1 = m 2 = 40 nm. The RI of air is 1, and the RI of the fiber materials is fixed at 1.45 in order to clearly show that the RI of the analyte can either be higher or lower Sensors 2020, 20, 1009 3 of 8 than that of the fiber materials. In addition, the complex dielectric constant (ε(ω)) of gold is defined by using the Drude-Lorentz model [30]: where ω D represents the plasma frequency, γ D is the damping frequency. Ω L , Γ L and ∆ε can be interpreted as the oscillator strength, spectral width of the Lorentz oscillators, and weighting factor [30].
In addition, we use the artificial boundary condition of the outermost perfect matching layer (PML) to absorb the radiant energy as shown in Figure 1b [13,19,31].
Because the core mode with the electric field predominantly orthogonal to the metal surface can be more readily coupled to the SPP modes on the metal surface [8,9,18,22,[32][33][34], in this design the y-polarized core mode has a better SPR phenomenon than the x-polarized core mode, thus providing a better sensing performance. In what follows, we mainly investigate the sensing performance of the y-polarized core mode. In Figure 2a, we plot the real part of the n eff (Re(n eff )) curves of the y-polarized core mode and SPP modes when the RI of the analyte (n a ) is 1.43, 1.45, and 1.47, respectively, to indicate that the proposed sensor has potential for RI sensing that can be higher or lower than the RI of fiber materials. The black solid line represents the Re(n eff ) of y-polarized core mode, whereas the red solid, red dashed and red dotted lines respectively represent the Re(n eff ) of y-polarized SPP modes at n a = 1.43, 1.45, and 1.47, as shown in Figure 2a. Take the case of n a at 1.43; the core mode and SPP mode are coupled where their n eff curves intersect (C point in Figure 2a). Losses of the core mode increase sharply near this intersection (resonance wavelength) as shown in Figure 2b, because the energy of the core mode transfers to SPP modes which can be observed from the inset C in Figure 2c. Similar processes of this energy transfer also occur at the intersections D and E when the n a is 1.45 and 1.47, respectively, which can be seen from Figure 2b and the insets D and E in Figure 2c. In Figure 2a,b, we also observed that the wavelength of resonance peak is 1006 nm, 1367 nm, and 1791 nm when n a is 1.43, 1.45, and 1.47, respectively. That is, as n a increases, the resonance peak shifts to longer wavelengths. This peak behavior can be used to measure the change of the analyte RI.
where ωD represents the plasma frequency, ϒD is the damping frequency. ΩL, ГL and Δε can be interpreted as the oscillator strength, spectral width of the Lorentz oscillators, and weighting factor [30]. In addition, we use the artificial boundary condition of the outermost perfect matching layer (PML) to absorb the radiant energy as shown in Figure 1b [13,19,31].
Because the core mode with the electric field predominantly orthogonal to the metal surface can be more readily coupled to the SPP modes on the metal surface [8,9,18,22,[32][33][34], in this design the y-polarized core mode has a better SPR phenomenon than the x-polarized core mode, thus providing a better sensing performance. In what follows, we mainly investigate the sensing performance of the y-polarized core mode. In Figure 2a, we plot the real part of the neff (Re(neff)) curves of the y-polarized core mode and SPP modes when the RI of the analyte (na) is 1.43, 1.45, and 1.47, respectively, to indicate that the proposed sensor has potential for RI sensing that can be higher or lower than the RI of fiber materials. The black solid line represents the Re(neff) of y-polarized core mode, whereas the red solid, red dashed and red dotted lines respectively represent the Re(neff) of y-polarized SPP modes at na = 1.43, 1.45, and 1.47, as shown in Figure 2a. Take the case of na at 1.43; the core mode and SPP mode are coupled where their neff curves intersect (C point in Figure 2a). Losses of the core mode increase sharply near this intersection (resonance wavelength) as shown in Figure 2b, because the energy of the core mode transfers to SPP modes which can be observed from the inset C in Figure  2c. Similar processes of this energy transfer also occur at the intersections D and E when the na is 1.45 and 1.47, respectively, which can be seen from Figure 2b and the insets D and E in Figure 2c. In Figures 2a and 2b, we also observed that the wavelength of resonance peak is 1006 nm, 1367 nm, and 1791 nm when na is 1.43, 1.45, and 1.47, respectively. That is, as na increases, the resonance peak shifts to longer wavelengths. This peak behavior can be used to measure the change of the analyte RI.

Sensing Performance
By measuring the shift of the peak wavelength, the change in n a can be determined. The sensitivity of the sensor is given by [8,9,12,[14][15][16][17][18][19][20][21][22]24]: where, ∆λ peak denote the shift of peak wavelength and ∆n a is the change of n a . To give an example in Figure 2b, n a changes from 1.45 to 1.47, and the corresponding peak wavelength shifts ∆λ peak = 424 nm, which means that the sensitivity of the sensor is 21,200 nm/RIU (RI units). Figure 3b,d respectively depict the peak wavelengths and sensitivities curves of the sensor when the n a changes from 1.33 to 1.49. On the whole, as n a increases with the same ∆n a , the ∆λ peak of the peak wavelength also becomes larger, according to Equation (2), the sensitivity of the sensor also increases correspondingly, reaching a maximum value of 25,900 nm/RIU when the n a range of 1.47-1.48 as shown in Figure 3d. This sensing performance make it very suitable to measure some high RI organic chemical analytes, such as chloroform toluene or benzene [35].

Sensing Performance
By measuring the shift of the peak wavelength, the change in na can be determined. The sensitivity of the sensor is given by [8,9,12,[14][15][16][17][18][19][20][21][22]24]: where, Δλpeak denote the shift of peak wavelength and Δna is the change of na. To give an example in Figure 2b, na changes from 1.45 to 1.47, and the corresponding peak wavelength shifts Δλpeak = 424 nm, which means that the sensitivity of the sensor is 21,200 nm/RIU (RI units). Figures 3b  and 3d respectively depict the peak wavelengths and sensitivities curves of the sensor when the na changes from 1.33 to 1.49. On the whole, as na increases with the same Δna, the Δλpeak of the peak wavelength also becomes larger, according to Equation (2), the sensitivity of the sensor also increases correspondingly, reaching a maximum value of 25,900 nm/RIU when the na range of 1.47-1.48 as shown in Figure 3d. This sensing performance make it very suitable to measure some high RI organic chemical analytes, such as chloroform toluene or benzene [35]. The thickness of the metal film is a significant parameter affecting the resonance coupling between the core mode and the SPP modes [14][15][16]. Figure 3a shows the loss spectra of the y-polarized core mode at na = 1.43 for various thicknesses of gold film (m1 = m2) 30 nm, 40 nm, and 50 nm. As can be seen from the figure, with the thickness of the gold film becoming thicker, the

Gold-Film Thickness
The thickness of the metal film is a significant parameter affecting the resonance coupling between the core mode and the SPP modes [14][15][16]. Figure 3a shows the loss spectra of the y-polarized core mode at n a = 1.43 for various thicknesses of gold film (m 1 = m 2 ) 30 nm, 40 nm, and 50 nm. As can be seen from the figure, with the thickness of the gold film becoming thicker, the corresponding peak wavelength shifts towards longer wavelengths and, meanwhile, the peak loss shows a downward trend. This peak behavior is also consistent with that at the other n a , as shown in Figure 3b,c. The main reason for these phenomena is that the increase of gold-film thickness increases the distance between the core area and the gold surface, and only at longer wavelengths can the electric field of the core mode penetrate the gold film, coupling with the SPP modes on the gold surface. The increase of gold-film thickness also reduces the coupling intensity between the core mode and the SPP modes, thus reducing the peak loss. Note that the curves of peak loss appear to significantly decline in the vicinity of 1.45. This is due to the fact that the n a is not very different from the RI of the background material, the confinement of the core mode becomes weaker and more energy of the core mode leaks out to the analyte region. To further study the effect of gold-film thickness on sensing performance, we also present the sensitivities of the sensor at different n a with gold-film thickness at 30 nm, 40 nm, and 50 nm in Figure 3d. In general, the sensor shows a higher sensitivity with the thicker gold film, especially at the larger n a range.

Fabrication Tolerance
Coating with gold film on surfaces of such grooves in this design is much simpler than that on inner surfaces of the air holes in the other designs [13][14][15][16][17]20,24]. In actual manufacturing, however, it is difficult to accurately deposit the gold film on the surface of the two grooves under the same thickness. It is necessary to investigate the effect of the fabrication tolerances of the gold film on the sensing performance of the sensor. Due to the symmetry of its structure, we only consider the case in which the variation of ±10% of m 2 affects the sensing performance of the proposed sensor when the m 1 is fixed to 40 nm. Figure 4 shows the loss spectra with slight variation of ±10% of m 2 at n a = 1.47. When m 2 varies from -10% to +10%, the loss spectra present a slight change.
can the electric field of the core mode penetrate the gold film, coupling with the SPP modes on the gold surface. The increase of gold-film thickness also reduces the coupling intensity between the core mode and the SPP modes, thus reducing the peak loss. Note that the curves of peak loss appear to significantly decline in the vicinity of 1.45. This is due to the fact that the na is not very different from the RI of the background material, the confinement of the core mode becomes weaker and more energy of the core mode leaks out to the analyte region. To further study the effect of gold-film thickness on sensing performance, we also present the sensitivities of the sensor at different na with gold-film thickness at 30 nm, 40 nm, and 50 nm in Figure 3d. In general, the sensor shows a higher sensitivity with the thicker gold film, especially at the larger na range.

Fabrication Tolerance
Coating with gold film on surfaces of such grooves in this design is much simpler than that on inner surfaces of the air holes in the other designs [13][14][15][16][17]20,24]. In actual manufacturing, however, it is difficult to accurately deposit the gold film on the surface of the two grooves under the same thickness. It is necessary to investigate the effect of the fabrication tolerances of the gold film on the sensing performance of the sensor. Due to the symmetry of its structure, we only consider the case in which the variation of 10% of m2 affects the sensing performance of the proposed sensor when the m1 is fixed to 40 nm. Figure 4 shows the loss spectra with slight variation of 10% of m2 at na = 1.47. When m2 varies from -10% to +10%, the loss spectra present a slight change.
In order to further investigate the effect of the m2 on sensing performance of the proposed sensor, we summarize the peak wavelengths, peak losses and sensitivities for variation of 10% of m2 in Table 1 when m1 is fixed at 40 nm and na changes from 1.33 to 1.49. In general, as m2 changes from −10% to +10%, the peak wavelength shows a slight decrease in the low na range and then follows an opposite trend in the high na range, and the peak loss shows a small decrease in the whole na range. Those slight changes have negligible influence on the sensitivities of the sensor as shown in Table 1, which indicates that the sensor has good stability within the variation of 10% fabrication tolerances for the thickness of the gold film and low requirements of manufacturing precision.  Table 1. Summary of peak wavelengths, peak losses and sensitivities of y-polarized core mode at the na range of 1.33-1.49, when m1 is fixed at 40 nm and m2 changes in the range of ±10%. In order to further investigate the effect of the m 2 on sensing performance of the proposed sensor, we summarize the peak wavelengths, peak losses and sensitivities for variation of ±10% of m 2 in Table 1 when m 1 is fixed at 40 nm and n a changes from 1.33 to 1.49. In general, as m 2 changes from −10% to +10%, the peak wavelength shows a slight decrease in the low n a range and then follows an opposite trend in the high n a range, and the peak loss shows a small decrease in the whole n a range. Those slight changes have negligible influence on the sensitivities of the sensor as shown in Table 1, which indicates that the sensor has good stability within the variation of ±10% fabrication tolerances for the thickness of the gold film and low requirements of manufacturing precision. Table 1. Summary of peak wavelengths, peak losses and sensitivities of y-polarized core mode at the n a range of 1.33-1.49, when m 1 is fixed at 40 nm and m 2 changes in the range of ±10%.

Conclusions
In this paper, we propose a novel design of an open structure H-shaped PCF with a capability of a wide RI-detection range. The gold film and the analyte are placed on the surface of the grooves in the H-shaped PCF, making the fabrication of the sensor much easier than traditional PCF-SPR sensors in which the gold film and the analyte are placed in the air holes. The results demonstrate that the proposed sensor can work well in a large n a range, and has good stability within tolerances of ±10% of the gold-film thickness. Compared with the other types of SPR sensor, our proposed SPR sensor has the advantages of convenient operation, simple fabrication, good stability, large detection range, high sensitivity, and is reusable, which make it more competitive in physical-, biological-and chemical-sensing fields.