3.1 Coupling properties
Figure 2 depicts the dispersion curves and loss spectra of core mode and surface plasmon polariton (SPP) mode at an analyte RI na of 1.25. The insets ((a)-(d)) show the y- and x-polarized core modes at resonance, as well as the corresponding SPP modes. It can be observed that as the wavelength increases from 0.75 to 1.25 µm, the real part of the effective RI of core mode gradually decreases. Moreover, the real parts of the effective RI of y- and x-polarized core modes undergo abrupt changes near the wavelengths of 0.845 and 1.095 µm, respectively, and intersect with that of SPP modes in the same polarization direction. That is to say, the core mode and SPP mode at the above two wavelengths satisfy the phase matching conditions. From the electric field distributions (a) and (c), it can be found that near the resonant wavelength, part of the energy of core mode is transferred from the core region to the surface of gold film and a stronger coupling resonance occurs in the y-polarization direction. Therefore, the loss peaks as high as 678.91 and 471.53 dB/cm are generated at the two resonance wavelengths, respectively.
3.2 Sensing performance
Figure 3 plots the loss of y- and x-polarized core modes as a function of wavelength ((a)-(b)), as well as the corresponding peak loss and resonant wavelength (c), when the analyte RI na increases from 1.19 to 1.37 in steps of 0.02. From Fig. 3, it can be observed that the peak losses of y- and x-polarized core modes exhibit an overall trend of increasing first and then decreasing with the increase of na. This is because the increase of na changes the RI of the environment near the gold film, the RI difference between the core mode and SPP mode gradually decreases. The limit ability of the fiber core to the electric field decreases, more energy transfers from the core region to the surface of gold film, and the SPR effect is enhanced. However, as na further increases, the RI difference between the two resonance modes increases, more electric field energy is confined in the core region, and the mode coupling is weakened.
In addition, the resonant wavelengths in the y- and x-polarization directions undergo red-shifted with increasing na. Figure 3(c) specifically depicts the corresponding resonant wavelengths in two polarization directions under different na. The increase of na leads to an increase in the real part of the effective RI of SPP mode, while that of core mode remains essentially unchanged, resulting in the increase of the phase matching condition between the two modes, which provides the possibility for the realization of the sensing function. Research has found that when na increases from 1.19 to 1.37, the resonant wavelength in the x-polarization direction shifts from 0.92 to 1.72 µm. The maximum wavelength sensitivity is up to 12500 nm/RIU. Assuming the resolution of the spectrometer is 0.10 nm, the maximum resolution of the sensor can reach 3.64 × 10− 5. Meanwhile, within the low RI detection range of 1.19 to 1.33, the x-polarization direction has good linearity. Moreover, in the RI sensing detection range of 1.19 to 1.37, the y-polarization direction can also be used for auxiliary detection to improve detection accuracy.
3.3 Influence of structural parameters on sensing performance
3.3.1 The air hole diameters d1 and d2
The structural parameters of MOF waveguide have a crucial impact on the sensing performance. Figure 4 investigates the effect of the variation of large air hole diameter d1 ((a)-(b)) and small air hole diameter d2 ((c)-(d)) on the loss when na is 1.31 and 1.33. The inset shows the amplitude sensitivity (AS) at na of 1.31 [14]. From Fig. 4, it can be obtained that the change of air hole diameters d1 and d2 under the same na has little changed to the surrounding environment near the core region and gold film, so it causes little change in the RI difference between the core mode and SPP mode. Therefore, the energy transfer between the two resonance modes has no significant change, and the peak loss does not change much.
At the same time, when the large air hole diameter d1 and small air hole diameter d2 vary from 2.20 to 2.40 µm and 1.00 to 1.20 µm, respectively, there is no significant shift in the resonant wavelengths of y- and x-polarization directions at na of 1.31 and 1.33. This is due to the fact that the above two air hole diameter changes have little effect on the real parts of the effective RI of core mode and SPP mode, so the phase matching points of the two resonance modes with different air hole diameters do not change significantly. This performance of resonant wavelength and peak loss indicates that the fiber has a good structural tolerance for the air hole diameters d1 and d2, which reduce the difficulty of fabrication. However, considering that the x-polarized core mode has a large AS and a narrow full width at half maximum (FWHM) at d1 of 2.40 µm, so d1 is selected as 2.40 µm. And d2 chose a scaled-down 1.20 µm.
3.3.2 The distance h
Figure 5 shows the loss spectra of core mode at na of 1.31 and 1.33 for an increase in the distance h between the core and the side polished surface from 2.25 to 2.27 µm. The illustration shows the corresponding amplitude sensitivity for na of 1.31. When h changes from 2.25 to 2.27 µm, the peak loss of y-polarized core mode increases and then decreases at na of 1.31, while that changes in the opposite direction at na of 1.33, showing a decrease and then an increase. This is because as h increases, the proportion of silicon near the gold film increases, and the real part of the effective RI of SPP mode increases. The RI difference between the core mode and SPP mode decreases and then increases with the increase of h at na of 1.31, while increases and then decreases at na of 1.33. This resulted in different changes in the SPR effect during the change of h. Meanwhile, due to the asymmetry of the fiber structure, the overall RI difference between the two resonant modes in the x-polarization direction becomes larger with the increase of h, and the coupling strength decreases, so that the peak loss of x-polarized core modes show a decreasing trend as a whole.
As h increases, the resonant wavelength of core mode shifts towards longer wavelengths. The reason for this phenomenon is that with the increase of h, the proportion of silicon near the gold film increases, leading to an increase in the real part of the effective RI of SPP mode, while that of core mode remains basically unchanged, resulting in the phase matching point redshift. To obtain narrow FWHM and higher AS, h is set to 2.25 µm.
3.3.3 The open-loop channel diameter r
Figure 6 describes the variation of open-loop channel diameter r varying from 0.70 to 0.90 µm, the loss spectra of core mode at na of 1.31 and 1.33 ((a)-(b)), and resonant wavelengths for different na (c). When r increases from 0.70 to 0.90 µm, the peak loss of y-polarized core mode shows decreases and then increases, and continuously decreases at na of 1.31 and 1.33, respectively. The corresponding peak loss of x-polarized core mode at the above two na is in contrast, with changes of first increasing and then decreasing, and continuously increasing, respectively. As r increases, the liquid filling the open-loop channel with RI lower than that of silicon RI increases, which changes the environment around the gold film, and the real part of the effective RI of SPP mode reduces. The RI difference between the y-polarized core mode and SPP mode increases with the increase of r when na is 1.31. But as r further increases, the real part of the effective RI of core mode is enhanced by the influence of r, and its value decreases. So the RI difference between the two resonant modes decreases, resulting in the SPR effect in the y-polarized direction at na of 1.31 first weakening and then strengthening. However, the RI difference between the two resonant modes in the y-polarization direction increases with the increase of r when na is 1.33, and the coupling strength weakens. The peak loss of x-polarized core mode has a different optimal coupling state than that in the y-polarized direction at different r due to the birefringent characteristics of the fiber.
From Fig. 6(c), it can be observed that the resonant wavelength of y-polarized core mode does not change very much with increasing r, while that of x-polarized core mode undergoes a significant blue shift overall. The blue-shifted of resonant wavelength in the x polarization direction is due to the fact that the increase of r, which increases the amount of liquid filled in the open-loop channel with RI lower than that of silicon. The RI of the environment near the gold film is altered, resulting in a decrease in the real part of the effective RI of SPP mode, while that of core mode remains essentially unchanged. As a result, the resonant wavelength undergoes a blue shift. The x-polarized core mode of the sensor achieved a maximum sensitivity of 12500 nm/RIU at r of 0.70 µm.
3.3.4 The gold film thickness t
Figure 7 illustrates the loss spectra (((a) - (b)) of core mode at na of 1.31 and 1.33 when the gold film thickness t increases from 30 to 60 nm, and the corresponding resonant wavelengths at different na (c). Figure 7(a) and (b) reveal when t increases from 30 to 60 nm, the peak loss of y-polarized core mode increases and then decreases under the same na, while that of x-polarized core mode decreases with the increase of t. For example, when na is 1.33, the corresponding peak losses of the former are 1409.50, 1161.91 and 1296.00 dB/cm, while the corresponding peak losses of the latter are 967.80, 734.24 and 691.95 dB/cm, respectively. Due to the stronger asymmetry of the proposed MOF, for the y-polarization direction, the free electrons on the surface of the gold film increase as t increases, and the mode coupling is enhanced. However, when t exceeds the critical value, the evanescent wave intensity decreases and the SPR effect becomes weaker. And in the variation range of t studied, for the x-polarization direction, the thickness of the gold film leads to the reduction of the penetration thickness of the evanescent field, which makes the peak loss of x-polarized core mode decreases with the increase of t.
From Fig. 7(c), it can be observed that as t increases from 30 to 45 nm, the resonant wavelength is blue-shifted in the y-polarization direction. When t is 45 and 60 nm, the position of the resonant wavelength in this direction changes little. The resonant wavelength shows no consistent change with the increase of t in the x-polarization direction. This is because the propagation constant of SPP mode on the metal waveguide will change when t varies, but there is an optimal phase matching point between the core mode and SPP mode but during this change. So, the modulation of resonant wavelength can be realized by controlling the thickness of the gold film within a certain range. When t is 60 nm, the sensor achieves maximum sensitivity.
Table 1. shows the comparison between the proposed SPR-based MOF sensor with a single-layer cladding air-holes and the reported sensors. Compared with Ref. [7], the proposed MOF avoids the challenges of coating and liquid selective filling in the internal hole of the optical fiber, and improves the reusability of the optical fiber. Meanwhile, compared with the SPR-based MOFs reported in Table 1, the proposed MOF has a wide RI sensing range and high sensitivity, and its unique and simple structure makes it a strong candidate for biological and chemical RI sensing.
Table 1. Performance comparison of SPR-based MOF RI sensors