The radius of the nanoparticle plays an important role in the performance of the biosensor. Figure 4 shows the effect of the nanoparticle’s radius r_g on the resonant wavelength, spectral loss, and spectral sensitivity. Figure 4A shows the relationship between the resonant wavelength and r_g when n_a is 1.33. With the increase of r_g, the resonant wavelength of the FM-MCF LSPR sensor exhibits a red shift, this is because the nanoparticle’s radius affects the maximum light coupling between the fiber mode and gold nanoparticle. Although resonant wavelength has a red shift, the change of adjacent resonance peaks gradually decreases. The relationship between r_g and spectral loss when n_a = 1.33 is shown in Figure 4B. In Figure 4B, the peak loss of LP_01x mode increases with the radius of the nanoparticle initially, when r_g = 90 nm, at this moment LP_01x has the maximum loss, and then peak loss begins to decrease. However, the peak loss of LP_01y mode always increases as the radius increases, when r_g = 150 nm, LP_01y has the maximum loss. When n_a varies from 1.33 to 1.34, the spectral sensitivity of FM-MCF LSPR biosensor for different nanoparticle’s radius is presented in Figure 4C. As the radius increases, the sensitivity continues to increase, reaching its maximum when the radius is 150 nm. Therefore, by changing the radius of the gold nanoparticle, we can adjust the resonant wavelength, spectral loss, and the spectral sensitivity of the biosensor.

Meanwhile, the influence of nanoparticle positions on FM-MCF LSPR biosensor performance is also analyzed in this paper. The gold nanoparticle is initially placed tangent to the core, as illustrated in Figure 1A. When the nanoparticle rotates clockwise around the center of the open air-hole to the next position, the angle between the original position and the next position is described by θ.

Figure 5 depicts fundamental mode loss spectra of n _a = 1.33 when θ is 0°, 5°, 10°, and 15°, respectively. We found that as θ increases, the peak losses of the two polarizations gradually decrease but the resonant wavelength remains almost the same. The reason is that the evanescent wave has a certain penetration depth, and its amplitude decreases exponentially with the increase of the distance from the interface so peak loss varies when the nanoparticle is placed at different angles (Chiavaioli et al., 2017b).

The FM-MCF we use only supports two modes (LP₀₁ and LP₁₁) at the communication band. At visible wavelengths, plenty of high order modes can be transmitted in the fiber core. Transmission mode in the fiber is also a significant factor that affects the performance of the presented biosensor. As mentioned above, we fix the radius of the gold nanoparticle to 150 nm and the best position to θ = 0°. Loss spectra of different modes when biological liquid analyte RI ranges from 1.33 to 1.39 with a step of 0.01 is shown in Figure 6, where the dash lines represent the loss spectra of the x polarization while the solid lines represent the y polarization. It can be seen that loss spectra excited by y polarization have higher losses than x polarization in the same mode and the resonant wavelength of x polarization is also longer than that of y. When using high order modes to excite LSPR, high order modes usually have higher losses than the fundamental mode, and hence their LSPR loss curves are steeper than that of the fundamental mode, the narrower the loss curve, the better the resolution of the sensor. Therefore, the performance of LSPR biosensor excited by the high order mode is better than the fundamental mode.

Figure 7 shows the relations between n _a and the resonant wavelength. The average sensitivity and highest sensitivity can be obtained according to (3). The average sensitivity of the LP_01x, LP_01y, LP_11x, LP_11y, LP_21x, LP_21y, LP_02x, and LP_02y mode is 2467.9, 2257.9, 2528.2, 2310, 2640, 2428.6, 2557.1, and 2313.9 nm/RIU, respectively. The LP_21x mode has the maximum highest sensitivity of 3478.28 nm/RIU among all modes when n _a = 1.39. It can be seen that x polarization has a higher sensitivity than y polarization in the same mode. In addition, high order modes have higher sensitivity than fundamental mode in the same polarization state. Therefore, using high order mode to excite LSPR can improve the sensitivity of the sensor.

It has been shown experimentally that the shape of the gold nanoparticle plays a vital role in determining the sensitivity (Mayer and Hafner, 2011). Several gold nanoparticles with different geometric shapes are illustrated in Figures 8A–D, all the nanoparticles are filled in the air hole of the FM-MCF and are tangent to the core. From the previous discussion, when the radius of the circumferential circle is 150 nm, the LSPR excited by gold nanoparticles has the highest sensitivity. When biological liquid analyte RI is set as 1.33, the loss spectra of LSPR excited by four different shapes of gold nanoparticle are shown in Figure 8E.

It can be seen that the loss spectra exhibit a red shift as nanoparticle gets sharper in Figure 8E. The resonant wavelength of hexagon nanoparticle is close to that of the circular nanoparticle, and the triangle nanoparticle’s resonant wavelength is in the near-infrared while circular is in the visible light range. By using different shapes of nanoparticle, we can adjust the resonant wavelength of the FM-MCF LSPR biosensor. Figure 8 shows the optical field distribution of LSPR excited by different shapes of nanoparticle at the peak of a, b, c, d, e and f in Figure 8E, the red arrows represent the direction of the electric field. When nanoparticles have sharp tips or features, the LSPR energy is mainly concentrated at the tip position. The coupling between LP₀₁ mode and SP mode excited by triangle nanoparticle is the best, then square, and finally hexagon nanoparticles. This is because of the sharper the angle, the greater the density of the free electrons at the tip, and the stronger the electric field that can be excited. The strong electric field enhancement at the sharp tips makes it possible to excite surface plasmon resonance with only a small amount of incident light energy, so the sharper the nanoparticle, the longer the resonant wavelength.

In the arrangement shown in Figures 8A–D, only one corner of the nanoparticle is in contact with the air hole. For the first three shapes in Figures 8A–D, we rotate the nanoparticles 60°, 45°, and 30° counterclockwise along the center as shown in Figures 9A–C such that two corners of these nanoparticles are in contact with the air hole. Loss spectra of LP_01x and LP_01y when different shapes of gold nanoparticles excite LSPR after rotation and moving are shown in Figure 9D.

Compare Figure 9D with Figure 8E, it can be seen that the loss spectra of all shape nanoparticles have changed after rotation and moving. Since the hexagon is closest to the circle, its loss curve does not change significantly after rotation, however, the difference between the triangle and the circle is the largest, so the loss spectra vary obviously. After the triangle nanoparticle rotates 60°, the resonance peak of LP_01y moves from 850 to 963 nm (red shift), while the resonance peak of LP_01x moves from 950 to 895 nm (blue shift).

Nanoparticle arrays also affect the performance of the FM-MCF LSPR biosensor. In Figure 10 gold nanoparticles with a radius of 150 nm are filled symmetrically in the air hole, the angle between adjacent nanoparticles is represented by δ and the minimum value is 2.7°, which means that two adjacent nanoparticles are tangent at this time. When δ = 2.7°, the entire air hole can be filled with 81 gold nanoparticles.

Since the air hole range has been determined, the number of nanoparticles n and the angle between adjacent nanoparticles δ simultaneously affect the property of the gold nanoparticle arrays. The influence of n has been studied at first, the loss curves excited by LP_01y mode when δ = 2.7°, n_a = 1.33, and n are set as 81, 41, 21, 11, 9, 7, 5, and 3, respectively are shown in Figure 14. Because the loss curves of n = 41 and 21 are very close to n = 81, so they are not given in Figure 11A. It can be found that compared with single nanoparticle, nanoparticle array has many resonance peaks. When n = 81, the resonant wavelength locates in 680 nm, as n decreases to 11 the loss curves begin to show two peaks, and the resonance peaks at longer wavelength have higher confinement loss. When n = 3, there is an ultra-high loss peak at 1042.4 nm, and the confinement loss can reach 13.5 dB/cm, far exceeding the peak loss at other nanoparticle numbers.

In addition, the loss curves when n_a = 1.34 have also been calculated, the resonant wavelength and sensitivity vary with different n, as shown in Figure 11B. For the same n_a, when n decreases from 81 to 21, the resonance wavelength remains basically unchanged, and as n continues to decrease, the second resonance peak begin to appear at longer wavelength, so the resonant wavelength of n = 11 have a significant red shift. However, as n decrease to 5, the second resonance peak gradually blue shifts so the resonant wavelength decreases. The average sensitivity can be calculated by Eq. 3, it can be found that initially when the n decreases, the sensitivity is basically unchanged, when n = 11, the second resonance peak has higher sensitivity but as n continues to decrease the sensitivity decreases. When n = 3, the sensitivity can reach 2850 nm/RIU, which is higher than the sensitivity of other number of nanoparticles. Therefore, the number of nanoparticles n is set to 3.

Secondly, the influence of δ has been studied. The loss curves for different δ are shown in Figure 12 where δ = 3°, 5°, 7°, 9°, and 11°. When δ varies from 11° to 3°, the resonance peaks have an obvious red shift and the confinement loss gradually increases. It can be interpreted as when δ is large, each gold nanoparticle can independently excite the LSPR without coupling to each other. With the decrease of δ, the local surface plasmon waves excited by each gold nanoparticle begins to show weak coupling and lead to the red shift of resonance peak. When the distance between gold nanoparticles is close to their own size, the local surface plasmon waves show strong coupling, so the confinement loss gradually increases.

The variation of resonant wavelength and sensitivity with δ is plotted in Figure 13. When n_a = 1.33 and δ increases from 3° to 5°, the resonant wavelength declines from 1037.7 to 838.2 nm while δ increases from 9° to 11°, the resonant wavelength declines from 728.7 to 722 nm. It can be found that although changing δ can adjust he resonance wavelength’s position, the adjustment effect is limited. The sensitivity change with δ can also be obtained from Figure 13. When δ = 5°, it reaches the sensitivity of 3610 nm/RIU, which is the largest of all δ. Therefore, the angle between adjacent nanoparticles δ = 5°.

The FM-MCF LSPR sensor can work in the RI range of 1.33–1.39 which covers the RI of the BSA solution and human Immunoglobulin G. Therefore, the sensor can be used as a biosensor to detect the biological liquid analytes. The loss curves excited by LP_01y and LP_11y mode when n = 3, δ = 5° and biological liquid analyte RI is from 1.33 to 1.39 and loss curves excited of LP_21y and LP_02y mode and biological liquid analyte RI is from 1.33 to 1.38 is shown in Figure 14. With the increase of biological liquid analyte RI, the resonance peaks have a red shift and at the same RI, the loss curves of LP_11y have a more obvious red shift than that of LP_01y. Figure 15 illustrates the relationships between na and resonant wavelengths for LP_01y mode and LP_11y mode when n_a = 1.33–1.39. The average sensitivity of LP_01y and LP_11y mode when n_a is from 1.33 to 1.39 is 4497.1 and 4704.6 nm/RIU, respectively, while the highest sensitivity for each mode is 5732.1 nm/RIU and 6055.36 nm/RIU when n_a = 1.39, respectively. In addition, when the wavelength of incident light along the core is 800–1300 nm, LP_21y and LP_02y modes can also be transmitted stably, and the RI range at this time is 1.33–1.38. In Figures 14C,D, the loss spectra become not smooth, this is mainly because LP_21y and LP_02y are more likely to resonate with the core mode, and the energy is basically coupled to the plasmon mode. However, when the wavelength has a slight change, the phase matching condition is no longer satisfied. Therefore, the average sensitivity of LP_21y and LP_02y mode when n_a = 1.33–1.38 is 4888 nm/RIU and 5114 nm/RIU, respectively, and the highest sensitivity for each mode is 6209.6 nm/RIU and 7,351.6 nm/RIU when n_a = 1.38. It is demonstrated that the FM-MCF LSPR biosensor has high sensitivity and is ideal for real-time detection of biological substances.