## 3 Results and Analysis  
Based on the above introduction, the paper analyzes the field enhancement effect, the transmission loss spectrum and the relationship between the diameter and spacing of the gold cylinder, and obtains the optimal structural parameters of the SPR sensor finally. Then the sensitivity of these structures is analyzed to find the optimal structural parameters.  
Firstly, we set the distance between the gold cylinder constant 1 nm, set the measured liquid refractive index \(n_{a}\) = 1.333, gradually changing the diameter \(  
Based on the optimal value of the diameter of the gold cylinder \(d=55\) nm, we study the optimal gap parameter of the gold cylinder. We set the gold cylinder diameter \(d=55\) nm, gradually changing the gap between the gold cylinder in the range of 0.5-30 nm, while the measured liquid refractive index is \(n_{a}=1.333\). As shown in Figure 5, with the gap increases, the mode loss changes with wavelength. It can be seen from Figure 5 that as the gap increases in the range of 0.5-30 nm, the resonant wavelength shifts to the longer wavelength. However, the peak loss at the resonant wavelength first increases significantly and then decreases, obtaining the maximum at \(gap=20\) nm.  
Therefore, the gold cylinder spacing theory is not the bigger the better, but instead there is an optimal value, making the formation of a resonant cavity between the gold cylinder. The plasmon resonate with each other in the resonator to enhance the SPR effect, so that the energy of the incident light can be transformed into plasma energy to a large extent. This shows that the effect on the transmission loss spectrum is that the resonance peak is the sharpest.  
Based on the above analysis and simulation, this study is to choose the diameter of the gold cylinder and the corresponding gap, to optimize the sensitivity of the proposed fiber SPR sensor. As shown in Figure 6, the sensitivity of the three sensor structures was analyzed. The first structure was \(d=45\) nm, \(gap=20\) nm, the second structure was \(d=50\) nm, \(gap=20\) nm and the third structure was \(d=55\)nm, \(gap=20\) nm, assuming that the receiving end can detect the change of 1% of the transmission power. According to the sensitivity calculation formula \(S=(\Delta\alpha/\Delta n)/\alpha_{a}\), the sensitivity of the first  
Figure 4: Relationship between transmission loss spectrum and gold cylinder diameter.  
Figure 3: Relationship between the field enhancement of the fundamental mode and the diameter of the gold cylinder.  
structure was S-94, that was, the change of the liquid refractive index in the order of \(10^{-4}\) RIU/nm can be detected. the sensitivity of the second structure was S-189, that was, the change of the liquid refractive index in the order of \(10^{-5}\) RIU/nm can be detected. Meanwhile, the sensitivity of the third structure was S-178, that is, the change of the liquid refractive index in the order of \(10^{-5}\) RIU/nm can be detected. At the same time, it could be found that although the sensitivity of the first structure was relatively low, the sensitivity can maintain a high level in a long wavelength band. The second and third sensor structures have higher sensitivity, but the maximum sensitivity can only be maintained in a smaller band. Therefore, in practical applications, the working method can be selected reasonably to obtain the highest sensitivity or better sensitivity in a longer wavelength band.  
The region of refractive index used for the calculation is 1.333, which is close to the RI of water. Considering the detected RI value are near the index of water in most label-free sensing applications, the influence of RI was neglected. At the same time, in actual application, the sensor's structural parameters can be flexibly adjusted to meet different work requirements. For example, we can choose a long wavelength range of work or high sensitivity mode of operation.