## 4 Simulations and Discussions
### Discussions  
In this section, we will discuss the reliability and drawbacks of the simulation model. Additionally, the experimental feasibility and strategies to improve the performance of our sensor are described through the theoretical analysis and existing technology. The model of the sensing area is inferred to be reliable based on the following reasons. Firstly, the simulation results are consistent with the theoretical analysis results. This indicates that the higher-order mode has a high energy proportion in the cladding, and can fully excite SPR; therefore, in the sensing area, the RI sensitivity and resolution of higher-order modes are much higher than those of the fundamental mode. Secondly, the reliability of the model is verified from the experimental results of others. According to Table 1 and \(I_{min}\), the RI sensitivity of the fundamental mode is \(1.1\times 10^{-3}\) RIU. This result roughly equals the experimental results of [PERSON] et al. (1.83 \(\times\) 10\({}^{-3}\)RIU) [16], but is slightly lower than that of [PERSON] et al. (\(6.1\times 10^{-4}\)RIU) [17]. The reason is that there is still a small part of cladding left in the sensing area. The cladding is not completely removed, which fails to fully utilize the energy of the cladding in the sensing area to excite SPR. Although the reliability of the model is verified, it also shows that the shortcoming of the model is that it cannot fully utilize the energy in the cladding. As we use the LP\({}_{11}\) and the LP\({}_{21}\) mode to excite SPR, these modes can be obtained only by partially stripping the  
Figure 10: The loss of the LP\({}_{\rm mm}\) mode under different RI. cladding in the simulations, which is different from the results in the actual experiments. In reality, these modes propagate in the core of fiber without cladding, exposed to the solution with high loss. However, this cannot be acquired in the simulations, since the simulations need to meet the boundary condition. The proposed sensor is experimentally feasible, using higher-order modes. In the experiment, the usage and generation of the LP\({}_{11}\) and the LP\({}_{21}\) mode is of great necessity and importance. First, the loss of these modes is low, which has little effect on the intensity modulation compared to other higher-order modes, such as the LP\({}_{0\text{m}}\) (m \(\geq\) 2), the LP\({}_{1\text{m}}\) (m \(\geq\) 2), and the LP\({}_{2\text{m}}\) (m \(\geq\) 2) mode. Second, it is possible to fabricate a few-mode fiber with low loss in the visible band. On the one hand, in the area of communication, a few-mode fiber has already been developed which can support the LP\({}_{01}\), LP\({}_{11}\), and LP\({}_{21}\) mode, propagating with a loss of less than 0.21 dB/km (FM GI-4, 1550 nm, Yangtze Optical Fiber and Cable Co., Ltd., Shanghai, China). The processing experience and fabricating procedures of this fiber may be helpful to make a few-mode fiber in the visible band. On the other hand, the length of few-mode fiber is short (\(\sim\)cm) in the sensor, resulting in low loss of transmission, which can be ignored. Third, it is realistic to make the LP\({}_{01}\)-LP\({}_{11}\) coupler and the LP\({}_{01}\)-LP\({}_{21}\) coupler with high \(\gamma\) in a wide range of visible bands due to the former coupler has been fabricated [11]. Finally, the processes associated with the manufacture of sensing zones are well established. The sensing area can be processed by the wheel-based side grinding method [18; 19]. Then, Ag layers (40 nm in thickness) can be deposited on the sensing area using a vacuum deposition machine (ZZS-700B, Chengdu Vacuum Machinery, Chengdu, China) at a certain working pressure and specific rates [20]. To further improve the performance of our sensor, we present two methods. One is to replace the sensing area with a new structure. In view of the experiment, the performance of the sensor might be improved by removing all the cladding or replacing the sensing area by some complex structures which can leak more power [21; 22; 23; 24].