## 2 Modeling  
Figure 1 is the cross-sectional schematic diagram of the opened three-hole suspension SPR sensor designed in this paper. There are three macropores in the suspension core fiber. One of the macropores is an open design for filling the fluid to be measured. The remaining two macropores are sealed and filled with air. The open pores are arranged with nanometer gold cylinders of the same size and pitch along the axial direction of the core. In practice, the above structure can be realized by self-assembly or nanoimprint method. The diameter of the gold cylinder is d, the distance between the gold cylinders is dgap, and the refractive index is denoted by nd. In the modeling process with COMSOL, we choose the core curvature \(r\) = 4 \(\upmu\)m, cantilever thickness \(c\) = 0.4 \(\upmu\)m, under this condition the structure can be maintained single-mode conditions [8]. The suspended optical fiber-based material is silica, whose refractive index \(n_{c}\) under different wavelength conditions could be obtained by the Sellmeier equation [17]. Gold cylinder refractive index n\({}_{\rm d}\) parameters can be obtained by reference to the relevant literature [18]. To implement the opened suspended core fiber-based SPR sensors for analytes, the opened holes could be coated with the gold nano cylinder using high pressure chemical vapor deposition (CVD) technique, wet chemistry deposition technique or nanoskiving [19; 20; 21; 22; 23], and then filled with the analytes.  
In microstructured optical fiber sensors, the mode power loss propagating forward along the \(z\)-axis can be expressed by Equation (1):  
\[P=P_{0}\mathrm{e}^{-\alpha z} \tag{1}\]  
where \(P_{0}\) is the power at plane \(z=0\). The mode attenuation constant is proportional to the imaginary part of the effective refractive index of the mode:  
\[\alpha=2k_{0}\mathrm{Im}(n_{eff}) \tag{2}\]  
Therefore, the attenuation coefficient can be used to quantify and evaluate Gaussian guided mode transmission loss.  
In addition, the sensitivity of the SPR sensor can be expressed as:  
\[S=(\Delta\alpha/\Delta n)/\alpha_{a} \tag{3}\]  
where \(\Delta n\) represents the offset value of the measured liquid refractive index value from \(n_{a}=a\), \(\Delta a\) represents the change value of the transmission loss for the wavelength when the liquid refractive index changes, \(a_{a}\) represents the measured liquid refractive index \(n_{a}=a\) fiber transmission loss spectrum.  
Figure 1: Schematic cross-section of the proposed fiber SPR sensor.  
Figure 2: Spatial distribution of the sensor pattern.  
Figure 2 analyzes the spatial energy distribution of the proposed sensor pattern (gold cylinder diameter \(d\) = 35 nm, transmission wavelength \(l\) = 530 nm). The gap of the gold cylinders is set as 0.5 nm, while for the entire loss peak, the energy distribution in the sensor-mode cantilever region is very close to the Gaussian type. The gold cylinder region has a strong energy distribution (field enhancement), the gold cylinder also formed a direct resonance effect. The mode field amplitude locally attenuates at the interface between the gold cylinder and the liquid being measured, which is characteristic of the surface plasmon resonance effect. Here the color/unit definition of the intensity bar is consistent with the intensity of Y axis, as it originates from the Multiphysics COMSOL software (COMSOL, Inc., Burlington, MA, USA) and is a relative magnitude.