## 3 Numerical Results and Discussion
### Structural-Parameter Determination  
It is well known that the influence of PCF structural parameters is sensitive on sensing characterization. In this section, diameter of central two holes \(d_{2}\), thickness of gold layer \(T_{Au}\), channel length \(\Lambda_{2}\), and hole diameter \(d_{3}\) were considered for numerical investigation. Figure 4a depicts loss spectra for different diameters of central holes \(d_{2}\) with \(d_{1}\) = 2.8 \(\upmu\)m, \(d_{3}\) = 7.0 \(\upmu\)m, \(\Lambda_{1}\) = \(\Lambda_{2}\) = 6.0 \(\upmu\)m, \(T_{Au}\) = 50 nm, and \(n_{a}\) = 1.36, making \(d_{2}\) 6.0, 7.0, and 8.0 \(\upmu\)m, respectively. The position of resonance wavelength occurred as a redshift with the increase of d\({}_{2}\). Simultaneously, the corresponding resonance signal was also changed; especially in the case of \(d_{2}\) = 8 \(\upmu\)m, the signal was reduced and widened because diameter d\({}_{2}\) was too large, and the area of the core was reduced, which made it difficult to maintain good single-mode transmission of the PCF, so y-polarization FM could not generate a strong mode-coupling effect with the SPP mode. Thus, we should avoid the value of d\({}_{2}\), which was too large in the sensor design. Under conditions of \(d_{2}\) = 6 and 7 \(\upmu\)m, the energy produced by the latter was also slightly larger than that of the former in calculation; if more loss energy could be generated, the signal would be easier to detect, so the case of \(d_{2}\) = 7 \(\upmu\)m was selected for the next analysis. Figure 3: Dispersion relations of y-polarization core FM and SPP mode in this sensor. Illustration of resonance mode displayed when \(d_{1}\) = 2.8 \(\upmu\)m, \(d_{2}\) = \(d_{3}\) = 7.0 \(\upmu\)m, \(\Lambda_{1}\) = \(\Lambda_{2}\) = 6.0 \(\upmu\)m, \(T_{Au}\) = 50 nm, and \(n_{a}\) = 1.36. Figure 2: Mode patterns of fundamental modes (FMs) and plasmonic mode: (**a**) x-polarization core FM; (**b**) y-polarization core FM; (**c**) surface-plasmon-polariton (SPP) mode in sensing layer. Obviously, the role of excitation-gold-layer thickness in sensing is very important. So, the influence of different gold-layer thicknesses \(T_{Au}\) on the sensor was considered, as shown in Figure 4b. We observed that, when \(T_{Au}\) increased, the CL peak was blue-shifted, and the loss peak was reduced. The reason for this phenomenon was the thinner thickness of the gold layer; the more obvious the effect of light-matter interaction, the more that free oscillation was enhanced. This process also enhanced the evanescent field near the dielectric interface, which distinctly led to strong energy generation that would be weaker. However, in the course of use, the gold layer would certainly be consumed and it could not be designed to be very thin in a one-sided pursuit of high-loss signals. So, \(T_{Au}\) = 40 nm was selected as a compromise between gold-layer thickness and signal strength. Figure 4c displays loss spectra for different channel lengths \(\Lambda_{2}\) with \(d_{1}\) = 2.8 \(\upmu\)m, \(d_{2}\) = \(d_{3}\) = 7.0 \(\upmu\)m, \(\Lambda_{1}\) = 6.0 \(\upmu\)m, \(T_{Au}\) = 40 nm, and \(n_{a}\) = 1.36. The \(\Lambda_{2}\) variation also induced the changes of resonance wavelength and loss peak. It was obvious that, with the increase of \(\Lambda_{2}\), the loss peak shifted towards the shorter wavelength direction, and signal peak increased. The cause of this phenomenon was that, as \(\Lambda_{2}\) is increased, light in the core region penetrated more into the cladding, and the evanescent field increased, so the CL increased. Figure 4d displays loss spectra for different \(d_{3}\) with \(d_{1}\) = 2.8 \(\upmu\)m, \(d_{2}\) = 7.0 \(\upmu\)m, \(\Lambda_{1}\) = 6, \(\Lambda_{2}\) = 6.2 \(\upmu\)m, \(T_{Au}\) = 40 nm, and \(n_{a}\) = 1.36. When \(d_{3}\) was 2.8 \(\upmu\)m, the surrounding medium of the \(d_{3}\) hole had a binding effect on the light, and the light travelling in the PCF core dissipated to a certain extent.