## 3 Simulations and Results
Therefore, the sensitivity of the sensor, which was 2260 nm/RIU with a FOM of 56.5, could be obtained from the slope after linear fitting, leading us to obtain the best result for the optimal parameter of the structure. To investigate the influences of different external radii of the outer ring of the CCDRR on Fano resonance, \(R_{1}\) was set to increase from 200 nm to 240 nm at an interval of 10 nm, while keeping other arguments fixed at \(R_{2}=110\) nm, \(H=540\) nm, \(h=150\) nm, and \(g=10\) nm. The transmission spectra are displayed in Figure 5a. With the increase of \(R_{1}\), there is an obvious red shift at the dip point of Fano resonance, and the transmittance of this position increases slightly. The simulation result shows that \(R_{1}\) determines the dip wavelength of Fano resonance. This phenomenon can be explained in other words as a scenario where the dip wavelength depends on the CCDRR corresponding to the narrowband pattern, with \(R_{1}\) as an important parameter of the CCDRR. As shown in Figure 5b, by linear fitting, five solid lines representing the sensitivities of the different structures were obtained. As the external radius \(R_{1}\) of the outer ring increases, the sensitivity becomes higher. The maximum sensitivity was obtained via calculation, which was 2200 nm/RIU when \(R_{1}\) was  
Figure 3: Normalized H\({}_{\text{Z}}\) field distributions at \(\lambda=1459\) nm of: (**a**) the unitary two rectangular baffles; (**b**) the whole structure; electric field distributions at \(\lambda=1459\) nm of: (**c**) the unitary two rectangular baffles; (**d**) the whole structure. 240 nm, and the maximum FOM was 47.8. Thus, in practical applications, the radius \(R_{1}\) should be appropriately increased to obtain a better sensing performance. The effects of different external radii \(R_{2}\) of the inner ring of the CCDRR on the transmission capabilities were investigated as 90, 100, 110, 120, and 130 nm, while setting the parameter value \(R_{1}\) as 240 nm and keeping the other parameters the same. As shown in Figure 6a, the dip wavelength of Fano resonance was almost constant. When \(R_{2}\) increases, the dip point of Fano resonance has a slight red-shift and the transmittance of the dip marginally decreases, and there is a slight increase in sensitivity, which is described in Figure 6b. When \(R_{2}\) = 130 nm, the sensitivity of the structure attained the highest value: 2260 nm/RIU with a FOM of 56.5. Figure 4: (**a**) Transmission spectrum of the whole system for various refractive indexes; (**b**) variation of the dip point’s wavelength in Fano resonance (\(\Delta\lambda\)) with a changed refractive-index (\(\Delta n\)). Figure 5: (**a**) Transmission spectrum of the outer ring of CCDRR for different external radii \(R_{1}\); (**b**) shifts of the dip point in Fano resonance (\(\Delta\lambda\)) with a changed refractive-index (\(\Delta n\)). Afterward, the effect of the separation \(H\) of the two symmetric rectangular baffles on the propagation performance was studied. The transmission spectra that are displayed in Figure 7a were calculated at different separations for \(H\) = 540, 560, 580, 600, and 620 nm, while the other geometric parameters were kept the same. It was found that no matter how \(H\) changed, the dip wavelength of Fano resonance remained almost unchanged, though the FOM obviously decreased, as represented in Figure 7b. There was an optimal simulation result: the sensitivity was 2260 nm/RIU and FOM was 56.5. Then, the other geometric parameters were kept the same, except for increasing the height of the rectangular baffle \(h\) from 130 to 170 nm in steps of 10 nm. The transmission spectra and the change of FOM of the diverse heights of the rectangle baffles are shown in Figure 7c,d, respectively. As shown in Figure 7c, with the increase of \(h\), the dip wavelength only demonstrates a slight blue-shift, while the Fano line shape changes significantly. According to the calculation, when \(h\) = 150 nm, the maximum sensitivity is 2260 nm/RIU with a FOM of 56.5.