## 3 Simulations and Results  
When comparing the performance of the double-ring cavity and the CCDRR, it was found that their sensitivity was almost the same in the range of the agreed refractive index change, but that the CCDRR had a higher FOM, so the CCDRR was chosen for further study. To gain a distinct understanding of the propagation characteristics of the proposed structure, it was necessary to compare the whole system with the single CCDRR structure and the unitary two rectangular baffle structure. The unitary two rectangular baffle structure and the unitary CCDRR structure are shown in Figure 2a,b, respectively. The transmission spectra of the three structures are shown in Figure 2c. The geometric parameter settings are as follows: \(R_{1}=190\) nm, \(R_{2}=130\) nm, \(H=540\) nm, \(h=150\) nm, and \(g=10\) nm. The transmission spectra of the unitary two rectangular baffle structure, the unitary CCDRR structure, and the whole system are represented by the black, red, and blue solid lines, respectively. In Figure 2c, the black solid line representing the unitary two rectangular baffle structure has a positive slope, and it has relatively high transmittance in the range of 0.35 to 0.6. Hence, it can be regarded as a continuous wide-band mode. The transmission spectrum of the unitary CCDRR structure approximates the Lorentz line, which is considered as representing the discrete narrowband mode. It is obvious that the transmission spectrum of the whole structure (blue line) has an asymmetric shape, which indicates that Fano resonance is generated by the interaction of the successive wide-band mode and discrete narrow-band mode. To better comprehend the inner theory of the black line's role in the Fano resonance of the whole structure, the magnetic field distributions and the electric field distributions of the unitary two rectangular baffles and the whole system at the resonance dip point (\(\lambda=1459\) nm) were demonstrated, which are shown in Figure 3a-d, respectively. In Figure 3a, there is a distinct resonance in the MIM waveguide, with only one bus waveg  
Figure 2: (**a**) Two-dimensional schematic diagram of the unitary two rectangular baffle structure; (**b**) 2D schematic diagram of the unitary CCDRR structure; and (**c**) the transmission spectrum of the unitary two rectangular baffle structure (black line), the unitary CCDRR structure (red line), and the whole system (blue line). uide and two rectangular baffles. As shown in Figure 3b, for the whole structure, the firm resonance occurs only on the left side, while infirm resonance occurs on the right. Additionally, the upper and lower parts of the outer ring in the CCDRR are anti-phase. Figure 3b,c provides insight into the actual energy distribution in the waveguides and the CCDRR cavity. In Figure 3c, there is an obvious energy distribution in the MIM waveguide. However, as shown in Figure 3d, the energy of SPPs is intensified at the CCDRR cavity and decreased at the right side of the waveguide. It was found that SPPs was directly coupled to the unitary two rectangular baffle structure and stimulated the resonance corresponding to the successive wide-band state, while the discrete narrow-band state in the CCDRR was indirectly stimulated by the SPPs in the two symmetrical rectangular baffles. Thus, the interaction of the two states produced the Fano resonance. For further investigation of the influences of the different refractive indexes (\(n\)) on the transmission spectrum of the Fano resonance, six refractive indexes were simulated: 1.00, 1.01, 1.02, 1.03, 1.04, and 1.05 RIU. The structural arguments were as follows: \(R_{1}=240\) nm, \(R_{2}=130\) nm, \(H=540\) nm, \(h=150\) nm, and \(g=10\) nm. Figure 4a,b shows the simulation results. In Figure 4a, with the increase of \(n\), the transmission spectra have an approximately equidistant red-shift. As shown in Figure 4b, when the refractive index changes, the change of dip wavelength-shift is linear.