Based on the concept of surface plasmon polaritons (SPPs), we confine the SPPs to metal or insulator interfaces through a metal-insulator-metal (MIM) waveguide. This approach breaks the classical diffraction limit and allows light to be manipulated at the nanoscale. The study of sensing characteristics by modifying the resonant cavity coupled to the straight waveguide has become a research hotspot. However, achieving optimal solutions for the transmission spectrum, sensitivity, number of peaks, and figure of merit (FOM) of the MIM waveguide coupled resonant cavities remains challenging. To meet the requirements of high sensitivity, high FOM, and multiple Fano resonance peaks for waveguide structures and optical refractive index sensors, the transmission characteristics of SPPs are deeply explored, and an innovative structural design is proposed based on this. This design features a single baffle MIM waveguide coupled with two different types of resonant cavities: an octagonal cavity above and a notched ring cavity below. The clever combination of this structure enables interference effects under near-field coupling, eliminates narrow discrete states formed by the metal baffle and wide continuous states formed by the octagonal and notched ring cavities, and results in three different modes of Fano resonance. This model not only effectively improves the sensor’s sensitivity but also significantly enhances the FOM through reasonable structural design. Different coupling paths and coupling strengths excite the three modes of Fano resonance, each exhibiting unique spectral characteristics.

The proposed MIM waveguide consists of a straight waveguide with a metal baffle, an upper octagonal resonant cavity, and a lower notched ring cavity. The coupling distance between the resonant cavities and the straight waveguide with the metal baffle g=10 nm. The width of the metal baffle in the straight waveguide d=20 nm. The widths of the octagonal resonant cavity, the notched ring resonant cavity, and the straight waveguide w=50 nm. The side length of the octagonal resonant cavity is defined as S, the radius of the notched ring resonant cavity as R, and the notch size of the notched ring cavity as θ. Based on the coupled mode theory, we analyze the generation mechanism of these three Fano resonances in detail. To verify the accuracy of our theoretical analysis, we conduct numerical simulations of the structure using the finite element method, which effectively handles complex geometric structures and boundary conditions. During the simulation, we perform detailed scanning and in-depth analysis of various key parameters, focusing on their impact on refractive index sensing characteristics and FOM. We perform detailed scanning and in-depth analysis of various key parameters, focusing on their impact on refractive index sensing characteristics and FOM.

The three Fano resonance peaks generated by this model are defined as FR 1, FR 2, and FR 3. Our results show that varying the radius of the ring cavity and the angle of the notched ring cavity directly affects the shifts of FR 1 and FR 3 at the peak wavelengths of the transmission spectrum [Figs. 4(a) and 5(a)]. These parameters also impact the FOM of FR 1 [Figs. 4(a) and 5(b)]. Changing the side length of the octagonal cavity affects the shift of FR 2 at the peak wavelength and the fluctuation of its FOM (Fig. 6). We conclude that the resonance peaks of FR 1 and FR 3 can be controlled by adjusting the radius and angle of the notched ring cavity, while FR 2 can be controlled by adjusting the side length of the octagonal cavity. This allows for flexible wavelength selection and adjustment to cope with varying external environments (e.g., air or liquids with different refractive indices). We provide the optimal FOM values corresponding to the structural parameters and determine the adjustment range. By optimizing the system’s structural parameters, we demonstrate the relationship between the refractive index change and wavelength and transmittance [Fig. 7(a)]. As the refractive index changes, the positions at the wavelengths the positions of FR 1, FR 2, and FR 3 shift. The peak transmittance of FR 1 is highly sensitive to the refractive index, while the peak transmissivity of FR 2 increases, and that of FR 3 decreases with increasing refractive index. The position changes of the peak wavelengths of FR 2 and FR 3 are also significant. Fig. 7(b) shows a linear relationship between the refractive index change and the resonance wavelength position. With further optimization of structural parameters and material selection, this model is expected to play a significant role in future practical applications, such as biosensing, chemical analysis, and environmental monitoring.

The results show that the three Fano resonance modes generated by the model exhibit extremely high sensitivity in refractive index sensing. Specifically, when the side length of the octagonal cavity S=268 nm, the radius of the notch ring cavity R=268 nm, and the angle of the notched ring cavity θ=220°, the sensitivities of these three modes are 650 nm/RIU (refractive index unit), 1000 nm/RIU, and 1250 nm/RIU, respectively. This indicates that the sensor can detect significant spectral shifts with small changes in the refractive index of the surrounding environment, which is crucial for high-precision sensors. The FOMs for these modes are 1.6047×10⁴, 3.8852×10⁴, and 1842.54, respectively, demonstrating excellent performance in sensing. Future research could explore integrating multiple similar structures to achieve more complex functions and improve sensor performance with new materials. Continuous optimization and innovation in this field are expected to yield significant breakthroughs, leading to more efficient and accurate optical sensing technologies.