As an optical device that can regulate light waves on the nanoscale, the optical micro-nanostructure has the characteristics of simple fabrication and easy integration. With the rapid development of modern optics, micro/nanostructures have been widely adopted in environmental monitoring, biosensing, medical sample detection, and other fields. Conventional attenuated total reflection sensing structures usually exhibit ohmic loss, whereas molybdenum disulfide (MoS₂) nanomaterials have good optical properties. Therefore, we considered two-dimensional materials instead of metallic materials to construct an all-medium multilayer membrane structure. However, the global optimization of the sensor structure cannot be realized using only parameter scanning. Therefore, a multilayer composite structure model based on the MoS₂ hybrid-coupled waveguide mode was proposed. The light transmission characteristics and generation mechanism of the double-waveguide mode were analyzed in combination with the reflection angle spectrum, and the physical mechanism of the Fano resonance and plasmonic induced transparency (PIT) formation was explained. Finally, within a certain parameter range, a deep extreme learning machine model was incorporated to establish the mathematical relationship between the structural parameters, figure-of-merit (FOM) value, and sensitivity. Multiple optimization algorithms were used to determine the extreme values of the DELM neural network model and obtain the best structural parameters.

To develop a multilayer composite structure model based on a MoS₂ hybrid coupled waveguide mode, a geometric model was established using the finite element analysis software, COMSOL Multiphysics. The prism layer comprises chalcogenide glass. The Teflon-PTFE and ZnS waveguide layers doped with polycarbonate (PC) are separated with MoS₂ layers. The ZnS layer supports the waveguide mode in which electromagnetic waves can propagate. To analyze the sensing performance of the sensor structure in detail, the optical transmission characteristics were explored under angle modulation. The formation mechanism of the Fano resonance was examined via analysis of the distribution of electromagnetic fields. The influences of the thickness of each medium layer and the number of MoS₂ layers on the spectral response of the Fano resonance were further explored to determine the structural parameters that have a greater influence on the spectrum. Finally, a mathematical relationship between the structural parameters and the FOM value was determined to establish the DELM model. Cuckoo Search (CS), Bat Algorithm (BA), Gray Wolf Algorithm (GWO), and Whale Optimization Algorithm (WOA) were selected to optimize the parameters of the DELM. An optimal GWO-DELM optimization model was obtained. The model was then used for multiple-iteration optimization, and the average value of the structural parameters was considered the optimal parameter, so the sensor performance could be significantly improved.

Comparing the spectral responses of the partial and whole structures (Fig. 2), the two discrete states coupled to form a Fano resonance, accompanied by energy migration. Subsequently, the influence of various structural parameters on the spectral response of the Fano resonance was explored. The variation trend of the FOM value was analyzed using the different spectral responses of each structural parameter, and the structural parameters that predominantly influence the spectral response of the Fano resonance were determined. A mathematical model was built between the structural parameters and the FOM value. The iterative optimization diagram of different models (Fig. 8) show that, the BA and CS clearly fall into the local optimal solution at the beginning, and the WOA converges quickly. However, the GWO is superior to other algorithms in terms of convergence speed and searchability. Comparing the errors of different optimization algorithms (Table 2 and Fig. 9), the values of the three error indices obtained by the GWO-DELM are all optimal; thus, the GWO-DELM model exhibits a better prediction performance. As a result, the GWO-DELM residual error is the most concentrated, and its optimization performance is the best. The sensing performance of the proposed structure was compared with those of other structures, and the results are listed in Table 3. Compared with other sensing structures, the FOM value in this study is significantly improved, and the sensor exhibits excellent sensing performance.

In this paper, we propose a multilayer composite structure of a MoS₂ mixed-coupled double waveguide, in which MoS₂ is intermixed between two layers of dielectric materials to achieve the coupling of two waveguide modes. The two waveguide modes generate wide and narrow resonances, respectively, owing to the different quality factors of MoS₂, and the coupling then generates the Fano resonance. The mechanism of the Fano resonance is described, and the influence of the structural parameters and the number of MoS₂ layer on the sensing characteristics is discussed. A high FOM was achieved under optimal conditions. Global optimization of structural parameters was conducted using the GWO-DELM optimization algorithm, and the optimization performances of different optimization algorithms for the DELM were compared. The FOM value was improved by one level to reach the highest level, reflecting the effectiveness of the global optimization algorithm in optical-sensor design and the significance for further optical-sensor research.