Design and optimization of a compact dual band metal insulator metal filter for high sensitivity refractive index sensing using particle swarm optimization

Abstract

This paper presents a highly optimized metal-insulator-metal (MIM) filter designed for لrefractive index sensing applications, with dual cut-off bands at 1008 nm and 1348 nm. The filter's dimensions are optimized using the Particle Swarm Optimization (PSO) algorithm, ensuring maximum sensitivity and miniaturization. The Finite-Difference Time-Domain (FDTD) method is employed for simulations, while the Drude-Debye model accurately captures the dispersive dielectric properties of the metallic layers. Also, the optimized sensor exhibits high sensitivity, with values of 7504 nm/RIU for the first cut-off band and 8000 nm/RIU for the second, demonstrating enhanced responsiveness in the longer-wavelength range. The figure of merit (FOM) values of 250.13 (1/RIU) and 250 (1/RIU) for the two cut-off bands, respectively, along with detection limits of 0.0039 RIU and 0.004 RIU, further highlight the sensor's precision and reliability in detecting small refractive index changes. Furthermore, this dual-band MIM filter is well-suited for real-time refractive index detection, providing a compact, efficient design with excellent filtering capabilities. The integration of the PSO algorithm ensures optimal performance across both wavelength bands, making the sensor a promising candidate for applications in biosensing, chemical detection, and environmental monitoring. The high sensitivity, combined with the dual-band functionality, enables versatile sensing applications with enhanced precision.

Keywords: Drude–Debye model; High sensitivity; MIM filter; Particle swarm optimization; Refractive index sensor.

Fig. 1

Schematic of the proposed MIM filter with stubs and holes.

Fig. 2

Simulation results of the transmission rate for different geometric parameters: (a) W₁, (b) L₁, (c) L₂/L₃, and (d) d. In (a), the parameters are L₁ = 160 nm, L₂/L₃ = 1.2, and d = 12.5 nm; in (b), W₁ = 60 nm, L₂/L₃ = 1.2, and d = 12.5 nm; in (c), W₁ = 60 nm, L₁ = 160 nm, and d = 12.5 nm; and in (d), L₁ = 160 nm, L₂/L₃ = 1.2, and W₁ = 60 nm.

Fig. 2

Simulation results of the transmission rate for different geometric parameters: (a) W₁, (b) L₁, (c) L₂/L₃, and (d) d. In (a), the parameters are L₁ = 160 nm, L₂/L₃ = 1.2, and d = 12.5 nm; in (b), W₁ = 60 nm, L₂/L₃ = 1.2, and d = 12.5 nm; in (c), W₁ = 60 nm, L₁ = 160 nm, and d = 12.5 nm; and in (d), L₁ = 160 nm, L₂/L₃ = 1.2, and W₁ = 60 nm.

Fig. 3

Simulation results of the transmission rate for different angles (θ) with W₁ = 60 nm, L₁ = 160 nm, L₂/L₃ = 1.2, and d = 12.5 nm.

Fig. 4

PSO algorithm workflow for the designed MIM filter.

Fig. 5

Comparison of transmission spectra for initial and optimized filter dimensions.

Fig. 6

Field profile of ∣Hz∣ for the designed filter at passband and cutoff wavelengths: (a) 750 nm, (b) 1008 nm, and (c) 1600 nm.

Fig. 7

(a) Full transmission spectrum from 600 nm to 1800 nm for different refractive indices, and magnified view of transmission spectrum around (b) 1008 nm, and (c) 1348 nm.

Fig. 7

(a) Full transmission spectrum from 600 nm to 1800 nm for different refractive indices, and magnified view of transmission spectrum around (b) 1008 nm, and (c) 1348 nm.