## 3 Results and Discussion  
Detectors and sensors operating in the medium and long infrared bands are widely utilized in photoelectric detection systems [27; 28; 29]. Specifically, medium infrared detectors and sensors typically operate in the 3.7-4.8 \(\upmu\)m range [30; 31], while long infrared devices operate in the 8-12 \(\upmu\)m range [32; 33]. The geometric parameters of the circle hole structure were optimized under different metal thin film materials (Au, Ag, and Al), as shown in Figure 3. Upon analysis, it has been discovered that the transmission spectrum remains largely consistent between 3.7-4.8 \(\upmu\)m when the thickness of the metal film (\(h_{1}\)) is altered from 50 nm to 300 nm. Meanwhile, it is noted that, when the radius (\(r\)) of a circle hole changes from 1.3 \(\upmu\)m to 1.7 \(\upmu\)m, the transmission peak remains stationary, but the peak width increases. From the previous work [34], in a square array, if \(\varepsilon_{d}\) and \(\varepsilon_{m}\) have been determined, then the period \(P\) of the structure is one of the main factors controlling the position of the transmission peak when the incident light is perpendicular to the metal film. When \(P\) (4 \(\upmu\)m) remains constant, only the radius \(r\) can be altered and the transmission peak will remain unchanged. However, if \(P\) increases (meaning that the proportion of the circle hole structure in the same area decreases), the electric field localization on the metal surface becomes stronger. This results in an enhanced coupling of the charge density on the circle wall, causing the effective refractive index \(n_{\mathit{eff}}\) to increase. As a result, the transmission peak will experience a redshift. It is important to note that the intensity of the transmission peak decreases as a result of the duty cycle reduction. The change of structure has a nonnegligible effect on the infrared transmission characteristics [35; 36; 37]. In cases where the polarization effect of the incident light is weaker, other structures besides the circle hole structure may be present. The Figure 4 provides the transmission spectrum of four different structures (all with the same duty cycle) in the middle infrared band. Additionally, the electric field distribution of the corresponding structure at the wavelength with the maximum transmission peak intensity is included for a more in-depth analysis of the physical mechanism. It is clear that the full width at half maximum (FWHM) of the transmission peak is wider when the periodic structure is connected as a whole (circle and cross-shaped) than when it is not connected (cylinder and hollow cross-shaped) as shown in Figure 4a. Moreover, the connected periodic structure exhibits a broader response range in the infrared band. As a continuous conductor structure, the electromagnetic SE in the radar band is higher. Additionally, as depicted in Figure 4b-e, the charge distribution is more localized for cylinder and hollow cross-shapedstructures, resembling metal nanoparticles. As known in reference [38], metal nanoparticles in close proximity to one another are impacted by external light fields. The dipole radiation field of one nanoparticle can disrupt the dipole radiation field of the other, altering the force of free electrons and subsequently changing the resonance frequency and distribution of electron clouds. On the other hand, the interaction between metal nanoparticles is more significant in terms of frequency selection, resulting in a narrower FWHM of the transmission peak. Meanwhile, the cylindrical structure and the circular hole structure are complementary structures, and their light propagation paths are completely opposite. In a circular hole structure, the propagation path of light is within the circular hole, and the charge distribution is more compact compared to the entire periodic structure. However, the light propagation path of the cylindrical structure is between adjacent cylinders.