# Broadband Plasmonic Metamaterial Optical Absorber for the Visible to Near-Infrared Region
## 2 Geometric Structure of the Absorber Unit Cell  
The proposed MA structure consists of silicon dioxide (SiO\({}_{2}\)) and tungsten (Tu). SiO\({}_{2}\) is used for the dielectric substrate layer and the antireflection coating, while Tu has been employed for the resonators and the ground layer. SiO\({}_{2}\) coats the Tu resonator layers to stop incident wave reflection and layer oxidation. Figure 1 illustrates the MA unit cell's physical structure. Despite having significant intrinsic losses, Tu was chosen for optical wavelength applications because of the excellent impedance matching with open space. Because weak transmission and reflection quality leads to increased absorption behavior [26]. SiO\({}_{2}\) was chosen as a dielectric substrate material because it is lossless in the optical wavelengths. These characteristics of SiO\({}_{2}\) lead to a broader absorption bandwidth and good impedance matching [26]. The nanoarchitecture design and the proposed MA characterizations were done using Computer Simulation Technology (CST). As the MA stricter is with curvature, tetrahedral mesh was used in simulation for extracting result more accurately. The estimated free space propagation impedance of the substrate's dielectric characteristics is 377 \(\Omega\). The minimum and maximum edge lengths in this tetrahedral mesh analysis--which has a quality between 0.176825 and 0.999151--are 5.250000 nm and 141.421476 nm, respectively. The simulation was run with a mesh with a total of 12,424 tetrahedrons and an average quality of 0.781090 in order to produce the most accurate results. The unit cell boundary condition has been applied to the x- and y-axes, and the open add space condition has been applied to the z-axis. By using Equation (1), the absorption property \(A(\omega)\) was calculated. Where the reflection coefficient is \(S_{11}\), and the transmission coefficient is \(S_{21}\). \[A(\omega)=1-|S_{11}(\omega)|^{2}-|S_{21}(\omega)|^{2}=1-R-T \tag{1}\]  
Here \(S_{21}\) is zero as the thick Tu back layer blocks the transmission of the electromagnetic wave, which can be explained by skin depth calculation from Equation (2). So, Equation (1) can be written as Equation (3). \[\text{skin depth }(\delta)=\sqrt{\frac{\rho\omega}{\pi\text{C}\mu}} \tag{2}\]  
\[A(\omega)=1-|S_{11}(\omega)|^{2}=1-R \tag{3}\]  
In Equation (2), the resistivity (\(\rho\)) of Tu is 5.60 \(\times\) 10\({}^{-8}\) (\(\Omega\)m\({}^{-1}\)), \(\omega\) = 2600 nm is the maximum wavelength, and permeability \(\mu\) is 1. According to Equation (2), the skin depth for this MA is 0.0125 nm, which prevents waves with a wavelength of less than 2400 nm from transmitting. The unit cell design parameters are listed in Table 1. Figure 2 shows the absorption properties of the unit cell as the design gradually evaluates toward the final structure of the MA. The MA offers very weak absorption when the unit cell only has the dielectric substrate layer of SiO\({}_{2}\) and the ground. As there is no resonating element in the unit cell at this stage, all incident waves are reflected from the ground layer. After introducing the first Tu resonating layer, the MA shows a peak of 95% absorption at 400 nm wavelength. However, it is weak for the remaining wavelengths. That is mainly because the incident light is reflected from the metal resonator layer. Then a coating of SiO\({}_{2}\) was introduced to prevent the incident light from reflecting. With this coating, the MA shows a 96% average absorption in the visible spectrum from 400 nm to 700 nm. But there is still a very weak absorption in the near-infrared region. A second Tu resonator layer has been added above the SiO\({}_{2}\) coating to improve absorption in the near-infrared spectrum. Figure 1: The design of the internal structure and ingredients of the layers of the unit cell. That second Tu layer effectively increased average absorption in the near-infrared spectrum but failed to achieve adequate absorption in the visible spectrum.