# Combined Mie Resonance Metasurface for Wideband Terahertz Absorber
## 2 Structure Design and Simulation  
The schematic diagram of our combined Mie resonance metasurface is shown in Figure 1a, and the enlarged view of one unit cell (circled by a yellow box) is shown in Figure 1b. The dielectric blocks were arranged periodically on the aluminum reflective layer. Here, nine dielectric blocks were incorporated into one unit cell. The virtual yellow dashed line in Figure 1b (this is for illustration only and was not in the structure) divides the unit cell into nine spaces--similar to the Sudoku. The nine blocks were located at the center of each of these spaces. The side lengths of the square blocks in the \(x\)-\(y\) plane (a\({}_{1}\sim\) a\({}_{9}\)) were from 31 um to 35 um, with a step of 0.5 um. The periods in both \(x\) and \(y\) directions were maintained to be \(p_{x}=p_{y}=120\) um. The thickness of the blocks were all \(t=30\) um, and the thickness of the metallic layer for reflection was 0.5 um. As metal is a perfect electrical conductor in the terahertz band as their properties are similar, we could have used any kind of metal. At the same time, the material of the structure is not limited to titanium dioxide, and other dielectric with high refractive index, such as silicon or barium strontium titanate (BST), are also feasible. We chose TiO\({}_{2}\) in this paper to get larger frequency interval between the fundamental mode and the higher-order mode so that it would be convenient for our analysis. In manufacturing, the substrate under the metal reflective layer can be a quartz substrate or a silicon wafer; this only plays a role as support because there will be no transmission through the metal layer. The dielectric blocks that act as resonators were constructed from titanium oxide (TiO\({}_{2}\)) with a relatively large permittivity of 114 and a loss tangent of 0.01 at terahertz frequencies [27]. The spectra of the absorbers were numerically calculated using the commercial simulation software CST Microwave Studio (CST Studio Suite 2014, CST Company, Darmstadt, Germany) with the finite-element frequency-domain solver. The calculation procedure was similar to what other people in our research group had previously done in their papers [28; 29]. Periodic boundary conditions were used in both \(x\)- and \(y\)- directions, while open boundary condition was used in \(\pm z\) direction. Both normal-incident TE\({}_{00}\) (the electric fields of the light polarized along the \(y\)-axis) and TM\({}_{00}\) (the electric fields of the light polarized along the \(x\)-axis) modes were defined at the receiving ports to ensure that any polarization conversion was accounted for. At least four mesh steps per wavelength were used to ensure the accuracy of the calculated results. The absorption was obtained by subtracting the transmission and reflection from 1. As for the transmission and reflection, they could be directly obtained in the S-parameters, which were calculated by the software. We assumed the plane wave, with a wave vector of \(k\), propagated along the opposite direction of the \(z\)-axis. The magnetic and electric fields of the light were polarized along the \(x\) and \(y\) axes, respectively. Figure 2 shows the absorption (black curve), transmission (red curve), and reflection (blue curve) spectra of our combined Mie resonance metasurface. The transmission could be negligible to zero because of the metal layer. The reflection and absorption added up to 1. The absorption was stable at a high level with a few fluctuations within a certain frequency range, while the spectra of traditional dielectric resonators usually had the Gaussian shape, as shown in Figure 3. Three absorption peaks and two absorption valleys were labeled as \"P1\", \"P2\", \"P3\", \"V1\", and \"V2\", respectively, and are pointed with green arrows in Figure 2.  
Figure 2: Simulated absorption/transmission/reflection spectra of our proposed wideband Mie resonance-based metasurface absorber.