# High-Aspect-Ratio Silicon Metasurfaces: Design, Fabrication, and Characterization. _Applied_
## 2 Design of the Transmissive Silicon Meta-Atom
We now illustrate how the structural effects, including the sidewall profile and thickness of the continuous substrate, affect the performance of our designed MHWP, numerically calculating the transmittance and transmission phase with a Finite Difference Time Domain (FDTD) simulation. In our simulations, the refractive index of silicon is set as \(\mathrm{n}_{\mathrm{Si}}=3.45\). The simulated results in Figure 2 illustrate the influence of the sidewall profile on the performance of the designed MHWP with three typical cases. Here, we only consider the sidewall profile in one direction, defined as the ratio between the bottom width (\(\mathrm{d}_{2}\)) and the top width (\(\mathrm{d}_{1}\)) of the micro-pillar, with all other parameters fixed as the designed ones (see the inset in Figure 2c). The designed meta-atom has a straight sidewall profile with \(\mathrm{d}_{2}/\mathrm{d}_{1}=1\), as shown in Figure 1a. Usually, the sidewall slope will decrease with the \(\mathrm{d}_{2}/\mathrm{d}_{1}\) due to the imperfect lateral control of the DRIE fabrication process. The simulationresults shown in Figure 2a illustrate that the PCR of the designed MHWP will significantly decline with the decrease in d\({}_{2}\)/d\({}_{1}\). Here, the simulated spectra of the PCR were obtained by calculating the power ratio between the LCP transmitted THz wave and the incident RCP THz wave based on the FDTD simulation. The simulated transmission amplitude spectra along the x and y direction shown in Figure 2c,d illustrate that the sidewall slope slightly influences the transmission of the meta-atom. Meanwhile, it did largely modify the phase difference between two crossed-polarized THz waves, as shown in Figure 2b. In particular, the phase difference changed from 180\({}^{\circ}\) to 90\({}^{\circ}\) and to 45\({}^{\circ}\) for these three cases, respectively. The underlying physics of this effect is related to the anisotropic design of the micro-pillar with rectangular shape. The sidewall profile reduces the effective refractive index of the silicon pillar at different vertical positions, making the meta-atom exhibit less anisotropic properties, which results in the decrease in the phase difference of the two cross-polarized transmitted THz wave. In addition, the pronounced dip in the spectra of the PCR origins from a Fabry-Perot resonance of the anti-reflection layer, which can be remedied by optimizing the geometrical parameter of the micro-resonators, or shifted away from the working bandwidth of our device by changing the periodicity of the structure, as shown in the Supplementary Materials. To illustrate the influence of the connecting layer thickness on the performance of the MHWP, we perform a similar FDTD simulation with three different thickness of the connecting silicon layer d\({}_{3}\) (see the inset to Figure 3c). Here, all the parameter of the tri-layered meta-atom are fixed, except the height of the micro-pillar determined by H = 400 \(-\) d\({}_{3}\). As can be seen in Figure 3a, d\({}_{3}\) can significantly affect the polarization conversion performance of the designed MHWP. The simulated results plotted in Figure 3b illustrate that the imperfect thickness control on d\({}_{3}\) slightly affects the phase difference between the two linearly cross-polarized THz waves, since the VTD almost did not influence the anisotropy property of the micro-pillar design with a straight sidewall. Meanwhile, the variation in the VTD of the meta-atom will lead to a frequency shift of the prefect transmittance for both the x- and y-polarized THz waves, as shown in Figure 3c,d, respectively. The underlying physics  
Figure 2: Simulated spectra of the polarization conversion ratio (**a**) and phase difference (**b**) between the x- and y-polarized transmissive THz wave, and the transmission amplitudes for the x-polarized (**c**) and y-polarized (**d**) transmissive THz light for the meta-atom with different sidewall slopes characterized by d\({}_{1}\) and d\({}_{2}\), the gray area in the figure covers the meta device working frequency.