# Ultrathin Acoustic Metasurface Holograms with Arbitrary Phase Control
## 2 Results and Discussion
Thickness of the inner cavity \(w\) is a dependent variable which satisfies \(w=t-2h\)) determined  
Figure 2: Calculated acoustic field distributions in the single-focal scenario. (**a**) Desired acoustic field pattern for the hologram. The black square is the image plane, and acoustic fields are expected to concentrate on the orange spot. (**b**) Calculated amplitude distribution of the acoustic field on the hologram plane. (**c**) Calculated phase distribution of the acoustic field on the hologram plane. (**d**) Calculated amplitude distribution of the acoustic field on the image plane. The distance between the two planes is 20 mm. its viscous property and the corresponding metasurface. The reflected amplitudes, as well as phase shifts of each unit cell with and without considering thermoviscous effects, were, therefore, carefully simulated, as demonstrated in Figure 3d. We found that both the amplitude and phase shift variation were negligible. Simulation results indicated that the inaccuracy caused by the thermoviscous effect is small enough to be ignored. Concerning the aforementioned continuous phase distribution on the hologram plane, together with 8 different reflection phases brought by 8 types of unit cell, we calculated a discrete reflection phase distribution, as illustrated in Figure 4a. Although uniform amplitudes and discrete approximations of the phases were used in the calculation, a fine focal effect was achieved. The image reconstruction of the proposed acoustic metasurface hologram was further simulated. By observing the reflected sound pressure field, the amplitude distribution on the image plane was acquired, as illustrated in Figure 4b. Most of the acoustic energy focused on the center of the image plane, rendering a spot pattern. It indicates that the simulation result is in good agreement with the numeric calculation result, and our metasurface hologram is feasible. In addition, the amplitude distribution considering thermoviscous effects was simulated, as illustrated in Figure 4c, demonstrating a very limited difference compared to the ideal one. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Phase [deg]** & **a [mm]** & **b [mm]** & **h [mm]** & **w [mm]** \\ \hline
1 & \(-\)135 & 2.2 & 9.5 & 0.50 & 1.5 \\
2 & \(-\)90 & 2.7 & 9.5 & 0.25 & 2.0 \\
3 & \(-\)45 & 3.0 & 9.0 & 0.35 & 1.8 \\
4 & 0 & 0.4 & 8.5 & 0.50 & 1.5 \\
5 & 45 & 1.6 & 9.5 & 0.50 & 1.5 \\
6 & 90 & 1.8 & 9.0 & 0.35 & 1.8 \\
7 & 135 & 1.8 & 8.5 & 0.30 & 1.9 \\
8 & 180 & 2.2 & 9.5 & 0.35 & 1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometry parameters of unit cells in a period (f = 7.0 kHz). To demonstrate the flexibility of the acoustic metasurface hologram, we also introduced multi-focal holography based on the same methods that single-focal holography uses. Similar to the previous case, we first determined the original imaging patterns, which were 2 to 6 circular spots, respectively. Figure 4: Acoustic field distributions in the single-focal scenario. (**a**) Calculated discrete phase distribution of the acoustic field on the hologram plane. (**b**) Simulated amplitude distribution of the reflected acoustic field on the hologram plane without considering thermoviscous effects. (**c**) Simulated amplitude distribution of the reflected acoustic field on the hologram plane considering thermoviscous effects. The simulation settings were kept consistent with the calculated ones. Figure 3: Unit cell of the hologram and the thermoviscous analysis. (**a**) Perspective view of an acoustic metasurface hologram. The designed hologram consisted of 400 unit cells. (**b**) A typical unit cell of the metasurface. The side length and the thickness of each unit cell were determined (d = 10 mm, t = 2.5 mm) while other three parameters (i.e., a, b, and h) were variable. (**c**) The reflected amplitudes and phases of unit cells under the frequency range between 6.5 kHz and 7.5 kHz. The scattering phase can be modulated by altering the geometry characteristics of the cavity.