# Ultrathin Acoustic Metasurface Holograms with Arbitrary Phase Control
## 2 Results and Discussion
(**d**) Amplitude and phase shift profiles at 7.0 kHz with and without considering thermoviscous effects. The radius of each spot was 5 mm, while other parameters and settings were identical with the previous case. The phase distributions were calculated afterward. Utilizing the 8 types of the unit cell designed before, we discrete the phase information into 8 levels as well. The phase distributions when 2 to 6 spots were focused on the image plane can be easily calculated using the Rayleigh-Sommerfeld integrals. Referring to these discrete phases, along with the uniform amplitude generated from the unit cells, focal images on the image plane can be calculated, as illustrated in Figure 5a-e.  
One can see from the calculation results that discrete phases and uniform amplitudes are capable of realizing good multi-focal effects. Therefore, we conducted simulations on the metasurface-based holograms to validate our theory. The simulation results are illustrated in Figure 5f-j. It indicates a good consistency with the calculated ones, showing a clear multi-focal imaging effect. To further show its ability of holographic effect in a certain frequency range, simulations were also performed at different frequency range with the structures of the metasurface kept unchanged. To give an example, here we present a 3-spot focal pattern at the frequency of 6.9, 6.95, 7.05, and 7.1 kHz, respectively, to verify its performance. The results are shown in Figure 6. As aforementioned, the adjacent unit cells have an almost same phase difference in this frequency range, that is to say, the whole metasurface will introduce a global phase deviation in every unit cell, which will not influence the imaging effect at all. However, since the sizes of the whole structure compared with the working wavelength were changed, it shows little divergence in contrast with the original one, as shown in Figure 5g. Nevertheless, the results illustrate equivalent fine imaging performances, validating its capability as a hologram in a certain frequency range. It should be noted that these unit structures in the metasurface which constitute the holograms have the ability to arbitrarily control the reflection phases. Hence, they are equipped with the potential to render any holographic image at will. In addition, the unit structures are easy to fabricate. With the aid of 3D printing technique, it is convenient to get the entire sample of the metasurface hologram. We may also stitch the separate unit cells together, just like building blocks, to obtain a whole hologram. Due to the advantages mentioned above, the proposed acoustic metasurface holograms may open the gate for various applications in real life. Figure 5: Amplitude distributions in multi-focal scenarios. (**a–e**) Calculated amplitude distributions of the acoustic field on the image plane when 2 to 6 spots were projected as the focal pattern, respectively. These amplitude distributions were rebuilt by discretized phases and a constant amplitude on the metasurface hologram planes. (**f–j**) Simulated amplitude distributions of the scattered acoustic field on the image plane. The distance between the two planes was 20 mm.