# Ultrathin Acoustic Metasurface Holograms with Arbitrary Phase Control
## 1 Introduction  
Acoustic imaging and acoustic focusing have many essential uses in modern science and industry, such as diagnosing disease [1], sensing natural gas seepage [2], visualizing earthquake sources [3], and microfluidic particle separation [4]. Generally, structures such as the concave mirror, convex mirror, and wedge are used to realize focal and imaging effects. However, these structures are bulky and have limited imaging effects. Holography, a revolutionary technique which can realize three-dimensional optical imaging, has gained increasing attention over the last few decades. The traditional optical hologram first records the interference patterns of the scattered light and a coherent reference beam [5; 6; 7; 8], and then, with the recorded phase and amplitude information, it reconstructs the light field to achieve optical imaging. In recent studies, the hologram can also be generated by calculating the phase distribution of the field on the hologram and transforming the phase information into unit structures, a method also known as computer-generated holography (CGH) [9; 10; 11].  
Consisting of only a single layer or a few layers of planar metallic structures, planar metamaterials with subwavelength, or metasurface [12; 13; 14; 15; 16; 17; 18; 19], show a rapidly growing interest in this field of research. By making use of the metasurface, the wave front, polarization, phase, and amplitude of the electromagnetic wave can all be manipulated. Unlike conventional optical devices, the metasurfaceis thin, compact, and capable of controlling phases. Owing to these advantages, the metasurface is opening the path to various applications, such as ultrathin flat lenses [20; 21; 22], carpet cloaks [23; 24; 25], and polarization conversion [26]. It has also made compact, efficient, and versatile optical holograms come true [27; 28; 29].  
The holography technique is receiving remarkable success in optical applications, and several acoustic holography imaging regimes are raised due to its promising characteristics [30; 31]. Yet, acoustic hologram applications are far less developed compared with optical ones since conventional means of the acoustic hologram requires cumbersome phase-shifting elements which are difficult to fabricate.  
Metasurfaces are also applicable in the acoustic field for the manipulation of sound wave propagation. A variety of acoustic metasurfaces have been designed to enable complex and unprecedented functionalities, such as the acoustic cloak [32], beam focusing [33], super absorbers [34], and so on. As one of the bases of the acoustic metasurfaces, Helmholtz-like elements can freely tailor the wave fields by controlling the resonance of the entire structure, such that the phase is fully manipulated [33; 35; 36]. With the ease of fabrication and facility to control the acoustic wave, such structures have been widely used to showcase multiple features. In analog with the optical metasurface hologram, the acoustic hologram based on the metasurface is accomplished by recording and manipulating acoustic field information.  
In this paper, we introduce a reflection type acoustic hologram utilizing ultrathin Helmholtz-like structures. Unlike previous acoustic metasurfaces which work only at a single frequency, the structures of the unit cells are adjusted carefully for the desired manner, which can achieve an arbitrary phase control in a certain frequency range. The phase deviations of these unit cells brought by thermoviscous effects are sufficiently investigated. A single-focal effect is achieved while the multi-focal scenarios are further promoted, showing its ability for arbitrary hologram imaging. Simulations are performed, and the results all possess good consistency with the theoretical prediction, validating the effectiveness in our design.