## 2 Acoustic Metasurfaces
### Phase-Modulating Metasurfaces  
Phase-modulating metasurfaces control the phase delay of transmitted or reflected waves by tuning the geometry, depth, or material properties of unit cells. This enables the manipulation of acoustic wavefronts, beam steering, and focusing. Gradient Index Metasurfaces (GIMs) are a representative example, providing spatially varying phase profiles for advanced wavefront control. Such structures are used in ultrasonic imaging. [PERSON] et al. developed a membrane-based acoustic metamaterial that can be actively adjusted through external voltage application [53]. Their experimental configuration was made of a rubber membrane for vibration, a central disk with gold-coated gold acting as both a mass load and an electrode, a gold-coated rigid ring for electric field generation and sound transmission, and a solid ring for fixing. Experiments show that when a DC voltage is applied, the resonance frequency can be modulated and the phase can be tuned, and it acts as a phase modulator in a phase array that can manage the sound wave at will. When the AC voltage is applied, it acts as an extra vibration source and amplifies or attenuates the vibration through phase control to achieve a noise reduction performance of up to 52 dB, experimentally demonstrating that the sound switch function can be realized. [PERSON] et al. presented a multifunctional smart window based on the dielectric elastomer actuator (DEA), which can electrically tune the acoustic absorption performance [40]. The structure consists of a microperforated dielectric elastomer actuator (MPDEA) fabricated using an acrylic-based dielectric elastic body (3M VHB 4910) with an inner diameter of 20.5 mm and an outer diameter of 28 mm, and a rigid glass backplate with a depth of 40 mm. In addition to serving as a light-scattering layer, the MPDEA incorporates a Helmholtz-like configuration that enables an acoustic control mechanism focused on phase modulation. The applied voltage alters the perforation radius and membrane tension, dynamically tuning not only the resonant frequency but also the phase response, and both single- and double-layer configurations exhibit electrical tunability. The double-layer device achieves a 15% reduction in perforation size and absorbs sound in the 846-1290 Hz range with absorption coefficients above 0.8. The system demonstrates an active electrostatic control mechanism along with a high level of post-fabrication tunability through voltage modulation. [PERSON] et al. proposed an acoustic gradient-index (GRIN) metasurface based on soft graded-porous silicone rubber [41]. The structure enables broadband three-dimensional wavefront shaping in underwater ultrasound environments, with spatial porosity control allowing acoustic refractive indices ranging from 1.4 to 7.5. Composed of a graded porous film supported by a rigid frame, the metasurface induces frequency-dependent phase delays by microscale reconfiguration of its internal pore structure in response to external mechanical inputs, enabling precise control over acoustic scattering even in ultrathin formats. As illustrated in Figure 5, this structural design enables advanced functionalities such as three-dimensional acoustic focusing and vortex beam generation. This 2 mm-thick metasurface demonstrated 5\({}^{\circ}\) beam steering, acoustic focusing with a 50 mm focal length (NA = 0.82), and vortex beam generation with a topological charge of +1 using a single transducer. These functions were experimentally verified in free space without the need for phased arrays. The authors further highlighted the feasibility of scaling up the design using conventional polymer processing and precision patterning techniques, referencing existing acoustic lens fabrication strategies as a potential pathway [54]. [PERSON] et al. proposed a spatial acoustic modulator (SSM), an electrically reconfigurable phase-adjustable acoustic metasurface, to actively control the acoustic field in the echo environment [42].