## 2 Acoustic Metasurfaces
### Resonance-Based Metasurfaces
For simulations involving oblique incidence, such as focusing or wave bending, perfectly matched layers (PMLs) and background pressure fields were added to suppress boundary reflections. Structural deformation was analyzed using geometrically nonlinear static analysis, while acoustic responses were computed using linear acoustic-structure coupling in the frequency domain. [PERSON] et al. proposed a membrane-based acoustic metasurface with a central mass, in which the resonant frequency can be tuned by adjusting membrane tension through an external magnetic field [38]. A nanocomposite membrane made of poly (vinyl alcohol)/graphene (PVA/GR) and an aluminum central mass was used within a plastic frame to support the structure. This configuration enables strong low-frequency absorption and qualifies the system as active, based on the use of static magnetic control. In addition, the nanocomposite membrane shifts its resonant frequency in response to temperature changes  
Figure 3: Magnetically tunable mass-weighted membrane structure that shows controllable acoustic trans-mission loss and phase response under different magnetic forces. (**a**) Image of the mass-weighted membrane. (**b**) Diagram of the measurement setup. (**c,d**) Acoustic transmission loss and phase measurement results under different magnetic forces.. Reproduced under a Creative Commons Attribution International 4.0 license [37], scientific reports, 2017.  
induced by DC voltage, thereby effectively attenuating sound. The ability to modulate the magnetic field after fabrication also provides tunability in the resonant response. [PERSON] et al. proposed an ultrathin acoustic metasurface (thickness \(\approx\) 10-300 \(\upmu\)m, up to \(\lambda/650\)) based on a spring-mass resonator model, composed of a flexible fiber/bead network formed by electrospinning soft polymer fibers and rigid copper beads [39]. As shown in Figure 4, the metasurface features a porous network structure that enables subwavelength thickness and tunable phase modulation. This design addresses the structural complexity, rigidity, and high loss of conventional acoustic metamaterials. The system demonstrates active responsiveness, as the resonance behavior can be tuned by applying an external magnetic field. It also provides post-fabrication tunability by adjusting the magnetic field strength to shift the resonant frequency. The metasurface achieves a near-\(\pi\) phase shift and maintains acoustic transmittance above 80%, enabling effective wavefront control. Through hollow-out patterning using a paper-cutting technique, diverse phase control functions such as acoustic vortex generation, sound focusing, and ultra-vibration manipulation are demonstrated within a single device, highlighting both its multifunctionality and large-area fabrication potential. Figure 4: Design and characterization of a soft fiber/rigid bead-based ultrathin acoustic metasurface. (**a**) Spring-mass resonator model schematic. (**b**) Polymer fiber/rigid bead spring-mass resonator analog. (c) Flexible soft fiber/rigid bead network enabling near-\(\pi\) phase shift. (**d**) Large-area metasurface sample photograph. (**e–g**) SEM images and experimental results showing the relationship among metasurface thickness, phase shift, and transmittance across various frequencies and material configurations. (**h,i**) Phase shift and transmittance measurement of metasurface with fixed copper beads/PVA ratio and thickness. Reproduced with permission from [39], Advanced Functional Materials, 2018.