Acoustic analog computing system based on labyrinthine metasurfaces

Acoustic computing devices, including switches, logic gates, differentiator and integrator, have attracted extensive attentions in both academic research and engineering. However, no scheme of acoustic computing device with more complex functionality has been proposed, such as ordinary differential equation (ODE) solver. Here, we propose an acoustic analog computing (AAC) system based on three cascaded metasurfaces to solve the nth-order ODEs. The metasurfaces are constructed with layered labyrinthine units featuring broad amplitude and phase modulation ranges. The simulated transmitted pressure of the AAC system agrees well with the theoretical solution of ODE, demonstrating the excellent functionality. Unlike the optical ODE solver based on differentiator or integrator, whose geometry becomes more complicated for solving higher order ODE, the proposed AAC system with fixed geometry can be designed for arbitrary nth-order ODE in principle. The proposal may find applications in various scenarios such as acoustic communication, analog computing and signal processing.