Inverse Design of Nonlocal Coiling-Up Space Acoustic Metasurfaces Based on Surface Coupling Approach

Acoustic metasurfaces have emerged as a promising platform for wavefront engineering, yet traditional designs relying on local phase gradients face limitations in control precision and flexibility under complex conditions. To address these limitations without computationally intensive full-wave simulations, this work proposes an inverse design framework for nonlocal coiling-up space acoustic metasurfaces based on the surface coupling approach (SCA). The SCA analytically captures the mutual impedance interactions between adjacent units, offering a theoretical model that accelerates the optimization process compared to purely numerical methods. By employing a nonlinear optimization algorithm, the structural parameters of the coiling-up units are iteratively adjusted to minimize the deviation between the SCA-predicted pressure field and a target Gaussian distribution. The proposed method is validated through the design of metasurfaces for both near-field and far-field focusing. Comparative results demonstrate that the nonlocal design significantly outperforms traditional local methods by effectively suppressing parasitic side lobes and enhancing energy utilization, achieving a peak sound pressure intensity 1.25 times higher in far-field applications. Furthermore, the optimized metasurfaces exhibit robust broadband performance, maintaining effective wave manipulation and stable focal positions across a wide frequency range. This work provides a framework for advanced acoustic metasurface design in noise control, imaging, and underwater detection.