Monolithic Elastic Metasurface Design for Advanced Wave Manipulation via a Direct Wave-Shaping Topology Optimization Approach

Abstract: Elastic metasurfaces offer precise control over elastic waves for applications such as vibration isolation, sensing, and imaging. However, achieving high-efficiency and scattering-free performance with complex functionalities remains a fundamental challenge. While conventional Generalized Snell's Law (GSL) designs suffer from inherent inefficiencies and parasitic scattering, recent alternatives--including impedance-matching methods and diffraction-grating-based metagratings--have sought to overcome these drawbacks. While efficiency improvement has been demonstrated, both methods are limited in generating complex wavefields such as focusing. Here, we propose a direct wave-shaping (DWS) topology optimization framework that bypasses these intermediate concepts and automates the design of high-performance, monolithic elastic metasurfaces. To mitigate the high computational expense, we parameterize the geometry with movable, deformable and interactable elliptical voids, thereby drastically reducing the design variables while enabling holistic optimization that inherently accounts for nonlocal inter-cell couplings. We demonstrate the framework by designing metasurfaces for challenging tasks including high-efficiency longitudinal-to-transverse wave conversion with large-angle beam steering, wavelength-multiplexed beam steering, and both reflective and transmissive metalenses with numerical apertures exceeding 0.99. Compared to state-of-the-art gradient-index, impedance-based, and hybrid designs, our metasurfaces consistently exhibit superior efficiency, significantly reduced spurious scattering, and enhanced focusing capability, with the most demanding transmissive metalens validated experimentally. This work establishes a scalable and computationally efficient pathway to realizing practical, high-performance elastic metasurfaces for advanced wave manipulation.