Double-wavelength perfect negative reflection of water waves

When water waves are reflected by a rigid boundary, classical Snell's law dictates that the incident and reflected waves should lie on opposite sides of the surface normal. However, phase gradient metasurfaces/metagratings (PGMs) can overcome this constraint by enabling higher-order diffraction, giving rise to negative reflection—a phenomenon in which both incident and reflected waves appear on the same side of the normal. While in the fields of electromagnetics and acoustics, PGMs are typically constructed by embedding materials with varying refractive indices to achieve phase modulation. However, the effective refractive index of water waves depends jointly on both water depth and wavelength, and the complex wavelength distribution in natural environments significantly limits the applicability of such designs for water waves. In this work, we propose a different reflective PGM for water waves, which realizes the phase change through path differences rather than effective refractive index. This design enables nearly perfect negative reflection at both a target wavelength λ0 and its half λ0/2. The incident water wave can be almost entirely coupled into the ±1 diffraction orders, effectively suppressing specular reflection. The experimental results show good agreement with theoretical predictions. This study offers a different approach for multi-wavelength water wave manipulation and exhibits broad application potential in wave cloaking, riverbank protection, and wave energy utilization.