Shallow-water waveguide with hybrid boundaries for underwater acoustic metamaterial measurements

Experimental studies of low-frequency underwater acoustic metamaterials are constrained by the need for large-scale three-dimensional anechoic environments. The lack of rigid boundaries in water further impedes the construction of planar waveguides, limiting experimental progress in characterizing such structures. Here, we propose a shallow-water waveguide with hybrid boundaries, combining the natural soft water-air interface with an absorbing bottom layer. A theoretical model based on the Helmholtz equation is developed to analyze wave propagation under three types of boundary conditions: rigid-rigid, soft-soft, and soft-absorbing. Analytical results reveal that the soft-absorbing configuration exhibits mixed propagation characteristics of the other two, which also makes it suitable for quasi-two-dimensional measurements. Numerical simulations are carried out to characterize the resulting sound field, and water-tank experiments confirm the formation of expected propagation modes using a single cylindrical source. Finally, underwater measurements of both periodic cylindrical arrays for acoustic scattering and the designed two-bit coding metasurface for axial focusing show good agreement with theoretical predictions and simulations, validating the effectiveness of the testing platform. This proposed shallow-water waveguide with hybrid boundaries provides a compact and practical solution for underwater acoustic measurements, particularly in the low-frequency regime.