Acoustic metamaterials coupled with topological waveguide array for robust sound energy transmission across the water–air interface

• We propose a composite structure consisting of Floquet topological waveguide array and acoustic metamaterials. • The operating frequency of metamaterial is located at the frequency band of π-mode topological edge state. • The membrane satisfying soft boundary condition is introduced to improve the robustness against interface fluctuations. • Correction coefficient in metamaterial during the process of impedance matching is modified. Efficient and robust transmission of sound energy across the water–air interface remains challenging due to severe impedance mismatch and environmental perturbations. Here, we propose and experimentally demonstrate a composite structure by coupling impedance matching acoustic metamaterials with Floquet topological waveguide array for sound transmission through different media. The metamaterials, whose operating frequency is located at frequency band of topological edge state, are employed to compensate the impedance mismatch. By engineering the driving pulse protocol of waveguide array, π-mode edge state is selectively excited while bulk states degenerate, enabling robust energy transmission under topological protection. A thin membrane is introduced to improve the robustness against the interface fluctuations when the water-immersion depth is less than 60 mm. The discrepancy between analytical and simulation results is reduced according to the approximation of aperture radiation impedance and the correction coefficient in metamaterials. This work provides a paradigm for combining topological physics with acoustic metamaterials, and offers new opportunities for robust cross-medium communication, sensing and energy transmission.