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Abstract The valley degree of freedom in crystals offers great potential for manipulating classical waves, however, few studies have investigated valley states with complex wavenumbers, valley states in graded systems, or dispersion tuning for valley states. Here, we present tunable valley phononic crystals (PCs) composed of hybrid channel-cavity cells with three tunable parameters. Our PCs support valley states and Dirac cones with complex wavenumbers. They can be configured to form chirped valley PCs in which edge modes are slowed to zero group velocity states, where the energy at different frequencies accumulates at different designated locations. They enable multiple functionalities, including tuning of dispersion relations for valley states, robust routing of surface acoustic waves, and spatial modulation of group velocities. This work may spark future investigations of topological states with complex wavenumbers in other classical systems, further study of topological states in graded materials, and the development of acoustic devices. 

Abstract Metasurfaces open up unprecedented potential for wave engineering using subwavelength sheets. However, a severe limitation of current acoustic metasurfaces is their poor reconfigurability to achieve distinct functions on demand. Here a programmable acoustic metasurface that contains an array of tunable subwavelength unit cells to break the limitation and realize versatile two‐dimensional wave manipulation functions is reported. Each unit cell of the metasurface is composed of a straight channel and five shunted Helmholtz resonators, whose effective mass can be tuned by a robust fluidic system. The phase and amplitude of acoustic waves transmitting through each unit cell can be modulated dynamically and continuously. Based on such mechanism, the metasurface is able to achieve versatile wave manipulation functions, by engineering the phase and amplitude of transmission waves in the subwavelength scale. Through acoustic field scanning experiments, multiple wave manipulation functions, including steering acoustic waves, engineering acoustic beams, and switching on/off acoustic energy flow by using one design of metasurface are visually demonstrated. This work extends the metasurface research and holds great potential for a wide range of applications including acoustic imaging, communication, levitation, and tweezers.