A method for calculating acoustic scattered field for planar metasurfaces

The propagation of sound in materials is closely related to their geometric and physical properties, and people have been trying to construct metamaterials to modulate sound. These metamaterials are typically constructed with specific geometric patterns to scatter acoustic waves; therefore, understanding sound propagation passing through these structures is essential. This article proposes a convenient method to analyze how the scattered field is distributed after the incident wave passes through a metasurface composed of multiple materials and meta units with arbitrary geometrical configurations. The key to realizing it is that each term of the Fourier expansion of the distribution of a specific property of the metasurface corresponding to a harmonic branch after the incident wave is coupled with localized vibration of the metasurface. This method is validated by simulation and can be used to construct metasurfaces at the sub-wavelength scale for flexible control of scattered waves, and it can guide the design of acoustic lenses, devices that collect sound energy using surface waves, and acoustic diffusers inside rooms.