Abstract
An analytical model is built to predict the acoustic fields of acoustic metasurfaces. The acoustic fields are investigated for a Gaussian sound beam incident on the acoustic metasurfaces. The Gaussian sound beam is decomposed into a set of discrete elementary plane waves. The diffraction caused by the acoustic metasurfaces can be obtained using this analytical model, which is validated with the numerical simulations for the different incident angles of the Gaussian sound beam. This model overcomes the limitation of the method based on the generalised Snell's law which can only predict the direction of a specific diffracted order. Actually, this analytical model can be also used to predict the sound fields of acoustic metasurfaces under any incident sound if its Fourier transforms exist. This conclusion is demonstrated by studying the sound field for a point sound source incident on the acoustic metasurface. The acoustic admittances of acoustic metasurfaces are required in the calculation of the analytical model. Therefore, a numerical method for obtaining the effective acoustic admittances is proposed for the structurally complex metasurfaces without the analytical expressions of material properties, such as equivalent density and sound speed.
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