Acoustic transmission resonance and suppression through double-layer subwavelength hole arrays

We present a theoretical study of acoustic waves passing through double-layer subwavelength hole arrays. The acoustic transmission resonance and suppression are observed. There are three mechanisms responsible for the transmission resonance: the excitation of geometrically induced acoustic surface waves, the Fabry-Perot resonance in a hole cavity (I-FP resonance) and the Fabry-Perot resonance between two plates (II-FP resonance). We can differentiate these mechanisms via the dispersion relation of acoustic modes supported by the double-layer structure. It is confirmed that the coupling between two single-layer perforated plates, associated with longitudinal interval and lateral displacement, plays a crucial role in modulating the transmission properties. The strong coupling between two plates can induce the splitting of the transmission peak, while the decoupling between plates leads to the appearance of transmission suppression. By analyzing the criterion derived for transmission suppression, we conclude that it is the destructive interference between the diffracted waves and the direct transmission waves assisted by the I-FP resonance of the first plate that leads to the decoupling between plates and then the transmission suppression.