Phononic crystal diffraction gratings

Abstract

When a phononic crystal is interrogated by an external source of acoustic waves, there is necessarily a phenomenon of diffraction occurring on the external enclosing surfaces. Indeed, these external surfaces are periodic and the resulting acoustic diffraction grating has a periodicity that depends on the orientation of the phononic crystal. This work presents a combined experimental and theoretical study on the diffraction of bulk ultrasonic waves on the external surfaces of a 2D phononic crystal that consists of a triangular lattice of steel rods in a water matrix. The results of transmission experiments are compared with theoretical band structures obtained with the finite-element method. Angular spectrograms (showing frequency as a function of angle) determined from diffraction experiments are then compared with finite-element simulations of diffraction occurring on the surfaces of the crystal. The experimental results show that the diffraction that occurs on its external surfaces is highly frequency-dependent and has a definite relation with the Bloch modes of the phononic crystal. In particular, a strong influence of the presence of bandgaps and deaf bands on the diffraction efficiency is found. This observation opens perspectives for the design of efficient phononic crystal diffraction gratings.