Subwavelength waveguiding of surface phonons in pillars-based phononic crystal

Abstract

In this study, we theoretically analyze the guiding of surface phonons through locally resonant defects in pillars-based phononic crystal. Using finite element method, we simulate the propagation of surface phonons through a periodic array of cylindrical pillars deposited on a semi-infinite substrate. This structure displays several band gaps, some of which are due to local resonances of the pillar. By introducing pillar defects inside the phononic structure, we show the possibility to perform a waveguiding of surface phonons based on two mechanisms that spatially confine the elastic energy in very small waveguide apertures. A careful choice of the height of the defect pillars, allows to shift the frequency position of the defect modes inside or outside the locally resonant band gaps and create two subwavelenght waveguiding mechanisms. The first is a classical mechanism that corresponds to the presence of the defect modes inside the locally resonant band gap. The seconde is due to the hybridation between the phonon resonances of defect modes and the surface phonons of the semi-infinite homogenous medium. We discuss the nature and the difference between both waveguiding phenomena.