Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface

Abstract

International audienceWe investigate theoretically the propagation of acoustic waves in a two-dimensional array of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the band structure of the periodic array and of the transmission of waves through a finite length array, we show that the phononic crystal can support a number of surface propagating modes in the nonradiative region of the substrate, or sound cone, as limited by the slowest bulk acoustic wave. The modal shape and the polarization of these guided modes are more complex than those of classical surface waves propagating on a homogeneous surface. Significantly, an in-plane polarized wave and a transverse wave with sagittal polarization appear that are not supported by the free surface. In the band structure, guided modes define band gaps that appear at frequencies markedly lower than those expected from the Bragg interference condition. We identify them as originating from local resonances of the individual cylindrical pillars and show their dependence on the geometrical parameters, in particular with the height of the pillars. The transmission of surface acoustic waves across a finite array of pillars shows the signature of the locally resonant band gaps for surface modes and their dependence on the symmetry of the source and its polarization. Numerical simulations are performed by using the finite element method and considering silicon pillars on a silicon substrate

Waveguiding by a locally resonant metasurface

“…It should be noted that the propagation of surface acoustic waves in structures comprising periodic or aperiodic arrays of pillars has been investigated in a number of experimental and theoretical studies [30][31][32]. While the main emphasis of these studies was on sagittally polarized surface waves, the existence of guided SH waves associated with the resonances of the pillars has been predicted and their dispersion calculated numerically using the finite elements analysis [30].…”

Phonon and heat transport control using pillar-based phononic crystals

“…The flattening of the dispersion branches due to both Bragg diffraction and the local resonances can form phononic bandgaps—the ranges of frequency, in which phonons cannot propagate [27,35,36]. The frequency of the Bragg bandgap is linked to the period of the PnCs and thus affects only phonons with the wavelengths of about the characteristic size of the system [27,35,37].…”

“…The frequency of the Bragg bandgap is linked to the period of the PnCs and thus affects only phonons with the wavelengths of about the characteristic size of the system [27,35,37]. The frequencies of the local resonance bandgaps are linked to the resonant frequencies of the pillars [27], which can be tuned via structural parameters, such as pillar diameter [30,38] and height [25,26,30,38,39], or material parameters, such as density and Young modulus [25,30].…”

Band structure analysis of leaky Bloch waves in 2D phononic crystal plates

“…[9] as well as Finite Element (FEM)-based absorbing regions [10,11,12] and Perfectly Matched Layers [13,14], while the so-called Plane Wave Expansion (PWE) method has been used in [15,16,17].…”