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

Abdelkrim Khelif*, Younes Achaoui, Sarah Benchabane, Vincent Laude, Boujamaa Aoubiza

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

245 Citations (Scopus)

Abstract

We 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.

Original languageEnglish
Article number214303
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume81
Issue number21
DOIs
Publication statusPublished - 10 Jun 2010
Externally publishedYes

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