Abstract
In this chapter we investigate 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 acoustic band diagram and transmission spectra of periodic pillars arranged in different symmetries, we show that these structures possess acoustic metamaterial features for surface acoustic waves. The pillars on the top of the surface introduce new guided modes in the non-radiative region of the substrate outside the sound cone. The modal shape and 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 addition, the band diagram of the guided modes defines band gaps that appear at frequencies markedly lower than those expected from the Bragg mechanism. We identify them as originating from local resonances of the individual cylindrical pillar and we show their dependence on the geometrical parameters, in particular with the height of the pillars. The frequency positions of these band gaps are invariant with the symmetry, and thereby the period, of the lattices, which is unexpected in band gaps based on Bragg mechanism. However, the role of the period remains important for defining the non-radiative region limited by the slowest bulk modes and influencing the existence of new surface modes of the structures. The surface acoustic wave transmission across a finite array of pillars corroborates the signature of the locally resonant band gaps for surface modes and their link with the symmetry of the source and its polarization. Numerical simulations based on an efficient finite element method and considering Lithium Niobate pillars on a Lithium Niobate substrate are used to illustrate the theory.
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The authors thank Prof. Vincent Laude and Dr. Sarah Benchabane for fruitful discussions.
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Khelif, A., Achaoui, Y., Aoubiza, B. (2013). Locally Resonant Structures for Low Frequency Surface Acoustic Band Gap Applications. In: Craster, R., Guenneau, S. (eds) Acoustic Metamaterials. Springer Series in Materials Science, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4813-2_2
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DOI: https://doi.org/10.1007/978-94-007-4813-2_2
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