We study theoretically, by means of layer-multiple-scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in a polyester matrix, embedded in air. In particular, we focus on the study of modes localized on the surfaces of the structure. Their origin and behavior, as well as the physical parameters that influence and determine their appearance, are investigated in detail. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. © 2008 The American Physical Society.

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