Surface and interface acoustic waves in solid-fluid superlattices: Green's function approach

Y. El Hassouani (1) , E.H. El Boudouti (1) , Bahram Djafari-Rouhani (2) , H. Aynaou (1) , L. Dobrzynski (2)

1 Université Mohammed Premier [Oujda]
2 IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520

We study the propagation of acoustic waves associated with the surface of a semi-infinite superlattice (SL) consisting of alternating elastic solid and ideal fluid layers or its interface with a semi-infinite fluid. We present closed-form expressions for localized surface and interface waves depending on whether the SL is terminated with a fluid layer or a solid layer. We also calculate the corresponding Green’s function and densities of states. These general results are illustrated by a few applications to periodic Plexiglas-water and Al-water SLs. In the case of a fluid layer termination, we generalize a rule obtained previously about the existence and behavior of surface waves in the case of pure transverse or longitudinal waves in solid-solid SLs, namely (i) the creation from the infinite SL of a free surface gives rise to δ peaks of weight (−1∕4) in the density of states, at the edges of the SL bulk bands, (ii) by considering together the two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane lying within the fluid layer and parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of the wave vector k∥ (parallel to the interfaces). However, this rule is not fulfilled when the cleavage is carried out inside the solid layer. Indeed, in this case, the dispersion curves may present zero, one, or two modes inside each gap of the two complementary SLs depending on the position of the plane where the cleavage is produced. Finally, we investigate the localized and resonant modes associated with the presence of a fluid cap layer made of mercury, with finite or semi-infinite extent, on top of the above-mentioned SLs. Different guided modes induced by the adsorbed fluid layer are obtained and their properties are investigated.

Domaines: Matière Condensée [cond-mat]; Acoustique [physics.class-ph]

Y. El Hassouani, E.H. El Boudouti, Bahram Djafari-Rouhani, H. Aynaou, L. Dobrzynski. Surface and interface acoustic waves in solid-fluid superlattices: Green's function approach. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2006, 74 (14), pp.144306. ⟨10.1103/PhysRevB.74.144306⟩. ⟨hal-00154926⟩