Surface acoustic waves on one-dimensional phononic crystals of general anisotropy: Existence considerations

Existence of surface acoustic waves on the boundary of half-infinite one-dimensional phononic crystals is investigated. The structure is formed of perfectly bonded solid nonpiezoelectric layers of general anisotropy. The layers are parallel to the substrate surface. It is shown that at most three surface waves can exist in a stopband. The number of surface waves on the structure with a given order of layers is correlated with the number of surface waves on the structure where the order of layers is reversed, namely, in total at most three surface waves occur within a stopband. However, if the layers are arranged so that the period is symmetric with respect to its midplane, "symmetric" period, then at most one surface wave exists per stopband on the phononic crystal-vacuum boundary. A criterion of the occurrence of such a wave in the lowest stopband is found. No surface acoustic wave exists in the lowest stopband on the mechanically clamped surface but one surface wave can occur in the other stopbands. The case of "symmetric" period has no relation to crystallographic symmetry. In particular, it occurs in half-infinite two-layered phononic crystals where the thickness of the exterior layer of the substrate is half the thickness of the interior layers of the same material.