We have used a plane-wave-expansion model to study the out-of-plane propagation of elastic waves in a two-dimensional phononic band-gap material. The case of quartz rods embedded in an epoxy matrix has been computed. Band gaps for nonzero values of the wave-vector component parallel to the rods are shown to exist and are investigated. For wavelengths smaller than the period of the structure, modes are found that are localized in the epoxy intersites, and propagate perpendicularly to the plane of the structure.

• Received 7 March 2003

DOI:https://doi.org/10.1103/PhysRevE.67.065602