We present the first full band-structure calculations for periodic, elastic composites. For transverse polarization of the vibrations we obtain a ‘‘phononic’’ band gap which extends throughout the Brillouin zone. A complete acoustic gap or a low density of states should have important consequences for the suppression of zero-point motion and for the localization of phonons, and may lead to improvements in transducers and in the creation of a vibrationless environment.

• Received 11 February 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.2022