Abstract
The band-structure results for elastic and acoustic waves propagating in a composite (consisting of periodically placed spheres in a host material) are analyzed by employing the frequency dependence of the scattering cross section from a single sphere. Two limiting modes of propagation can be visualized. According to the first the wave propagates mainly through the host material; according to the second the wave hops coherently from a sphere to its neighbors using the resonances in the single-sphere scattering cross section. This second mode is the analog of the linear combination of atomic orbitals in electronic propagation, with the atomic orbitals replaced by the resonances.