Phononic crystals with planar defects

We study the effect of planar defects in phononic crystals of spherical sca tterers. It is shown that a plane of impurity spheres introduces modes of v ibration of the elastic field localized on this plane at frequencies within a frequency gag of a purl phononic crystal: these show up as sharp resonan ces in the transmittance of elastic waves Incident on a slab of the crystal . A periodic arrangement of impurity planes along a given direction creates narrow impurity bands with a width which depends on the position of these bands within the frequency eap of the pure crystal and on the separation be tween the impurity planes. We show how a slight deviation from periodicity (one impurity plane is different from the rest) reduces dramatically the tr ansmittance of elastic waves incident on a slab of the crystal.