Peculiarities of propagation of acoustic excitations through an imperfect 1D-superlattice

Virtual crystal approximation is adapted to address peculiarities of propagation of acoustic waves through a 1D 'sandwich' superstructure consisting of alternating layers of two types randomly substituted by foreign layers of the third type. Same-parity layers are of the same width and constitute a sublattice. Dependence of the lowest forbidden acoustic zone width of the described structure on concentrations of impurity layers in the two sublattices is numerically evaluated for longitudinal and transverse excitations. Values of substitute concentrations making the structure completely transparent prove to be independent of the relative widths of the 1st and 2nd type layers.