Surface acoustic waves in the continuous spectrum of Bloch waves in piezoelectric one-dimensional phononic crystals

This paper theoretically investigates surface acoustic waves (SAWs) which emerge within the continuous spectrum of bulk Bloch waves in piezoelectric one-dimensional phononic crystals. Accordingly, these SAWs may be treated as an example of the bound states in the continuum (BIC). The equations which determine the existence of such BIC-SAWs have been derived. Unlike SAWs in the frequency intervals forbidden for bulk Bloch waves, BIC-SAWs are governed not by a single purely real dispersion equation but by sets of equations, so BIC-SAWs prove to be robust only to a consistent change of a definite number of free parameters characterizing the wave propagation. The form of the derived equations allows the establishment of the conditions on the frequency and other parameters under which the BIC-SAW exists. The number of conditions depends on the number of bulk waves in the frequency interval under consideration. In the case of generic crystallographic symmetry, there are three, five, and seven conditions which have to be fulfilled for a BIC-SAWs to coexist with one pair, two pairs, and three pairs of bulk Bloch waves, respectively. It is shown that the crystallographic symmetry may reduce the number of conditions to two, three and four, respectively. Numerical computations confirm analytic results.