Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.