Bleustein–Gulyaev SAW and its associated quasi-particle

Following a previous work that dealt with the case of Rayleigh surface waves in pure elasticity, here it is shown that a quasi-particle with Newtonian point-like mechanics (equation of inertial motion, expression of the kinetic energy) can be associated with the celebrated Bleustein–Gulyaev surface waves of linear piezoelectricity. This association is based on the integration over a vertical band of the sagittal plane of the canonical balance laws that accompany, via Noether’s theorem, the basic field equations. It accounts for the boundary conditions at the limiting surface, the periodicity of the solution in propagation space, and the vanishing of all fields at infinity in the substrate or in the outside vacuum. The proof benefits from the fact that the average (over one wavelength of propagation) of the Lagrangian density at the limiting surface is proportional to the satisfied “dispersion relation”, and hence is zero. The expression found for the “mass” of the said quasi-particle is informative in that it contains information about the frequency, the amplitude of the signal, and the electromechanical coupling.