Theory of nonlinear electroacoustics of dielectric, piezoelectric, and pyroelectric crystals

Based on a fully electrodynamic Lagrangian theory of elastic dielectrics, a completely deductive derivation of the dynamical equations and constitutive relations for elastic, electric, and electroelastic phenomena is presented. The equations apply to crystals of arbitrary symmetry, structural complexity, and nonlinearity. These include pyroelectrics as well as dielectrics and piezoelectrics. Emphasis is placed on the lowest order nonlinearities, that is, ones depending either bilinearly or quadratically on the elastic and electric variables. A relation between the electrostriction tensor and the low-frequency limit of the elasto-optic tensor, different from any previous relation in the literature, is derived and discussed.