Electric componentes of acoustic fields in piezoelectrics and some their topological features

The existence conditions of zero electric fields E and zero electric displacements D are studied for bulk acoustic waves in piezoelectric crystals. General equations are derived for lines of zero electric fields, E(m) = O, and for specific points mo of vanishing electric displacements, D(mo) = O, on the unit sphere of propagation directions m2 = 1. It is proved that the both types of specific directions must exist in any (even triclinic) crystals.The obtained equations are solved for a series of examples of particular crystal symmetry. It is shown that the vectors D(m) being generally orthogonal to the wave normal m are characterized bydefinite orientational singularities in the vicinity of mo and can be described by the poincare indices n+O, +- 1 or +-2. The algebraic expressions for indices n are found both for unrestricted anisotropy and for a series of particular cases.