Existence of extraordinary zero-curvature slowness curve in anisotropic elastic media.

Acoustic wave propagation in elastic media is characterized by the slowness surface. The slowness surface consists of three sheets associated with three modes of wave propagation and the two outer sheets can have zero-curvature locally. It is shown that the outmost sheet can admit extraordinary zero-curvature and the slowness curve can appear as a straight line locally. Using the perturbation method, the conditions for the extraordinary zero-curvature are derived analytically without violating the thermodynamic condition for elastic media. The results can be applied to crystals with higher symmetry and to the study of phonon focusing and surface waves.