Evolution of phonon-focusing caustics under linear spatial dispersion

Linear dispersion of elastic constants in non-centrosymmetric crystals has the effect of lifting phase-velocity degeneracy along those acoustic axes w hich do not lie in symmetry planes. The separating of the sheets of the iso frequency (or slowness) surface, even though slight at low frequencies, nev ertheless has a striking effect on the phonon intensity pattern near to the removed degeneracy. Phonon focusing abides by the shape of the slowness su rface. whose curvature is singular at the degeneracy point. Hence, a small perturbation breaking the degeneracy entails a large change of the curvatur e in a small region scaling in size with the magnitude of the perturbation. As a result, new phonon focusing caustics may arise, and existing caustics may undergo major changes near acoustic axes. Theoretical analysis reveals possible patterns of local transformation of the slowness surface leading to different types of critical behaviour of phonon focusing. Criteria, in t erms of the elastic constants of a given crystal are obtained for the emerg ence of focusing caustics.