Effects of first-order spatial dispersion on phonon focusing: Application to quartz

First-order spatial dispersion has a considerable impact on phonon focusing in the vicinity of the acoustic axes of crystals, even for frequencies well below 1 THz. Subject to certain symmetry requirements, the degeneracy of the transverse sheets of the acoustic slowness surface is removed at finite wave vector and frequency. As a result, the phonon intensity anticaustic associated with a conical degeneracy is transformed into a similarly shaped caustic. Intersecting line caustics associated with a tangential degeneracy at a fourfold axis break apart and form cusps. Lines of wedge-shaped degeneracy in hexagonal crystals are removed, thereby giving rise to pairs of circular caustics. It is shown that a simple treatment of first-order spatial dispersion is well able to explain a number of anomalies in the published phonon images of quartz.