General analytical scheme for determining the characteristic caustic points in phonon focusing patterns of cubic crystals

Phonon focusing patterns are dependent on the existence of concave/saddle regions and acoustic axes in the slowness surface. The main feature of the focusing patterns in cubic crystals can be characterized by the cuspidal and swallowtail points in the symmetry planes. By applying the Stroh formalism, these points are investigated in relation to degeneracies in the Stroh eigenvalue equation. Explicit expressions for these points are derived.