Structure of phonon focusing patterns in tetragonal crystals.

A set of critical conditions for the characteristic caustic points in the phonon focusing patterns in tetragonal crystals is formulated. A caustic line segment in the focusing pattern is generally associated with either a fold or a cusp on the wave surface. Most of the caustic lines are symmetrical with respect to the principal symmetry plane and can be characterized by the caustic points at the centers of the caustic lines. These characteristic caustic points originated from inflection/parabolic points with zero in-plane/ex-plane curvature, respectively. By employing the Stroh formalism, the inflection/parabolic points on the slowness surface are studied in terms of the so-called zero-curvature transonic states. Since these transonic states are related to extraordinary degeneracies in the Stroh eigenvalue equation, the conditions for the degeneracies can be regarded as critical conditions for the characteristic caustic points. These conditions provide an overview of global structure of the phonon focusing patterns in tetragonal crystals. A set of caustic lines in vicinity of (001) plane is also investigated and exemplified.