Department of Mathematics and Physics, Ostfold University College, 1757 Halden, Norway.
J Acoust Soc Am. 2010 Feb;127(2):746-53. doi: 10.1121/1.3273901.
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.
一组用于描述四方晶体中声子聚焦模式特征焦散点的临界条件被提出。聚焦模式中的焦散线通常与波面的折叠或尖点有关。大多数焦散线相对于主对称面对称，可用焦散线中心的焦散点来描述。这些特征焦散点分别起源于面内/面外曲率为零的拐点/抛物线点。通过采用 Stroh 形式，利用所谓的零曲率跨声速态，研究了慢度面上的拐点/抛物线点。由于这些跨声速态与 Stroh 特征方程中的特殊简并有关，因此这些简并条件可视为特征焦散点的临界条件。这些条件提供了四方晶体中声子聚焦模式整体结构的概述。还研究并举例说明了（001）面附近的一组焦散线。
