Formation of phonon-focusing caustics in crystals.
Formation of phonon-focusing caustics in crystals.
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晶体中声子聚焦焦散的形成。
DOI：
10.1103/physrevb.34.2852
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
Every
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文献类型：
--
作者：
Every
在晶体的声子图像中可以观察到各种各样的焦散。这些结构是声子聚焦的结果，即由弹性各向异性引起的声子射线矢量方向的聚集。在这些焦散中可以识别出许多基本的灾变。本文认为，如果把弹性常数之比作为控制参数，补充声子通量方向规范中出现的两个参数，则对声子焦散线有更透彻的理解。通过这种方式，人们可以解释为什么在声子图像中存在略微展开的高阶灾变部分，如蝴蝶和双曲脐带。本文的主要目的是引起人们对晶体弹性波动方程的特殊形式以及不同声子分支之间对称性和简并性的限制所引起的各种特殊焦散的注意。给出了焦散的全球发展的例子，并讨论了外锥折射现象及其在对称破缺扰动下的展开。探讨了简并性与焦散线的存在之间的密切联系。文中考虑了锥形、切线、直线、曲面和三重简并，并描述了由改变简并形式的微扰引起的焦散线中的变换。这些发现表明，声子成像可以用来研究相变和测量某些难以获得的弹性常数。预计这些结果也将有助于对低对称性晶体的声子聚焦模式进行分类。
A great variety of caustics are observed in the phonon images of crystals. These structures are the result of phonon focusing, ie, the crowding together in direction of phonon ray vectors that is brought about by elastic anisotropy. Many of the elementary catastrophes can be identified in these caustics. It is argued in this paper that a more penetrating understanding of phonon caustics is arrived at if the ratios of the elastic constants are regarded as control parameters supplementing the two that arise in the specification of the direction of the phonon flux. In this way one can explain the presence in phonon images of slightly unfolded sections of higher-order catastrophes such as the butterfly and hyperbolic umbilic. The main thrust of this paper is to draw attention to a variety of extraordinary caustics occasioned by the particular form of the elastic wave equation for crystals, and by the constraints of symmetry and degeneracy between the different phonon branches. Examples are given of the global development of caustics, and the phenomenon of external conical refraction and its unfolding under a symmetry-breaking perturbation is treated. The close link between degeneracy and the existence of caustics is explored. Conical, tangential, line, surface, and triple degeneracies are considered, and the transformations brought about in the caustics by perturbations that change the form of the degeneracy, are described. These findings suggest a route by which phonon imaging could be used in the study of phase transitions and for measuring certain hard-to-obtain elastic constants. It is anticipated that these results should also assist in the classification of the phonon-focusing patterns of lower-symmetry crystals.