PHONON FOCUSING AND THE SHAPE OF THE RAY SURFACE IN CUBIC CRYSTALS

Abstract
A systematic study has been carried out on the dependence of the phonon ray surface of cubic crystals on elastic constants. The correspondence between folds in this surface and the presence of caustics in the flux of phonons emanating from a localised heat source is explored. The line, cusp, butterfly and hyperbolic umbilic elementary catastrophes as well as some remarkable types of structural instability are shown to occur in these caustics. A method is demonstrated for portraying the ray surface which provides an immediate indication of the number of separate components a ballistic heat pulse will split up into on propagating in various directions, and what the relative intensities and the spacings of these components will be.