Applicability and limitations of the phonon-focusing theory based on geometrical acoustics

A detailed discussion is given on the applicability and limitations of the naive phonon-focusing theory by Taylor, Maris, and Elbaum. Comparing it with the characteristic behavior of ballistic-phonon propagations detected recently in heat-pulse experiments, we find that the theory predicts correctly the locations of various sharp peaks observed in flux enhancement of transverse phonons. When emissivity of phonons excited in a heat source into an anisotropic crystal is properly taken into consideration, the relevant theory accounts quantitat\`{}vely for (a) the relative magnitudes of highly enhanced phonon flux of different polarizations measured along the principal crystallographic axes (i.e., the [001], [110], and [111] axes) of a cubic crystal, and (b) the angular dependence of the phonon intensity for the longitudinal mode. On the contrary, in the neighborhood of sharp peaks of the flux, the theory becomes invalid by yielding much larger intensity than that observed in the experiments, which suggests the breakdown of geometrical acoustics on surfaces called caustics.