Geometrical factors in the dispersion of ballistic heat pulses

The dispersion of ballistic heat pulses in dielectric crystals can partly be ascribed to geometrical factors that include the sample thickness, the contact areas of the source and detector and their relative positioning, and the acoustic anisotropy of the transmission medium. These factors are involved in determining the spread in the path lengths and group velocities of the phonons that are transmitted. In this paper we derive a simple expression, valid when the source and detector dimensions are small compared with the thickness of the slab-shaped sample, which relates the temporal width of a ballistic heat pulse to the average in-plane component of the slowness vector s of the transmitted phonons. A comparison is made between the predictions of this expression, Monte Carlo simulations and published experimental ballistic heat pulse data on paratellurite.