Photoacoustic group velocity

Abstract The concept of photoacoustic (PA) group velocity ( v g ) is largely missed in the related transport theory. Generally it is assumed that the PA signal propagation occurs at a constant velocity, and thus overlooking the attenuation and dispersion effects. In practice, the PA signals propagate as material waves coupled to the sample, and thus inherently experiencing wave dispersion. In this work, such limitation is bypassed using a modified wave-function formulation in which both amplitude attenuation and wave dispersion arise naturally from a Heaviside-type (Cattaneo) transport equation operating on the velocity potential. Thus the approach, is valid for homogeneous media, characterised by a frequency-dependent PA absorption coefficient and an explicit expression for the group velocity. The resulting model accurately predicts the experimentally observed amplitude decay, bandwidth reduction, and peak-frequency shifts of PA spectra as functions of propagation distance. Furthermore, it is consistent with local thermal equilibrium and energy conservation requirements, and provides the necessary framework to satisfy Biot’s group-velocity theorem and, consequently, the macroscopic Debye kinetic theory. This analysis also supports the interpretation of the PA signal as a dispersive wave packet propagating with an average group velocity, whose velocity distribution is governed by its spectral content.