Three-dimensional elasto-optical interaction for reflectometric detection of diffracted acoustic fields in picosecond ultrasonics

Abstract

The three-dimensional (3D) photoelastic interaction involved in the detection mechanism of picosecond ultrasonics is investigated in micrometric metallic films. In pump-probe experiments, the laser source beam is focused to a spot size of less than $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. A 3D diffracted acoustic field is generated at high frequencies of several tens of gigahertz, containing longitudinal and shear waves altogether. Their propagation changes the dielectric permittivity tensor and the material becomes optically heterogeneous. Consequently, the detection process is modeled through the propagation of the laser probe beam in a material with dielectric properties varying in all directions. Thus, the solution of Maxwell's equations leads to a differential system, the source term of which is proportional to the acoustic field itself. In the frame of small perturbation theory, the latter is decomposed into a continuous sum of monochromatic plane waves. The scattered electromagnetic field is described using the matricant, and the ensuing analytical solution then allows analyzing the 3D photoelastic interaction. The contribution of acoustic diffraction and shear wave detection to the reflectometric signal is put into relief. Good agreement with experiments performed in a $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ thick aluminum film is found.