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 less than 1 µm. 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 solving of Maxwell equations leads to a differential system, the source term of which is proportional to the acoustic field itself. The scattered electromagnetic field is described using the matricant and the ensuing analytical solution allows then analyzing the 3D photoelastic interaction. Good agreement with experiments performed in a 1 µm thick aluminum film is found.