Analytical one-dimensional model for laser-induced ultrasound in planar optically absorbing layer

Ultrasound generated by means of laser-based photoacoustic principles are in common use today and applications can be found both in biomedical diagnostics, non-destructive testing and materials characterisation. For certain measurement applications it could be beneficial to shape the generated ultrasound regarding spectral properties and temporal profile. To address this, we studied the generation and propagation of laser-induced ultrasound in a planar, layered structure. We derived an analytical expression for the induced pressure wave, including different physical and optical properties of each layer. A Laplace transform approach was employed in analytically solving the resulting set of photoacoustic wave equations. The results correspond to simulations and were compared to experimental results. To enable the comparison between recorded voltage from the experiments and the calculated pressure we employed a system identification procedure based on physical properties of the ultrasonic transducer to convert the calculated acoustic pressure to voltages. We found reasonable agreement between experimentally obtained voltages and the voltages determined from the calculated acoustic pressure, for the samples studied. The system identification procedure was found to be unstable, however, possibly from violations of material isotropy assumptions by film adhesives and coatings in the experiment. The presented analytical model can serve as a basis when addressing the inverse problem of shaping an acoustic pulse from absorption of a laser pulse in a planar layered structure of elastic materials.