Laser-induced ultrasound in multiple thin layers—An analytical solution

Laser-induced ultrasound is based on the thermo-elastic conversion of absorbed short light pulses to pressure pulses. In the work presented here, laser-induced ultrasound in a planar structure of interconnected layers with variations in optical, thermal, and mechanical properties is studied. Layered structures can be used for generating wideband ultrasonic pulses specific to a chosen application. An analytical time-domain solution is derived for the resulting pressure transmitted from the layered structure. The solution is derived for an arbitrary number of layers with an arbitrary optical absorption profile. Free space Green's functions with image sources are used to derive the solution. A solution employing the Beer-Lambert law is also proposed. The simplification with reflections only at the boundaries is in agreement with previous published results. The spectral properties of the generated pulse are derived, where the effects of optical absorption coefficients and layer thicknesses are shown. The analytical solution is compared to one-dimensional (1D) simulations and a three-dimensional (3D) simulation, realised as a two-dimensional (2D) axially symmetric case, using the matlab toolbox k-Wave. The 3D simulation on-axis pressure agrees well with the 1D analytical solution when the diameter of the laser beam is larger by approximately 1 order of magnitude than the thickness of the planar layered structure.