Photoacoustic generation by a gold nanosphere: From linear to nonlinear thermoelastics in the long-pulse illumination regime

We investigate theoretically the photo-acoustic generation by a gold nano-sphere in water in the thermoelastic regime. Specifically, we consider the long-pulse illumination regime, in which the time for electron-phonon thermalization can be neglected and photo-acoustic wave generation arises solely from the thermoelastic stress caused by the temperature increase of the nano-sphere or its liquid environment. Photo-acoustic signals are predicted based on the successive resolution of a thermal diffusion problem and a thermoelastic problem, taking into account the finite size of the gold nano-sphere, thermoelastic and elastic properties of both water and gold, and the temperature dependence of the thermal expansion coefficient of water. Our results suggest that the critical energy scales as the volume of water over which heat diffuses during the illumination pulse. Finally, we show that the relationship between the photo-acoustic amplitude and the equilibrium temperature at sufficiently high fluence reflects the thermal diffusion at the nano-scale around the gold nano-sphere.