We investigate theoretically the photoacoustic generation by a gold nanosphere 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 photoacoustic wave generation arises solely from the thermoelastic stress caused by the temperature increase of the nanosphere or its liquid environment. Photoacoustic 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 nanosphere, thermoelastic and elastic properties of both water and gold, and the temperature dependence of the thermal expansion coefficient of water. For sufficiently high illumination fluences, this temperature dependence yields a nonlinear relationship between the photoacoustic amplitude and the fluence. For nanosecond pulses in the linear regime, we show that more than $90\%$ of the emitted photoacoustic energy is generated in water, and the thickness of the generating layer around the particle scales close to the square root of the pulse duration. The amplitude of the photoacoustic wave in the linear regime is accurately predicted by the point-absorber model introduced by Calasso et al. [Phys. Rev. Lett. 86, 3550 (2001)], but our results demonstrate that this model significantly overestimates the amplitude of photoacoustic waves in the nonlinear regime. We therefore provide quantitative estimates of a critical energy, defined as the absorbed energy required such that the nonlinear contribution is equal to that of the linear contribution. Our results suggest that the critical energy scales as the volume of water over which heat diffuses during the illumination pulse. Moreover, thermal nonlinearity is shown to be expected only for sufficiently high ultrasound frequency. Finally, we show that the relationship between the photoacoustic amplitude and the equilibrium temperature at sufficiently high fluence reflects the thermal diffusion at the nanoscale around the gold nanosphere.

• Received 16 February 2015
• Revised 8 September 2015

DOI:https://doi.org/10.1103/PhysRevB.92.115450