Influence of the temperature-dependent dielectric constant on the photoacoustic effect of gold nanospheres

Photoacoustic imaging techniques with gold nanoparticles as contrast agents have received a great deal of attention. The photoacoustic response of gold nanoparticles strongly depends on the far-field optical properties, which essentially depend on the dielectric constant of the material. The dielectric constant of gold not only varies with wavelength but is also affected by temperature. However, the effect of the temperature dependence of the dielectric constant on gold nanoparticles' photoacoustic response has not been fully investigated. In this work, the Drude-Lorentz model and Mie theory are used to calculate the dielectric constant and absorption efficiency of gold nanospheres in aqueous solution, respectively. Then, the finite element method is used to simulate the heat transfer process of gold nanospheres and surrounding water. Finally, the one-dimensional velocity-stress equation is solved by the finite-difference time-domain method to obtain the photoacoustic response of gold nanospheres. The results show that under the irradiation of a high-fluence nanosecond pulse laser, ignoring the temperature dependence of the dielectric constant will lead to large errors in the photothermal response and the nonlinear photoacoustic signals (it can even exceed 20% and 30%). The relative error of the photothermal and photoacoustic response caused by ignoring the temperature-dependent dielectric constant is determined from both the temperature dependence of absorption efficiency and the maximum temperature increase of gold nanospheres. This work provides a new perspective for the photothermal and photoacoustic effects of gold nanospheres, which is meaningful for the development of high-resolution photoacoustic detectors and nano/microscale temperature measurement techniques.