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In this work, quite different from many previous studies in the ultrafast region, we study the thermo-optical nonlinearity of a single metal nanoparticle and many-nanoparticle composite under continuous-wave illumination. For single metal nanoparticle system, we show that the thermal effect is able to qualitatively explain the experimental results of the strong nonlinear scattering from sufficiently small Au nanoparticle. To characterize the thermo-optical nonlinearity of single nanoparticle of finite size, we use the best experimentally measured data of the temperature dependent permittivities of bulk gold and calculate the temperature and scattering cross-section of the nanoparticle. We show that, quite counterintuitively, the particle temperature changes with its size non-monotonically. Furthermore, our numerical model shows much better agreement with the nonlinear scattering measurement results than the previous studies. The results of the single nanoparticle system are then used to study the thermo-optical nonlinearity of many-nanoparticle composites. Specifically, the temperature distribution of the many-nanoparticle composite is calculated by properly summing the heat generated by all nanoparticles in the composite as well as modeling by simulation. We show that, in contrast to the case of a single nanoparticle, the temperature distribution and thus the thermo-optical nonlinearity of the composite are weakly dependent on the illumination wavelength, nanoparticle size, and density, but is strongly sensitive to the beam size and the thermal conductivity of the host material. These results are critical for the optimization of the photo-thermal effect in many applications. More importantly, since photo-thermal effects were shown to be responsible for observations of faster chemical reactions, our results can be used to interpret correctly the differences in chemical reaction enhancements originating from the thermo-optical nonlinearity at different illumination intensities.
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