Vibrational Response of Nanorods to Ultrafast Laser Induced Heating: Theoretical and Experimental Analysis

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Abstract
In this paper, we elucidate the vibrational response of cylindrical nanorods to ultrafast laser-induced heating. A theoretical analysis of the expected behavior is first presented. This analysis predicts that both extensional and breathing vibrational modes of the rods should be excited by laser-induced heating. Analytical formulas are derived assuming that the heating/expansion process is instantaneous, and that the lengths of the rods are much greater than their radii. These results show that the breathing mode dominates the mechanical deformation of the rod. However, because the frequency of the extensional mode is much lower than that of the breathing mode, the extensional mode will dominate the response for a real experiment (a finite-time heating/expansion process). The results of this model are compared to data from transient absorption experiments performed on gold nanorods with average lengths between 30 and 110 nm. The transient absorption traces show pronounced modulations with periods between 40 and 120 ps, which are only observed when the probe laser is tuned to the longitudinal plasmon band. The measured periods are in good agreement with the expected values for the extensional modes of the rods. For rods wider than 20 nm, the breathing mode can also be observed and, again, the measured periods are in good agreement with the theoretical calculations. The breathing mode is not observed for thinner rods (<20 nm width) because, in this case, the period is comparable to the time scale for lattice heating.