Coherent vibrational motion in metal particles: Determination of the vibrational amplitude and excitation mechanism

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Abstract
Ultrafast laser excitation of metal particles coherently excites the symmetric breathing mode. This changes the electron density in the particle, which produces a periodic redshift in the position of the plasmon band. In this paper transient absorption data recorded over a range of wavelengths are analyzed to determine the amplitude of the breathing motion for 24.2 nm radius Au particles. The results are compared to a model calculation where the expansion coordinate is treated as a damped harmonic oscillator and the driving force is thermal expansion due to lattice heating (the temperature rise is determined from the energy absorbed by the sample). The only adjustable parameters in these calculations are the dephasing time of the oscillations and the time scale for energy transfer to the solvent. The experimental and calculated vibrational amplitudes are in excellent agreement, which shows that all the absorbed energy goes into expansion. However, the phases of the calculated and experimental traces do not match. The calculations can be brought into almost perfect agreement with the experimental results by including hot-electron pressure effects in the coefficient for thermal expansion of the particles. This contribution is significant in our experiments because laser excitation initially creates a very high electronic temperature. A simple expression for the time dependence of the transient absorption signal is also derived that explicitly accounts for sample polydispersity. In this expression the beat period is related to the mean radius, and the damping time to the mean radius and the width of the size distribution. Thus, time-resolved laser experiments can be used to obtain accurate information about the size distribution of metal particle samples.