Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the transient absorption data depends on s/T, which is inversely proportionalto j R /R. Thus, the sample quality can be judged simply by the number of beatsin the experimental traces.Time-resolved experiments were performed over a range of wavelengthsfor the sample in Fig. 1. The transient absorption versus wavelength data atdifferent times was then analyzed to determine the position and width of theplasmon band versus time [36]. In this analysis, the Au plasmon band wasmodeled as a Lorentzian function. The peak position versus time data wasthen be converted to radius versus time through the Mie theory expression forthe absorption cross section of small particles. Specifically, assuming that thedielectric function of the metal is dominated by free-electron (Drude model)contributions, it can be shown that the maximum of the plasmon band occursat [37].N pN max ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ð3Þ1 þ 2e mwhere q m is the dielectric constant of the medium and N p is the plasmafrequency. The plasma frequency is given by N p = (ne 2 /q 0 m e ) 1/2 , where n is theelectron density, m e is the effective mass of the electrons, and q 0 and e havetheir usual meanings. Equation (3)pshowsffiffiffithat the frequency of the plasmonband maximum is proportional to n . This proportionally allows the peakwavelength versus time data to be converted into size versus time. The resultsof these calculations are shown in Fig. 3. The key points to note are that (1)laser excitation produces an overall increase in the radius of the particles of0.4%, just after the electrons and phonons have reached equilibrium (10ps); (2) the oscillations in the radius have an amplitude that is 50% of theoverall size increase.A simple way to understand how the beat signal is generated is to considerthe lattice heating process. The pump laser deposits energy in the electronicdegrees of freedom, which subsequently flows into the phonon modeson a picosecond timescale. This increases the temperature of the nuclei, whichcauses the particles to expand. Because the lattice heating is faster than thephonon mode that correlates with the expansion coordinate, the nuclei cannotrespond instantaneously. Thus, following laser excitation, the nuclei will startto move along the expansion coordinate (the symmetric breathing mode) andpick up momentum. When they reach the equilibrium radius of the hot particles,their inertia will cause them to overshoot. The elastic properties of theparticle then provide a restoring force that makes the nuclei stop and reversetheir motions. The competition between the impulsive kick from the rapidlaser-induced heating and the restoring force from the elastic response of theparticles causes the nuclei to ‘‘ring’’ around the new equilibrium radius—thevalue of which is determined by the temperature rise in the particles.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.