Coherent and Incoherent Ultrafast Dynamics in Colloidal Gold Nanorods

The study of the mechanisms that control the ultrafast dynamics in gold nanoparticles is gaining more attention, as these nanomaterials can be used to create nanoarchitectures with outstanding optical properties. Here pump–probe and two-dimensional electronic spectroscopy have been synergistically employed to investigate the early ultrafast femtosecond processes following photoexcitation in colloidal gold nanorods with low aspect ratio. Complementary insights into the coherent plasmonic dynamics at the femtosecond time scale and incoherent hot electron dynamics over picosecond time scales have been obtained, including important information on the different sensitivity to the pump fluence of the longitudinal and transverse plasmons and their different contributions to the photoinduced broadening and shift.

particle's surface with a solution of Au 3+ .All the solvents and reactants were obtained from Sigma-Aldrich (Merck KGaA, Darmstadt, Germany) and used as received without further purification.
TEM Measurements and Extinction Spectra.TEM analysis was performed with a jeol 300 PX electron microscope, while extinction spectra were recorded with a Cary 5000 spectrophotometer.
Ten images with approximately 300 NRs were analyzed for the dimensional dispersion of the colloidal nanosystems.The results are shown in Figure S1.Pump-probe Measurements.The pump and the probe beams are generated by an amplified Ti:Sapphire laser (Spitfire, Spectra Physics) seeded by a femtosecond pulsed Ti:Sapphire oscillator (Mai-Tai, Spectra Physics).The laser pulses are emitted at 800 nm, with an energy of 0.8 mJ per pulse, a repetition rate of 1 kHz, and a 180 fs pulse duration.The output laser beam is split by a 4% beam splitter into two paths.The weaker one generates a supercontinuum white light in a thin sapphire plate and is used as the probe.The stronger portion is instead used to generate the pump pulse at 400 nm via second harmonic generation in a BBO thin crystal.The pump fluence is tuned from 100 to 700 μJ/cm 2 using OD filters and its repetition rate is halved to 500Hz through an optical chopper.The collimated pump pulse and the focused probe pulse hit the samples in an overlapping region within the sample.The delay between pump and probe pulses is controlled with a motorized linear stage.
The transmitted light is dispersed and directed to a linear CMOS diode array.The quality of the TA signal, i.e.,  values (differential absorption), is improved through repeated measurements and averaging (200 measurements were averaged to obtain a sufficient signal-to-noise ratio).The obtained spectra are numerically processed to minimize white light chirping effects by using a homemade Matlab routine.Each measure is repeated at least twice to verify the reproducibility of the phenomena.
A TA spectrum plots the differential absorption Δ( !, ) as a function of the probe energy  at a fixed value of the time delay  ! after pump excitation: where  "# () and  # ( !, ) are the intensity of the signal at probe energy  without pump excitation and at a time delay  ! after pump excitation, respectively.2DES Measurements.The experiment is conducted using a 3 KHz Ti:Sapphire Coherent® Libra laser system coupled with a commercial NOPA (Light Conversion® TOPAS White) to generate pulses centered at about 600 nm.A compression of about 11 fs at the sample position is achieved through a prism compressor coupled with a Fastlite Dazzler pulse shaper for fine adjustment, as determined through frequency-resolved optical gating (FROG) experiments (Figure S2).The 2DES experiment relies on the passively phase stabilized setup, where the laser output is split into four   (within a ± 10% interval) did not show significant differences.Furthermore, considering that the TSPR has S7 energy closer to the interband transitions (2.4 eV for Au), 4 it is expected to exhibit a larger homogeneous width due to interband scattering effects. 4,6In light of these considerations, the parameters  .,  ., and  .for i=TSPR were selected to achieve the best fit with the data for each TA spectra while still maintaining the constraints mentioned before.The select parameters are summarized in Table S1.
where  is the Voigt's area,  % is the frequency center,  the Lorentzian's width and  the Gaussian's width.
For a better estimation of the short-time behavior, the Δ() and Δ() dynamics were fitted using a function that incorporates the convolution of the system's response function with the instrumental response function (IRF), which is approximated as a Gaussian pulse with a duration of 150 fs ( *@)A( of 63.7 fs): () = M () e − ′; 0,  *@)A( f ′ : ,: where RDD is the function described in Eq.1 or Eq.3 of the main text.
The 2DES data analysis was performed through a complex multi-exponential global fitting model which has been proposed in our group. 7The fitting function  = ∑  B  .C #  ,D " E # ⁄  ,.< # D "  a Error represent the 95% confidence interval obtained from linear fitting of data collected at various pump fluences.
b Error of the parameters that remain constant with respect to the pump fluence, determined by the standard deviation of multiple measurements.
Table S3.Results from the analysis of 2DES data.a Error of the parameters determined by the standard deviations of four different measurements at the same laser fluence (9 µJ/cm 2 ).

Figure S1 .
Figure S1.Dimensional characterization.a) TEM images of CTAB capped Au NRs dispersed in identical phase-stable beams (three exciting beams and a fourth beam further used as Local Oscillator, LO) in a BOX-CARS geometry using a suitably designed 2D grating.Pairs of four CaF2 wedges modulate time delays between pulses.Delay times  $ (coherence time between first and second pulse),  & (population time between second and third pulse), and  ' (rephasing time between the third pulse and the emitted signal) are defined.The rephasing and non-rephasing parts of the signal are recorded by acting on the pulse sequence.The coherence time is scanned from 0 to 80 fs with steps of 2 fs for the rephasing experiments and from 0 to 64 fs with steps of 2 fs for the non-rephasing experiments.The population time is scanned from 0 to 200 fs with steps of 3 fs in the first series of experiments and from 0 to 1000 fs with steps of 7.5 fs in the second series.The energy per pulse at the sample position is set to about 8 nJ, which corresponds to a fluence of about 9 µJ/cm 2 .The purely absorptive signal is then calculated as the sum of the rephasing and non-rephasing signals.The heterodyne detected third order signal is collected using a double lock-in method.For a more detailed description of the setup and data processing procedures, see ref.3 Each experiment is repeated at least 4 times to guarantee reproducibility.

Figure S2 .
Figure S2.Pulse width characterization.FROG measurement performed in the 2DES setup at the

Figure S3 .
Figure S3.Characteristic electron-phonon time determination.Linear fit of all the  (,*+ values obtained from Δ .and Δ .traces as a function of the pump fluence.The points are obtained as the mean of the four values at that specific fluence, and the error bar is estimated through their standard deviations.The extrapolation at zero fluences gives a characteristic electron-phonon time of about 1.16 picoseconds.

Figure S4 .
Figure S4.Gold Nanorods LSPR vs AR.Linear relationship between the LSPR wavelength and the simultaneously all the signal decay at each coordinate of the 2DES maps, and it allows simultaneous access to both the oscillating ( B ≠ 0) and non-oscillating ( B = 0) components, each one associated with a specific kinetic constant  B .S9S3.ADDITIONAL DATA

Figure S5 .
Figure S5.  and   dynamics.Normalized time traces of broadening and red shift of

Figure S7 .
Figure S7.2DES and pump-probe.The phasing of the 2DES data was performed through the

Figure S8 .
Figure S8.Amplitude of .From the linear fit of the amplitude of Δ as a function of pump fluence,

Table S2 .
Results from the analysis of pump-probe data.