174
F. Vallée and N. Del Fatti
This polarization decay, frequently discussed in terms of surface plasmon resonance dephasing in nanoparticles has been investigated using time-resolved second
and third harmonic generation in large noble-metal plasmonic objects [46, 48, 49,
89]. Sub-10 to -20 fs decay times have been deduced, consistent with the estimated
bulk scattering times α bulk in noble metals (confinement effects are negligible for
the investigated sizes). In the spectral domain hole burning measurements have been
performed to estimate the homogeneous SPR linewidth as a function of the size,
shape and environment of oblate particles. Dephasing times in the same ranges are
inferred by these spectral results [90–92]. More generally, for optical pulses down
to 15–20 fs, no deviation from “instantaneous” single electron excitation has been
observed in metal film consistent with polarization decay with the electron scattering time α bulk [26]. Similar results were obtained in metal nanoparticles, where this
decay is expected to be even faster, due to increase of the intrinsic scattering rates
and additional electron surface scattering (Eq. 5.5). In particular, ultrafast sub-10 fs
Landau decay has been confirmed probing the induced depopulation of electronic
states well below the Fermi energy in few nanometer silver nanoparticles [47]. For
optical frequencies larger than the interband threshold, ω e ≥ ω ib , interband interaction with light also takes place. It corresponds mostly to excitation of an electron from
the d-band to the conduction band. Ultrafast dephasing of the conduction electron-d
band hole pair is also expected due to ultrafast few-fs dephasing of carriers in metal
[93, 94].
Electronic nonlinear coherent polarization due to interaction with an intense electromagnetic pulse is at the origin of the observed nonlinearity of metal nano-materials
leading to emission of new frequencies radiated by the nonlinear dipoles, such as
in harmonic generation [48, 62–64]. It also contributes to excitation of high energy
states leading to new frequency creation by anti-Stokes photoluminescence [95, 96],
multi-step nonlinear absorption due to electronic state excitation also taking place.
However, its damping involves similar processes as for the linear coherent polarization and is thus expected to also take place on a few to a few tens of femtoseconds.
Due to this ultrafast damping, this coherent contribution is usually weaker than incoherent ones when they are involved. This is the case in nonlinear processes where
no new frequency is created such as those leading to optical Kerr effect. This has
been confirmed by the absence of coherent response in pump-probe experiments with
pulses in the 20 fs range [26, 52, 53]. In the following only resonant incoherent contributions due to metal absorption, and the associated electron and lattice relaxation
kinetics, will thus be considered.
5.3.2 Ultrafast Electron Kinetics
If only intraband excitation is considered, in both bulk and confined metallic materials
optical absorption leads to excitation of single electrons, each of them increasing its
energy by ω (i.e., an electron hole-pair is created in the conduction band). Electrons
with an energy E between E F − ω e and E F are excited above the Fermi energy
F. Vallée and N. Del Fatti
This polarization decay, frequently discussed in terms of surface plasmon resonance dephasing in nanoparticles has been investigated using time-resolved second
and third harmonic generation in large noble-metal plasmonic objects [46, 48, 49,
89]. Sub-10 to -20 fs decay times have been deduced, consistent with the estimated
bulk scattering times α bulk in noble metals (confinement effects are negligible for
the investigated sizes). In the spectral domain hole burning measurements have been
performed to estimate the homogeneous SPR linewidth as a function of the size,
shape and environment of oblate particles. Dephasing times in the same ranges are
inferred by these spectral results [90–92]. More generally, for optical pulses down
to 15–20 fs, no deviation from “instantaneous” single electron excitation has been
observed in metal film consistent with polarization decay with the electron scattering time α bulk [26]. Similar results were obtained in metal nanoparticles, where this
decay is expected to be even faster, due to increase of the intrinsic scattering rates
and additional electron surface scattering (Eq. 5.5). In particular, ultrafast sub-10 fs
Landau decay has been confirmed probing the induced depopulation of electronic
states well below the Fermi energy in few nanometer silver nanoparticles [47]. For
optical frequencies larger than the interband threshold, ω e ≥ ω ib , interband interaction with light also takes place. It corresponds mostly to excitation of an electron from
the d-band to the conduction band. Ultrafast dephasing of the conduction electron-d
band hole pair is also expected due to ultrafast few-fs dephasing of carriers in metal
[93, 94].
Electronic nonlinear coherent polarization due to interaction with an intense electromagnetic pulse is at the origin of the observed nonlinearity of metal nano-materials
leading to emission of new frequencies radiated by the nonlinear dipoles, such as
in harmonic generation [48, 62–64]. It also contributes to excitation of high energy
states leading to new frequency creation by anti-Stokes photoluminescence [95, 96],
multi-step nonlinear absorption due to electronic state excitation also taking place.
However, its damping involves similar processes as for the linear coherent polarization and is thus expected to also take place on a few to a few tens of femtoseconds.
Due to this ultrafast damping, this coherent contribution is usually weaker than incoherent ones when they are involved. This is the case in nonlinear processes where
no new frequency is created such as those leading to optical Kerr effect. This has
been confirmed by the absence of coherent response in pump-probe experiments with
pulses in the 20 fs range [26, 52, 53]. In the following only resonant incoherent contributions due to metal absorption, and the associated electron and lattice relaxation
kinetics, will thus be considered.
5.3.2 Ultrafast Electron Kinetics
If only intraband excitation is considered, in both bulk and confined metallic materials
optical absorption leads to excitation of single electrons, each of them increasing its
energy by ω (i.e., an electron hole-pair is created in the conduction band). Electrons
with an energy E between E F − ω e and E F are excited above the Fermi energy