5 Ultrafast Nonlinear Plasmonics
173
Fig. 5.2 Time scale of the different nonequilibrium electron relaxation processes in a metal film
or nanoparticle after excitation by a femtosecond pulse: coherent polarization decay (few to 10 fs),
electron-electron energy exchanges (establishment of the electron temperature in few hundred fs),
electron-lattice energy transfer (on a picosecond scale) and damping of the nanoparticle energy to
its environment (in few to few hundred ps). Acoustic vibrations take place on a picosecond to few
tens of picosecond scale depending on the film thickness or nanoparticle size and geometry
5.3.1 Coherent Electron-Light Coupling
In a bulk metal, the optical electric field couples with the electrons in the conduction band inducing their forced oscillation at the optical frequency ω e . The electron
motion generates a polarization (or equivalently a current) that radiates an electromagnetic field, this simple picture leading to the Drude expression for the quasi-free
electron dielectric function (Eq. 5.1). Light absorption takes place with polarization
decay due to electron scattering, leading to excitation of single electron-hole pairs
in the conduction band (Landau damping, where an electron is excited in a E energy
state above the Fermi energy, E F , leaving a hole in the E − ω e energy state below
E F ). It can be globally interpreted in the quasi-particle interaction model of the free
electron absorption: one photon is absorbed by one conduction band electron with
assistance of a third quasi-particle [66], the time scale for this process being then the
electron scattering time α bulk = 1/λ bulk (Eq. 5.1).
In metal nanoparticles a similar process takes place, taking into account nanoscale
electron localization. The optical field induces oscillation of the electron density at
the optical frequency ω e in the nanoparticles. This electron movement generates an
oscillating dipole in each particle that radiates at the same frequency (which is at
the origin of the particle Rayleigh scattering). A coherent superposition of material
polarization and electromagnetic field is created, light absorption taking place with
decay of the induced material polarization. As discussed by Kawabata and Kubo,
this decay takes place with single electron excitation, which is similar to Landau
damping of the collective plasmon mode in a plasma [2]. As in bulk metal, decay
is induced by electron scattering in each nanoparticle, the relevant time being then
α n = 1/λ n (Eq. 5.5).
173
Fig. 5.2 Time scale of the different nonequilibrium electron relaxation processes in a metal film
or nanoparticle after excitation by a femtosecond pulse: coherent polarization decay (few to 10 fs),
electron-electron energy exchanges (establishment of the electron temperature in few hundred fs),
electron-lattice energy transfer (on a picosecond scale) and damping of the nanoparticle energy to
its environment (in few to few hundred ps). Acoustic vibrations take place on a picosecond to few
tens of picosecond scale depending on the film thickness or nanoparticle size and geometry
5.3.1 Coherent Electron-Light Coupling
In a bulk metal, the optical electric field couples with the electrons in the conduction band inducing their forced oscillation at the optical frequency ω e . The electron
motion generates a polarization (or equivalently a current) that radiates an electromagnetic field, this simple picture leading to the Drude expression for the quasi-free
electron dielectric function (Eq. 5.1). Light absorption takes place with polarization
decay due to electron scattering, leading to excitation of single electron-hole pairs
in the conduction band (Landau damping, where an electron is excited in a E energy
state above the Fermi energy, E F , leaving a hole in the E − ω e energy state below
E F ). It can be globally interpreted in the quasi-particle interaction model of the free
electron absorption: one photon is absorbed by one conduction band electron with
assistance of a third quasi-particle [66], the time scale for this process being then the
electron scattering time α bulk = 1/λ bulk (Eq. 5.1).
In metal nanoparticles a similar process takes place, taking into account nanoscale
electron localization. The optical field induces oscillation of the electron density at
the optical frequency ω e in the nanoparticles. This electron movement generates an
oscillating dipole in each particle that radiates at the same frequency (which is at
the origin of the particle Rayleigh scattering). A coherent superposition of material
polarization and electromagnetic field is created, light absorption taking place with
decay of the induced material polarization. As discussed by Kawabata and Kubo,
this decay takes place with single electron excitation, which is similar to Landau
damping of the collective plasmon mode in a plasma [2]. As in bulk metal, decay
is induced by electron scattering in each nanoparticle, the relevant time being then
α n = 1/λ n (Eq. 5.5).