254
M. B. Raschke et al.
Ag and Au particles as a function of their geometrical aspect ratio found that the
dephasing times for higher aspect ratios are longer than for similarly sized spherical
particles. Larger particles have shorter radiative dephasing times, consistent with
observations from Mie theory and the quasistatic approximation. The SPP decay
time for long rods approaches 20 fs, indicating that dephasing for these geometries
is dominated by nonradiative Drude relaxation τ D .
The different geometric behavior is important for applications of plasmonic structures. For mediating the coupling of nanoscopic emitters to far-field emission, increased radiation rates and spherical particles are preferred. However, the dephasing
time is directly related to the field enhancement T 2 ◦ F, so for many applications it
is desirable to instead maximize the plasmon lifetime.
There are various momentum scattering contributions to the T 2 SPP dephasing
discussed above. Electron–electron, electron–phonon, electron-defect, impurity, and
surface scattering can all contribute, so that the total decay rate is the sum of these
different contributions,
Γ =
i
τ
−1
i
= τ
−1
e−e + τ
−1
e− ph + τ
−1
e−de f ect
(7.24)
All of these processes have been found to be largely temperature independent with
the exception of electron–phonon scattering, which shows a linear increase with
temperature, explained with a Debye model for the material-dependent electron–
phonon interaction [19].
In addition to the extrinsic dependence of particle plasmon properties on size,
with dielectric constant ε = ε bulk , intrinsic size effects occur for particles where the
size approaches the mean free path of the conduction electrons. This regime, relevant
for few nanometer sized particles, is characterized by increased electron scattering
from the particle surface and ε ≤ = ε bulk . A radius-dependent correction to the Drude
damping can be introduced empirically [12, 20]:
Γ (R) = Γ ≈ +
Av F
R
(7.25)
with the bulk Drude damping Γ ≈ and Fermi velocity v F . A has a value near unity
depending on particle geometry and the 1/R-dependence follows from the ratio of
the surface area to particle volume.
The short timescales and multiple relaxation processes involved in SPP dephasing
lead to difficulty in interpreting results and separating the various effects in both frequency and time domain measurements. For time domain measurements, a challenge
arises that for plasmon resonances in the visible to near-IR, the SPP dynamics on few
femtosecond timescales are comparable to the shortest possible laser pulses in that
energy range (e.g. ∝2 fs optical cycle period at λ SPP = 600 nm). In the following
section as an application of the nonlinear SPP response we will also discuss nonlinear optical time-resolved techniques for the investigation of the ultrafast plasmon
dynamics.
M. B. Raschke et al.
Ag and Au particles as a function of their geometrical aspect ratio found that the
dephasing times for higher aspect ratios are longer than for similarly sized spherical
particles. Larger particles have shorter radiative dephasing times, consistent with
observations from Mie theory and the quasistatic approximation. The SPP decay
time for long rods approaches 20 fs, indicating that dephasing for these geometries
is dominated by nonradiative Drude relaxation τ D .
The different geometric behavior is important for applications of plasmonic structures. For mediating the coupling of nanoscopic emitters to far-field emission, increased radiation rates and spherical particles are preferred. However, the dephasing
time is directly related to the field enhancement T 2 ◦ F, so for many applications it
is desirable to instead maximize the plasmon lifetime.
There are various momentum scattering contributions to the T 2 SPP dephasing
discussed above. Electron–electron, electron–phonon, electron-defect, impurity, and
surface scattering can all contribute, so that the total decay rate is the sum of these
different contributions,
Γ =
i
τ
−1
i
= τ
−1
e−e + τ
−1
e− ph + τ
−1
e−de f ect
(7.24)
All of these processes have been found to be largely temperature independent with
the exception of electron–phonon scattering, which shows a linear increase with
temperature, explained with a Debye model for the material-dependent electron–
phonon interaction [19].
In addition to the extrinsic dependence of particle plasmon properties on size,
with dielectric constant ε = ε bulk , intrinsic size effects occur for particles where the
size approaches the mean free path of the conduction electrons. This regime, relevant
for few nanometer sized particles, is characterized by increased electron scattering
from the particle surface and ε ≤ = ε bulk . A radius-dependent correction to the Drude
damping can be introduced empirically [12, 20]:
Γ (R) = Γ ≈ +
Av F
R
(7.25)
with the bulk Drude damping Γ ≈ and Fermi velocity v F . A has a value near unity
depending on particle geometry and the 1/R-dependence follows from the ratio of
the surface area to particle volume.
The short timescales and multiple relaxation processes involved in SPP dephasing
lead to difficulty in interpreting results and separating the various effects in both frequency and time domain measurements. For time domain measurements, a challenge
arises that for plasmon resonances in the visible to near-IR, the SPP dynamics on few
femtosecond timescales are comparable to the shortest possible laser pulses in that
energy range (e.g. ∝2 fs optical cycle period at λ SPP = 600 nm). In the following
section as an application of the nonlinear SPP response we will also discuss nonlinear optical time-resolved techniques for the investigation of the ultrafast plasmon
dynamics.