7 Ultrafast and Nonlinear Plasmon Dynamics
253
For an atomic emitter with typically μ ba = (1 electron charge)·(0.1 nm) (or 1.602
×10 −29 C·m), and ω 0 = 2 eV/ = 3.04×10 15 rad/s, the corresponding spontaneous
emission lifetime is τ = 1/Γ sp = 33 ns. Since the results in the weak perturbation
regime are similar for the classical and quantum treatment (oscillator strength ∝ 1),
we can rewrite Eq. 7.22 in the following semi-classical form:
Γ sp =
8e 2 π 2
3ε 0
r
λ 0
2 1
λ 0
.
(7.23)
This equation highlights the size mismatch r/λ 0 giving rise to the long ns radiative
lifetimes for atomic emitters. Considering the SPP nanoparticles as an optical dipole
with r = 10...100 nm, compared to the 0.1 nm of atomic dimensions, will increase
the effective size of the dipole moment and thus reduce the radiative impedance
mismatch. For a one-electron oscillator of that size the radiative rate would increase
by 10 2 − 10 6 and with that the dephasing time would decrease from the ns into
the fs regime as seen for a localized SPP of a metal nano-particle. Note that this
model merely qualitatively describes the general trend of an increase in radiative
rate with increasing oscillating charge separation, with details depending sensitively
on geometry.
7.2.2 Experimental Studies of Plasmon Lifetimes
A range of studies have investigated dephasing times from both time resolved and
spectral line width analysis (see, e.g., [16, 17] and references therein). Here we discuss frequency-domain measurements of T 2 , with further time-resolved experiments
provided in Sect. 7.4. Since the time scales for plasmon dephasing are in the few femtosecond regime and the relative contributions of radiative and nonradiative decay
pathways are size-dependent, accurate measurements of the intrinsic dephasing time
usually require either a homogeneous sample or individual nanostructure, and various model assumptions are employed. Dark field scattering of individual particles
or persistent spectral hole burning give access to the homogeneous sub-ensemble
of an inhomogeneous sample. In hole burning, for example, the sub-ensemble with
resonance close to that of the exciting laser frequency is bleached, and the linewidth
of the spectral hole at different fluences is extrapolated to zero fluence to establish
the dephasing time.
As shown in Figs. 7.5 and 7.6, the linewidth and related quality factor Q =
ω 0 /Γ can be derived with a particle SPP calculation using either the Drude model
or experimental dielectric values. Most experimental results indicate 5–10 fs for
dephasing time T 2 , i.e. reduced from the theoretical maximum nonradiative value
of ∝18 fs. While the limiting nonradiative case has been demonstrated [18], the
shorter dephasing times often reported may result from structural inhomogeneities,
surface scattering, and radiation damping. Measurements of the dephasing times of
253
For an atomic emitter with typically μ ba = (1 electron charge)·(0.1 nm) (or 1.602
×10 −29 C·m), and ω 0 = 2 eV/ = 3.04×10 15 rad/s, the corresponding spontaneous
emission lifetime is τ = 1/Γ sp = 33 ns. Since the results in the weak perturbation
regime are similar for the classical and quantum treatment (oscillator strength ∝ 1),
we can rewrite Eq. 7.22 in the following semi-classical form:
Γ sp =
8e 2 π 2
3ε 0
r
λ 0
2 1
λ 0
.
(7.23)
This equation highlights the size mismatch r/λ 0 giving rise to the long ns radiative
lifetimes for atomic emitters. Considering the SPP nanoparticles as an optical dipole
with r = 10...100 nm, compared to the 0.1 nm of atomic dimensions, will increase
the effective size of the dipole moment and thus reduce the radiative impedance
mismatch. For a one-electron oscillator of that size the radiative rate would increase
by 10 2 − 10 6 and with that the dephasing time would decrease from the ns into
the fs regime as seen for a localized SPP of a metal nano-particle. Note that this
model merely qualitatively describes the general trend of an increase in radiative
rate with increasing oscillating charge separation, with details depending sensitively
on geometry.
7.2.2 Experimental Studies of Plasmon Lifetimes
A range of studies have investigated dephasing times from both time resolved and
spectral line width analysis (see, e.g., [16, 17] and references therein). Here we discuss frequency-domain measurements of T 2 , with further time-resolved experiments
provided in Sect. 7.4. Since the time scales for plasmon dephasing are in the few femtosecond regime and the relative contributions of radiative and nonradiative decay
pathways are size-dependent, accurate measurements of the intrinsic dephasing time
usually require either a homogeneous sample or individual nanostructure, and various model assumptions are employed. Dark field scattering of individual particles
or persistent spectral hole burning give access to the homogeneous sub-ensemble
of an inhomogeneous sample. In hole burning, for example, the sub-ensemble with
resonance close to that of the exciting laser frequency is bleached, and the linewidth
of the spectral hole at different fluences is extrapolated to zero fluence to establish
the dephasing time.
As shown in Figs. 7.5 and 7.6, the linewidth and related quality factor Q =
ω 0 /Γ can be derived with a particle SPP calculation using either the Drude model
or experimental dielectric values. Most experimental results indicate 5–10 fs for
dephasing time T 2 , i.e. reduced from the theoretical maximum nonradiative value
of ∝18 fs. While the limiting nonradiative case has been demonstrated [18], the
shorter dephasing times often reported may result from structural inhomogeneities,
surface scattering, and radiation damping. Measurements of the dephasing times of