5 Ultrafast Nonlinear Plasmonics
185
-0.02
0.00
0.02
0.04
0.06
0.08
(b)
Δε
2
ib
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
(c)
Δε
1
ib
(x 10
-3
)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
(d)
Δε
2
ib
(x 10
-3
)
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
(a)
Δε
1
ib
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
2.0
ω (eV)
(e)
Δε
1
in
(x 10
-3
)
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
2.0
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
ω (eV)
(f)
Δε
2
in
(x 10
-3
)
Δε
2
in
(x 10
-4
)
ω (eV)
Fig. 5.5 Computed absolute values of the changes of the real (left) and imaginary (right) parts of
the interband, ε ib , and intraband, ε in , contributions to the gold dielectric function after excitation
with a 25 fs pulse with ω e = 1.5 eV and ωT me
e = 100 K and time t = 0 fs (dash-dotted line), 500
fs (full line) and 3 ps (dashed line) after the maximum of the excitation pulse. Different mechanisms
are considered: a and b: effect of electronic distribution change on ε ib for t = 0 fs, 500 fs and 3
ps (Sect. 4.1.1); c and d: effect of the volume change on ε ib for t = 500 fs and 3 ps (Eq. 5.33);
effect of the volume change on ε in e: for t = 500 fs and 3 ps (Eq. 5.35); f: effect of increase of
electron-electron scattering λ e−e for t = 0 fs (lower dashed line) and 500 fs (upper full line, almost
overlapping that due to ωλ e− ph ) (Eqs. 5.31 and 5.32) and of electron-phonon scattering λ e− ph for
t = 500 fs (lower full line, almost overlapping that due to ωλ e−e ) and 3 ps (upper dashed line)
(Eq. 5.34); insert of f: effect of the electron surface contribution for a 10 nm gold nanosphere for
t = 500 fs and 3 ps (Eqs. 5.7 and 5.31). All the ωε amplitudes associated to mechanisms due to
electronic or lattice heating decrease or increase with time, respectively. Note the different ωε scales
for the different mechanisms
where ωλ stand for ωλ bulk or ωλ n in film and nanoparticles, respectively. ωε in
2 is
thus much larger than ωε in
1 (ωε in
1 /ωε in
1 ≈ 2λ / ω << 1). Only the former gives a
significant contribution and will be considered in the following.
185
-0.02
0.00
0.02
0.04
0.06
0.08
(b)
Δε
2
ib
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
(c)
Δε
1
ib
(x 10
-3
)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
(d)
Δε
2
ib
(x 10
-3
)
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
(a)
Δε
1
ib
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
2.0
ω (eV)
(e)
Δε
1
in
(x 10
-3
)
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
2.0
1.5
2.0
2.5
3.0
3.5
0.0
0.5
1.0
1.5
ω (eV)
(f)
Δε
2
in
(x 10
-3
)
Δε
2
in
(x 10
-4
)
ω (eV)
Fig. 5.5 Computed absolute values of the changes of the real (left) and imaginary (right) parts of
the interband, ε ib , and intraband, ε in , contributions to the gold dielectric function after excitation
with a 25 fs pulse with ω e = 1.5 eV and ωT me
e = 100 K and time t = 0 fs (dash-dotted line), 500
fs (full line) and 3 ps (dashed line) after the maximum of the excitation pulse. Different mechanisms
are considered: a and b: effect of electronic distribution change on ε ib for t = 0 fs, 500 fs and 3
ps (Sect. 4.1.1); c and d: effect of the volume change on ε ib for t = 500 fs and 3 ps (Eq. 5.33);
effect of the volume change on ε in e: for t = 500 fs and 3 ps (Eq. 5.35); f: effect of increase of
electron-electron scattering λ e−e for t = 0 fs (lower dashed line) and 500 fs (upper full line, almost
overlapping that due to ωλ e− ph ) (Eqs. 5.31 and 5.32) and of electron-phonon scattering λ e− ph for
t = 500 fs (lower full line, almost overlapping that due to ωλ e−e ) and 3 ps (upper dashed line)
(Eq. 5.34); insert of f: effect of the electron surface contribution for a 10 nm gold nanosphere for
t = 500 fs and 3 ps (Eqs. 5.7 and 5.31). All the ωε amplitudes associated to mechanisms due to
electronic or lattice heating decrease or increase with time, respectively. Note the different ωε scales
for the different mechanisms
where ωλ stand for ωλ bulk or ωλ n in film and nanoparticles, respectively. ωε in
2 is
thus much larger than ωε in
1 (ωε in
1 /ωε in
1 ≈ 2λ / ω << 1). Only the former gives a
significant contribution and will be considered in the following.