linear and nonlinear optical properties of metal nanoparticlescophen04/talks/delfatti.pdffundamental...
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Linear and nonlinear optical properties
of metal nanoparticles
Arnaud Arbouet
Cyril Guillon
Natalia Del FattiPierre Langot
Fabrice Vallée
Semiconductor or metal nanoparticlesin a transparent matrix or deposited
• Quantum confinement: - modification of the electronic wave functions- quantized vibration modes
• Dielectric confinement:- Sizes << optical wavelength
→→→→ Modification of the optical properties
Semiconductor nanoparticles →→→→ quantum confinementMetal nanoparticles →→→→ dielectric confinement
→→→→ " small solids " + modifications due to confinement (N > 300 atoms / particle ⇔⇔⇔⇔ nanosphere with diameter D > 2nm)
Noble Metals (Ag, Au) : synthesis - model
Nanomaterials
Metal nanoparticles : optical properties at equilibrium
Interfaces :Visible absorption enhancement
Surface Plasmon Resonance
200 250 300 350 400 450 5000
1
2
3
4
5
Interband Transitions
Surface Plasmon Resonance
α L
Wavelength (nm)
Surface Plasmon Resonance
ΩR
Silver nanoparticles in glass matrix
Optical Properties of Metal Clusters (I)
Medium absorption (spheres):
→→→→ Resonance for εεεε1 + 2 εεεεm = 0: surface plasmon resonance
→→→→ Resonance frequency depends on: - shape- structure- environment
REO
Eint
εεεε(ωωωω)
εεεεm
+
+
+
+( )mm
mm p ε−ε
ε+εε+ε=ε2
3~
Metal Nanospheres (ε = εε = εε = εε = ε1 1 1 1 + + + + iεεεε2222) (R << λλλλ) in a matrix (εεεεm):
→→→→ effective dielectric constant:
(p << 1 : volume fraction)
( ) )(2)(
)()(
22
21
2
ωε+ε+ωεωε∝ωα
m
Optical Properties of Metal Clusters (II)
EFintrabandtransitionsinterband
transitions
CB
d - bands
Ag - D = 13 nm - p = 2x10-4
200 250 300 350 400 450 5000
1
2
3
4
5
ΩRInterband Transitions
Surface Plasmon Resonance
α L
Wavelength (nm)
ΩΩΩΩRInterband Transitions
Threshold
ΩΩΩΩib
Surface Plasmon Resonance
Wavelength (nm)
( )τ+ωωω−ωε=ωε ipb 2)()(
bound electrons (interband)
free electrons (intraband)
Metal dielectric function:
mRb
pR ε+Ωεω=Ω 2)(1
Surface Plasmon Resonance
- frequency :
- width : Γ = 1/τ = 1/τo + g vF/R
Non-equilibrium Femtosecond studies
Fundamental properties of metal nanoparticles (Silver or Gold in a matrix, solution or deposited)
→→→→ out-of-equilibrium electronic propertiesOptical excitation →→→→ Ultrafast response
of an ensemble of nanoparticles or a single unit
• Size evolution of the properties
• Mechanisms of energy and charge transfer at interfaces
Experiments: femtoseconde pump-probe setup
Optical « pump » pulse :
modification of the electronic and optical properties of the system
Optical « probe » pulse :
optical transmission changes ∆∆∆∆T/T
Experimental setup : femtosecond pump - probe
Chopper ( ω)
Computer
Variable Delay
Lock-inAmplifier
ω
+ -
Signal Reference
Argon Laser
Reference
BBO
Sample
Signal
Ti:sapphire laser
800 - 900nm1W - 25fs
prismpair
Pump: infrared pulses (25 fs)Probe: infrared pulses (25 fs)
blue (30 fs)or UV (55 fs)
Weak perturbation : ∆∆∆∆Te ~ 100KSensitivity: ∆∆∆∆T/T ~ 10-7
ω2ω3ω
(f)
f
Sample
Pump
Probe
∆T/T
Nanomaterials : Ag, Au nanoparticles in a matrix
10 11 12 13 14 15 16 17 180
5
10
15
20
Rel
ativ
e n
umbe
r
Nanoparticle radius (nm)
TEM
Hoya - Japan LASIM - Lyon LM2N - Paris / ICMCB - Bdx
Synthesis : fusion + trait. th. deposition (LECBD) chemicalDiameter D : 4 < D < 30 nm 2 < D < 4 nm 4 < D < 10 nmDispersion : < 10 % ~ 10 % 10 - 30 %Vol. Fraction : ~ 2.10-4 ~ 2 % tunableMatrix : 50 BaO - 50P2O5 Al2O3 ou MgF2 colloïde, polymer, deposited
Femtosecond investigations
Selective electron excitation (hνννν) →→→→ response of nonequilibriumelectrons
→→→→ Intrinsic electron scattering processes- Internal thermalization ( →→→→ Te) →→→→ electron-electron : ττττth ~
300 fs- External thermalization (Te →→→→ TL) →→→→ electron-lattice : ττττe-ph ~ 1
ps
→→→→ Confined vibrational modes
MatrixLattice
ττττe-ph
e ↔ eττττth ττττp-mττττp-m
Matrix
hν
Femtosecond excitation and probing
f
E
f(0)
F E F
0f(t)
E F
Te = T0 Te > T0
+ωP
ωP
t = 0 t > 0t < 0
Femtosecond excitation: intraband absorption
→→→→ Athermal electron distribution →→→→ Thermalization + Cooling
Femtosecond probing: • Transmission change ∆∆∆∆T/T ⇔⇔⇔⇔ dielectric function change ∆ε∆ε∆ε∆ε(tD)
• Probe wavelength →→→→ different electron interactions
IS T x IS∆∆∆∆T/T
Sample
Probe
Pump
*First hundreds fs :
→ Internal thermalisation of
the electron gaz at Te >To
* First ps :
→ Energy transfer from
the electrons to the lattice
* Longer time scale :
→ Energy transfer to the matrix
→ Acoustic vibrations
Ultrafast dynamics
τth (Ag) = 350 fs dans le massif
Electron dynamics
Lattice dynamics
τ e-ph (Ag) = 850 fs dans le massif
Internal Thermalization of the electron gaz
Energy transferto the lattice
Acoustic vibrations of the particles
Energy transferto the matrix
0 2 4 6 8 10 12
0.0
0.5
1.0
∆T
/ T
(n
orm
.)
Retard sonde (ps)
Metal Nanoparticles (I)
Internal electron thermalization
Internal electron thermalization: Ag - Au
• Probing energies close to the Fermi level from d-bands→→→→ electronic distribution close to EF →→→→ Internal electron thermalization
• Probe pulse : - Ag : ΩΩΩΩib ~ 4eV (310nm) →→→→ Titane - Saphir x 3 - Au : ΩΩΩΩib ~ 2.5eV (500nm) →→→→ Titane - Saphir x 2
• Low perturbation regime : dynamics independent from Ipompe
0 ∆∆∆∆fe
EF
∆∆∆∆fe
EF
bandes d
B.C.
EF
Probe UV or visible
d-bands
PumpIR
Athermal Thermal
Electron thermalization kinetics (Ag nanoparticles)
Rise time : thermalization time Phenomenological response:
Faster thermalizationfor the smaller sizes
caracteristic time ττττth
0.0 0.5 1.0 1.5 2.0
0.0
0.5
1.0
τth = 250 fs
Ag - R = 3 nm
∆T
/T
(nor
m.)
Probe Delay (ps)
BttAth relth +τ−τ−−= )/exp()/exp(1)(
Ag - D = 6 nm
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
3.2 nm
6 nm
D = 24 nm
- ∆
T/T
(
norm
aliz
ed)
Probe Delay (ps)
Electron internal thermalization: size dependence(C. Voisin et al. , PRL 85 , 2200 (2000))
• Increase of electron – electron scattering: intrinsic effect
• Modification of the electronic environment at surfaces:
- spill-out →→→→ reduction of the electron density ne →→→→ R + b - reduced polarisability of d-electrons →→→→ R - a
Fermi liquid Theory (bulk):
increase of e-e scattering close to the surfaces (screening reduction)
0 5 10 15 20 25100
200
300
400
500
colloidAl2O3
Au
τ th
(fs)
Nanoparticle diameter (nm)0 5 10 15 20 25
150
200
250
300
350
BaO-P2O5
Al2O3
Deposited
Nanoparticle diameter (nm)
Ag
τ th
(fs)
R-aR
R+b2/16/5 )()( deee n ε∝τ −
Metal Nanoparticles (II)
Electrons - lattice energy transfer
Electron energy losses: electron-phonon couplingAg - D = 3 nm in Al2O3
UV probe : Risetime: electron thermalization →→→→ electron-electron interactionsDecay: energy transfer to the lattice →→→→ electron-lattice coupling
Blue probe: ∆∆∆∆T/T ∝∝∝∝ excess energy in the electron gas →→→→ electron-lattice coupling
→→→→ Size effect ?
bandes d
B.C.
EF
UV probe
d-bands
Blue probe
0 1 2 3
0.2
0.4
0.6
0.8
1.0
∆T
/T
Probe Delay (ps)
0 1 2
0.01
0.1
1
∆T
/T
Probe Delay (ps)
pump: IR (930nm)probe: Blue (465nm) or UV (310 nm)
Electron - Phonon Coupling in Ag Clusters: Size effect
Exponential decay : electrons - lattice energy transfer time,
ττττe-ph
• Large nanoparticles: same as bulk
• Small nanoparticles: increased electron-lattice energy
exchanges
0 1 2 310
-2
10-1
100
23 nm film
D = 26 nm
D = 6 nm
Ag
∆T
/T
(no
rmal
ized
)Probe delay (ps)
0 1 2 3
0.0
0.5
1.0 Ag - clusters in Ba0-P2O5
D = 26 nm D = 6 nm
∆T
/T
(no
rmal
ized
)
Probe delay (ps)
Electron - phonon scattering : size effects (A. Arbouet et al., PRL 90, 177401 (2003))
• Similar to electron-electron scattering modifications
• Tin and Gallium: ττττe-ph ∝∝∝∝ D (M. Nisoli et al., PRL 78, 3575 (1997))
• Theory : coupling modification (electron-ion screening →→→→ full line) ? Quantized vibrations?
0 5 10 15 20 25 30
0.5
0.6
0.7
0.8
0.9
BaO-P20
5
Al2O
3
MgF2
PMMAdeposited
Nanoparticle Diameter (nm)
Ag
τ e-ph
(ps)
0 5 10 15 20 25 300.4
0.6
0.8
1.0
1.2
Al203
Colloid Colloid
Au
τ e-ph
(ps)
Nanoparticle Diameter (nm)No matrix or growing method dependence Intrinsic effect
Metal Nanoparticles (III)
Acoustic Vibrations of nanospheres
Electron-lattice quasi-equilibrium: acoustic modeAg spherical nanoparticles in glass
Transmission change probed at the surface plasmon resonance :
Oscillating signal ∆∆∆∆T/T ∝∝∝∝ A e - γγγγ t cos ( ωωωω t + ϕϕϕϕ ) Coherent (in phase) motion of the spherical nanoparticles
R
D = 26 nm
D = 6 nm
10 20 30 40-1
0
1
(ps)
( ∆T
/T) os
c
0 10 20 30
0.0
0.5
1.0
Retard sonde (ps)
∆T/T
(n
orm
.)
Fundamental radial mode (n = 0): "breathing" of an elastic sphere
Excitation mechanism
Fast lattice heating by the electrons: ττττe-ph < Tosc
fast increase of the equilibrium size Req(TL) (dilation)
(C.Voisin et al., J. Phys. Chem B 105, 2264 (2001))
Displacive excitation
cosine oscillations0 10 20 30
0
1
- Sin
Cos Ag - R = 13nm
( ∆T
/T )
osc
Probe Delay (ps)
Lattice heatingAg - D = 26 nm
Probe mechanism
Modulation of the position of the surface plasmon resonance :
Ensemble of nanoparticles:
Coherent (in-phase) oscillations
R
3 40
1
2
3
α L
Energy (eV)
ω-pr ω+
pr
ΩR
0 10 20 30-2
-1
0
1
2
3
ω-pr
ω+pr
∆T
/T
x 1
0 3
Probe Delay (ps)
0 4 8
-0.1
0.0
0.1
∆γ
(meV
)∆Ω
R
(meV
)
Probe Delay (ps)
mRb
pR ε+Ωεω=Ω 2)(1
Vibration modes of a sphere
• Silver nanoparticles in glass matrix :elastic homogeneous media
• Vibration modes of a free sphere : Lamb (1882)• Embedded sphere :
• Excitation mechanism : isotrope (via the electrons)→ radial vibration modes (dilation and contraction)
Size effects
Size reduction :
→ smaller period
→ stronger damping
R = 13 nm
R = 3 nm
RRTosc ∝=∝=γ
τωπ 12
Dependence of period and damping with nanoparticle size
1 2 3 4 5 6 7 8-0.02
0.00
∆T
/T (
norm
alis
é)
Retard sonde (ps)1 2 3 4 5 6 7 8
-1.0
-0.5
0.0
0.5
1.0
103 ∆∆ ∆∆
T/T
Retard sonde (ps)
Damping : environment effect
Origin of damping : homogeneous and inhomogeneous
Inhomogeneous : nanoparticle size distribution
Homogeneous : energy transfer to the matrix → nanoparticle - matrix acoustic coupling
Ag - R = 3nm in glass Ag - R = 2.5nm in water
R
Acoustic vibrations : fundamental radial mode
Fundamental radial mode (n = 0) :
Period Tn=0 →→→→ average diameter
Homogeneous damping : →→→→ matrix energy transfer
R
R
RdtdE
Esurface
volumeh ∝
∝τ
0
2
4
6
8
10
Osc
illat
ion
peri
od
(ps)
0 5 10 15 20 25 30 350
4
8
12
Dam
ping
tim
e (
ps)
Nanoparticle Diameter (nm)→→→→ contact / interface quality
Higher order radial modes
FFT
R
n = 0
with : Tn=1 = Tn=0 / 2.1 (period)ττττn=1 ≈≈≈≈ ττττn=0 (damping)
lower excitation (1:6)(dilation model )
n = 1
0 10 20 30 40-4
-2
0
2
4
Experimental Fit (one mode)
Ag in glassR = 13 nm
∆T
osc
(x
104 )
Probe Delay (ps)
Ag - D = 26 nm
0.0 0.2 0.4 0.6
0.2
0.4
0.6
0.8
1.0
experimental calculated (2 modes)
Ag in glass R = 13nm
Frequency (THz)
FF
T
Am
plitu
de
Ag - D = 26 nm
n=0 n=1
Conclusion
• Femtosecond perturbation of the electron gas→→→→ Electron interaction processes in a nanoparticle
• Nonequilibrium electrons: establishment of a collective response
• Electron dynamics: e - e and e - phonon interactions increase for D ≤≤≤≤ 10nm Confinement effects
• Nanoparticle lattice dynamics
Real time detection of nanoparticle coherent oscillations Radial mode frequency and damping - Optical control
• Charge transfer• Single nanoparticle
Acknowledgements
E. Cottancin LASIM - Univ. Lyon I - France
J. Lermé
M. Pellarin
M. Broyer
M. Maillard LM2N - Univ. P. et M. Curie - France
L. Motte
M. P. Pileni
M. Treguer ICMCB – Univ. Bordeaux I - France
Y. Hamanaka Nagoya University - Japan
A. Nakamura
S. Omi Hoya Corporation - Japan
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