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