linear and nonlinear optics with a single metal nanoparticle

Linear and Nonlinear Optics with

a Single Metal Nanoparticle

Natalia Del FattiFemtoNanoOptics GroupLASIM, Lyon - France

Outlook

I. Introduction: optical response of metal nanoparticles

- Properties of spherical nanoparticles: Mie theory- Size, shape and environment effects

II. Linear Optics: detection and spectroscopy of a single metal nanoparticle

- Far-field detection of a single nano-object - “SMS” : Spatial Modulation Spectroscopy

- Optical characterization of a single nano-object

III. Nonlinear Optics: ultrafast dynamics of a single metal nanoparticle

- Femtosecond time resolved pump-probe technique- Electronic and Vibrational response (acoustic oscillations)

Chartres cathedral - France(red color: gold nanoparticles in glass)

Metallic particles in glasses: stained glass windows

Metal Nanoparticles... and colors

Metallic particles in glasses: jewelry, ornament

Lycurgus Cup: a Roman NanotechnologyRoman Era (4th Century A.D).It appears green in reflected light...and red in transmitted light.

from IV ... to XXI century

Ag Au

Ancient cup (Central Europe)

Metal Nanostructures

Metallic nanostructured materials :

- Physical and chemical synthesis, different shapes, different matrices (solid, liquid, deposited, ...)

100 nm

- Intermediates between bulk / molecular systemsD = 40 nm : ~ 2 million atomsD = 20 nm : ~ 250 000 atomsD = 4 nm : ~ 4000 atomsD = 2 nm : ~ 250 atoms

D = 3 nm : same number of atoms at the surface / core

- Specific properties, « Small is different » Confinement effects (dielectric and quantum)

- Applications in optics, chemistry, biology,...

Part I

Introduction: optical response of metal nanoparticles

- Spherical nanoparticles: Mie theory- Dielectric constant of a metal- Size, shape and environment effects

Linear Optics: detection and spectroscopy of a single metal nanoparticle

Nonlinear Optics: ultrafast dynamics of a single metal nanoparticle

Optical response of metal nanoparticles

• Experimental studies: characteristic length → optical wavelength λ small objects (<< λ): M. Faraday (Philos. Trans. R. Soc. 147, 145 (1857))

• Theoretical model:- Absorption/Scattering by a nano-sphere → Mie theory (Am. Phys. (Leipzig) 25, 377 (1908))

- Small nano-spheres: quasi-static approximation → generalization: - nano-ellipsoids

- core-shell particles- Numerical calculations

F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles, John Wiley (1998)

U. Kreibig & M. Vollmer, Optical Properties of Metal Clusters, Springer Verlag, Berlin (1995)

Optical response of a nano-object

- Nano-sphere with radius R = D/2 and dielectric constant: ε = ε1 + iε2

in a non absorbing homogeneous dielectric environment: εm (real)- Incident e.m. field: Ee (He) → scattered field: ES (?)

→ internal field: Ei (?)

- Cross sections (?) : scattering σs (scattered power PS = σS Ie) absorption σa (absorbed power Pa = σa Ie) extinction σe = σs + σa

REe

Ei

ε(ω)εm

ES

Spherical dielectric inclusion in adielectric matrix: optical response?

Constituting materials: dielectric constants

The nano-sphere: Mie theory

Electromagnetic problem:- Maxwell’s equations- Boundary conditions: continuity of E et H parallel to the surface (and D et B orthogonal)

E ∧ n =cste ; H ∧ n =cste

- Incident field: linearly polarized plane wave

But: mathematically complex:- nanosphere: spherical symmetry → boundary conditions: spherical coordinates- e.m. field: plane wave, Cartesian coordinates

Solution: development of the fields in spherical harmonics → internal and scattered electromagnetic field ⇒ σa et σs (and σe) expressed in terms of spherical Bessel functions ⇒ power series expansion in D / λ → numerical calculations

cceAxE tkziee += − )(ˆ ω

Ee + EsEi

ε(ω)εm

n

Small size: D < λ/10 (~ 30 nm)→ lowest order development of Mie theory (dipolar)⇔ quasi-static approximation

with kz-ω t constant over the sphere → incident e.m. field constant over the nanosphere (at each time)

Electrostatic problem: much simpler → scalar potential

Poisson’s equation:

surface continuity:

- incident:

- internal: → internal electric field

Small size D << λ: dipolar approximation

xAee −=Φ

0=∆Φ

rrise

mise ∂Φ∂

=∂

Φ+Φ∂Φ=Φ+Φ εε )(;

eem

mi EfEE )(

23 ω

εεε

=+

=xAem

mi εε

ε2

3+

−=Φ

cceAxE tkziee += − )(ˆ ω

cceAxE )tkz(iii += ω−

xAii −=Φ

0=∆Φ z

Proportionality factor f : local field factor (or dielectric confinement factor)

Small size: quasi-static approximation

- scattered: with

→ scattered field: induced dipole p at the sphere center

30m

s r4r.pεπε

=Φ em

mnpm EVp ⎥

⎦

⎤⎢⎣

⎡+−

=εε

εεεε2

3 0

Ee k z

x

y

pEe

electrons

Displacement of electrons (-) / (+) lattice ions (fixed)→ two displaced charged spheres ⇔ dipole (outside field)→ oscillating dipole (dipolar approximation), electron oscillation at ω

+ restoring force (→ resonance)

→ large size: retardation effect (non uniform field over the sphere)

Simple interpretation

Optical response of a nano-sphere: cross-sections

- Scattering cross-section:

→ proportional to the square of the nano-sphere volume

- Absorption cross-section:

→ proportional to Vnp

• for small nano-spheres, absorption dominates: σe ≈ σa >> σs (σs / σa ∝ (D/λ)3)

• both cross-sections depend on

2npV

2

m

m2m4

2np

3

s 2V24

ε+εε−ε

ελ

π=σ

2m

22/3m

npa

2

V18

ε+ε

εε

λ

π=σ

2m2ε+ε

Resonance for ε1 + 2εm = 0 ⇒ ε1 < 0 → metals

→ ε2 weakly dispersed:

→ Surface plasmon resonance Dielectric confinement effect (resonant collective oscillation)

emkE

2)(

22h=k

Parabolic conduction band:

bandes d

B.C.

E F

E

k

Dielectric constant of bulk (noble) metals

⇓

EF

Métal Structure a (Å) ne (x 1022 cm-3) me/m0 EF (eV)

Ag [Kr] 4d10 5s1 4.08 5.86 1 5.49

Au [Xe] 4f14 5d10 6s1 4.07 5.90 1 5.53

Cu [Ar] 3d10 4s1 3.61 8.47 1.5 4.67

Ag

• Optical absorption : occupied to unoccupied states

- interband transitions: d electron state → conduction band state (E > EF)

⇒ threshold hω > hΩib

- intraband transitions: Drude model ⇒ ε2 ∝ 1/τ collision assisted (phonon)

Dielectric constant of bulk (noble) metals

EF intrabandtransitionsinterband

transitions

C.b.

d-bands

( )τ+ωωω−ωε=ωε i)()( 2p

b

bound electrons(interband)

free electrons(intraband)

• Dielectric constant of a noble metal

Métal Ag Au Cu

hΩib (eV) 3.9 2.4 2.1

)/( 022

eep menwith εω = 1 2 3 4 5 6

-40

-20

0

hω ( eV )

ε 1 ;

ε 2

ε2

ε1

2 4 60

2

4

6 εib1

εib2

Ag

UV - VIS

Metal nanoparticle (D> 2nm ~ 250 atoms): “Small solid”

Dielectric function of the confined metal:

- Intraband contribution:

• classical model:

electron mean free path: l ≈ vFτ ≈ 30 nm (vF ≈ 1.4 106 m/s, τ ≈ 10-20 fs)

l comparable to D → electrons-surface interaction time: ∝ D/vF

with 1/τnano = 1/τ + 2g vF/D (g ≈ 1)

• quantum mechanics: → transition between confined states (k is no more a good quantum number)

- Interband contribution:non modified down to D > 2nm (experimental)

Dielectric constant of nanoparticles: confinement effects

EF intrabandtransitionsinterband

transitions

Cond.band

d-bands

( )nanopb i τωωωωεωε +−= 2)()(

-20

-10

0

10

Wavelength (nm)700 500 300

hΩ R

-2εm

ε2

ε1

ε

2 3 40

1

2

3

hΩ ib

AgD = 13 nm

αL

hω (eV)

Extin

ctio

n (O

D)

Surface plasmon resonance: noble metals

1.5 2.0 2.5 3.00.00

0.05

0.10

hΩ ib

AuD = 10 nm

hω (eV)

-20

-10

0

10

hΩR

Wavelength (nm)400500600700800

-2εm

ε2

ε1

____ experimental- - - - computed

ε1 + 2εm = 0

ε1 + 2εm = 0 → Surface plasmon resonance:

mRb

pR εεω 2)(1 +Ω=Ω

bound electronsenvironment

)(122

3R

ib

p

R

nanoΩ

Ω+=Γ ε

ωτ

increase with size decrease (surface: g) overlap with interband transitions: broadening

Frequency:

Width:

Surface plasmon resonance: noble metals

350 400 450 5000

1000

2000

3000

x10

absorption scattering

Ag in glassD = 20 nm

σa

; σ

s

(nm

2 )

Wavelength (nm)500 600 700 800

0

100

200

300

400

absorption scattering

x100

Au in glassD = 20 nm

σa

; σ

s

(nm

2 )

Wavelength (nm)

22

4

23

224

mm

mnp

sV

εεεε

ελ

πσ

+−

= 222/3

2

18

mm

npe

V

εε

εελ

πσ

+=Scattering: << absorption:

Ag Au

Deviation from the dipolar (quasi-static) approximation

Displacement of electrons / lattice ions

large size: retardation effectnon uniform field over the particle

cceAxE )tkz(iii += ω−

xAii −=Φ

0=∆Φ

Ee

k

electrons

+ +

+

- - - -

- +

++ + ...

dipole quadrupole

→ Multipolar expansion of the nanoparticle response

Surface plasmon resonance: size effect

3.0 3.5 4.00.0

0.1

0.2

hω (eV)

300350400

Wavelength (nm)

D=40nm D=20nm D=10nm D=5nm

Ag - Vacuum g = 1

σ s /D

3 ;

σe /

D3

(nm

-1)

400 500 600 7000

10

20

σ e (1

04 nm2 )

Wavelength (nm)

0

1

2

3

4

3.5 3 2.5 2hω (eV)

Na - Vacuum D = 40 nm D = 80 nm D = 120 nm D = 160 nm D = 200 nm

σ a (1

04 nm2 )

• Dipolar approximation (few nm - few 10 nm): - ΩR size independent - width size (electrons-surface interaction)

• Mie theory (D ≥ 30-50 nm): - red shift - broadening (radiative damping) - multipolar resonances

Surface plasmon resonance: environment effect

2 3 40.0

0.5

1.0

800 700 600 500 300 400 500 600

Ag - D = 26 nm

α

(nor

mal

ized

)

hω (eV)2.0 2.5 3.0

Wavelength (nm)Wavelength (nm)400

εm=1 εm=1,77 εm=2,15 εm=3,1

Au - D = 20 nm

hω (eV)

Nanoparticles in vacuum (εm = 1), water (1.77), silica (2.15) or alumina (3.1)

mRb

pR εεω 2)(1 +Ω≈Ω


Gold colloidal solution (different solvents)

S. Underwood and P. Mulvanay, Langmuir 1994

Au, D ~ 16nm

Ag deposited on SiO2 + oil oil removed dark blue: spheres 50-90 nm light blue: hexagon nanoparticles J. J. Mock, D. R. Smith and S. Schultz red: triangles Nano Letters 2003

Single nanoparticle (scattering)

Environment sensitivity → local nanosensors (bio-sensors)

22

2/3

2

4

223

)1(

2

)1(3

8

mii

mnpie

mii

mmnpis

LL

V

LLV

εε

ελ

επσ

εεεε

λ

επσ

−+=

−+−

=

Surface plasmon resonance: shape effect

Small ellipsoids

quasi-static approximation (Mie-Gans), for light polarized along the axes i :

0)1/1()(1 =−+Ω→ miiR LResonances εε

x

z

y

ac

b

- Sphere: Li = 1/3 )1L(i

i =∑

Li : geometrical factorsdepending on the aspect ratio

∑=i

isese

N,, 3

σσ

Ensemble of randomly

oriented ellipsoids (density N):

2 3 40.0

0.5

1.0

Wavelength (nm)

Ag - Prolate

σ e

hω (eV)

X Y,Z

700 500 300

→ Tuning the SPR spectral position

Surface plasmon resonance: other shapes

K. L. Kelly et al, J. Phys. Chem. B 2003

Ag prisms, thickness 16 nm. DDA calculations with a 2 nmcubic grid (for snip = 0: 68 704 dipoles are used)

Ag prismsexternal E-field enhancement contours

at 770nm → tip effect

Numerical approaches:

• Discrete Dipole Approximation (DDA), Goodman, Draine & Flatau, Opt. Lett. 1991 → breaking up particle into small volumes, each of which carry dipole moment• Finite Element Method (FEM), ex. COMSOL Multiphysics software → numerical solution of differential equations• ...

Practical Work...

Question 1: Why does it appeargreen or red depending on theillumination conditions ?

400 500 600 700 800

0.0

0.5

1.0

Absorption

σ a (a

rb. u

nits

.)Wavelength (nm)

400 500 600 700 800

0.0

0.5

1.0

Scattering

σ s (a

rb. u

nits

.)

Wavelength (nm)

Gold nanospheres in glass

Hint ...

Question 2: What is the size ofthe nanoparticles ??

Licurgus Cup

Part II



- Far-field experimental techniques - Optical signature: Gold nanospheres - Shape effect: Gold nanorods


Non luminescent object: → Detection of light scattering or absorption

♦ Near field: local environment perturbationT. Klar et al., Phys. Rev. Lett. 1998

♦ Far field: focused beam 300 - 500 nm → diluted sample ( < 1 particle / µm2 ) - Scattering (∝ V2 ; size ≥ 20 nm): → Dark field microscopy

C. Sönnichsen et al., Appl. Phys. Lett. 2000, New J. of Phys. 2002 (Heterodyne detection) K. Lindfords et al. Phys. Rev. Lett. 2004

- Absorption (∝ V ; small particle): Gold nanosphere D = 20 nm - 5 nm absorption of ∆P/P ~ σext / Slaser ~ 10-3 - 10-5 of the incident light

→ Photothermal techniqueD. Boyer et al., Science 2002, S. Berciaud et al. Phys. Rev. Lett. 2004

→ Spatial modulation technique (quantitative)A. Arbouet et al., Phys. Rev. Lett. 93, 127401 (2004)O. Muskens et al., Appl. Phys. Lett. 2006

Optical study of a single metal nanoparticle

Ensemble measurement: 104 to 106 particles⇒ Size and shape fluctuations ⇒ Single nano-object study

Dark Field Microscopy

Blocking the direct incoming light: collection of scattered light

condenser

scattered light

blue: Ag spheregreen: Au sphereorange: Au rods

scatteringspectrum

22m4

2np

3

s )(f3

V8ωε−ε

λ

π=σ

Single particle detection (D ≥ 20 nm)

Size dependent dark-field scattering spectra

Single particle detection (D ≥ 20 nm)

Normalized scattering spectra

Au: experimental + Mie theory

(radiation damping, quadrupolar effects)

C. Sönnichsen et al., New J. of Phys. 4 (2002)

• Dipolar approximation (few nm - few 10 nm): - ΩR size independent - width > size < (electrons-surface interaction)

• Multipolar Mie theory (D ≥ 30 - 50 nm): - red shift - broadening (radiative damping) - multipolar resonances

Spatial Modulation Spectroscopy (SMS)Modulation of the nanoparticle position ⇔ Modulation of the transmitted light

A. Arbouet et al., Phys. Rev. Lett. 2004

∆T/T

f 2f

X (µm) X (µm)

Y (µm) Y (µm)

Gold nanoparticles<D> ~ 16 nm

diluted on glass

λ = 532 nm

lock-in amplifier

Transmitted power P

f

piezo f

objective100x

f , 2f

XY scanner

Y (µm)

λ = 633 nm

X (µm)

Metal nanoparticle ⇒Surface Plasmon Resonance

Au - D = 20 nm :σext (532 nm) ≈ 10 σext (633 nm)

400 500 600 7000

100

200

300

400

633 nm

532 nm

Au - 20nm

σex

t (nm

2 )

Wavelength (nm)

λ = 532 nm

Y (µm)

X (µm)

TT∆

Metal Nanoparticles ?

detection at f

yδy << spot size

detection at 2f

y

Modulation of the position at f : y0 → y0 + δysin(2πft)

)2(sin2

)2sin(),( 222

2

0000

ftyIft

yIyxIPP y

y

exty

yextextit πδ

∂

∂σ−πδ

∂∂

σ−σ−≈

yy0

I(x0,y0)δy

Nanoparticle at position (x0, y0) ⇒

Transmitted power :

I : intensity profile at the focal spot

( )00,yxIPP extit σ−=

Spatial Modulation : model

Absorption cross-section of a single nanoparticle

Au nanoparticle <D> = 10 nm

λ = 532 nm

dFWHM = 0.34 µm

δy = 0.27 µm

f 2f

Absorption cross-section

σabs = (53 ± 2) nm2

@ λ = 532 nm-0.50 -0.25 0.00 0.25 0.50

-4

-2

0

2

4

∆P /

P x

10 4

y - y0 (µm)-0.50 -0.25 0.00 0.25 0.50

-1

0

1

2(d)

∆P /

P x

10 4

y - y0 (µm)

SMS microscope

grating

Non-linearphotonic crystal fiber

Supercontinuum λ > 450 nm

Ti- sapphirefemtosecond oscillator

100 mW - 780 nm - 20fs

Optical absorption signature

Absorption spectroscopy of a single nanoparticle

Quasi-spherical gold nanoparticles

Single particle: Size effect

450 500 550 6000

100

200

300

400

σ abs

(nm

2 )

Wavelength (nm)

White light

Spectroscopy

19.5 nm

18 nm

• Absolute value of the extinction (absorption) cross-section:

→ Mie theory: optical determination of the particle size D → good agreement with TEM (mean diameter and size dispersion)

12 13 14 15 16 17 18 19 20 210

5

10

15

<D > = 16.6 nm

Coun

ts

D iam eter (nm )

N anoscope

12 13 14 15 16 17 18 19 20 210

10

20

30

40

50

60<D > = 16.2 nm

Coun

ts

D iam eter (nm )

TE M

• Surface Plasmon Resonance (SPR) spectrum

Unpolarized light: Small sphere model

2m

22/3mabs

218V

ε+ε

εελπ=σ

0

30

6090

120

150

180

210

240270

300

330

450 500 550 600 6500

50

100

150

200

250

300

350

400

Angle polarisation

σ ab

s (n

m2 )

Longueur d'onde (nm)

Single particle: Anisotropy

Au

Polarizationangle

Wavelength (nm)

a

c

Nanoellipsoids: SPR splitting ⇒ Aspect ratio: c/a = 0.92

22

2

2/3

1

2

mi

ii

miabs

LLL

V

ε−

+ε

ε

λ

επ=σ

Linearly polarized light → two "extreme" directions

Optical identification of a nanoobject: size, anisotropy and orientation→ studies of surface effects ; local environment effects ; …

0 .5 0 .6 0 .7 0 .8 0 .9 1 .00

4

8

12 < η > = 0 .9

Coun

ts

A spect ra tio c/a

N anoscope

0 .5 0 .6 0 .7 0 .8 0.9 1 .00

20

40

60

< η > = 0 .9

Coun

ts

A spect ra tio c/a

T E M

Aspect ratio statistics

O.Muskens et al., Appl. Phys. Lett. 2006

Shape effect: gold nanorods

100 nm

Shape effect: Gold nanorods (in PVOH)

Ensemble

90 nm

M.P. Pileni - LM2N, Paris A. Brioude, G. Bachelier - Lyon

15 - 20 nm

40 - 60 nm

450 475 500 525 550 575 600 625 650 675 7000

2

4

6

8

10σ ex

t (x

10-1

5 m2 )

Wavelength (nm)

35 nm

Single nanorod

0

10

20

0

30

6090

120

150

180

210

240270

300

330

0

10

20

630 nm

- Longitudinal SPR

0

2

4

0

30

6090

120

150

180

210

240270

300

330

0

2

4

510 nm

- Transverse SPR

- Interband absorption

Gold nanorods

450 500 550 600 650 7000

2

4

6

8

10

0

30

6090

120

150

180

210

240270

300

330

σ ext (

x 10

-15 n

m2 )

λ (nm)

Extin

ctio

n (n

orm

.)

450 500 550 600 650 700 7500.0

0.2

0.4

0.6

0.8

1.0 ext abs scatt

x 9

Extin

ctio

n (

norm

.)

λ (nm)

Finite element model / DDAfor fixed: - shape (cylinder with hemisphere caps)

- environment refractive index→ aspect ratio L/D = 2→ Length (volume): L ≈ 50 nm

L

D

Transverse Longitudinal

New information ( / scattering experiments): O.Muskens et al., J. Phys. Chem. C 2008 - Volume - Longitudinal / Transverse SPR amplitude (better agreement for sharper tips)

Dominated by absorption

One-by-one correlation with TEM:nanoparticles on silica grids

Optical TEM

1 µm

0° 90°

D = 102 nm

400 500 600 700 8000

1

2

3

4

5

σ ext(λ

) (1

04 nm

2 )

Wavelength (nm)

Agreement withMie theory

Au

Ag@Si02

P. Billaud et al., JPCC 2008

Environment effect: “local” refractive index

Local environment: fixed size (D = 16 nm)

Effect on amplitude and SPR frequency→ nm = 1.5→ nm = 1.4→ nm = 1.25

450 500 550 6000

100

200

300

400

500

σ abs

(nm

2 )

Wavelength (nm)

→ Probe of its nano-environment: local refractive index

2m

22/3mabs

218V

ε+ε

εελπ=σ

Single nanoparticles: local environment

Au - 16nmin PVOH

Single nanoparticles: local environment statistics

Mean refractive index:- on glass: 1.34- embedded in polymer (PVOH): 1.45

Statistics: fluctuations of the “local” environment

Au/air

glass

glass

PVOH

PVOH added after /before spin coating

→ “Local” refractive index of the nano-environmentO.Muskens et al., Phys. Rev. B 2008


0 1 2 30.0

0.2

0.4

0.6

0.8

1.0

∆λ R /

∆λm

axR

Shell thickness / Core radius

Au

SiO2

water

Environment sensitivity: scale ?

→ Core-shell nanoparticle

(quasi-static approximation σe, σs)

Surface plasmon resonance shift asa function of shell thickness

Almost complete shift forshell thickness ≡ core radius

Sensitivity to the environment overa nanoscale (about its size)

⇔ extension of the local field

waterR

SiORR λλλ −=∆ 2max

Optical response: field (Ag)

2 3 4

0

5

10 |f(ω)| ϕ σe

ϕ

|f

(ω)|

hω (eV)

f(ω) = |f(ω)|eiφ

0 1 2 30

5

10

hω=hΩR hω=hΩR+0,2 eV hω=hΩR-0,2 eV

|Ei,

e+s /

Ee|

z / R

Internal/external field

xz

Ei

B2

m1 )(fp αωε

ε=α

Absorption:

Local field factor:m

mfεωε

εω2)(

3)(+

=

eem

mi EfEE )(

23 ω

εεε

=+

=

Enhancement of the internal field

and of the external field,on a scale of about the radius R

Ag

Surface plasmon resonance: nanoparticles as sensors

Environment sensitivity → local nanosensors (bio-sensors)

G. Raschke et al., Nano Letters 3, 935 (2003)

Improved sensitivity: shape (nanorods, triangle, ...), structure (core-shell)

Confinement effect: SPR width and quality factor

Single particle: width of the SPR

2223

2

18

mm

abs

nn

V+ε

ελπ

=σ

Electron scattering impact on absorption spectra: width of the SPR

Width:DgvF

Rib

p

RR

p

RR

21)()()(0

22

322

3+

τ+Ωε

ω

Ω≈Ωε

ω

Ω≈ΩΓ

( )τ+ωωω−ωε=ωε ipb 2)()(

DgvF211

0+

τ=

τwith

Electron scattering rate(τ0: e-phonons, g: e-surface)

g-surface scattering coefficient: fundamental problem quantum mechanical predictions (Kubo, 1966)

→

More precise studies: Ag@Si02

Large width fluctuations:Single Au colloids:g surface factor : 0.2 ≤ g ≤ 2

→

... but hard to study:- Ensembles: inhomogeneous effects

(shape and environment distribution)- Single: Exp. : non-controlled environment (chemical damping)

Th. : g extracted by Mie theory fits (dependence on ε tabulated values)

in air on glass embedded in PVOH with PVOH after spin-coating

g = 0

1

2

Surface plasmon resonance damping: size dependence

Controlled environment: Ag@SiO2 nanoparticles Luis Liz-Marzán, Universidad Vigo, Spain

Ag

2SiOnm15e =

Silver sphere mean diameter:<D> = 12 nm<D> = 25 nm<D> = 50 nm

Ag: surface plasmon resonance away from

the interband absorption:

→ SPR width: size dependence

→ no surface effects visible on ensemble spectra 300 350 400 450 500 550 6000.0

0.5

1.0

Extin

ctio

n (n

orm

.)

Wavelength (nm)

0.03 0.06 0.09

0.2

0.4

0.6

0.8<D> (nm)

Γens

R

(eV

)

1 / <D> (nm-1)

50 30 20 10

0)(2 ≈Ωε Rib

DgvF

Rp

RR

21)()(0

22

3+

τ≈Ωε

ω

Ω≈ΩΓ

0.02 0.04 0.06 0.08 0.10

0.1

0.2

0.3

0.4

0.5

Diameter (nm)

Γ R

(eV

)

1 / Deq (nm-1)

0.04 0.06 0.08 0.100.1

0.2

0.3

Γ R (eV

)

1/Deq (nm-1)

605040 30 20 10 50

0

1τ

eq

FR D

gv21

0

+≈Γτ

• Small particles:

• Big particles : radiative damping

Single nanoparticles: e-surface scattering in AgPolarization dependent spectra by SMS → aspect ratio η , equivalent diameter Deq

375 400 425 450 475 500 5250

200

400

600

800

1000 80°170°

σ ext (

nm2 )

Wavelength (nm)

350 400 450 5000

200

400

σ ext (

nm2 )

λ (nm)

Deq = 13.2 nm (14.2 nm)

η = 0.97

→ Quantitative analysis of surface scattering at the single particle level

→ g coefficient measured from exp. slope

g = 0.7 ≈ quantum-box Kubo model g’ = 0.45 including size-dependent 1/τ0

⇒ more realistic quantum calculations : g’ ~ 0.4

g = 0.7

1/τ0(D)

H. Baida et al., Nano Letters 2009

Part III




- Femtosecond time resolved pump-probe technique- Electron-lattice coupling: Silver nanosphere

- Acoustic vibrations of a single nano-object

Ultrashort pulse laser: Titanium - Sapphire

→ pulse duration ~ 20 fs→ repetition rate ~ 100 MHz→ infrared central wavelength tunable λ : 680 → 1080 nm→ average power 1 W (peak power 500 kW, focused

peak intensity 1015 W/m2 )

There are as many femtoseconds in one second …

than seconds in 30 million years !!1 fs = 10-15 s

The femtosecond laser

See Prof. Chang Hee Nam’s lesson, Monday 30 November

Non-linear optics

Second Harmonic Generation ω + ω → 2ωE(t) = A cos(ωt)

→ PNL ∝ E . E ∝ cos(2ωt)

Non linearcrystal

ω

2ω

ω

-100 -50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

25 fs

Temps ( fs )

Cor

réla

tion

cr

oisé

e

420 430 440 4500.0

0.2

0.4

0.6

0.8

1.0

16nm

Inte

nsité

(

un. a

rb.)

Longueur d'onde ( nm )

From IR fs pulses → blue / green fs pulses

...)2(00 +⋅χε+χε= EEEP

Nonlinear response of a material under strong em fields:

⇒ Polarization: P = PL + PNL

χ(2) = 2nd order non-linear susceptibility

→ generation of fs pulses at different wavelengths

Pump pulse: ultrafast perturbation of thesystem : modification of the mediumelectronic and optical properties

Delayed Probe pulse: probe the system andits relaxation to equilibrium.The transmission change, ∆T/T,induced by the pumpis measured as a function of the tunablepump-probe delay, tD

Time resolved pump-probe spectroscopy

Sample

Pump

Probe

∆T/T

0 5 10 15 20 25 30

∆T/

TPump - probe delay (ps)

Pump-probe: high sensitivity Lock-in detection scheme

Pump

Retardvariable

Pompe

Sonde

Chopper

Echantillon

Signal Réfèrence

LOCK-IN+

Probe

Sample

Pump

Pump- ProbeDelay

0 5 10 15 20 25 30

∆T/

T

Pump - probe delay (ps)

Sample

Pump

Probe

∆T/T

Pump intensity modulated at frequency ω (chopper).For a fixed pump-probe delay tD:

Sample Transmission: )()( )(DpumpD tTTtT ω∆+= 0

Photodiode: ipumpiT ITITI ×∆+×= ω)(0

Lock-in amplifier: ω modulated part

→ sensitivity down to ∆T/T ~ 10-6 or better

Fs experimental set-up in Lyon

• Home-made 18 fs oscillator, 76 MHz

• Coherent Chamaleon 680 - 1080 nm

• Coherent MIRA 100 fs oscillator

• Coherent REGA amplifier, 250kHz

• Coherent OPA system

• Non-linear SHG, THG

• Supercontinuum generation

• High sensitivity pump-probe setup

• SMS single nanoparticle setup

• Femtosecond Pump: selective electron excitation (temperature increase ~ few 100 K)

MatrixLattice

τe-ph

e ↔ eτth τp-mτp-m

Matrix

hν

Femtosecond investigation of metal nanoparticles

Sample

Pump

Probe

∆T/T

• Investigation of the nonequilibrium electron kinetics (fs – ps time scale): → Intrinsic electron interaction processes (electrons-electrons / electrons-lattice) → Confined vibrational modes → Nanoparticle - environment coupling

Te = T0 Te > T0

+hωPp

hωPp

t = 0 t > 0t < 0

f

E

f(0)

F E F

0 f(t)

E F

hωPphωpr

*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 in metal nanoparticles

τth = 350 fs (Ag-bulk)

Electrondynamics

Latticedynamics

τ e-ph = 850 fs (Ag-bulk)

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

(nor

m.)

Retard sonde (ps)

Many studies in ensembles (J. Phys. Chem. B 105, 2264 (2001))→ Single nanoparticle

Femtosecond spectroscopy of a single nanoparticle

IS T x IS∆T/T

Sample

Probe

Pump femtosecond pump - probe:

probe around the SPR wavelength

Linear absorption: probe beam

detection and optical characterisation

Nonlinear femtosecond response

pump (2ω) & probe (ω)

probe

ext

lenanopartic STT σ∆

−=∆

1

First measurements: single silver nanospheres 20 - 30 nmO.Muskens, N. Del Fatti and F. Vallee, Nano Letters 6, 552 (2006)

Electron-lattice energy exchanges: single Ag nanosphere

350 400 450 500 5500

5

10

σ ext

(x 1

0-15 m

2 )

Longueur d'onde (nm)

Ag - D = 30 nm

D = 21 nm

IR excitation / SPR probing (425 nm)

0 1 2 3

0.0

0.4

0.8

1.2

∆T/T

(x

10-4)

Probe delay (ps)

0 200 4000.0

0.5

1.0

∆T/T

max

(x

10 -4

)

PP (µW)

probe

ext

pumpext

ext

lenanopartic STT σ

σσ

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−=

∆

1

TransmittedPower

MicroscopeObjective

100x

Femtosecond spectroscopy of a single Ag nanosphere

Optical characterisation of a single nanoparticle (linear absorption spectrum) & femtosecond pump - probe study :

0.0 0.2 0.40.6

0.9

1.2

1.5

τ e-ph

(p

s)

Pump power (mW)

• ∆T/T ∝ electron excess energy⇒ Decay: electron-lattice energy exchange → τe-ph

0phe−τ

Strong excitation regime

excitation dependent decay: τe(Te)

Weak excitation regime

∆T decay with τ0e-ph = c0 T0 / G

⎪⎪⎩

⎪⎪⎨

⎧

−=

−−=

)(

)()(

LeL

L

Lee

ee

TTGdt

dTC

TTGdt

dTTCThermal distributions: Two temperature model

Te ; TL ; G = e-lattice coupling constant

Ce(Te) = c0 Te ; CL : heat capacities

Electron-phonon energy exchange in single Ag nanospheres

0.0 0.2 0.40.6

0.9

1.2

1.5

τ e-ph

(p

s)

Pump power (mW)

Known nanoparticle ⇒ known excitation Te - T0

→ comparison with the two-temperature model

max

Electron-phonon coupling in single Ag nanospheres

Comparison wih two temperature model: → Same electron-phonon coupling as in ensemble measurements (in glass) → No environment dependence (large excitation) → No e-ph coupling dependence on excitation regime

0.1 1

1.0

1.5

2.0

τ e-ph

/ τ 0 e-

ph

(T max e -T0) / T0

pump power⇒ T

emax

O. Muskens, N. Del Fatti and F. Vallee, Nano Letters 2006

∆Temax : 110 - 430 K (30nm)

∆Temax : 220 - 380 K (21nm)

Non-linear SPR response: single Au nanorod

i) Detection and optical characterizaion

500 600 700 8000

2

4

6

8

Abso

rptio

n (a

rb. u

nits

)

Wavelength (nm)

nano-batonnet unique ensemble

ii) Ultrafast nonlinear response

pump & probe

Linear absorption spectroscopy

Ultrafast nonlinear response of a gold nanorod

0.0 0.5 1.0 1.5 2.0-6

-3

0

3

6

9 780 nm 800 nm 830 nm

∆T/T

(x

10-5

)

Probe delay (ps)0.0 0.5 1.0 1.5 2.0

-1.0

-0.5

0.0

0.5

1.0

1.5

∆T/T

(n

orm

aliz

ed)

Probe delay (ps)

Simulations

Optical nonlinearityof a single nanorod:

Quantitative interpretation(no size, shape or orientation

averaging)

60 nm

15 nm

Shape, size, orientation

Acoustic vibrations of a nano-object

Vibrational acoustic modes:

- Frequency: size and shape dependent → Single nanoparticle- Damping: environment, size-shape distribution

Optical Excitation and Detection of acoustic vibrations

• Ultrafast Pump pulse : → launches the vibration

• Delayed Probe pulse :→ Volume-dependent signal→ sensitive to vibrations

Breathing nanoparticles...

Acoustic breathing mode of a Ag nanoparticle with R = 12 nm :

Vibration period ~ 7 ps

T0

Single Ag@SiO2 nanoparticle: pump-probe and TEM study

Single particle oscillation (Ag@Si02):

spherical model ω = ξ vL/D

→ Deq ~ 45 nm

Pump / Probe 830 / 415 nm

0 10 20 30 40

0.0

0.5

1.0

1.5

∆T

/ T (

x 10

-3)

Time Delay (ps)

L. Liz-Marzan, Univ. Vigo, Spain

From TEM : a = 38 nm / b = 47 nm.

Ag2SiO

nme 15~

400 420 440 460 4800.0

0.5

1.0

1.5

2.0

2.5

Ex

tinct

ion

σ ext (

x 10

4 nm

2 )

λ (nm)

Size ~ 40 nm

Acoustic vibrations of a nano-prism

Gold nanoprisms: detection

M. El-SayedGeorgia Inst. Tech., Atlanta

Nanosphere lithography:Organized nanoprisms: size 120 nm

thickness 30 nm

SEM image

AFM image

5 x 5 µm2

Optical image (at 410 nm)

⇒ Optical observation of prism pairs

Two main modes: period: T1 = 64 ps ; T2 = 49 ps damping: τ1 = 120 ps ; τ2 = 45 ps

FFT

T1

T2

Gold nanoprisms: acoustic vibrationsGold nano-prisms: acoustic vibrations

Time resolved spectroscopy of a single nanoprism pair

Thickness breathing mode: T3 = 14 ps (film - 30 nm : 2e/vL → 18 ps)

400 600 8000.0

0.1

0.2

OD

λ (nm)

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

∆T/T

(

x10-3

)

Probe delay (ps)

electronic response

pump

probe

acoustic vibrations

0 50 100 150

0.0

0.1

0.2∆T

/T

(x1

0-3)

Probe delay (ps)

• Period fluctuations: → mean values: <T1> = 68 ps ; <T2> = 51 ps → agreement with ensemble measurements → Correlated fluctuations → shape/size effect

Gold nanoprisms: acoustic vibrationsGold nanoprisms: acoustic vibrations

Main mode periods:T1 and T2

60 65 70 75

45

50

55

60

T1 (ps)

T2

(ps)

60 65 70 750

200

400

600

τ 1 (p

s)

T1 (ps)

• Damping: Energy transfer to the substrate - 100 ps ≤ τ1 ≤ 600 ps → <τ1> ≈ 360 ps - ensemble measurement: τ1 ≈ 70 ps (inhomogeneous damping) - No τ1 - T1 correlation → fluctuation of the prism-substrate contact

Gold nanoprisms: acoustic vibrations

50 100 150 200 2500

25

50

75

100

125

Pe

riod

T1

(ps)

Prism size (nm)

→ Weak substrate influence: free nanoprisms

→ Shape effect: truncated pyramid

J. Burgin et al., J. Phys. Chem. C 2008

Free prism: fundamental mode Truncatedpyramid

Gold nanoprisms: acoustic vibrations

• M.A.El Sayed et al.,J. Phys. Chem. B 109, 18881 (2005) Finite Element Method (FEM) simulations

• Single metal nanoparticle detection→ Spatial Modulation Technique: direct absorption measurement

→ absorption cross section down to a few nm2

→ far-field technique ⇒ dilute sample (< 1 particle per µm2)→ spectroscopy: optical identification of a single nanoobject→ combined optical response and electron microscopy

• Femtosecond time-resolved spectroscopy→ electron-phonon coupling in a single metal nano-object→ acoustic vibration: acoustic properties at a nanoscale→ nonlinear optics with a single nanoobject→ combination with electron microscopy

Conclusion

Acknowledgements

Universidad Vigo - SpainProf. L. Liz-Marzan

Université Paris VI - FranceProf. M.P. Pileni

Georgia Institute of Technology - USAProf. M. El-Sayed

FemtoNanoOptics group Lyon, France

H. Baida (PhD student) V. Juvé (PhD student)

D. Mongin (PhD student)

Dr. Paolo Maioli Dr. Aurélien Crut

Prof. Fabrice Vallée Prof. Natalia Del Fatti

Université Bordeaux -France- Université Lyon

Dr. D. Christofilos Prof. M. Broyer Dr. O. Muskens Prof. M. Pellarin Dr. A. Arbouet Prof. J. Lermé Dr. J. Burgin Dr. E. Cottancin Dr. P. Langot Dr. G. Bachelier

Dr. A. Brioude

linear and nonlinear optics with a single metal nanoparticle

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