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
Surface plasmon resonance: environment effect
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
Introduction: optical response of metal nanoparticles
Linear Optics: detection and spectroscopy of a single metal nanoparticle
- Far-field experimental techniques - Optical signature: Gold nanospheres - Shape effect: Gold nanorods
Nonlinear Optics: ultrafast dynamics of a single metal nanoparticle
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
Surface plasmon resonance: environment effect
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
Introduction: optical response of metal nanoparticles
Linear Optics: detection and spectroscopy of a single metal nanoparticle
Nonlinear Optics: ultrafast dynamics of a single metal nanoparticle
- 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