Size dependence of dipole and quadrupole plasmon resonances Size dependence of dipole and quadrupole plasmon resonances of lightof light--induced sodium clustersinduced sodium clusters

Anastasiya Derkachova, Krystyna Kolwas

Institute of Physics, Polish Academy of Sciences, Al.Lotników 32/46, 02-668 Warsaw, Poland

5,4 5,6 5,8 6,00

5

10

15

20

t = 5.58 s

v458 : 1th point h458 : 2th point v514 : 3th point h514 : 4th point v568 : 5th point h568 : 6th point v647 : 7th point h647 : 8th point

Sca

tter

ed i

nten

sity

[ a

. u. ]

Time [s]95 100 105 110 115

0

15

30

45

60

R = 104.8 nm

Sca

tter

ed i

nten

sity

[ a

. u. ]

Radius [nm]

1 2 3 4 5 6 7 80,0

0,2

0,4

0,6Average concentration: N

c = 0.2747

Standard deviation: Sx = 0.1435

Variability coefficient: Vx = 52.24 %

Con

cent

ratio

n [a

.u.]

Measurement points (v458, h458, v514 ... )

Looking for the best radiusLooking for the best radius

0 2 4 6 8 10 12 140

40

80

120

160

R(t

) [n

m]

Time [s]

0 2 4 6 8 10 12 1410

1

103

105

107

Con

cent

rati

on [

a.u.

]

Time [s]

Evolution of cluster radius Evolution of cluster radius and concentrationand concentration

Identification of plasmons in Identification of plasmons in scattered lightscattered light

50 100 150 200 250 3000,0

0,5

1,0

1,5 Rl=2

Rl=1

quadrupole

I|| (H)

( l=1...6)

I|| (H)

( l=2, TM)

I|| (H)

(l=1,TE; l=2,TM)

I || (H

) / NR

2 [a.u

.]

Radius [nm]

0 50 100 150 200 250 3000,0

0,5

1,0

1,5

2,0dipole

I (V)

(l=1,TM)

IV ( l=1...6)

= 2.54eV

p= 5.6eV

I V

/ NR

2 [a.u

.]

Plasmon resonance frequenciesPlasmon resonance frequencies

0 50 100 150 2000

1

2

3

4

l(R

) [e

V]

l=4

l=6

l=3

l=2Rl=1

R [nm]

Rl=2

403,4

457,9496,5514,5568,2

647,1

l=1

0 50 100 150 2000

1

2

3

4

dipole quadrupole

dipole quadrupole

647,1

496,5

457,9

403,4

514,5

l=1

l(R

) [e

V]

R [nm]

l=2

568,2

experimental

Mie theory with Drude dielectric function

We study the dependence of the optical properties of large sodium clusters as a function of their size. Sodium clusters are light induced [1,2] giving the unique opportunity of observing the smooth change of their sizes as a result of the spontaneous nucleation process in supersaturated vapor. Supersaturation is due to dissociation of Na2 molecules initiated by switching-on of the laser light at frequency resonant with some transition frequencies in sodium Na2 molecules. We measure the scattered intensities of the probe laser beam with polarization parallel and perpendicular the observation plane. The measurement is performed for several wavelengths of the probe light scattered by clusters growing with time. The full Mie scattering theory is used to describe intensities of light scattered by growing clusters in directions orthogonal to the direction of the incident light beam. The Drude dielectric function of free-electron metal is used to describe the optical properties of studied clusters. The method of finding the dependence of cluster radius and relative concentration is presented. We combine the formalism of the classical Mie scattering theory for arbitrary large size and the concept of the collective electron oscillations (plasmons) [3,4]. The maxima in normalized intensities of light scattered by single cluster we attribute to resonant excitation of dipole and quadrupole plasmon oscillation respectively. We show that plasmon resonances take place for different cluster sizes when excited with different wavelength. We compare these results with expectations resulting from solving the problem of eigenfrequencies of free-electron sphere with the dielectric function described within Lorentz-Drude model.

This work was partially supported by the Polish State Committee for Scientific Research (KBN), grant No. 2 PO3B 102 22.

References: 1. K. Kolwas, M. Kolwas, D. Jakubczyk, Appl. Phys. B 60, 173 (1995), 2. Demianiuk S, Kolwas K. J. Phys. B, 34, 1651 (2001), 3. K. Kolwas, S. Demianiuk, M. Kolwas, J. Phys.B, 29, 4761 (1996), 4. K. Kolwas, S. Demianiuk, M. Kolwas, J. Chem. Phys., 106(20), 8436 (1997)

AbstractAbstract Experimental setupExperimental setup

Polarization geometryPolarization geometry

incident light Polarization of

Polarization ofdetected light

IIV V (I(I))

IIH H (I(IIIII))

Cell

Mirror

ComputerSSD spectrometer

Induced beam source

Probe Beam source

Polarizer 1

Polarizer 2

Shatter

Half-transmitting mirror

Mechanism of sodium Mechanism of sodium clusters condensation clusters condensation

Scattered intensities : a) experimental; Scattered intensities : a) experimental; b) Mie theoryb) Mie theory

40 80 120 160 2000

3

6

9

12

15

IV

457,9 514,5 568,2 647,1

Inte

nsiti

es [

a.u.

]

R [nm]

IH

b)b)

0 2 4 6 8 10 12 140

2

4

6

8

10

12 457.9 514.5 568.2 647.1

Inte

nsit

ies

[a.u

.]

Time [s]

IV

IH

a)a)

40 60 80 100 120 140 1600

4

8

12

16

20

24

Inte

nsit

ies

[a.u

.]

R [nm]

457,9 514,5 568,2 647,1

IH

Iv

Plasmon resonances: Plasmon resonances: a) experimental;a) experimental;

b) Mie theoryb) Mie theorya)a)

b)b)

20 40 60 80 100 120 140 1600

2

4

6

8

10

12

14

I/NR

2 [a.

u.]

R [nm]

IV

IH

The spontaneous nucleation process of clusters induced by light [1,2] gives the unique opportunity of observing the smooth change of cluster size up to the macroscopic droplet of radius of about 150nm. That enables the study of optical properties of free-electron clusters as a function of sizes in wide range up to hundreds of nanometers.

The presented experimental results seams to be the first observation of manifestation of:

• the dipole plasmon resonance in clusters of so large sizes as few tens of nanometers, • the quadrupole plasmon resonance

The presented experimental results are not contradictory with theoretical predictions of the problem of eigenfrequencies of free-electron sphere with the dielectric function described within Lorentz-Drude model

SummurySummury

Resonance excitation of dimers

488 nm488 nmNaNa22 Na Na22

**

Collision assisted dimers dissociation

collisionscollisions NaNa22

** Na+Na Na+Na**

Sodium vapour supersaturationSodium vapour supersaturation

Clusters condensationClusters condensation