Photo-induced Multi-Mode Coherent Acoustic Phonons in the Metallic Nanoprisms

Po-Tse Tai1, Pyng Yu2, Yong-Gang Wang2 and Jau Tang* 2, 3 1Chung-Shan Institute of Science and Technology, Taoyuan, Taiwan

2Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan3Institute of Photonics, National Chiao-Tung University, Hsinchu, Taiwan

Abstract We report here experimental measurements of photoinduced ultrafast structural dynamics in metallic nanoprisms. Metallic nanoparticles could be strongly coupled to local optical fields via surface plasmon resonance (SPR). They are the best candidates for optoelectronic applications, including sub-wavelength optical devices and data storage, as well as for biomedical applications, including fluorescence labels, sensors and contrast enhancers in photoacoustic imaging.

Time-Resolved Experiment - Thin Film

Conclusions

(a) Excitation of acoustic oscillations of triangular plate with 49.8 nm bisector and (b) the oscillation periods versus triangle bisector.

Introduction

Laser

heat up of surface electrons by photons

ballsitic and diffusive dynamics of electrons

heat up of phonons viae-p interactions

thermal relaxation of phonons

time

100 ps10 p

s1 ps

100 fs

Metal

Electrons

Quantitative Model : Fermi-Pasta-Ulam (FPU) Model + TTM

Conventional pump-probe setup & up-conversion setup

•Ti:sapphire oscillator + regenerating amplifier + OPA

•> 10J/pulse @ 1KHz (320nm~2000nm)

•Time resolution ~100fs (Pulse duration 90fs)

Femtosecond Laser System

(a) Pump-probe data of a 50-nm gold film at different laser fluence and the fitted solid-line curves by the TTM-FPU model. (b) The dependence of the initial phase on pump fluence. The initial phase data represented by open circles with an error bar determined by fitting the experimental curves to a damping sinusoid. The dependence of the phase on pump fluence allows us to determine the electronic Grüneisen parameter.

We illustrated a non-thermal equilibrium approach to measure e unambiguously using optical pump-probe experiments.

The TTM-FPU model provides a better quantitative description of metal laser-heating and a deeper physical insight into coherent acoustic wave excitation in metallic thin films.

0 20 40 60 80 100 120

R/R

(a.

u.)

Delay Time (ps)

2.3 mJ/cm2

3.2 mJ/cm2

4.1 mJ/cm2

5.0 mJ/cm2

(a)0 1 2 3 4 5 6 7 8

240

260

280

Init

ial

Ph

as

e (

de

gre

e)

Pump fluence (mJ/cm2)

e=1.0

e=1.6

e=2.2

Exp data

(b)

Gold film

0 10 20 30

0.0000

0.0005

0.0010

s

/ s

Time (ps)

Fermi-Pasta-Ulam Model + TTM Experimental UEC data

Al, N = 67

The experimental data of time-resolved electron diffraction by Nie at al. for a polycrystalline aluminum thin film of about 20 nm in thickness (open circle). The data curve for the changes of the diffraction ring position can be fitted by using the FPU-TTM model (blue line).

Electron Grüneisen Parameter e

UEM Experiment

Z

1

32

4 5 6

7 8 9 10

1514131211

0 50 100 150 20049.5

49.6

49.7

49.8

49.9

50.0

50.1

simulation data fitted curve

Bis

ec

tor

(nm

)

Time (ps)

30 40 50 60 70 80 900

10

20

30

40

50

Pe

rio

d (

ps

)

Bisector (nm)

breathing mode totally symmetratic mode

(a) (b)

Optical Control of Coherent Acoustic Vibration

Anisotropic Thermal Expansion Model for Triangular Plate

We combined two kinds of impulsive forces, namely, FD and FI, representing the thermal stress from laser-heated electrons and lattice with a 2-D FPU model to simulate lattice vibration. Two vibration modes, which are breathing mode and totally symmetric mode, can be directly observed.

Simulation Results

fcc (1,1,1) triangular plateSince the SPR the metal nanoparticle have strong coupling with optical field, and allow the higher linear and nonlinear optical effect. In our lab, we have ability to synthesize different size and shape nanoparticles.

First, the laser pulse heat up the surface electrons, then the energy would spread through thermal diffusion and electron ballistic motion. After several pico-seconds, the hot electron relax energy to phonon through electron-phonon coupling. The electron and phonon temperature change induces thermal stress. Two different types of thermal stresses work on the lattice and cause the lattice vibration.

•Lasr-Heating Process

•Metal Nanoparticles & SPR

•Two-Temperature Model

tz,Stz,T-tz,Tg-tz,Tz

kz

tz,Tt

TC peeeee

tz,Stz,T-tz,Tg-tz,T

zk

ztz,T

tTC peeeee

tz,T-tz,Tg-tz,Tz

ktz,Tt

C epp2

2

Lpp

tz,T-tz,Tg-tz,T

zktz,T

tC epp2

2

Lpp

•FPU model+ Gruneisen relationship

Thermal stress

Electron temperature

Phonon temperature

z-zm-P-tFPdt

d

z-z-2zm-P-tFPdt

d

z-zm-P-tFPdt

dm

Pz

dt

d

1-nn2

NNN

1)-N ... 2 1,(n 1n1-nn2

nnn

102

000

nn

z-zm-P-tFPdt

d

z-z-2zm-P-tFPdt

d

z-zm-P-tFPdt

dm

Pz

dt

d

1-nn2

NNN

1)-N ... 2 1,(n 1n1-nn2

nnn

102

000

nn

0 10 20 30 40 50 60

T/T

(a.

u.)

Delay Time (ps)

2.3 mJ/cm2

1.84 mJ/cm2

1.38 mJ/cm2

0.92 mJ/cm2

0 10 20 30 40 50 60

T/T

(a.

u.)

Delay Time (ps)

2.3 mJ/cm2

1.84 mJ/cm2

1.38 mJ/cm2

0.92 mJ/cm2

Copper filme = 0.9

T = 29.4 ps T = 18 ps

From JPC B 107,668 (2003)

Localized field enhance higher absorption thermal gradientanisotropic thermal expansion

•Photo-induced acoustic phonons of the nanoprisms, which are breathing mode and totally symmetric mode, have been studied. •We used two properly timed pump pulses to directly excite totally symmetric mode of the nanoprisms.

(a) Initial phases depend on the electron phonon coupling time. We arranged the numerical results by the open squares representing breathing mode and open circles for the totally symmetric mode, and corresponding solid spots are from the experimental observation. (b) The mode weight of totally symmetric mode depends on the electron phonon coupling time. The mode weight of totally symmetric mode is defined by the divided amplitude of totally symmetric mode on the breathing mode. The open circles and solid circle represent the numerical and experimental results respectively.

3 4 5 6 7 8 9 10 110

5

10

15

20

25

30

35

mo

de

we

igh

t (%

)

e-ph

(ps)3 4 5 6 7 8 9 10 11

0

20

40

60

80

100

120

140

e-ph

(ps)

ph

as

e (

de

gre

e)

(a) (b)

Simulation Model & Experimental Results

Tips effect

we presented here a simulation model to explain and to quantity the experimentally observed dependence of the electron-photon coupling time constant and the phase of the acoustic oscillations. According to this model based on the notion of enhanced optical field localized around the sharp tips of a nanoprism, we theorized that the geometrical distribution of thermal gradient on the triangular plate were the sources for causing anisotropic thermal expansion. Two planar coherent acoustic modes, namely, the breathing mode and the totally symmetric mode, could be directly observed, as inferred by this anisotropic expansion model.