Transcript 投影片 1 - National Chiao Tung University

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, Taiwan
3Institute 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.
Anisotropic Thermal Expansion Model for Triangular Plate
Introduction
•Metal Nanoparticles & SPR
Since 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.
•Lasr-Heating Process
fcc (1,1,1) triangular plate
1
Z
2
3
5
4
time
Laser
Tips effect
6
Metal
100 fs
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.
7
ballsitic and diffusive
dynamics of electrons
1 ps
Electrons
heat up of surface
electrons by photons
9
8
11
12
13
10
14
15
10 ps
heat up of phonons via
e-p interactions
100 ps
From JPC B
107,668 (2003)
thermal relaxation
of phonons
Quantitative Model : Fermi-Pasta-Ulam (FPU) Model + TTM
We combined two kinds of impulsive forces, namely, FD and FI, representing the
Localized field enhance 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
higher absorption
totally symmetric mode, can be directly observed.
thermal gradient
anisotropic thermal expansion
•Two-Temperature Model

  

Te z, t    k e Te z, t  - gTe z, t  - Tp z, t   Sz, t 
t
z  z


2
Cp Tp z, t   k L 2 Tp z, t  - gTp z, t  - Te z, t 
t
z
Simulation Results
(a)
50.1
Electron temperature
Phonon temperature
+ Gruneisen relationship
•FPU model
(b)
50
breathing mode
totally symmetratic mode
50.0
40
d
P
zn  n
dt
m
d
P0  F0 t  - gP0 - m 2 z 0 - z1 
dt
d
P n  Fn t  - gPn - m 2 2zn - z n -1 - z n 1 
dt
d
P N  FN t  - gPN - m 2 z n - z n -1 
dt
49.9
Period (ps)
Thermal stress
Bisector (nm)
Ce T 
49.8
49.7
30
20
10
49.6
simulation data
fitted curve
(n 1, 2 ...N -1)
49.5
0
50
100
150
0
200
30
40
50
70
80
90
Bisector (nm)
Time (ps)
Femtosecond Laser System
60
(a) Excitation of acoustic oscillations of triangular plate with 49.8 nm bisector and (b) the oscillation
periods versus triangle bisector.
Conventional pump-probe setup & up-conversion setup
Optical Control of Coherent Acoustic Vibration
•Ti:sapphire oscillator + regenerating amplifier + OPA
•> 10mJ/pulse @ 1KHz (320nm~2000nm)
•Time resolution ~100fs (Pulse duration 90fs)
Time-Resolved Experiment - Thin Film
UEM Experiment
0.0010
Al, N = 67
T = 18 ps
0.0005
Fermi-Pasta-Ulam Model + TTM
Experimental UEC data
0.0000
0
10
20
30
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).
Time (ps)
Simulation Model & Experimental Results
Electron Grüneisen Parameter ge
Gold film
(a)
2
4.1 mJ/cm
2
5.0 mJ/cm
2
20
40
60
80
100
120
30
ge=1.6
ge=2.2
Exp data
260
240
Copper film
(b)
0
1
2
3
4
5
6
7
8
ge = 0.9
T/T (a.u.)
0
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.
2
1.38 mJ/cm
2
0.92 mJ/cm
2
10
We
20
30
40
Delay Time (ps)
20
15
10
50
60
100
80
60
40
20
0
0
The
2
25
5
(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.
1.84 mJ/cm
120
3
illustrated a non-thermal equilibrium approach
to measure ge unambiguously using optical pumpprobe experiments.
4
5

6
e-ph
Pump fluence (mJ/cm2)
Delay Time (ps)
2.3 mJ/cm
(b)
35
140
ge=1.0
mode weight (%)
3.2 mJ/cm
280
Initial Phase (degree)
2
R/R (a.u.)
2.3 mJ/cm
(a)
0
•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.
phase (degree)
 s / s
T = 29.4 ps
7
(ps)
8
9
10
11
3
4
5

6
e-ph
7
8
9
10
11
(ps)
(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.
Conclusions
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.