MASTER of PHYSICS We consider the following properties of two metals (copper and titanium) given in the table. Lejman et al.
2014
a significant
3), the pump
different fs
apphire cave laser beam
be beam by
es through a
al to obtain
opped by an
Both beams
spot size of
r, measured
larger than
on is approof coherent
plane-wave
corded with
-in amplifier
d setup emh. The laser
probe beam,
OPO) having
O allows the
0 nm with a
ped with an
he transient
todiode and
dulation fre2 and that of
n all experieen checked
iable probe
transport of
. First, elecpaths of the
a small elec15
Table 1. Some Physical Properties of
Copper and Titanium
Optical Properties: skin depth (nm)
[29,30], Wavelength (nm)
400
572
780
800
Mechanical Properties
Sound velocity V S "m∕s#
Density ρ "kg∕m3 #
Thermal and Transport Properties
Thermal expansion (K−1 ) [31]
Lattice heat capacity (at 300 K)
(J · mol−1 · K−1 )
Electronic heat capacity (J · m−3 · K−1 ),
Te is the electronic temperature
Electron–phonon coupling constant g
(1015 W · m−3 · K−1 ) [4,6,28]
Heat conductivity κ (W · m−1 · K−1 ) [31]
Copper
Titanium
∼14.5
∼14.5
∼12.4
∼12
∼14.4
∼16.8
∼18.8
∼19.3
4730
8960
5090
4500
16 × 10−6
24.4
8.5 × 10−6
25.06
96.6 Te [31]
20–60
313 Te
[31,32]
200–500
400
80
(Table from Lejman et al JOSA B 2014) RESULTS
We 3.consider that aAND
pulse DISCUSSION
laser of 100 fs interacts with the metal. This laser energy pulse is 1A.
nJ. Generation
The laser eof
xcite a surface of the m
etal of 0by
.1mm * 0.1 mm. Coherent
Acoustic
Phonons
Superdiffusive
Hot
Electrons
Following
thevalue classical
picosecond
scheme,
wemetal just after the laser light 1) Give the of the electronic tacoustic
emperature in both performed
experiments
in
front–back
configuration
1
[see
absorption. Fig. 2(a)]. In this case, the laser pump excites the titanium film
and,
through a thermoelastic
process, leads
to the generation
2) Considering the electron-­‐phonon coupling parameters given in the table, can you of picosecond
acoustic
pulses
that
propagate
within the
estimate the characteristic time after which the electron subsystem has given its copper
film, band
atsthe
front surface. The tranenergy ack are
to tdetected
he lattice ubsystem. sient optical reflectivity signal exhibits different features. We
can easily observe some periodic events at time around t ≈ 45,
3) Give the final value of the lattice temperature. 145, and 230 ps. Two of these successive events are separated
by a time interval very close to 2τCu ! 2H∕V Cu . This time exactly corresponds to a round trip time of the longitudinal
acoustic phonons in copper. Consequently, we can attribute
these events to the acoustic pulse photo-generated in the titanium film, and traveling back and forth within the copper
film at the longitudinal acoustic speed V Cu ! 4730 m∕s
[34]. The short longitudinal acoustic pulses in metals and de-