Thermal Approaches to Interpret
Laser Damage Experiments 13
that the laser damage density globally decreases in the range [0
◦
,90
◦
]. If considering now
the black arrows, these points correspond to local generation of SHG. It has been noticed that
for these particular points (i.e. Ω =40
◦
and Ω =60
◦
) the laser damage density is punctually
altered as an indication that SHG tends to c ooperate to damage initiation.
Fig. 6. Evolution of laser damage density as a function of Ω,fortwodifferent1ω fluences.
Green triangles and orange squares respectively correspond to F
1ω
=19J/cm
2
and F
1ω
= 24.5
J/cm
2
. Modeling results are represented in dash lines, respectively for each fluence.
Modeling results are discussed in Sec. 3.1.3.
Many assumptions may be done to explain these observations. Crystal inhomogeneity, tests
repeatability, self-focusing, walk-off and SHG (Demos et al., 2003; Lamaignère et al., 2009;
Zaitseva et al., 1999;?) were suspected to be possible causes for these results due to their
orientation dependence they may induce. But it has been ensured that these mechanisms
were not the main contributors (even existing, participating or not) to e xplain the influence of

14 Will-be-set-by-IN-TECH
Where [a
−
(F), a
+
(F)] is the range of defects size activated at a given damage fluence level,
D
de f
(a ) is the density size distribution of absorbers assumed to be (as expressed in (Feit &
Rubenchik, 2004)):
D
de f
(a )=
C
de f
a
p+1
(15)
Where C
de f
and p are ad justing parameters. This distribution is consistent with the fact
that the more numerous the precursors (even small and thus less absorbing), the higher the
damage density. In Sec. 2.1.1, Eq. (5) has defined the critical fluence F
c
necessary to reach the
critical temperature T
c
for which a first damage site occurs, which can be written again as
(Dyan e t al., 2008):
F

. It is then supposed that the geometry of the precursor defect can explain the previous
experimental results.
Geometries of defects
As regards KDP crystals, lattice parameters a, b and c are such as a
= b = c conditions. The
defects are assumed to keep the symmetry of the crystal so that the defects are isotropic in
the
(ab) plane due to the multi-layered structure of KDP crystal. The principal axes of the
defects match with the crystallographic axes. Assuming this, it is possible to encounter two
geometries (either b/c
< 1orb/c > 1 ), the prolate (elongated) spheroid and the oblate
(flattened) s pheroid, represented on Fig. 7.
Fig. 7. Geometries proposed for modeling: (a) a sphere, which is the standard geometry
used, (b) the oblate ellipsoid (flattened shape) and (c) the prolate ellipsoid (elongated shape).
The value of the aspect ratio (between major and minor axis) is set to 2.
DDScat model
Defining an anisotropic geometry instead of a sphere implies to reconsider the set of equations
(i.e. Fourier’s and Maxwell’s equations) to be solved. Concerning Fourier’s equation, to
our knowledge, it does not exist a simple analytic solution. So temperature determination
remains solved for a sphere. This approximation remains valid as long as the as pect ratio does
230
Two Phase Flow, Phase Change and Numerical Modeling
Thermal Approaches to Interpret
Laser Damage Experiments 15
not deviate too far from unity. This approximation will be checked in the next paragraph. As
regards the Maxwell’s equation, it does not exist an analytic solution in the general case. It is
then solved numerically by using the discrete dipole approximation. We addressed this issue
by the mean of DDScat 7.0 code developed by Draine and co-workers (Draine & Flatau, 1994;
2008; n.d.). This code enables the calculations of electromagnetic scattering and absorption
from targ ets with various geometries. Practically, o rientation, indexes from the dielectric

= 6 ,000 K. This latter value agrees qualitatively with experimental results
obtained by Carr et al. (Carr et al., 2004), other value (e.g. around 10, 000 K) wo uld not have
significantly modified the results. Complex indices have been fixed to n
1
=0.30andn
2
= 0.11.
C
de f
and p necessary to define the defects size d istribution are chosen to ensure that damage
density must fit with experimentally observed probabilities (i.e. P =0.05toP =1).
Critical damage density T
c
n
1
n
2
C
de f
p Aspect ratio Rotation angle Ω
10
−2
d/mm
3
6,000 K 0.30 0.11 5.5 10
−47
7.5 2 0to90
◦
Table 2. Definition of the set of parameters for the DMT code at 1064 nm.
It is worth noting that these parameters have been fixed for F

abs
variations are correlated to t he variations o f ρ(Ω). As regards the
oblate one which has also been proposed, it has been immediately leaved out since variations
introduced by the Q
abs
coefficient were anti-correlated to those obtained experimentally. Note
that other geometries (not satisfying the condition a = b) have also been studied. Results (not
presented here) show that either the variations of Q
abs
are anti-correlated or its variations are
not l arge enough to r eproduce experimental results whatever t he 1ω fluence.
231
Thermal Approaches to Interpret Laser Damage Experiments
16 Will-be-set-by-IN-TECH
On Fig. 5, green and orange dash lines respectively correspond to fluence F
1ω
=19J/cm
2
and fluence F
1ω
= 24.5 J/cm
2
. As said in Sec. 3.1.1, one would note that it is important to
dissociate the impact of the SHG on the damage density from the geometry effect due to
the rotation angle Ω. For a modeling concern, it is thus not mandatory to include SHG as
a contributor to laser damage. So, in the range [0
◦
,90
◦
], one can clearly see that modeling

,F
1ω
), symbolized
by color contour lines.
Fig. 8. (a) Damage density versus fluence i n the mono-wavelength case: for 1ω and 3ω.(b)
Evolution of the LID densities (expressed in dam./mm
3
) as a function of F
3ω
and F
1ω
.The
color levels stand for the experimental damage densities. Modeling results are represented in
white dash contour lines for δ = 3. Modeling results are discussed in Sec. 3.2.3.
232
Two Phase Flow, Phase Change and Numerical Modeling
Thermal Approaches to Interpret
Laser Damage Experiments 17
A particular pattern for the damage densities stands out. Indeed, each damage iso-density
is associated to a combination between F
3ω
and F
1ω
fluences. If now we compare results
obtained in the mono- and multi-wavelengths cases, it is possible to observe a coupling
between the 3ω and 1ω wavelengths (Reyné et al ., 2009). Indeed, we can observe that:
ρ
= f (F
3ω
, F

higher. Other experimental results (DeMange et al., 2006) i ndicates that it is possible t o predict
the damage evolution of a KDP crystal when exposed to several different wavelengths from
the damage tests results. It can be said that mono-wavelength results are necessary but not
sufficient due to the existence of a coupling effect.
Besides, it is possible to define a 3ω-equivalent fluence F
eq
, depending both on F
3ω
and F
1ω
,
which leads to the same damage density that would be obtained with a F
3ω
fluence only. F
eq
can be determined using approximately a linear relation between F
3ω
and F
1ω
, linked by a
slope s resulting in
F
eq
= f (F
3ω
, F
1ω
)=sF
1ω
+ F

abs
(3ω,1ω)I
3ω
+ Q
(1ω)
abs
(3ω,1ω)I
1ω
(19)
Where Q
(3ω)
abs
(3ω,1ω) and Q
(1ω)
abs
(3ω,1ω) are the absorption efficiencies at 3ω and 1ω.Itis
noteworthy that apriorieach absorption efficiency depends on the two wavelengths since both
participate into the plasma production. Thirdly, calculations are performed under conditions
where the Rayleigh criterion (a
≤ 100 nm) is satisfied: under this c ondition, an error less than
20 % is observed when the approximate expression of Q
(ω)
abs
is used. So, Q
(3ω)
abs
(3ω,1ω) and
Q
(1ω)
abs

(3ω)
e
+ n
(1ω)
e
,wheren
(3ω)
e
and n
(1ω)
e
are the electron densities produced by the 3ω and 1ω
pulses. Here the interference between both wavelengths are neglected. This assumption is
reliable since the conditions permit to consider that the promotion of valence electrons to the
Conduction Band (CB) is mainly driven by the 3ω pulse (F
3ω
≥ 5J/cm
2
). As a consequence,
we consider that the 3ω is the predominant wavelength to promote electrons in the CB.
So for the 3ω it results that Q
(3ω)
abs
(3ω,1ω) = Q
(3ω)
abs
(3ω) while for the 1ω,sinceQ
(1ω)
abs
∝ n

is obtained for δ
 3. These calculations have also been performed for various iso-densities
ranging from 2 to 15 d./mm
3
.
Fig. 9. Evolution of the modeling slopes s as a function of δ for the damage iso-density ρ =5
d/mm
3
. For this density level, the experimental slope is s
ex p
−0.3.
As a consequence, observations result in Fig. 10 which shows that δ
 3forρ ≥ 3d/mm
3
.
Actually, it is most likely that δ = 3 considering errors on the experimental fluences,
uncertainties on the linear fi t to obtain s
ex p
, and owing to the band gap value. Therefore, t he
comparison between this experiment and the model indicates that the free electron density
leading to damage is produced by a three-photon absorption mechanism. It is noteworthy
234
Two Phase Flow, Phase Change and Numerical Modeling
Thermal Approaches to Interpret
Laser Damage Experiments 19
Fig. 10. Evolution of the best p arameter δ which fits the experimental slope s
ex p
,asa
function of ρ. Given a damage density, the error bars are obtained from the standard
deviation observed between the minimum and maximum slopes.

consistent with δ
> 5 or more. In Fig. 10, it corresponds to the hashed region where the
modeling slopes do not intercept the experimental ones.
In other respects, the nature of the precursor defects has partially been addressed in the
mono-wavelength configuration (DeMange et al., 2008; Feit & Rubenchik, 2004; Reyné et al.,
2009). In the DMT
2λ
model, we consider a single distribution of defects, corresponding to a
population of defects both sensitive at 3ω and 1ω. Calculations with two d istinct distributions
have also been performed. It comes out that no significant modification is observed between
the results obtained with only one distribution: e.g. the damage densities pattern nearly
235
Thermal Approaches to Interpret Laser Damage Experiments
20 Will-be-set-by-IN-TECH
remains unchanged and the slopes s as well. Also these o bservations do not dismiss that
two populations of defects may exist in KDP (DeMange et al., 2008).
4. Conclusion
The laser-induced damage of optical components used in megajoule-class lasers is still under
investigation. Progress in the laser damage resistance of optical components has been
achieved thanks to a better understanding of damage mechanisms. The models proposed in
this study mainly deal with thermal approaches to describe the occurrence of damage sites in
the bulk of KDP crystals. Despite the difficulty to model the whole scenario leading to damage
initiation, these models acco unt f or the main trends of KDP laser damage in the nanosecond
regime.
Based on these thermal approaches, direct comparisons between models and experiments
have been proposed and allow: (i) to obtain some main information on precursor defects
and their link to the physical mechanisms involved in laser damage and (ii) to improve our
knowledge in LID mechanisms on powerful laser facilities.
5. References
Adams,J.,Weiland,T.,Stanley,J.,Sell,W.,Luthi,R.,Vickers,J.,Carr,C.,Feit,M.,Rubenchik,

355-nm p ulses, Appl. Phys. Lett. 89: 181922.
DeMange, P., Negres, R., Rubenchik, A., R adousky, H., Feit, M. & Demos, S. (2008). The energy
coupling efficiency of multiwavelenght laser pulses to damage initiating defects in
deuterated KH
2
PO
4
nonlinear crystals, J. Appl. Phys. 103: 083122.
Demos, S., DeMange, P., Negres, R. & F eit, M. (2010). Investigation of the electronic and
physical properties of defect structures responsible for laser-induced damage in
DKDP crystal, Opt. Express 18, 12: 13788–13804.
Demos, S., Staggs, M. & Radousky, H. (2003). Bulk defect formations in KH
2
PO
4
crystals
investigated using fluorescence microscopy, Phys. Rev. B 67: 224102.
236
Two Phase Flow, Phase Change and Numerical Modeling
Thermal Approaches to Interpret
Laser Damage Experiments 21
Draine, B. & Flatau, P. (1994). Discrete-dipole a pproximation for scattering calculations, J. Opt.
Soc. Am. B 11: 1491–1499.
Draine, B. & Flatau, P. (2008). The discrete dipole approximation f or periodic targets: theory
and tests, J. Opt. Soc. Am. A 25: 2693–2703.
Draine, B. & Flatau, P. (n.d.). User guide f or the discrete dipole approximation code DDScat 7.0.
Duchateau, G. (2009). Simple models for laser-induced damage and conditioning of potassium
dihydrogen phosphate crystals by nanosecond pulses, Opt. Express 17, 13: 10434–
10456.
Duchateau, G. & Dyan, A. ( 2007). Coupling statistics and he at transfer to study laser-induced

to femtosecond time scales: calculation of thresholds, absorption coefficients, and
energy density, IEEE J. Quant. Electron. 35: 1156–1167.
Numerical Recipies (n.d.).
O’Connell, R. (1992). Onset threshold analysis of defect-driven surface and bulk laser damage,
Appl. Optics 31, 21: 4143.
Picard, R., Milam, D. & Bradbury, R. (1977). Statistical analysis of defect-caused laser damage
in thin films, Appl. Opt. 16: 1563–1571.
Pommiès, M., Damiani, D., Bertussi, B., Pi ombini, H., Mathis, H., Capoulade, J. & Natoli,
J. (2006). Detection and characterization of absorption heterogeneities in KH
2
PO
4
crystals, Opt. Comm. 267: 154–161.
Porteus, J . & Seitel, S. (1984). A bsolute onset of optical surface damage using distributed
defect ensembles, Appl. Optics 23, 21: 3796–3805.
237
Thermal Approaches to Interpret Laser Damage Experiments
22 Will-be-set-by-IN-TECH
Reyné, S., Duchateau, G., Natoli, J Y. & Lamaignère, L. (2009). Laser-induced damage of KDP
crystals by 1ω nanosecond pulses: influence of crystal orientation, Opt. Express 17,
24: 21652–21665.
Reyné, S., Duchateau, G., Natoli, J Y. & Lamaignère, L. (2010). Pump-pump experiment in
KH
2
PO
4
crystals: Coupling two different wavelengths to identify the laser-induced
damage mechanisms in the nanosecond regime, Appl. Phys. Lett. 96: 121102–121104.
Reyné, S., Loiseau, M., Duchateau, G., Natoli, J Y. & Lamaignère, L. (2009). Towards a
better understanding of multi-wavelength ef fects on KDP crystals, Proc. SPIE 7361,

equilibrium severely for femtosecond laser ablation due to the femtosecond pulse duration
is quite shorter compared to the electron–phonon relaxation time. So, it is expected that the
basic theory for describing the femtosecond laser pulses interactions with metal is quite
different from that of nanosecond laser pulses. In general, for femtosecond laser pulses, the
heating involves high-rate heat flow from electrons to lattices in the picosecond domains.
The ultrafast heating processes for femtosecond pulse interaction with metals are mainly
consist two steps: the first stage is the absorption of laser energy through photon–electron
coupling within the femtosecond pulse duration, which takes a few femtoseconds for
electrons to reestablish the Fermi distribution meanwhile the metal lattice keep undisturbed.
The second stage is the energy distribution to the lattice through electron–phonon coupling,
typically on the order of tens of picoseconds until the electron and phonon reaches the
thermal equilibrium. The different heating processes for electron and phonon were first
evaluated theoretically in 1957 (Kaganov et al.,1957). Later, Anisimov et al. proposed a
Parabolic Two Temperature Model (PTTM), in which the electron and phonon temperatures
can be well characterized (Anisimov et al.,1974). By removing the assumptions that regard
instantaneous laser energy deposition and diffusion, a Hyperbolic Two Temperature Model
(HTTM) based on the Boltzmann transport equation was rigorously derived by Qiu (Qiu et
al.,1993). Further, Chen and Beraun extended the conventional hyperbolic two temperature
model and educed a more general version of the Dual-Hyperbolic Two Temperature Model
(DHTTM), in which the electron and phonon thermal flux are all taken into account (Chen et
al., 2001). The DHTTM has been well applied in the investigation of ultrashort laser pulse
interaction with materials. The mathematical models for describing the DHTTM can be
represented in the following coupling partial differential equations:

e
eeep
T
CqGTTQ
t
()

qkT qt (3)
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

241
here
e
k and
e
τ
denotes the electron heat conductivity and the electron thermal relaxation
time. Further, letting the electron thermal relaxation time
e
τ
be zero. Consequently the
DHTTM can be reduced to the Parabolic Two Temperature Model (PTTM), which had been
widely used for investigation of the ultrashort laser pulse interaction with metal films.
For the multi-layered metal film assembly, the PTTM can be modified from Eqs.(1)-(3) and
written as the following form for the respective layers:

i
iiii
e
eeep
T
CqGTTQ
t
()
() () () () (1)
()

layer number in the multi-layer assembly. The laser heat source term is usually considered
as Gaussian shapes in time and space, which can be written as

QSx
y
Tt
(1)
(,) ()=⋅ (6)
where

()
pb b s
yy
Rx
Sxy F
ty
2
0
4ln2 1
(,) exp
πδδ δδ



−
−


=×−−


p
t is the FWHM (full width at half maximum) pulse
duration,

b
δδ
+
is defined as the effective laser penetration depth with
δ
and
b
δ
denoting
the optical penetration depth and electron ballistic range, respectively.

F
is the laser fluence.
y
0
is the coordinate of central spot of light front at the plane of incidence and
s
y
is the
profile parameter. When a laser pulse is incident on metal surface, the laser energy is first
absorbed by the free electrons within optical skin depth. Then, the excited electrons is
further heated by two different processes, which includes the thermal diffusion due to
electron collisions and the ballistic motion of excited electrons. So, we use the effective laser
penetration depth in order to account for the effect of ballistic motion of the excited
electrons that make laser energy penetrating into deeper bulk of a material.
The calculation starts at time t=0. The electrons and phonons for the respective layers in the

nn
0
ΩΩ
∂
∂
==
∂∂
(11)
here,
Ω
represents the four borderlines of the 2-D metal film assembly.
For the interior interfaces of the multi-layer systems, we assume the perfect thermal contacts
for electron subsystem between the respective layers herein, leading to

i
ee e
TT T
(1) (2) ( )
ΓΓ Γ
==⋅⋅⋅= (12)

i
ee e
qq q
(1) (2) ( )
ΓΓ Γ
==⋅⋅⋅ (13)
where,
Γ
represents the interior interfaces of the multi-layer assembly. Additionally, the

τ
= and
e
pp
BT1
τ
= is temperature dependent electron-electron and the
electron-phonon scattering rates, with which the temperature dependent thermal
conductivity can be educed. We assume that the electrons and phonons are isotropic across
the target so that the isotropic thermal properties for the targets can be applied in the
current simulations. In the regime of high electron temperature, the electron-electron
interactions must be taken into account, leading to

e
eee
ee
pp
T
kBk
AT BT
1,0
2
=
+
(15)
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

243
However, when the electron temperature is low enough that electron-electron interactions

(Kanavin et al.,1998):

()
ee ee
CT BT= (17)
An analytical expression for the electron-phonon coupling strength was proposed by Chen
et. al., which can be represented as follows (Chen et al., 2006):

() ()
e
ep e p
p
A
GT T G T T
B
0
,1


=++






(18)
Fig.2 shows the electron-phonon coupling strength as a function of electron temperature for
the targets of Au and Al. We fix the phonon temperature at room temperature of 300K. It is
shown that the electron-phonon coupling strength increases obviously with increasing the

excitation, the total scattering rates can be written as

me b
p
vATBT
2
=+, in which the electron
and phonon temperatures can jointly contribute to the total scattering rates. The connection
between the metal surface reflectivity and the total scattering rate usually relates to the well-
known Drude absorption model. After some derivations from Drude model, the reflective
index
n and absorptive coefficient k can be immediately written as:

pp p
m
mm m
v
n
vv v
1
22
2
22 2
2
22 22 22
11
11
22
ωω ω
ωωω ω

22
ωω ω
ωωω ω



=− + −−



++ +


(20)
where

p
ω
denotes the plasma frequency of the free electron sub-system, expressed as
()
e
en m
2*
0
ε
,
ω
is the angular frequency of the laser field. Applying the Fresnel law at the
surface, we can get the surface reflectivity coefficient:


electron ballistic effect is included in the simulations. At time of 500 fs, the electron
subsystem for the film assembly is dramatically heated, the maximal electron temperature at
the front and rear surfaces of the two layer Au/Ag film assembly get 2955K and 1150K,
respectively. However, the phonon subsystem for the bottom Ag film layer of the assembly
is slightly heated at 500 fs, the phonon temperature field is mostly centralized at the first
layer, approximately 20 nm under the Au film surface, the maximal phonon temperatures at
front surface and the layer interface gets to 317K and 305K, respectively. At time of 1 ps, the
electron temperature field penetrates into deeper region of the assembly, indicating that the
electron heat conduction amongst electron subsystem is playing an important role during
this period. The maximal electron temperature at the front surface drops down to 2100K and
rises to 1500K at the rear surface. Simultaneously, the phonon temperature at the respective
Au and Ag layers begins to rise, the maximal phonon temperatures at the front and the rear
surfaces of the assembly climbs to 328 K and 313 K at 1ps. The bottom Ag layer phonon
thermalization can actually be attributed to the electron thermal transfer from the first layer
Au film to the Ag electron subsystem, and the following process in which the overheated
electron coupling its energy to localized Ag film phonon subsystem through electron-
phonon coupling. At time of 4ps, the electron temperature field is significantly weakened
across the Au/Ag assembly and the phonon temperature fields are mostly distributed near
the front surfaces of the respective Au and Ag layers at this time, the maximal phonon
temperature at the front surface of the Au film and the Ag layer is 353.3 K and 345 K,
respectively. With time, the electron and phonon subsystems ultimately would get the
thermal equilibrium state and bears the united temperature distribution across the
assembly. It should be emphasized that the temperature field distributions for electrons and
phonons are quite different at the middle interface layer which is actually originated from
the physical fact that phonon thermal flux can be ignored and electron presents excellent
thermal conduction at the middle interface of the assembly during the picosecond time
period.

Two Phase Flow, Phase Change and Numerical Modeling


energy to electron subsystem of bottom Al layer through electron thermal conduction.
Immediately after that the Al layer electron couples it’s energy to the local phonon, leading
to preferential heating of the bottom Al film. At time of 4ps, the phonon subsystem of the Al
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

247
film is further heated and the phonon temperature at Au layer continues to rise very slowly,
the maximal phonon temperature at front surface and the middle interface is 351K and 443K
at this time. In Fig.4(B), the electron temperature field evolution for Au/Al film assembly
dose not show significant difference from that of the Au/Ag film assembly. The electron
subsystem of the two layer Au/Al film assembly is dramatically overheated at 500 fs, the
maximal electron temperature at the front surface of the assembly reaches 2922 K. At time of
1ps, the electron subsystem continues diffusing it’s thermal energy to the Al substrate, and
the electron temperature for the surface Au film bears a severe drop. The maximal electron
temperature comes down to 1900K at the front surface, and rises to 750K at the rear surface
at 1ps. At time of 4ps, the electron temperature across the assembly goes down to 400K and
350K at front surface and rear surface, respectively. With time, the electron and phonon
subsystems also would get the thermal equilibrium state, and if the united electron and
phonon temperature in assembly is higher than padding layers melting point, the two layer
film assembly will be damaged. Fig. 4. The temporal evolution of electron and phonon temperature fields in two layer
Au/Al film assembly. (A) Phonon temperature fields at 500fs, 1ps and 4ps; (B) Electron
temperature fields at 500fs, 1ps and 4ps
Fig.5 presents the phonon temperature field distributions for the three layer film assemblies
with different layer configurations at 5 ps. The laser and film parameters for the simulations
are listed as follows: laser fluence is
F=0.1 J/cm

time. Finally, the surface phonon temperature gets 380K, 370K, 349K, and 386K at 15ps for
assemblies of Au/Au, Au/Ag, Au/Cu and Au/Al, respectively. Fig.6(b) shows the surface
electron temperature of the Au coated metals also evolutes synchronously before 1ps, but
becomes discrepantly after 1 ps. It should be noticed that the surface phonon and electron
temperatures at 15ps for the Au coated Al film substrate are obviously larger than that of the
assemblies with other metal film substrates. It is expected that the thermal properties for the
substrate layers can play an important role in enhancing surface temperature evolution on
the Au coated metal assemblies.

Parameters Au Ag Cu Al
G
0
(10
16
J m
-3
s
-1
K
-1
) 2.1 3.1 10 24.5
C
e0
(J m
-3
K
-2
)

68 63 97 135

11
s
-1
K
-1
) 1.25 1.02 1.23 3.9
Table 1. Thermal physical parameters for Au, Ag, Cu and Al, the datum are cited from
references (Chen et al., 2010 ; Wang et al., 2006)
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

249

(a) Phonon temperature (b) Electron temperature
Fig. 6. Temporal evolution of phonon and electron temperatures at center of laser spot on
surface of Au surfaced two layer metal film assemblies
In general, the physical mechanism in dominating the temperature field distributions has no
difference for the two layer and the three layer metal film assemblies because of the similar
physical boundary and the mathematical processing for them. So, the two layer Au coated
metal assembly is here taken as example in order to explore what causes can definitely give
rise to the distinct temperature field distributions in the metal film assembly with different
substrate configurations? Fig.7 shows effect of the substrates thermal parameters on surface
phonon temperature of the two layers Au coated assembly. The thermal parameters such as
electron thermal capacity, electron thermal conductivity, electron-phonon coupling strength
and phonon thermal capacity are all selected falling into the ranges for the actual materials
as listed in table 1. As shown in Fig.7(a) and (b), the surface Au layer phonon temperature
decreases slightly with increasing electron thermal capacity and electron thermal
conductivity of the substrates. However, increasing of electron-phonon coupling strength or
phonon thermal capacity for the substrate layers can both result in the dramatic drops of
surface phonon temperature as shown in Fig.7(c) and (d), indicating the substrate layer

250
at depths of 150 nm and 200 nm for the substrate layer. It indicates the phonon subsystem is
heated in priority from substrate to the surface layer for the Au/Al assembly. Fig. 7. Effect of thermal parameters of the substrate layer on surface phonon temperature of
the two layer Au/substrate assembly (a) Electron temperature (b) Phonon temperature
Fig. 8. Temporal evolutions of electron and phonon temperature for the Au/Al film
assembly at different depths of the target
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

251

(a) Electron temperature (b) Phonon temperature
Fig. 9. Temporal evolution of electron and phonon temperature for the Au/Ag film
assembly at different depths of the target
The temporal evolution of electron and phonon temperature for the Au/Ag film assembly at
different depths of the target are given in Fig.9. The laser parameters are
t
p
=65 fs, F=0.1
J/cm
2
, wavelength is 800 nm. As show in Fig.9(a), the electron temperature peak decreases
orderly with increasing the depth. As the depth exceeds 100 nm, the electron temperature
profile still maintains the pulse-like distribution, although the sharp pulse structure is

evaluated by the temperature dependent electron-phonon coupling strength is rather higher
than using the constant electron-phonon strength mainly after 300 fs. For femtosecond laser
ablation, material damage usually occurs after the electron-phonon relaxation termination
on timescale of picoseconds. So, it is important to use the temperature dependent electron-
phonon coupling strength to predict ultrafast heating characteristics in multi-layer metal
film assembly for target material ablation. Fig. 11. The surface phonon temperature of the two layer Au/Al film assembly under the
irradiation of laser spot at time of 15ps with respect to temperature dependent and constant
reflectivity
The surface phonon temperature fields in the two layer Au/Al film assembly at 15 ps under
range of laser spot with respect to the temperature dependent and the constant reflectivity
are shown in Fig.11. The laser parameters are
t
p
=150 fs, F=0.05 J/cm
2
, laser wavelength is
800 nm. It can be seen that the constant surface reflectivity definitely makes a low estimation
of the surface phonon temperature, especially at center of the laser spot. The results can be
explained as follows: When the femtosecond laser pulse irradiation on the target surface, the
electron subsystem can be rapidly heated and the electron temperature is immediately
evaluated to higher level during femtosecond laser pulse heating, causing dramatic increase
of the total scattering rates. The large particle scattering rate is beneficial for reducing
surface reflectivity as predicted by the Drude model with respect to temperature dependent
Ultrafast Heating Characteristics in
Multi-Layer Metal Film Assembly Under Femtosecond Laser Pulses Irradiation

253

375-377.
Chen A.; Xu H.; Jiang Y.; Sui L.; Ding D.;Liu H. & Jin M. (2010). Modeling of Femtosecond
Laser Damage Threshold on the Two-layer Metal Films.
Applied Surface Science, Vol.
257, No.5, (December 2010),pp.1678-1683. ISSN 0169-4332
Chen J. & Beraun J. (2001).Numerical Study of Ultrashort Laser Pulse Interactions with
Metal Films.
Numer. Heat Transfer A, Vol. 40, No.1 (July 2001),pp. 1-20, ISSN 1040-
7782