Appl Phys A
DOI 10.1007/s00339-009-5077-6
Measurement of femtosecond laser-induced damage and ablation
thresholds in dielectrics
N. Sanner · O. Utéza · B. Bussiere · G. Coustillier ·
A. Leray · T. Itina · M. Sentis
Received: 2 September 2008 / Accepted: 15 December 2008
© Springer-Verlag 2009
Abstract The paper is focused on the importance of accurate determination of surface damage/ablation threshold of a dielectric material irradiated with femtosecond
laser pulses. We show that different damage characterization techniques and data treatment procedures from a single
experiment provide complementary physical results characterizing laser–matter interaction. We thus compare and
discuss two regression techniques, well adapted to the
measurement of laser ablation threshold, and a statistical
approach giving the laser damage threshold and further information concerning the deterministic character of femtosecond damage. These two measurements are crucial for
laser micromachining processes and high peak-power laser
technology in general.
PACS 42.70.CE · 61.80.Ba · 42.62.Eh
1 Introduction
Femtosecond lasers are unique tools for micro- (nano-)
machining materials like transparent dielectrics, providing
benefits in terms of minimal invasiveness (reduced “HeatAffected Zone”) and precision over longer laser pulses. The
N. Sanner () · O. Utéza · B. Bussiere · G. Coustillier ·
A. Leray · T. Itina · M. Sentis
Laboratoire LP3, UMR 6182 CNRS—Université
de la Méditerranée, Campus de Luminy, case 917,
13288 Marseille cedex 9, France
e-mail: [email protected]
Fax: +33-4-91829289
B. Bussiere
Amplitude Technologies, 2 rue du Bois Chaland, CE2926,
91029 Evry cedex, France
peculiarity of using femtosecond pulses for processing materials is the possibility to separate in time the energy deposition (heating of electrons during the laser pulse) and the
damage appearance (energy relaxation occurring after the
pulse). The energy is deposited in the material by nonlinear absorption of photons via multiphoton or tunneling effects, followed by an avalanche mechanism leading to strong
ionization. This free-electron plasma initially enhances light
absorption, until a critical density is reached leading to a
metal-like behavior of the dielectric. Then electron transport
and different energy relaxation channels eventually leading to damage and ablation (plasma expansion and/or matter vaporization) are likely to occur in a quite complex
combination. The precise knowledge of these processes is
crucial for the comprehensive understanding of the experimental observations and for predicting the damage and/or
ablation thresholds of a material in the frame of micromachining process development and high peak-power laser
technology in general. Part of the answer could be provided
by parametric studies of laser-induced damage (and/or ablation) thresholds (LIDT/LIAT) with various experimental
conditions (wavelength, pulse duration, polarization, number of pulses, material bandgap). However, even for similar
experiments from different authors [1–6] reporting surface
LIDT/LIAT measurements for fused silica samples irradiated with single shot, ∼100 fs, 800 nm pulse, a large scattering of results, from 2 to 12 J/cm2 , exists. Unfortunately,
the dispersion of these measurements (F ≈ 10 J/cm2 ) is
largely superior to the absolute surface LIDT/LIAT value,
thus preventing the precise determination of accurate data.
This issue is even more critical in the context of femtosecond
laser-dielectric interaction as it is supposed to be extremely
deterministic owing to its highly nonlinear nature [7]. In addition, this particular feature is one of the main reasons why
N. Sanner et al.
ultrashort material processing is now acknowledged as a relevant technology for applications requiring a high level of
accuracy. In particular, the spatial extent of the processed
zone can be limited to the laser spot area for which the local
fluence exceeds the material threshold, enabling to reach [8]
or even beat [7] the diffraction-limited beam surface when
the LIDT is surpassed only in the central region of the focused Gaussian beam distribution. This sharp ‘threshold’ effect, arising from the highly nonlinear character of absorption, is of prime interest for emerging nanomorphing applications, and is only obtained for pulse energies very close
to the material ablation threshold. The precise and reliable
determination of material thresholds is then a crucial issue
for both fundamental and applicative breakthroughs.
The problem of laser damage and ablation measurement
in femtosecond regime has already been addressed in the
literature. There are ex situ investigations of the diameter,
depth and morphology of damages by AFM [9], SEM [3],
optical miscroscopy [10] or profilometry [11]. On the other
hand, a multitude of in situ procedures are applied like timeof-flight [12], light scattering [13], time-resolved plasma
formation [14], time-resolved interference [15, 16], plasma
radiation [17, 18], or transient reflectivity [9, 14]. Nevertheless, there is no general agreement on the definition of
thresholds (melting, damage, and ablation), and on the methods of measurements (with their different detection limits).
Moreover, one observes a large variety of experimental setups, laser beam and material parameters (chemical material
composition, surface state, etc.). As a consequence, it appears unavoidable to observe a large scattering of threshold
values, which makes the comparisons between experiments
very delicate.
In this paper, we present different techniques for surface LIDT/LIAT measurements used in the experiments
with femtosecond laser pulses. The proposed techniques are
based on a single experimental setup but different postmortem analysis and data treatment. Assumptions responsible for systematic errors are considered. We show that information on laser ablation and/or laser damage threshold
of a material are preferentially obtained, depending on the
applied technique and procedure of treatment of the experimental data.
The paper is organized as follows. Section 2 describes
the setup configuration including precise description of the
laser source, the diagnostics and the experimental protocol.
The appropriate definitions of material damage and ablation thresholds are discussed in the same section. Then we
present in Sect. 3 the measurement and data exploitation
techniques for surface LIDT/LIAT determination, which are
compared and discussed in Sect. 4.
Fig. 1 Experimental setup. M: mirrors; Pol.: reflective Brewster polarizer; BD: beam dump; L: lens f = 100 mm
2 Experimental setup
The experimental setup is presented in Fig. 1. The laser
source is a commercial S-pulse system from Amplitude Systèmes, delivering 450 fs (controlled by a second-order autocorrelator), 1 kHz, 200 µJ pulses at 1025 nm. The intensity
distribution is Gaussian with a M2 factor equal to 1.3. The
M2 value was determined by studying the beam propagation with a long focal lens (f = 300 mm) and a CCD Spiricon beam analyzer. The beam is linearly polarized, allowing simple energy adjustment by means of a half-wave plate
combined with a reflective polarizer used at the Brewster
angle. The incident beam on the sample is then s-polarized,
whatever the tuning of energy. For small values of energy,
calibrated neutral density filters are added, in order to benefit
from small and precise energy increment which is required
for an accurate LIDT determination. The beam is expanded
with an afocal system providing a beam radius w = 4 mm
at 1/e2 , and is focused onto the surface of the sample with a
standard plano-convex BK7 lens of 100 mm focal length.
The target consists of the most widely studied transparent dielectric material, i.e. fused silica (Heraeus HOQ310,
thickness 2 mm and diameter 25 mm). To compare the surface LIDT/LIAT results deduced from the three methods
presented below, and because these thresholds may depend
on surface imperfections (scratches, cracks, grooves, etc.),
roughness, exact chemical composition or contamination, all
experiments are performed on the same SiO2 sample polished with standard optical quality. The sample is mounted
on a three-axis computer-controlled translation stage and its
position is carefully adjusted by combined energy-scan and
z-scan procedures, allowing to precisely locate the surface
at the waist position with an accuracy much better than the
Rayleigh range, ensuring the accuracy of the measurements.
As an example, for the 100 mm focal lens used in this experiment, the half Rayleigh range is ∼350 µm and the final
z-scan step amounts to 10 µm. A far-field imaging system is
also implemented. This system consists of the focusing optics itself combined with a CCD camera and its objective,
providing real-time visualization of the target surface with
Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics
a high magnification. The target surface is illuminated with
incoherent grazing red light (Stocker Yale Specbright LED
spotlight centered at 630 nm), so that the imaging system
is the equivalent of an in situ dark-field microscope, which
collects the reflected and scattered light coming from permanent damages induced by the laser pulses. This setup enables to reveal damages smaller than the laser waist at the
focus. All experiments are performed under ambient air in a
single-shot regime, and the sample is systematically moved
to a fresh zone after each shot, even if no damage is detected.
Indeed, multi-shot experiments imply incubation effects due
to accumulation of pulses on the same site, which considerably lower the threshold [3] and lead to results more delicate
to interpret. Our damage diagnostic is based on ex situ optical and/or atomic force (AFM) microscopy analysis. Note
that the laser-induced modifications of the material are compatible with the accuracy and resolution of these characterization tools.
We define damage as a permanent irreversible modification of the morphology of the material surface, which
can be detected by an AFM or an optical microscope with
adapted magnification and illumination. Transient reversible
phase changes or permanent structural modifications (leading to different material properties like a refractive index
rise) without any change in surface topology are, thus, not
considered as damage. When the surface modification is accompanied by material removal, we speak about ablation.
The ablation of the material is easily put in evidence by the
AFM, enabling to measure the ablated volume, and qualitatively by the optical microscope by varying the focus to
detect the formation of a crater.
In short-pulse regime (nanosecond to femtosecond) and
for a given laser source (pulse duration and wavelength),
the usual parameter to express the surface LIDT/LIAT of
a material is the fluence (J/cm2 ), ratio of the energy to
the surface. The threshold fluence thus corresponds to the
minimum energy per unit surface required to induce a detectable change (in the sense of our previous definition of
damage or ablation) of the material surface. The energy is
an experimental parameter whose value is easily measured
by a joule-meter or a power-meter. Note that a femtosecond pulse produced by an amplifier could exhibit a somewhat complex temporal structure of energy distribution, potentially including amplified spontaneous emission (ASE),
residual pulse train from the femtosecond oscillator and pre(post-) pulses due to non-perfect extinction ratio of the internal Pockels driving the regenerative amplification in the
laser. Each of these structural components of the temporal
energy distribution could induce pre-excitation of the surface which may have a strong effect on the material thresholds. With our laser system, the ASE is negligible (contrast
ratio ∼10−8 , as measured with a third-order autocorrelator), and the residual pulse train from the 50 MHz oscilla-
tor is measured and subtracted from the recovered singleshot amplifier energy value. Note the pulse energy ratio,
E1shot,oscillator /Esingle-shot,amplifier ∼ 10−9 , is largely inferior
to any material modification threshold, even under multishot irradiation [13, 19]. The pre- and post-pulses are minimized by a fine tuning of the extraction delay of the regenerative amplifier (contrast ratio ∼250). The single-shot regime
is obtained by triggering of the internal Pockels cell, leading
to shot-to-shot fluctuations ≤20%. These fluctuations are attributed to the non-optimal management of the instant of extraction of the pulse from the regenerative amplification loop
when operating the laser in that single-pulse regime. This
could be optimized by implementing an additional Pockels
cell outside the laser, gating a single pulse from the nominal
kilohertz pulse train. Nevertheless, during the experiments,
the amplitude of shot-to-shot fluctuations can be controlled
by a photodiode.
In order to calculate the fluence, the parameter “surface”
has to be evaluated. In the frame of LIDT/LIAT measurements, the surface can be defined in two ways. On the one
hand, one can consider the real beam size in the plane of the
target as it can be characterized by a beam analyzer with a
CCD camera or a knife-edge scanning system. On the other
hand, one can extrapolate the beam size from laser-induced
transformation measurements of the surface of a material as
first suggested by Liu for 20-ps long Gaussian pulses [20].
Dealing with femtosecond laser pulses, one should consider the transport of the laser beam onto the target and,
in particular, the impact of the laser focusing system on
the beam characteristics (waist and pulse duration) at the
focal plane, where the sample is studied. In all the experiments described hereafter, the beam power P is below
3.77λ2
) for self-focusing in air
the critical power (Pcr = 8πn
0 n2
(P ∼ 2–20 MW < Pcritical,air ≈ 3.3 GW, with n2,air =
4.7 × 10−19 cm2 /W [21] and n0,air ≈ 1), thus avoiding spatial and temporal beam distortions caused by self-focusing
and other nonlinear effects during laser beam transport to the
target. Now, the beam power generally exceeds the critical
power of the material estimated for fused silica to 3.1 MW
(λ = 1025 nm, n0 = 1.45, and n2 = 3.47 × 10−16 cm2 /W
[21]). Nevertheless, filamentation-induced damage was not
observed during our experiments as confirmed by the postmortem examination of the sample with the optical microscope. During our study of surface LIDT in short-pulse
regime, the damage is always initiated on the front surface
and we have checked that there is no damage under the surface or on the rear surface. Using a lens is a convenient way
to reach high-peak fluences for LIDT/LIAT study of a material. The influence of geometric (spherical) and chromatic
aberration induced by a lens on a femtosecond laser pulse
has been extensively studied by numerous authors [22–25],
and in most cases, an estimation of the influence of the focusing lens on spatial and temporal pulse stretching of the
N. Sanner et al.
femtosecond beam can be derived from scaling equations
that can be found in classical textbooks [24, 25]. Considering our laser system (1025 nm, 450 fs, w = 4 mm) and
experimental arrangement, we thus verify that geometrical, chromatic and temporal aberrations play a negligible
role in each experimental case with the 100-mm focal lens
used thereafter. These calculations are in agreement with the
beam waist measurement (w0 = 10.7 µm, f = 100 mm).
This w0 value also agrees with the theoretical value issued
from Gaussian law propagation considering M 2 = 1.3. Note
that in case of shorter femtosecond laser pulses and/or strong
focusing (high numerical aperture), the impact of lens aberration can be evaluated by solving the diffraction integral
in the focal region requiring a numerical and more complex
approach as treated for instance in reference [23].
3 Approaches used for LIDT determination
Three independent techniques for LIDT/LIAT determination based on post-mortem analysis of the target surface
are presented in this section. It is important to notice that
at this stage we do not distinguish between the laser damage (LIDT) and laser ablation (LIAT) threshold of the material. The difference will be made evident in the discussion of the results in Sect. 4. The first two techniques consist of direct measurements of damage dimensions, from
which LIDT/LIAT results are inferred by numerical regressions, whereas the third one is based on a statistical approach
which provides other additional information. Results are reported in Table 1 and discussed in Sect. 4. Note that since the
fluence thresholds given hereafter arise from one single experiment, and in order to facilitate comparisons between different applied data treatment techniques, all thresholds are
calculated considering the beam waist experimentally measured with the beam analyzer (w0 = 10.7 µm).
3.1 Diameter-regression technique
This technique is based on the measurement of the damage
area of the material, here with an optical microscope. It was
first proposed for indirectly recovering the intensity distribution of a 20-picosecond laser [20] based on the fact that
the damage size depends on the pulse fluence. For the considered range of pulse duration, this method provides the
LIDT of the fused silica target by means of damage diameter measurements. The radial fluence distribution at the focal point of the Gaussian beam is given by [26]: F (r) =
2
2
2Emeas −2r 2 /w02
= Fmeas e−2r /w0 , Emeas being the measured
2 e
πw0
laser energy, r the radial coordinate and w0 the beam waist
radius measured at 1/e2 . The main assumption states that, if
the material is not damaged at the distance r from the center
of the beam, the corresponding value of fluence F (r) equals
Fig. 2 Squared crater diameter vs. laser fluence (logarithmic scale).
The D 2 data are averaged over 5 points; the vertical error bars shown
in the figure correspond to the amplitude of the standard deviation. The
threshold is determined by the fluence value attained when the fit goes
down to D 2 = 0
the threshold value Fth . Therefore, the interaction of such
a beam with the sample surface results in a damage whose
diameter D scales with a logarithmic law as a function of
the laser pulse fluence Fmeas : D 2 = 2w02 ln(Fmeas /Fth ). Experimental data (averaged over 5 points) are reported on a
graph plotting D 2 versus Fmeas (Fig. 2), and a numerical
fit enables to find the damage threshold, determined by the
fluence for which the linear fit goes down to D 2 = 0. The
inferred threshold fluence then corresponds to the fluence
of the equivalent “top hat” beam [26]. Here we find Fth =
3.7 J/cm2 and the corresponding threshold energy is Eth =
6.7 µJ. The slope of the curve is equal to 2w02 , therefore
readily providing a simple way to control the effective radius
of the laser spot at 1/e2 on the target surface. We obtained
w0 = 8.7 µm which is somewhat lower than the waist measured with the beam analyzer (w0 = 10.7 µm). This point
will be discussed in Sect. 4.
3.2 Volume-regression technique
Another regression technique can also be implemented by
using measurements of the ablated volume. Fig. 3 shows the
volume of ablated material (averaged over 6 points) measured by an atomic force microscopy system (AFM XE-100
from Park Systems, Inc.) versus the laser pulse fluence. The
linear shape of this curve might help for identification of
predominant absorption channels.
It is now well established that photo-ionization and
electron–electron impact ionization are responsible for the
optical breakdown in dielectrics [27–29], but their relative
importance strongly depends on laser parameters (mainly
intensity and pulse duration, as pointed out in reference
Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics
channel in our experimental laser conditions is most probably related to avalanche ionization, which is predicted to
scale linearly with the laser intensity according to standard
kinetic models [27]. This result further confirms previous
findings [31], though the latter were obtained in a multishot regime. Finally, with this volume-regression technique,
the threshold fluence (resp. energy) is then measured to be
Fth = 4.25 J/cm2 (resp. Eth = 7.65 µJ), in agreement with
the first regression method relying on diameter measurements.
3.3 Statistical approach
Fig. 3 Ablated volume vs. laser fluence. The data of ablated volume
are averaged over 6 points; the vertical error bars shown in the figure
correspond to the amplitude of the standard deviation. The threshold is
determined by the fluence value attained when the linear fit goes down
to V = 0
[30]). Concerning photo-ionization mechanisms, the intensities used here (I < 1013 W/cm2
) involve for the Keldysh
parameter (defined by γ = ω/e me cnε0 Eg /I , see [30])
a value ∼3, suggesting that multiphoton absorption prevails upon tunneling ionization for the generation of very
first free-electrons. In our case a minimum of eight photons of 1.21 eV energy is required to transfer an electron from the valence to the conduction band (fused silica
bandgap Eg = 8.9 eV). This population of seed electrons
undergoes a further rise by impact ionization, usually described by avalanche ionization models for dielectrics [27,
29]. However, the respective contributions and probable interplay of the two processes are still under discussion [29]
due to contradictory existing experimental results [27, 31,
32]. This is a fundamental question because the ratio between photo-excited and impact-ionized electrons enables
to estimate the temporal evolution of the electron density
in the material and hence the transient absorption of the
laser energy during the pulse (in other words, the dynamics of the laser energy deposition in the material) and the
dynamics of the plasma formation. The absorption itself is
indeed a quite complex phenomenon as the free-electron
plasma generated by the initial part of the pulse can either
absorb the later part more efficiently or act as a plasma mirror and reflect most of the incident energy [33, 34]. In a
complementary experiment [35], we measured a linear evolution of the material absorption with respect to laser fluence increase (for the range Fth ≤ F ≤ 3Fth ), in agreement
with other published results [5, 36]. A linear rise of the ablated volume with the pulse fluence was thus expected close
to threshold, and we therefore infer the damage threshold
by extrapolating the linear regression to zero. This experimental observation suggests that the dominant absorption
This method is usually used for laser damage studies with
long pulses (typically nanosecond). In this regime, laser
damage exhibits a probabilistic behavior, contrary to the expected deterministic one for ultra-short pulses. In fact, in the
nanosecond regime, damage occurrence is more dependent
on impurity concentration than on intrinsic material properties, therefore leading to a non-deterministic behavior [37]
and to damage dimensions which are not directly related to
the laser beam spot size. The technique used for the LIDT
determination relies, thus, on statistical experiments. For
constant laser fluence below the intrinsic material threshold,
damage will occur if the laser spot hits a defect while no
damage will be observed if no defect stands in the laser focus area. As a result, the answer is binary, that is to say we
only consider the presence or absence of any damage after
the laser shot [37].
Here, we use this technique for precisely determining
the surface LIDT of the sample irradiated with femtosecond pulses. We measure the probability to produce damage
for a set of different fixed laser energies. For each energy
case, 50 laser shots are applied on 50 different sites (singleshot regime) of the fused silica sample which is examined
afterwards under optical microscopy to count the number
of damaged sites. Only the occurrence of the damage is
reported in that approach without any need of quantitative
measurement of a physical data like the diameter of a damaged or ablated zone. This procedure automatically minimizes the errors related to the precision and sensibility of
the diagnostic system and of the operator as well. This last
point can be particularly important when dealing with (sub-)
micrometer laser damage, close to the limit of resolution and
detection of a classical optical microscope.
The results are plotted on Fig. 4. Two LIDT values can
be extracted: Fth,low = 2.2 J/cm2 (resp. Eth,low = 3.9 µJ)
and Fth,high = 3.5 J/cm2 (resp. Eth,high = 6.2 µJ). The low
threshold value is the highest fluence for which the damage
probability equals zero. Surface damage begins to appear
(but not systematically) if the pulse fluence is just superior.
The high threshold is the lowest fluence for which damage
is systematically produced for each of the 50 trials. In Table 1, high- and low-thresholds are reported, and also what
N. Sanner et al.
Table 1 Energy and fluence thresholds measured with the three independent techniques (see the text for details). Fluence thresholds are calculated
using the experimentally beam waist, w0 = 10.7 µm. When possible, the calculated beam waist inferred from the treatment of the experimental
data is given for comparison
Technique (used diagnostic)
Fluence threshold (J/cm2 )
Regression diameter (optical microscope)
3.7
Regression volume (AFM)
4.25
Statistical (optical microscope)
Low
High
Mean
2.2
3.5
2.8
Energy threshold (µJ)
6.7
7.65
3.9
6.2
5.0
w0 (retrieved) (µm)
8.7
–
–
–
–
Fig. 4 Damage probability vs. laser fluence. The high- and
low-fluence thresholds are defined respectively by damage probabilities equal to 1 and 0
can be called the mean-threshold, corresponding to the energy needed to obtain a 50% damage probability.
4 Discussion
The experimental results are summarized in Table 1. Evaluating fluence thresholds is not totally straightforward due
to the Gaussian intensity distribution of the focal spot. Indeed, the material response is sensitive to the local peak
fluence (that is why a smooth intensity distribution without any hot spots is of prime importance) which is different from the average value, integrated over the whole crosssectional area measured by a power-meter placed in front of
the beam. It is the reason why, in the previous section and
in Table 1, the fluence threshold was calculated by taking
into account the surface correction considering the equivalent “top-hat” laser beam surface (S = πw02 /2), a uniform
cylindrical beam with the same total energy and peak fluence [26]. The laser fluence threshold Fth was then simply
expressed by: Fth = 2Eth /πw02 . This expression yields the
threshold twice larger than that usually given in the literature.
At this point, important remarks concerning the reliability and the significance of the different material thresh-
old measurements are worth being underlined. The first two
techniques (diameter- and volume-regression) integrate by
definition the response of the material to the laser excitation
through the quantitative measurement of changes induced
on a physical parameter of the sample (diameter of the affected zone or of the drilled crater on the surface target, ablated volume, etc.). The diameter-regression technique relies on the assumption that the measured diameter of the
damage is equal to the diameter of the Gaussian beam for
a fixed fluence level. In other words, this technique assumes
that the material damaging is deterministic. The method is,
therefore, not adapted to threshold determination with laser
pulses longer than a few tens of picoseconds, for which the
damaged region can extend to a significantly larger area than
the irradiated zone, mostly because of thermal effects [38].
On the contrary, this technique is especially relevant for femtosecond laser pulses, which are known to drastically reduce
surrounding unwanted effects on the material target (e.g.
thermal or mechanical damage [39, 40]) for pulse energies
close to the threshold. This is due both to a better localization of energy absorption provided by its nonlinear nature,
and also to the relatively low dependence on the presence of
defects for which absorption cross sections are smaller [41],
thus theoretically favoring intrinsic phenomenon. Now, the
linearity of the fit in logarithmic scale (see Fig. 2) can be
discussed when incident laser energies are very close to the
threshold level. The corresponding points are not reported
on the graph because optical microscopy does not offer sufficient spatial resolution to carry out accurate measurements
(see for instance Fig. 5a). On the opposite, when the incident energy is high, the damages can exhibit a very irregular
spatial shape resulting from evident mechanical cracking or
spallation (see for instance Fig. 5c). These points are obviously not considered because the diameter measurements
are not representative. Actually, Fig. 5b shows typical damages, the diameter of which can be non-ambiguously measured. As a result, the diameter-regression technique often
does not consider a set of data fully representative of the
Gaussian beam (in other words, the feet and the peak of
the Gaussian beam can roughly be ignored in that analysis), thus potentially inducing error in the derivation of the
energy threshold and beam waist from the data.
Measurement of femtosecond laser-induced damage and ablation thresholds in dielectrics
Fig. 5 Photographs of laser-induced damage in SiO2 at low (a),
medium (b) and high (c) fluence. The analysis is made using the optical
microscope (magnification × 100)
The second regression technique using AFM volume
measurements is less questionable, even if the same difficulty of accurately measuring an ablated volume very close
to the threshold still exists. Indeed, near the threshold, the
surface topography can be altered showing small pits and/or
pikes, melted zones, etc., but not leading to a measurement
of an ablated volume. Now, in the considered fluence range
just above the threshold (see Fig. 3), the evolution of the
ablated volume with the pulse fluence follows a linear law
making it easy to extrapolate the fluence threshold from the
ablated volume data set. This determination of the fluence
threshold is done without any assumption concerning either
the focal spot energy distribution or the deterministic character of the material threshold. The AFM analysis can also
provide an independent estimation of the fluence threshold
and beam waist, by using the diameter-regression technique
presented in Sect. 3.1 with AFM measured data, respectively
giving Fth = 3.3 J/cm2 (Eth = 5.95 µJ) and w0 = 10.15
µm (in good agreement with the waist measured with the
beam analyzer). The discrepancy in the inferred Fth , Eth
and w0 data illustrates the high sensitivity of the regression techniques, related to the dispersion of the quantitative
data (crater diameter and ablated volume), the accuracy of
the numerical fit and the resolution of the diagnostic tools
(optical microscope and AFM). As a result, the regression
techniques are in general less accurate than the statistical
approach for which the vertical error bar is considerably
minimized when using a sufficient number of trials and an
adapted diagnostic tool. Note also that deviations from the
theoretical waist value, which was experimentally confirmed
by the beam analyzer, can be partly attributed to potential
experimental errors concerning the positioning of the surface with respect to the beam focus location and diameter
measurements in a misfit or incomplete fluence range (with
respect to the fluence threshold).
Finally, it is interesting to consider the physical meaning
of the information given by the two regression techniques.
We believe that these regression methods determine the ablation threshold (LIAT), rather than the damage threshold
(LIDT). This is largely due to the fact that they both utilize
quantitative data which have to be unambiguously defined
and further measured. As precise measurement of these
quantitative data can be challenging at fluences very close
to the LIDT threshold, they are systematically ignored, finally not leading to the determination of the damage threshold but of the laser ablation threshold (LIAT) of the material. Now, it should be emphasized that although arising
from totally independent techniques (different equipment
for damage measurements and different data treatment), the
two LIAT thresholds obtained by the two regression techniques (diameter and ablated volume) are in good agreement
(Fth,diameter = 3.7 J/cm2 and Fth,ablated volume = 4.25 J/cm2 ).
The third independent procedure is the statistical technique. This technique does not need any physical assumptions (neither on the material answer nor the nature and/or
precision of the measurement of the physical data) since it is
based on the observation of the damage occurrence, which
just depends on the sensibility of the used diagnostics. This
technique is therefore particularly well adapted to the measurement of the damage threshold (rather than the ablation
threshold) of a material as it does not reside on any quantitative measurement of a physical data. Such a measurement
then can provide different and complementary information
with respect to the regression techniques which are mostly
devoted to laser ablation threshold analysis of a material.
Actually, the low threshold (Fth,low = 2.2 J/cm2 ) has to be
related to the laser damage of the material (LIDT), which is
significantly lower than the LIAT threshold obtained by the
regression techniques (Fth = 3.7 J/cm2 ). Interestingly, the
high threshold (Fth,high = 3.5 J/cm2 ) is measured to be close
to the LIAT threshold. Note that the determination of this
high LIDT threshold is important for the technical development of material processing applications, because it corresponds to the lowest fluence for which the modification of
the processed material is assured. Therefore, this operating
laser condition should be appropriate in terms of minimal
invasiveness and optimal processing/machining quality.
Furthermore, unlike the two previous regression-based
techniques, the statistical study can easily include a large
number of shots, thus enabling to average both shot-to-shot
fluctuations of the laser energy and spatial heterogeneity of
the SiO2 target. High accuracy and reliability are then expected using this technique of LIDT characterization. Another valuable interest is that this technique does not require
to measure the damage dimensions (which could be not trivial to carry for example on biological tissues) and could
then been implemented as an in situ diagnostic, thus significantly increasing the treatment speed. Moreover, the statistical method also provides additional information about the
sharpness of the threshold, that is to say the deterministic
character of laser damaging. Note that the fluence difference
between high and low LIDT values is FL→H = 1.3 J/cm2
and seems to be rather high to describe what is usually believed to be a sharply deterministic phenomenon. Part of
N. Sanner et al.
FL→H should be attributed to laser shot-to-shot fluctuations (<0.6 J/cm2 ). Further investigations out of the scope
of this paper are today needed for explaining the observed
amplitude of FL→H . Now it shall be underlined that this
technique offers high potentiality to deeply investigate the
role of different laser–matter mechanisms by providing a
new way to obtain a quantitative measurement of the deterministic character (sharpness) of the damage threshold.
5 Conclusions
We have presented different experimental approaches for
determining the laser damage (LIDT) and laser ablation
(LIAT) thresholds of a material. Although the experimental arrangement is rather simple, the precise knowledge of
all experimental parameters is required to provide reliable
and reproducible LIDT/LIAT measurements. The three experimental techniques presented in this work are fully independent, and rely either on the measurement of quantitative
damage data of the material, e.g. the affected diameter or
less ambiguously the diameter of the formed crater and the
ablated volume, or simply (qualitatively) on damage detection.
The two main concluding remarks which we can draw
from our experiments, and which are important for developing laser micromachining processes and high peak-power
laser technology in general, are the following. Firstly, we
show that the regression technique based on the treatment
of quantitative damage data conveniently determines the
laser ablation threshold (LIAT) of the material. The statistical approach provides a strongly enhanced accuracy and
additional information, concerning the determination of the
damage threshold (LIDT) rather than the ablation threshold, as well as a quantitative measurement of the deterministic character of femtosecond laser damaging. Secondly, the
technique based on the statistical approach and optical microscopy analysis is highly promising as a relevant, rapid,
simple and inexpensive in situ diagnostic for parametric
studies of ultra-fast laser–matter interaction at the surface of
dielectrics. Moreover, this technique can be extended, without any supplementary difficulty, to the LIDT measurement
of bulk dielectrics, and can be fruitfully used with any other
material, especially with biological tissues, for which obtaining reproducible quantitative data can be problematic.
Acknowledgements The authors wish to thank J.Y. Natoli, M. Zerrad and M. Commandré from Institut Fresnel (UMR 6133 CNRS—
Universités Aix-Marseille) for valuable discussions on the topic of the
manuscript. This research was supported by the Region Provence–
Alpes–Côte d’Azur, the Department of Bouches-du-Rhône and the
French National Agency of Research (ANR) under contract FESTIC—
BLAN06-2_157374.
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