multiscale analysis of the laser-induced damage threshold ... et... · posted 9 september 2008...

Multiscale analysis of the laser-induceddamage threshold in optical coatings

Jérémie Capoulade,* Laurent Gallais, Jean-Yves Natoli, and Mireille CommandréInstitut Fresnel (UMR CNRS 6133), Université Aix Marseille, Ecole Centrale Marseille,

Domaine Universitaire de St Jérôme, 13397 Marseille Cedex 20, France

*Corresponding author: [email protected]

Received 29 April 2008; revised 29 July 2008; accepted 5 August 2008;posted 9 September 2008 (Doc. ID 95607); published 3 October 2008

We have investigated the influence of laser beam size on laser-induced damage threshold (LIDT) in thecase of single- and multiple-shot irradiation. The study was performed on hafnia thin films depositedwith various technologies (evaporation, sputtering, with or without ion assistance). LIDT measurementswere carried out at 1064nm and 12ns with a spot size ranging from a few tens to a few hundreds ofmicrometers, in 1-on-1 and R-on-1 modes. These measurements were compared with simulations ob-tained with the statistical theory of laser-induced damage caused by initiating inclusions.

We show how to obtain information on the initiating defect properties and the related physical da-mage mechanisms with a multiscale study. Under certain conditions, it is possible with this method todiscriminate different defects, estimate their densities, and follow the evolution of the defects under mul-tiple irradiation. The different metrology implications of our approach, particularly for obtaining a func-tional LIDT of optical components are discussed. © 2008 Optical Society of America

OCIS codes: 310.0310, 140.3330.

1. Introduction

In dielectric thin films, laser-induced damage in thenanosecond regime is due mainly to the presence ofnanometer-sized precursors in the material that in-itiate the damage mechanism. The origin of theseprecursors could be contaminants from polishingand cleaning processes or coating deposition [1–4].In most cases, however, these defects are not identi-fied and characterized. Therefore a lot of efforthas been made in recent years to develop tools andmethods for studying these defects, aiming for funda-mental understanding and feedback on the manufac-turing process.An approach that has proved to be of great interest

for studying defects and their implications in the la-ser damage resistance of thin films is the analysis oflaser damage measurements with statistical models[5–11]. Indeed, with appropriate modeling one canextract from laser damage statistics the defect den-

sities and discriminate different defect classes. In thepresent work we propose to investigate the potenti-alities of combining these statistical models for laserdamage measurements made with various spot sizes(from micrometer to submillimeter diameter sizes).The objective is to use the test beam as a probe, withdifferent spatial detection capacities, to discriminatedifferent types of defects on a sample and to studytheir properties independently.

In the first part of this paper, the samples used forthe study (hafnia monolayers) are described, as wellas the laser damage testing procedure and the statis-tical model for the interpretation of laser damagestatistics. In the second part, after reviewing the dif-ferent investigations of spot size effects on laser da-mage in the literature, we analyze the resultsobtained in coatings irradiated with different spotsizes under single-shot irradiation. The results willbe interpreted in terms of initiating defects and com-pared with simulations. To finish, the spot size ef-fects on the damage probability curves undersuccessive irradiation (R-on-1 mode) are investi-gated. The results are interpreted in terms of defect

0003-6935/08/295272-09$15.00/0© 2008 Optical Society of America

5272 APPLIED OPTICS / Vol. 47, No. 29 / 10 October 2008

properties in order to quantify the ability of the de-fects to be conditioned or, in contrast, to produce fa-tigue effects.

2. Materials and Methods

A. Samples Description

The samples under study are HfO2 monolayers. Thisis one of the most important high-index materials forthe production of optical coatings for infrared appli-cations. The substrates are 1 in. (2.54 cm) diameterfused silica substrates (Corning 7980) polished forhigh-power applications. All the substrates are fromthe same batch and were polished at the same time.The optical thickness of the layers is a half-wave at1064nm. Four different methods were used to man-ufacture the samples: electron beam deposition withand without ion assistance (either from hafnium orhafnia starting material), reactive low-voltage ionplating, and dual ion beam sputtering. The sampleswill be called EBD-Hf, EBD-HfO2, RLVIP, and DIBS,respectively. The different coating plants and deposi-tion parameters used to produce these coatings aredescribed in [12]. The parameters correspond tothe optimized processes developed at the InstitutFresnel for this material.

B. Experimental Tools

The laser damage facility, described in Fig. 1, isbased on an injected Nd:YAG laser (Quantel YG980) with a pulse duration of 12ns. The laser oper-ates at 1064nm with a maximum output energy of1200mJ, at a repetition rate of 10Hz. The beam islinearly polarized and irradiates the sample at nor-mal incidence. The available output energy allows usto vary the irradiation beam size from submillimetricto micrometric range by changing the focus lens. Inthis study two different spot sizes were used: 44 and320 μm (diameter taken at 1=e2). This energy is con-trolled with a variable attenuator (half-wave plateand polarizer). A mechanical shutter permits extrac-tion of single shots from the 10Hz source. Theobservation of the sample is done by imaging thebackscattered light (He–Ne probe) with a long-distance video lens (magnification 200×), which pro-

vides a detection limit of 10 μm. The damage detec-tion is performed by comparing the area beforeand after irradiation with image processing software.The damage criterion is then any visible modificationdetected with this system. The measured laser-induced damage threshold (LIDT) is defined as thehighest fluence that does not induce any detectabledamage.

Statistical measurements were made on the differ-ent samples by using two standard test procedures:1-on-1 [13] and R-on-1.

• For the 1-on-1 mode, 20 different fluences weretested, with 50 shots at each fluence for the 44 μmspot size and 20 shots at each fluence for the320 μm spot size. Fewer data points were taken forthe larger spot size because of the lack of availablespace on the samples: indeed, the distance betweentwo tested sites must be large enough to avoid anymeasurement artifact such as contamination orstress caused by previous damage. Thus the errorbars on the measurements are different.

• For the R-on-1 mode, 75 sites were tested. Oneach site the fluence was progressively increasedfrom half the LIDT previously measured in the 1-on-1 mode to the fluence leading to damage, with in-crements of 1 J=cm2 and a frequency of 1Hz. Forthose measurements, we used the same laser da-mage criterion as in the 1-on-1 mode.

The error bars for the probability measurementsare calculated by using the procedure described pre-viously [14]. They correspond to a confidence level of95%: the confidence that the estimated probability(measurement) is between the upper and lower le-vels of the error bars is 95%.

C. Theoretical Tools

Laser damage statistics obtained with the use of the1-on-1 mode can be modeled. Different phenomenolo-gical models have been developed and refined [5–11]through the years to link the laser damage probabil-ities to defect densities, spot size, fluence, etc. Themodel that is used in this study is the one developedby Krol et al. [11].

First, we consider a collection Ω0 of isolated defects(so-called precursor centers) with a random distribu-tion. The probability of damage at a fluence F is theprobability of the presence of a precursor center un-der the irradiation beam that receives more fluencethan its intrinsic LIDT T. This probability is given by

PðFÞ ¼ 1 − exp½−NðFÞ�; ð1Þ

whereNðFÞ is the number of precursor centers underthe laser spot, initiating damage at a fluence lowerthan F:

NðFÞ ¼Z

F

0gðTÞSTðFÞdT: ð2Þ

Fig. 1. Schematic setup of the laser damage test facility: ωdam,Nd:YAG laser at 1064nm; ωprobe, He–Ne laser; Pyr, pyrometerfor pulse energy measurement; L, lens for beam focusing; Ech,sample.

10 October 2008 / Vol. 47, No. 29 / APPLIED OPTICS 5273

Here, STðFÞ is the spot surface where the fluence ishigher than the defect threshold T:

STðFÞ ¼πw2

2ln�FT

�ð3Þ

with the spot size diameter w defined at 1=e2. NðFÞalso depends on gðTÞ, the defect ensemble function,representing the density of defects initiating damageat a threshold fluence T. This function is a Gaussiandistribution with three variable parameters: a da-mage threshold mean value T0, a threshold standarddeviation ΔT0, and a precursor defect density d0[Eq. (4)]:

gðTÞ ¼ 2d0

ΔT0

ffiffiffiffiffiffi2π

p exp�−

12

�T − T0

ΔT0=2

�2�; ð4Þ

Z∞

0gðTÞdT ¼ d0: ð5Þ

A Gaussian defect ensemble gðTÞ and its associatedtheoretical laser damage probability curve areplotted for illustration in Figs. 2(a) and 2(b).We can generalize this statistical model to a mate-

rial that contains n different defect classes Ωi, char-acterized by their own ensemble function giðTÞ, i.e.,their density di, their damage threshold mean value

Ti, and their threshold standard deviation ΔTi.Then, the total ensemble function gðTÞ is given by

gðTÞ ¼Xni¼1

giðTÞ; ð6Þ

gðTÞ ¼Xni¼1

2di

ΔTi

ffiffiffiffiffiffi2π

p exp�−

12

�T − Ti

ΔTi=2

�2�: ð7Þ

In the case of two defect classes, a Gaussian defectensemble gðTÞ and its associated theoretical laserdamage probability curve are plotted for illustrationin Figs. 3(a) and 3(b). It is apparent that the laserdamage probability curve has two slopes, each beinglinked to one defect class.

Statistics obtained by R-on-1 are not so easy tomodel, since several other parameters can be in-volved in the laser damage mechanism: the numberof shots on each site, the step between each fluence,and shot frequency. Each of these parameters canhave an influence on the LIDT [15]. If no conditioningor fatigue effects are involved in the tested material,and if one assumes that there is no spatial variationof the laser beam, the laser damage probabilityshould be the same as in the case of 1-on-1 tests.In other cases, fatigue or conditioning effects couldbe interpreted as a variation in the defect ensemblefunction. This will be described in detail in Section 4.

Fig. 2. (a) Defect class ensemble Ω0 with the following parameters: T0 ¼ 35J=cm2, ΔT0 ¼ 1J=cm2, d0 ¼ 103=mm2. (b) Simulation of theassociated laser damage probability curve (spot size diameter 50 μm). (c) Simulation of laser damage probability curves for different spotsize diameters. 1, 10 μm; 2, 15 μm; 3, 20 μm; 4, 30 μm; 5, 50 μm; 6, 500 μm.


3. Spot Size Effects on Damage Probability Curves

Laser damage studies on optical components rely onstatistical tests made at different fluences on thesample, with a given spot size diameter. The mostcommonly used test is the 1-on-1 test, defined byan ISO standard [13], which recommends the useof a spot size of at least 400 μm for laser damagetests. Other refined procedures such as raster scan-ning have also been implemented for specific studiesof large-area components [16,17]. In the case of 1-on-1 tests, the first experiments showed a LIDT depen-dence on spot size [5,18,19]. This was caused by aninadequate definition of the threshold, which was de-fined as a fluence leading to a damage probability of50%. Considering the curves of Fig. 2(c), we can ea-sily observe that such a definition will induce a spotsize dependence of LIDT. Using statistical modelsbased on defect considerations, Foltyn [20] and Por-teus and Seitel [6] studied theoretically and experi-mentally the influence of the spot size on laserdamage experiments. They have concluded that bytaking the “onset” (higher fluence for 0% damageprobability), a spot-size independent LIDT could beobtained. We have seen that the method could havelimitations when different kinds of defect are in-volved in the laser damage process.It has also been suggested that if neighboring de-

fects can collaborate in the damage process, spot sizedependence of the LIDT should also be expected [21].

Taking these studies into consideration, we choseto investigate the potential of using intentionally dif-ferent spot sizes in laser damage tests to obtain in-formation on the damage mechanisms in a particularmaterial.

A. Theoretical Analysis

The spot size dependence of the LIDT can be pre-dicted according to the model presented in Subsec-tion 2.C. First, we consider a material with asingle defect class, chosen arbitrarily for illustrationand denoted Ω0. For a given distribution functiongðTÞ, the laser damage probability curve can beplotted as a function of the spot size diameter[Fig. 2(c)]. In this case one should find the sameLIDT, independently of the spot size. An increaseof the laser beam size should only change the curveslope. Then the spot size should theoretically have noimpact on the measured LIDT.

In a second case we consider that different defectclasses can be embedded in the material. We haveplotted in Fig. 3(c) the case of two classes of defect,Ω1 andΩ2 (again chosen arbitrarily), with the densityof Ω1 being larger than the density of Ω2, and thethreshold of Ω1 defects being higher than the thresh-old of Ω2 defects.

From these simulations, we find that in the case ofbeam sizes in the range of few tens of micrometers,the measured LIDT will be 35 J=cm2, which is the

Fig. 3. (a) Two defect class ensembles Ω1 and Ω2 with the following parameters: T1 ¼ 35J=cm2, ΔT1 ¼ 1 J=cm2, d1 ¼ 103=mm2,T2 ¼ 17J=cm2, ΔT2 ¼ 1J=cm2, d2 ¼ 10=mm2. (b) Simulation of the associated laser damage probability curve (spot size diameter100 μm). The two damage probability curves corresponding separately to precursorsΩ1 and precursors Ω2 are also plotted (dashed curves).(c) Simulation of laser damage probability curves for different spot size diameters. 1, 15 μm; 2, 35 μm; 3, 100 μm; 4, 150 μm; 5, 250 μm; 6;600 μm.


intrinsic threshold of the defects Ω1. In this case, theprobability of finding a defect Ω2 under the laser spotis negligible. The same material tested with a largerbeam size (>100 μm) should exhibit another LIDT,around 15 J=cm2, close to the intrinsic threshold ofΩ2 defects. For intermediate spot sizes, a break inthe slope of the measured damage probability curvesis expected. It occurs when the probabilities of find-ing a defect Ω1 or Ω2 under the spot are similar.Therefore, if different classes of defect can initiatelaser damage, the LIDT is spot size dependent,and no scaling laws can be used to anticipate the da-mage threshold of an optic from tests made with asmall beam size (in comparison with the mean freedistance between defects).We notice that these considerations are valid only

in the case where the more populous class of defecthas a higher activation threshold fluence than theother. The opposite case, where the more populousclass of defect has a lower activation thresholdfluence, is similar to the one-defect case explainedabove.Apart from metrological considerations, the inter-

esting point shown by these simulations is that per-forming laser damage measurements with differentspot sizes can provide specific information about thelaser damage precursors. Indeed, knowing the den-sity and the number of defect classes can be helpfulfor the optimization of fabrication processes, asshown in [22,23], for the study of polishing and clean-ing processes.

B. Results and Discussion

Measurements have been made on the samples de-scribed above with different spot diameters, 44and 320 μm (at 1=e2). Results are shown in Fig. 4.The curves can be fitted with the model describedabove (solid curves in the figure).Each pair of curves illustrates a particular case of

what has been seen by simulations in the previouspart. For the EBD-HfO2 samples, the two curvescan be fitted with the same parameter values: onlyone class of defect is highlighted with a LIDT of14 J=cm2 and a density of 6 × 102=mm2. Here, wehave measured a single threshold for different spotsizes (14 J=cm2). This corresponds to what is showntheoretically in Fig. 2.The DIBS samples illustrate the case of two defect

classes: with the two spot sizes, two different LIDTsare observed, which are 12 J=cm2 for the test madewith the 44 μm beam size and 5 J=cm2 for the320 μm beam size. This can be interpreted withthe defect model: one class of defect has a LIDT of5 J=cm2 and a density of 10=mm2 (called Ω2); theproperties of the other class are a LIDT of12 J=cm2 and a density of 5 × 102=mm2 (called Ω1).For the other samples, EBD-Hf and RLVIP, inter-

mediate cases between EBD-HfO2 and DIBS arefound. Two classes of defect are found, but in thiscase, owing to the particular ratio between the den-sities, a slope change is observed for the larger beam

size. It corresponds to what is shown theoreticallyin Fig. 3.

Regarding the results obtained for the DIBS sam-ple, the defects of class Ω2 are expected to be, in the-ory, detected by the 44 μm beam size, provided thatthe statistic is improved, i.e., the number of testedsites is increased. However, this is limited by two fac-tors. Fist, it was demonstrated that the distance be-tween two tested sites is a very important parameterin laser-induced damage metrology [24]. Indeed, ow-ing to the fragment pollution, mechanical stress, andso on, a laser-induced damage can affect tests ofneighboring sites at distances greater than the da-mage size (typically a few hundred micrometers).To avoid this effect, one has to perform measure-ments with a minimal distance between two neigh-boring tested sites: in our case, 300 μm for the44 μm spot size and 600 μm for the 320 μm spot size.Moreover, the dimensions of the sample physicallylimit the tested site number.

Now, let us introduce the ratio ξðsample=spot sizeÞ, defined by

ξðsample=spot sizeÞ ¼ Ndef

Ntest; ð8Þ

where “sample” is the sample tested, “spot size” isthe spot size used for the test, Ndef is the maximumdefect number of a given class that can be interceptedwhen the whole sample is tested, and Ntest is themaximum number of sites irradiated when the wholesample is tested. For a good measurement, ξ shouldbe close to 1 or higher, in order to intercept at least 1defect at each test. A small value of this ratio meansthat we will not be able to detect this defect classwith this spot size, even when testing the entiresample.

Taking into account these limiting parameters, wecan deduce that Ntest ¼ 3364 sites with the 44 μmspot size and Ntest ¼ 841 sites with the 320 μm spotssize. That implies that a maximum of 1.65% of theentire surface sample can be tested with the 44 μmspot size (5:11mm2), and 21% with the 320 μm spotsize (67mm2) [25].

In the case of the EBD-HfO2 sample, we detectedjust one class of defect, with a density of 600=mm2.Thus, with the 44 μm spot, Ndef ¼ 5:11 × 600 ¼3066 defects. So, here ξðEBD-HfO2=44Þ ¼ 3066=3364 ¼ 0:91, and with a 320 μm spot size,ξðEBD-HfO2=320Þ ¼ 47:8. In this case, both spotsizes are appropriate for the detection of this defectclass. With the same argument, considering now thedefect class Ω2 detected by the 320 μm spot on theDIBS sample (density of 10=mm2), ξðDIBS=44Þ ¼0:015 and ξðDIBS=320Þ ¼ 0:79. As we can see,ξðDIBS=44Þ is very low, which means that even whentesting the entire DIBS sample, the detection of thislow-density defect class would still be difficult with avery focused laser beam (44 μm). Thus, for the detec-tion of the Ω2 defects, we need a larger spot (320 μmin our case) in order to increase the ξ value.


Thus, one aspect of this multiscale study is to ex-hibit different classes of defect that could exist in thematerial at different densities, depending on the spotsize used. We will see in the next section that themultiscale approach allows one to study the behaviorof the defects separately, for instance, under multipleirradiation.

4. Spot Size Effects in the Case of Cumulative Shots

The R-on-1 procedure is adapted to observe potentialconditioning effects, i.e., improvement of the LIDTdue to preirradiation. In the case of HfO2 tested withthe R-on-1 procedure, large conditioning effects (in-crease of the LIDT up to a factor of three) have beenreported in the literature [26]. In addition, the tests

Fig. 4. Laser damage probability measured in 1-on-1 mode (at 1064nm and 12ns), and the associated defect ensembles (superimposed oneach data plot), for hafnia films made with different technologies: electron beam deposition, starting from a (a) hafnia or (b) hafniumsource, (c) reactive low-voltage ion plating, and (d) dual ion beam sputtering. The fits of the experimental data (solid curves) are describedin detail in the text.


are faster to conduct than with the 1-on-1 procedure:fewer sites are necessary for testing, since eachtested site gives a threshold value. Accordingly, thismethod is commonly used in the laser damage com-munity. However, the spot size effects on the mea-sured LIDT in the case of R-on-1 tests are notobvious to interpret, given the fact that, as opposedto 1-on-1 tests, conditioning or fatigue effects can beinvolved. It appears useful, then, for the LIDT me-trology to study spot size effects in R-on-1 tests.In the case of several classes of defect, as evidenced

on some of our samples in the previous section, eachdefect may have its own evolution under successiveirradiation. The R-on-1 measurements with differentspot sizes should therefore give information on thebehavior of each defect, since we have seen that theycan be separated.

A. Theoretical Analysis

As seen in Subsection 2.C, fatigue or conditioning ef-fects in the case of R-on-1 tests can be interpreted asvariations in the defect distribution function. In afirst approach we have chosen to consider differentpossible evolutions:

• No evolution of gðTÞ under successive irradia-tion. Then the results obtained in R-on-1 modeshould be the same as in 1-on-1 mode• A reduction of the defect density d correspond-

ing to possible mechanisms of defect ejection or des-orption [27,28]• An increase or decrease of the threshold mean

value under successive irradiation corresponding topossible annealing or modification of the defect struc-ture [15,29,30]• The creation of new defects caused by irradia-

tion [15]

To illustrate the potential of our test method to de-scribe variations of the distribution function, wehave plotted in Fig. 5 the modifications induced onlaser damage probability curves by a variation of�10% of the parameters of the distribution function.

B. Results and Discussion

To investigate the spot size influence in the case ofmultishot testing, R-on-1 experiments were con-ducted on the samples, again with two different spotsizes (44 and 320 μm) and the test procedure de-scribed in Subsection 2.B. These experiments wereconducted on the RLVIP and EBD-HfO2 samples.The results are plotted in Fig. 6 and compared withthe 1-on-1 measurements. The R-on-1 results aloneare plotted in Fig 7.

Opposite effects on the two samples are observed,as well as a spot size dependence of these effects.

For the RLVIP sample, no significant effect of theR-on-1 test was observed on the LIDTobtained in thecase of the 44 μm diameter beam. However, in thecase of the large test beam, a fatigue effect (i.e., a de-crease of the LIDT with multiple shots) was ob-served. The fact that different behaviors areobserved depending on the spot size used to testthe sample can be explained by defect properties:we have seen previously that different classes of de-fect are involved for 44 and 320 μm spot sizes.

For the EBD samples, a conditioning effect wasmeasured for the 44 μm spot diameter as well asfor the 320 μm spot size. The same behavior was ob-served for the two spot sizes, in agreement with thefact that a single class of defect is involved.

To explain the differences between the two sam-ples, we have to consider their different physicalproperties. Indeed, coatings made with ion platingare very dense, with a density near the bulk one,whereas coatings obtained by electron beam techni-ques are rather porous. In our case the respectiverefractive indices of these two samples are 2.2 and1.9 [12]. The results are to be compared to those re-ported in the literature: conditioning effects are ob-served mainly in porous thin films (obtained by EBDor solgel process). In this case, under multiple irra-diation, the material porosity could imply a betterrelaxation of mechanical stress or allow the ejectionof defects without damage to the surroundingarea, since the defect is not strongly bonded to thematerial [31]. Moreover, studies on artificial metallic

Fig. 5. Influence of (a) a variation of �10% of the defect density on the laser damage probability curve and (b) a variation of �10% of thethreshold mean value of the defects.


nanodefects have shown that, under irradiations be-low the LIDT, these defects can be heated to theirmelting point and the metal can diffuse in the matrixwithout macroscopic damage, which may improvethe LIDT of the coating [32]. In the case of dense haf-nia coatings, however, no conditioning effects havebeen reported in the literature, to our knowledge.From our study it appears that under these condi-tions this material rather exhibits fatigue effects.Another important point is that in addition to the

observation that the LIDT is spot size dependent, thebehavior of the material under repetitive shots (con-ditioning or fatigue) is also spot size dependent. Thisis because different classes of defect, with different

potential behaviors, are highlighted when differentspot sizes are used for laser damage tests. This couldexplain discrepancies observed in the literature, i.e.,materials that exhibit conditioning effects under cer-tain test conditions and no effects or fatigue effectsunder other tests conditions [33].

5. Conclusion

Spot size influence on laser damage probability mea-surements has been theoretically and experimen-tally investigated in optical coatings under singleand multiple irradiations. The experiments wereconducted on hafnia coatings made with different de-position techniques: electron beam deposition with

Fig. 6. Comparison of results obtained in 1-on-1 and R-on-1 modes on samples (a), (b) EBD-HfO2 and (c), (d) RLVIP for two spot sizes. Thefitting parameters for the 1-on-1 curves are identical to those in Fig. 4. For the sake of clarity, the errors bars of the R-on-1 curves are notgiven for each point.

Fig. 7. Comparison of results obtained with the R-on-1 mode, on samples (a) EBD-HfO2 and (b) RLVIP, for two spot sizes. For clarity, theerrors bars of the R-on-1 curves are not given for every point.


and without ion assistance, reactive low voltage ionplating, and dual ion beam sputtering. Thanks to astatistical analysis of the results based on a defectmodel, we have demonstrated the potential of thismultiscale approach to highlight different classesof defect and study their properties separately, espe-cially when their surface densities are not of thesame order of magnitude. We have also shown thatthe behavior of a particular material under multipleshots can be spot size dependent when various de-fects with different potential behaviors are involved.Opposite behaviors, i.e., fatigue or conditioning ef-fects, were observed on the samples depending onthe deposition process used for their manufacturing.These effects were related to defects and mechanicalproperties of the coatings.

We acknowledge the RCMO team of the InstitutFresnel for fabrication of thin films.

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multiscale analysis of the laser-induced damage threshold ... et... · posted 9 september 2008...

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