Laser-induced damage of optical thinfilms submitted to 343, 515, and1030 nm multiple subpicosecondpulses

Dam-Bé DoutiLaurent GallaisMireille Commandré

Laser-induced damage of optical thin films submitted to343, 515, and 1030 nm multiple subpicosecond pulses

Dam-Bé Douti, Laurent Gallais,* and Mireille CommandréAix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, Marseille 13013, France

Abstract. Optical materials submitted to multiple subpicosecond irradiations are known to exhibit a decrease ofthe laser-induced damage threshold (LIDT) with the applied number of pulses, an effect referred to as “fatigue” or“incubation.” In this work, we experimentally investigate this effect for the case of optical thin films submitted tomultiple exposures with 500 fs pulses at different wavelengths: 1030, 515, and 343 nm. Niobia, hafnia, and silicafilms made with dense coating techniques (magnetron sputtering, ion-assisted deposition, and reactive low volt-age ion plating) are studied, as well as the surface of a fused silica substrate. These samples have been exposedto different pulse numbers (from 1 to 100,000) at a low-frequency repetition rate (less than 1 kHz) and the LIDThas been measured. The results reveal the differences between materials and for the various wavelengths suchas the decrease rate of the LIDT or the stabilization level that is reached after multiple exposures. All the resultsevidence the role of native- and laser-induced defects that we discuss on the basis of published works on thesubject. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.53.12.122509]

Keywords: laser damage; thin films; silica; niobia; hafnia.

Paper 140718SS received May 3, 2014; revised manuscript received Jul. 11, 2014; accepted for publication Jul. 14, 2014; publishedonline Aug. 6, 2014.

1 IntroductionWhen optical materials are submitted to multiple pulse irra-diations, a decrease of the laser-induced damage threshold(LIDT) is observed with the applied number of pulses, evenif some exceptions can be found. Because it is a mainlimitation for high power applications, this effect has beenextensively studied and documented for different irradiationconditions (nano, pico, and femtosecond pulses) and manymaterials of different classes: glasses,1–4 crystals,2,5 metals,6

polymers,7 or thin films.8 It is often referenced as “fatigue”9or “incubation,”10 suggesting that the modifications of thematerial take place under laser irradiation up to the pointwhere catastrophic damage (defined as a visible modificationthrough a Nomarski microscope) occurs. These modifica-tions can be macroscopic (temperature accumulation,6

building of stress, and ripples formation11) or microscopic(trapped charges and point defects) and it is often notpossible to detect any change before catastrophic damageoccurs. The physical processes can be “intrinsic” (linearphotoinduced processes12 and nonlinear ionization8) or“extrinsic” (inclusions in the material13 and contamina-tion14,15). It can also be the result of measurement artifactslinked to laser shot-to-shot fluctuations.16

In the present study, we investigate the particular case ofdielectric thin films submitted to multiple subpicosecondpulses. This topic has been mainly studied till now at800 nm for different materials: HfO2,

17 Sc2O3,18 Ta2O2,

8

and mixtures of TiO2–SiO2.19 Some studies were also con-

ducted in the case of functional multilayer coatings.20,21 Ithas been well established that the LIDT for multiple pulsesirradiation is lower compared to a single-pulse one, and adecrease of a few tens of percent can occur depending onthe material and irradiation conditions. The incubation effect,

in this case, is assumed to be related to the accumulation ofelectronic defects that act as reservoirs for the generationof free electrons in subsequent irradiations.8 The genera-tion of free electrons from these states requires less energythan the direct excitation of valence electrons and implies adecrease of LIDT in relation to the density of these defectstates. These defects can be native, particularly in nonperfectcrystals and materials in thin film form, or those that are laserinduced. This is of main importance for the choice of amaterial for a given application or for the design of opticalinterference coatings. However, the process is complex; forinstance, a dependence of the surface damage threshold onthe shot number that differs for different pulse durations hasbeen reported (200 fs to 5 ps in Refs. 10 and 22). This can berelated to the dependence of the contribution of physicalprocesses with the pulse duration: for instance, impactionization is more sensitive to defect states localized nearthe conduction band (referred to as shallow traps) and itscontribution increases with the pulse duration. By takinginto account trap densities and ionization cross-section ina rate equation model based on avalanche and multiphotonionization, Emmert et al.23 have been able to reproduce theexperimentally observed behaviors. The characteristic fea-tures of this accumulation effect are that there exists a stabi-lization (also called “saturation”) level of the LIDT andthat this stabilization level and the number of pulses requiredto reach it are dependent on material properties (nativedefect states and densities, susceptibility to the creation oflaser-induced defects) and irradiation conditions (pulse dura-tion/intensity). Based on the physical processes involved,the wavelength or photon energy should also have a majorinfluence on the accumulation effect, and the study ofthe LIDT dependence with the photon energy should helpto understand these processes. It is not possible, however,

*Address all correspondence to: Laurent Gallais, E-mail: laurent.gallais@fresnel.fr 0091-3286/2014/$25.00 © 2014 SPIE

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to find experimental data on this subject in the literature, andour contribution in this work aims to fill that gap.

The study has been conducted on very common opticalmaterials for laser applications: HfO2, Nb2O5, and SiO2.These three materials have very different bandgap energies,from 3.4 eV (Nb2O5) to 7.5 eV (SiO2); therefore, the mainrange of bandgaps for thin film optical materials is covered,24

with an intermediate as HfO2 (5.5 eV). It is of particularinterest to study the dependence of the LIDT with thebandgap values, as evidenced by Mero et al.25 at 800 nm.For each material, two different samples made with variousdeposition techniques have been tested in order to determinethe possible influence on the damage resistance of the defectslinked to the deposition conditions. Additionally, some mix-ture of HfO2 with SiO2 has been investigated. These sampleshave been tested with the three harmonics of an Yb:KGW500-fs laser (1030, 515, and 343 nm). The details of theexperiments are given in the first part of this paper. Then,we present and discuss the results in the second part.

2 ExperimentsAll samples have been measured in the same experimentalconfiguration and with the same S-on-1 procedure. However,the measurements have not been made with the same pulseduration for the wavelength of 1030 nm (375 fs) and for thewavelengths of 515 and 343 nm (550 fs). To make the resultscomparable, the data at 375 fs have been scaled to 550 fsusing a scaling law that we detail below. The objective ofthese experiments was to analyze the evolution of the dam-age threshold of optical thin film materials when exposed tomultiple subpicosecond pulses. Particularly, we were inter-ested in obtaining the stabilization level: the lowest valueof LIDT that can be reached under multiple exposures.However, in order to maintain reasonable test durations,the maximum pulse number has been set to 100,000. Asa consequence, the stabilization level was not reached forall samples. We describe, in the following experiment, thetest procedures that we have applied, and the samples underinvestigation.

2.1 Experimental Setup

The laser-damage test system is based on a commercialfemtosecond diode pumped Ytterbium amplified laser(Amplitude Systemes S-Pulse HP, Pessac, France) operatingat 1030 nm, with duration tunable from 400 fs to 3 ps. Acomplete description of the experiment can be found inRef. 26. Compared to this last reference, an additional wave-length conversion module with nonlinear crystals and dedi-cated lines has been implemented: from the infrared sourcewe get the second harmonic at 515 nm and the third har-monic at 343 nm. The three lines can operate from a singleshot up to 100 kHz with a maximum energy at 1 kHz of 1 mJfor the infrared (IR), 430 μJ for the second harmonic, and220 μJ for the third one. The configuration of the completesetup used in the present study is schematically shown inFig. 1.

The pulse duration is measured with a single-pulseautocorrelator. Because the system only operates in thenear-infrared (NIR), the green and ultraviloet (UV) pulsedurations were not measured. Following the manufacturer’sspecifications, we have assumed that the generation of sec-ond and third harmonics in these energy ranges do not have

significant effects on the pulse duration (less than �10%).Figure 2 shows the autocorrelation trace, with the sech2-shape profile associated with the pulse (555 fs in the illus-trated case). Temporal profile measurements have been madebefore and after the measurement campaign and the temporalprofile stays stable with the same range of temporal width.The damage tests have been made in two periods of time,separated by a complete laser revision: while making LIDTmeasurements in NIR, the pulse width was measured to be375� 10 fs at 1030 nm, and for the LIDT measurements invisible and UV, the pulse width was 555� 10 fs at 1030 nm.For the sake of comparison, the NIR results presented, in thispaper, were scaled at 555 fs according to the pulse temporalwidth scaling law presented in Ref. 25: Fth ¼ ðc1Eg þ c2Þτkpwhere Fth is the threshold fluence; c1 and c2 are the con-stants, τp is the temporal width of the pulse, and k ¼ 0.3.This scaling law has been measured at the wavelength of800 nm and is extended here to 1030 nm because the photonenergies are very close. We can note that there is no suchdemonstrated scaling law for the visible and UV regionsin the literature.

We used AR coated lenses (different lenses for each line,with a focal length of 150 mm) to focus the laser on the sam-ple. The pulse spatial width at the focus point is measuredwith a profiling camera (Dataray WincamD, Bella VistaUCD23). Figure 2 shows the measurement profiles for thethree wavelengths. The beams have a Gaussian shape andthe width at the 1∕e2 level is 75 μm for 1030 nm, 45 μmfor 515 nm, and 35 μm for 343 nm.

In this experiment, we used two repetition rates for theS-on-1 tests: 10 Hz for the tests 1-on-1, 10-on-1, 100-on-1, and 1000-on-1, and 1 kHz for the tests 100-on-1,1000-on-1, 10,000-on-1, and 100,000-on-1. Selection ofthe number of applied pulses was done with a mechanicalshutter with a transfer time of ≈4 ms. For the 1 kHz repeti-tion rate, this transfer time (opening and closing) can inducesome deviation in the number of pulses effectively receivedby the sample (typically from 1 to 10 shots). In our testconditions, the LIDT was found to be independent of therepetition rate for the 100-on-1 and 1000-on-1 tests, as pre-viously observed.8

2.2 Test Procedures

All the samples have been measured with the same experi-mental configuration and with the same procedure. In thisstudy, we present 1-on-1 and S-on-1 tests, as defined by

Fig. 1 Experimental setup for IR-visible-UV femtosecond laser dam-age measurement: Sh: mechanical shutter; HR: high reflective mirror;λ∕2: half-wave plate; Pol: thin film polarizer; BS: wedged beam-splitter; Pyro: pyroelectric detector for calibration; rHR: removablehigh reflective mirror; Calo: calorimeter for calibration; S: sampleholder; M: microscope for damage detection.

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the ISO standards.27 In the case of the 1-on-1 tests, each siteis irradiated one time at a specified fluence, and in the case ofS-on-1 tests, each site has been irradiated S times at a con-stant fluence. For each energy, we have tested five indepen-dent sites to make sure that the result is repeatable. Amaximum number of 100,000 shots has been defined inorder to obtain a reasonable duration of the experiments andto obtain the LIDT stabilization level. However, as we willsee in the results section, the stabilization level can beobtained above this number of pulses.

To evaluate the maximum fluence Fm on the sample, weused the effective area equation that links the total energyand the beam image in the sample plane (see Refs. 27and 26). With this method, we can determine a precisevalue of the fluence incident on the sample by taking thereal shape of the beam into account. Table 1 shows the sta-tistics of the measurement of the effective area of the beamand the temporal width. The damage threshold is calculatedto be between the highest fluence with no damage andthe lowest fluence at which damage occurred. The LIDT

is dependent on the electric field distribution in the film.The internal LIDT is then derived from the experimentalvalue and is more convenient for comparisons:

LIDTinternal ¼ jEmax∕Eincj2LIDTmeasured; (1)

with Emax∕Einc the ratio of the maximum of the standingwave electric field distribution in the film to the incident one.

The damage detection and the damage criterion are twokey elements of a test procedure. The detection is made insitu by a Nomarski microscope with a 50× Mitutoyo PlanApo SL infinity-corrected objective mounted on a BXFMOlympus (Tokyo, Japan) microscope. Before and after eachshot, an image of the irradiated area is done with a chargecoupled device (CCD) camera (COHU high performanceCCD). An image processing algorithm realizes the subtrac-tion, filtering, and binarization process to determine anychanged pixel value compared to a threshold defined bythe user. For some measurements, an ex situ observationthrough another Nomarski microscope with three objectives(20×, 50×, and 100×) is made. The damage criterion is thenany visible modification detected through this system. Thismodification can be mechanical as well as refractive indexchanges.

2.3 Samples

The S-on-1 laser damage measurement is time consuming;hence, we chose to concentrate our study on a few selectedsamples. The choice of the samples has been made firstaccording to their bandgaps: we chose to test Niobia(Nb2O5) which has a gap energy of 3.4 eV, Hafnia(HfO2) which has a gap energy of 5.2 eV, and Silica(SiO2) which has a gap energy of 8 eV. These materialscover the range of bandgap values of classical optical thinfilm materials: Nb2O5 is one of the optical dielectric thin

Table 1 Error budget on the experiment.

ParametersMean

value (nm) Minimum MaximumStandarddeviation

Pulsetemporalwidth

1030 556 fs 551 fs 563 fs 2.4 fs

Effectivearea

1030 2360 μm2 2256 μm2 2524 μm2 34 μm2

515 771 μm2 767 μm2 783 μm2 3 μm2

343 555 μm2 550 μm2 560 μm2 2 μm2

Fig. 2 (a) Autocorrelation trace of the temporal profile of the beamat 1030 nmwith sech2 fitting, (b) spatialprofile of the beam at the focus point on the sample for the three wavelengths.

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film materials with the lowest gap, silica is a higher one, andHfO2 has an intermediate value and is a very useful materialfor high power applications. Additionally, using materialwith different bandgap energies is of particular interest forthe study, because depending on the wavelength the multi-photonic absorption process will involve different numbersof photons (see Fig. 3).

In the case of single shot irradiation, the damage resis-tance is only slightly dependent on the deposition techniqueat 1030 nm.24 However, there has been no reported investi-gation for the case of visible and UV irradiations and themultipulse damage resistance can be linked to native defectsdependent on the deposition technique. Therefore, for eachmaterial we have chosen to test samples made in differentdeposition conditions. The samples were prepared withdifferent techniques giving dense coatings: Magnetron sput-tering, electron beam with ion assistance deposition, andreactive low voltage ion plating. The samples are referredto as “MS,” “IAD,” and “IP,” respectively. Table 2 detailsthe characteristics of the samples.

As explained in the previous section, the internal LIDThas been derived from the experimental value using a pro-portionality coefficient taking the electric field distribution

in the film into account. This distribution is due to the inter-ferences which take place in the film from the transmissionreflection on the interfaces. The assumption made in the cal-culation of the internal LIDT is that the damages are initiatedat the location of the maximums of the interference pattern.Since these interferences are wavelength dependent, itdoes appear to be very important to make that correction.According to the wavelength, the number of interferencemaximums and their positions in the sample, the value ofmaximum intensity changes. Figure 4 compares the distribu-tion in an Nb2O5 film for the different wavelengths. Asexpected, the number of maximums doubles on the secondharmonic and triples on the third harmonic according to theIR. The maximum of ðEmax∕EincÞ2 is equal to 0.6 for the IR,0.46 for the visible, and 0.41 for the UV. We can also noticethe effect of the absorption in UV: an exponential decrease ofthe intensity in the film.

3 Results and Discussions

3.1 Niobia

The results for the two samples of Niobia are reported inFig. 5. We can observe that for a given sample, the 1-on-1 LIDT is as expected, increasing with the wavelength.However, the decrease rate and its stabilization are dependenton both the wavelength and the sample, leading to a quitecomplex behavior.

In the NIR, we observe a drop of more than 60% in thefirst 1000 pulses, and then the saturation level is reached.Very similar behaviors are evidenced for the two samplesand there is no influence of the deposition process, whichsuggests that the same defects, intrinsic to niobia material,are involved. In the visible, the decrease takes place ata slower rate and the stabilization level is reached after100,000 pulses. The MS sample has a lower single pulsethreshold than the IAD sample, but the incubation effectis the same for the two samples, which suggests that thesame modification process of the material takes place. At343 nm, the photon energy is very close to the bandgapenergy and there is some linear absorption at this wavelength(see Table 2). We can note that the two samples, MS andIAD, have an extinction coefficient of the same order of

Fig. 3 Representation of the number of photons for a multiphotonicabsorption process for the three materials and three wavelengths ofthe present study.

Table 2 Sample properties. Band gap energies are estimated values based on previous studies24 (therefore, we have added a reasonable errorbar), thickness and refractive index have been determined by the analysis of spectrophotometric measurements.

SampleDepositiontechnology

Energy gap(eV)

Thickness(nm)

Refractive indexat 1030 nm

Refractive indexat 515 nm

Refractive indexat 343 nm

Nb2O5 IAD 3.4� 0.1 233 2.21 2.33 2.76þ 0.035i

MS 498 2.25 2.38 2.8þ 0.04

HfO2 IP 5.2� 0.2 80 2.1 2.15 2.22þ 0.00005i

IAD 260 1.98 2.06 2.1þ 0.003i

MS (with 5% silica content) 5.6� 0.2 500 2.02 2.07 2.14þ 0.0003i

SiO2 IAD 8� 0.5 317 1.47 1.48 1.5þ 0.0001i

MS 2207 1.47 1.48 1.49þ 0.0001i

Substrate 1.45 1.46 1.48

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magnitude, but we observe, however, different incubationbehaviors between the two samples: stabilization at 30% and70%, respectively. This can be added to the lower LIDT ofthe MS sample compared to the IAD one at 515 nm.However, we can only conclude that there is an influenceof the deposition technique without any knowledge of thepotential physical origin: niobia is a material that hasbeen less studied compared to silica and therefore it is diffi-cult at this point to form some hypothesis about the possibledefects involved.

3.2 Hafnia

The results of hafnia films are plotted on separate figures foreach sample (Fig. 6). We have also added another figure forcomparison between the different samples (Fig. 7).

We can globally observe that no matter what the sample,the LIDT increases with the wavelength, and this is true evenfor multiple irradiations. Moreover, for a given wavelength,the MS sample has the highest LIDT, and the IP and IADsamples have the lowest LIDT (The same scale is usedfor the different figures so that the results are comparable).

In the IR, the maximum drop in threshold occurs in thefirst 100 pulses for all samples, then the threshold eitherslowly stabilizes (MS and IP) or decreases (IAD). Takingthe error bars into account, it is possible that the stabilizationoccurs for all samples. This behavior is quite similar to whathas been measured by Nguyen et al.17 in IBS coatings withthe same irradiation conditions (800 nm, 1 ps, and 1 kHz).This behavior was attributed to the high densities of deepand shallow traps,23 i.e., electronic states in the forbiddenband that can trap the conduction band electrons after asubthreshold irradiation. These traps are the results of thedeposition conditions of the samples, which could explainthe differences between samples: the stabilization level inthis case is dependent on the defect nature and densities.Previous studies have shown that the photoluminescencespectra ofHfO2 films show significant differences dependingon the manufacturing conditions,28 which is again evidenceof electronic defects correlated to the deposition conditions.Depending on the wavelength, the decrease rate and its sta-bilization are different: for the case of MS the evolution isthe same for the three wavelengths, whereas in the case ofIAD there is a continous decrease in the UVand stabilizationafter few pulses in the visible.

3.3 Silica

The results obtained on the two silica films and on the silicasubstrate are reported in Fig. 8. For the wavelength of343 nm, the results for one sample only are given: indeedin the test conditions of this study, we have observed thatfor the two films and the substrate samples irradiated at343 nm, the damage occurs in the substrate, just beneaththe surface. This subsurface damage could be related toself-focusing of the laser beam. It has been also observedin Al2O3 samples22 at 850 nm∕2 ps. The critical powerfor reaching self-focusing depends on λ2,29 which couldexplain why, in our case, it is preferentially observed bythe UV radiation. As a consequence, it was not possibleto obtain the LIDT values for the films at 343 nm. In thecase of 1030 and 515 nm, we have also observed such an

Fig. 4 Electric filed repartition ðE∕E incÞ2 in the niobia film for the threewavelengths. E is the interference resulting electric field in the sampleand E inc is the incident electric field.

Fig. 5 Results of the S-on-1 LIDT measurements made on the two Nb2O5 samples (IAD: ion-assisteddeposition; MS: magnetron sputtering). (a) LIDT values as a function of the number of applied pulses andwavelength, (b) same results but normalized with the single-shot LIDT.

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Fig. 6 Results of the S-on-1 LIDT measurements made on the different HfO2 samples. (a) and (b) HfO2film made by ion-assisted deposition, (c) and (d) HfO2 film made by reactive low voltage ion plating, (e)and (f) mixture film of HfO2 and SiO2 made by magnetron sputtering. The same scale is used for allthe samples.

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effect but only after multiple irradiations: for a low numberof pulses, damage is initiated at the surface and for a largenumber of pulses damage initiates in the bulk. We have giventhe information about the damage location in the results dis-played in Fig. 8.

The results obtained on the three different silica samplesare very similar at 1030 and 515 nm: either in thin film orbulk form, the single pulse LIDT and the fatigue effect arethe same if we take the error bars on the measurements intoaccount. One possibility for such an observation would bethat the subtrate is limiting the LIDT of the film samples,so that we have measured the LIDT of the substrate threetimes. This is also corroborated by the fact that the damageinitiates in the bulk. Therefore, the damage threshold of thefilms is the same or higher than the values reported in Fig. 8

for bulk silica and the laser-induced damage resistance isthen linked to the intrinsic properties of silica.

At 1030 nm, the single-shot LIDT value is 4 J∕cm2 andthen continuously decreases with the applied number ofpulses: it is less than 50% of the single pulse value after100,000 shots.The single-pulse LIDT value is comparableto what has been measured by other groups at 800, 1030, or1053 nm (see a review on silica LIDT values in Ref. 24).There are, however, few systematic studies of the LIDTdependence with the number of pulses in the literature.Rosenfeld et al.10 have studied the dependence on thepulse number of the surface damage threshold for a-SiO2

with 100 fs∕800 nm pulses and they have observed a 70%decrease in the damage threshold in the first 20 shots, andthen a saturation of the incubation effect. In our case, the

Fig. 7 Results of the S-on-1 LIDT measurements made on the two HfO2 samples. (a): LIDT values asa function of the number of applied pulses and wavelength, (b) same results but normalized withthe single-shot LIDT.

Fig. 8 Results of the S-on-1 LIDT measurements made on the two thin films SiO2 samples (IAD: ion-assisted deposition; MS: magnetron sputtering) and the bare fused silica susbtrate. (a) LIDT values as afunction of the number of applied pulses and wavelength. The black circles/ellipses point out the casewhere damage initiates in the subsurface, (b) same results but normalized with the single-shot LIDT.

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decrease occurs at a slower rate with the pulse number andsaturation is not reached after 100,000 pulses (50% to 60%decrease). The main difference between the two experimentsis the pulse duration (100 fs versus 500 fs).

At 515 and 343 nm, there are no reported data, to ourknowledge, for the case of multiple irradiations. However,single-pulse values can be compared to published data: Jiaet al.30 have measured an LIDTof 1.05 J∕cm2 for fused silicaat 500 nm∕150 fs, and 0.9 J∕cm2 − 1.01 J∕cm2 at 267 to400 nm∕150 fs, respectively. There is no demonstrated tem-poral scaling at these wavelengths; however, if we assumea τ0.3 dependence as is observed in the NIR, a factor of 1.4needs to be applied for comparison to our measurements(They found 2 J∕cm2 for 150 fs∕800 nm).

Similarly for all wavelengths, the LIDT is monotonicallydecreasing with the number of applied pulses, and no stabi-lization value can be reached after 100,000 pulses. Sucha behavior cannot be explained with the native defects asshown in Ref. 23 (very high defect densities would beneeded, which is unrealistic for fused silica), but laser-induced defects should be involved. Such potential defectsin silica can be induced from the desexcitation of self-trapped excitons created by the laser irradiation:31 displacedoxygen atoms, vacancies, dangling bonds, and others.Assuming a probability of creation that depends on the flu-ence level, these defects can accumulate during successiveshots at a rate dependent on the fluence, up to a critical den-sity. They act as some reservoir of available electrons thatcan be excited with low intensities to seed the avalanche.The stabilization level, that is not reached in our experimen-tal conditions, could be related to the threshold for theircreation. Because defect formation appears to have no sharponset intensity,12 we have no indication yet of a possiblethreshold for stabilization of the LIDT.

3.4 Wavelength Dependence of Laser-InducedDamage Threshold

In the NIR and subpicosecond regime, there is a directdependence of the LIDT with respect to the bandgap foroptical materials, which can be explained by invoking thebandgap dependence of the multiphoton absorption coeffi-cient from the Keldysh photoionization theory.25 Foroxide thin films as for bulk materials, the dependence is lin-ear in a limited range of bandgap values and the result is notdependent on the manufacturing technique or depositionparameters.24 This is of particular interest for the choiceof materials for high power applications, even if some devi-ations from this linear behavior can be observed in the caseof mixtures of oxides.24 With the experimental data gatheredin this work, we have plotted the LIDT of the three testedmaterials as a function of their bandgap and for the threewavelengths (Fig. 9).

For the NIR, there is a linear dependence of the LIDTwiththe bandgap, as was previously discussed. The empiricaldescription that was found for the same test conditionsbut with more samples in Ref. 24 was applied and plottedin Fig. 9 (red line)

LIDT1030nm ¼ 0.63 ðJcm−2 eV−1Þ �Eg − 1.5 ðJcm−2Þ: (2)

Linear fits were also done for the case of 515 and 343 nmwith the present experimental data. In the UV, however, we

have chosen not to include the niobia sample because thebandgap and photon energy are very close and there issome linear absorption: it was shown, indeed, at 1030 nmthat the linear dependence of LIDT with bandgap wasonly observed in the regime of nonlinear absorption,24 andas previously discussed this linear dependence is related tothe bandgap dependence of the multiphoton absorption coef-ficient.25 The empirical relations that are found are

LIDT515 nm ¼ 0.53 ðJ cm−2 eV−1Þ � Eg − 1.7 ðJ cm−2Þ; (3)

for the case of 515 nm, and

LIDT343 nm ¼ 0.45 ðJ cm−2 eV−1Þ � Eg − 2 ðJ cm−2Þ; (4)

for the case of 343 nm.We can note that the slope is decreasing with the wave-

length and that the negative offset of the line equation isincreasing. A relatively simple and good approximation ofthese results is

LIDT ¼ 0.67 ðJ cm−2 eV−0.7Þ � Eg � E−0.3p − 1.42

� E0.3p ðJ cm−2 eV−0.3Þ; (5)

with Ep the photon energy.These results suggest that the same model could be used

to describe the single-pulse LIDT as a function of wave-length and material properties, from the UV to IR. However,some theoretical work needs to be done to analyze theseresults and find some relation with the physical processesinvolved, particularly with the Keldysh theory, which is out-side of the scope of this paper.

For practical applications, the single-pulse LIDT is notreally the relevant value. One has to take the incubationbehavior into account. We have then plotted for comparisonin Fig. 10 the incubation coefficients for the different testedsamples and the three wavelengths. The incubation coeffi-cient is defined as the ratio between the LIDT after N pulseson the single-pulse LIDT. We have plotted this coefficientfor S ¼ 1000 and S ¼ 100;000.

Of course, the incubation behavior is dependent on thematerial, which should be linked to the different kinds ofdefects that can trap electric charges induced by femtosecond

Fig. 9 Single-pulse LIDT (1-on-1) of the different samples as a func-tion their bandgap. The LIDT values are given at 500 fs for the differ-ent wavelengths.

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irradiation. The incubation coefficient can also be stronglydependent on the wavelength: different defects or channelsare possibly activated depending on the photon energy inthis case. If we look at details for the results for each materialbelow:

• Nb2O5: the results are the same for the two samples,except in the UV, but in this case the wavelength isvery close to the absorption edge and the materialhas no real significance for high power applications.In the IR and the UV, there is a significant differencebetween the incubation coefficient, but as was shownin the previous section, the stabilization regime was notreached at 515 nm after 100,000 pulses. So it is notpossible to compare the stabilization threshold forthese two wavelengths.

• In the case of HfO2, the results are similar no matterwhat the wavelength, except for one sample in the UVwith some correlation to a high extinction coefficient(compared to other samples). For this material, thestabilization threshold is reached: for instance, in thecase of the MS samples, we know the significant differ-ence between the incubation coefficient after 1000 or100,000 pulses no matter what the wavelength. Thismaterial is then of particular interest for high powerapplications. It could be a better choice compared tohigher bandgap materials that have a higher single-pulseLIDT (Sc2O3) but a higher incubation coefficient.18,22

• For SiO2, there is a continous decrease of the LIDTwith the number of applied pulses and it was not pos-sible to observe a stabilization threshold with the maxi-mum of pulses that we have applied. Considering alsothe results of Rosenfeld et al.10 with a measured incu-bation coefficient of almost 0.2 and the fact exposedpreviously, we have no indication yet of a possiblethreshold for stabilization of the LIDT. It appears thatin some conditions, after a large number of pulses thethresold of SiO2 can be the same as that of HfO2. This

is of main importance for the design, for instance, ofoptical interference coatings: the designs (optimizationof the electric field distribution) should be based on thelong-term laser damage resistance of the materials.

4 ConclusionA new experimental tool for the study of laser damage re-sistance from the UV to the NIR in the subpicosecond regimehas been introduced in this paper. Using this instrument, wehave reported on the experimental data that were not avail-able in the community until now: the laser damage resistanceof optical thin film materials for multiple pulse irradiationsfrom 343 to 1030 nm. These data are of particular interestfor various applications, but also for the comparison of theo-retical models in experiments, particularly the scaling law ofLIDT with the photon energy in the case of a single-pulseirradiation. Based on published works on the subject, the“fatigue” or “incubation” of the materials that has beenobserved could be related to electronic defects in thedifferent materials under study, but at this point only somespeculations about the defects involved could be done: toobtain more knowledge on these defects, further studiesare required using, for instance, specific experimental tech-niques such as pump/probe measurements or nondestructiveanalysis for the characterization of linear and nonlinearabsorptions (photothermal techniques, luminescence, etc.).

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Optical Engineering 122509-9 December 2014 • Vol. 53(12)

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Biographies of the authors are not available.

Optical Engineering 122509-10 December 2014 • Vol. 53(12)

Douti, Gallais, and Commandré: Laser-induced damage of optical thin films submitted to 343, 515, and 1030 nm multiple subpicosecond pulses