15 June 1998

Ž .Optics Communications 152 1998 168–174

Full length article

Single-shot measurement of laser-induced damage thresholdsof thin film coatings

F. Loewenthal 1, R. Tommasini, J.E. BalmerInstitute of Applied Physics, Sidlerstrasse 5, 3012 Berne, Switzerland

Received 4 January 1998; revised 9 March 1998; accepted 17 March 1998

Abstract

A novel method for single-shot measurements of laser-induced damage threshold of thin film coatings is presented. Usinga binary mask a laser beam is transformed into an ensemble of Gaussian-like spots at the position of the test sample.Comparing this fluence map with the observed damage on the sample, the damage threshold of the thin film of the samplecan be calculated using the data of only a single shot. q 1998 Published by Elsevier Science B.V. All rights reserved.

1. Introduction

Since the early days of high-power lasers the limita-tions of the output power were given by the damage

w xthreshold of the optical components 1–3 . Laser-induceddamage to conventional, multi-layer, thin-film coatingsusually limits the laser’s maximum power. Significanteffort has gone into the search of coating materials used

w xfor single- and multi-layer coatings 4 and different depo-w xsition techniques 5,6 . Also large efforts were undertaken

in theoretical studies of laser-induced damage in order tounderstand the fundamental mechanisms of damage to

w xdielectric optical coatings 7–11 .Laser damage testing makes it possible to monitor the

w xquality of thin-film optical coatings 12 . It is commonknowledge that the measurement of the laser-induced dam-

Ž .age threshold LIDT of the thin film is dependent on thetest conditions and preparation of the specimen as well asexperimental condition, i.e. spot size, wavelength, pulse

w xduration, etc. Eva et al. have also 13 demonstrated condi-tioning effects in LaF rMgF layers for the 248 nm laser3 2

line. In a round-robin experiment involving eight differentw xlaboratories 14 this aspect was pointed out. The ISO

w x11254 15 defines now a standard method for measuringthe LIDT on optical thin film coatings. In its conventional

1 E-mail: loewenthal@iap.unibe.ch

form, the damage test is a time-consuming, expensivemeasurement. A large number of shots are usually neces-sary to determine the LIDT with either the frequency or

w xthe mean-value method as described in Ref. 15 .Different methods have been established for measuring

the LIDT of optical dielectric coatings. A common methodis to focus a laser beam on the specimen which is to betested. After irradiation the coating is inspected for damage

w xusing Nomarski microscopy 16 . There are different LIDTsdefined depending on the irradiation procedure. For mea-

Ž .suring the single-pulse 1-on-1 damage threshold the sam-ple is irradiated one time. Regardless of whether damageoccurs or not the sample is moved to prevent conditioning

Ž .effect. In the N-on-1 conditioning the sample is irradi-ated with multiple pulses at a constant fluence below the1-on-1 damage threshold. Then single pulses with increas-

w xing energy density are added until damage occurs 13 .This more classical method can be extended by simulta-

neously measuring the change of the reflection of a secondlaser focused on the same spot where damage is to be

w xexpected 17,18 . LIDT evaluation by measuring thew xphotoacoustic deflection 19,20 of a second test-laser is a

common method in the laboratories. Also a N-on-1 testw xwith holographic interferometry is proposed 20 for LIDT

measurements.w xCommon to all methods described in Refs. 12–20 is

that they need multiple laser shots one by one for a singlemeasurement of the LIDT of a dielectric optical coating.

0030-4018r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved.Ž .PII S0030-4018 98 00157-6

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174 169

w xAlso single shot methods have been proposed 21,22 .Ebert et al. used a relation between damage radius on thecoating and the fluence map of the beam. Comparing theradius of the damage with the beam fluence map the LIDTcan be calculated approximately. This method has theadvantage of being very fast, but it does not take intoaccount the different morphology of damage due to laserirradiation and the statistical component of damage occur-

w xrence 23 . Wiggins et al. formed a small-spot pattern inthe Fourier plane of a lens using a binary mask.

In this work a single-shot method for measuring theLIDT of dielectric coatings is presented which is an exten-

w xsion of the method described in Ref. 22 . With a binarymask a diffraction pattern is generated in the near-field ofa lens. This pattern consists of an ensemble of Gaussian-likespots with a 1re2-diameter of about 100 mm. The peakfluences of the single spots are distributed over a largerange depending also on the beam profile of the incidentlaser. Comparing the fluence map of the beam with theresulting damage features, the LIDT of a dielectric coatingcan be determined with a single shot. With this modifica-tion the fabrication of the mask is less critical and themethod is extended to larger spot size.

2. Experimental setup

The experiments were performed using a Nd:glass lasersystem consisting of a Q-switched, mode-locked oscillatorfollowed by three rod amplifiers. A maximum pulse en-ergy of 4 J can be extracted with a pulse duration of 450

Ž .ps and a beam diameter of about 23 mm FWHM result-ing in a peak intensity of about 2 GWrcm2. The spatialbeam profile is super-Gaussian due to the gain profile ofthe rod amplifiers.

In Fig. 1a the focusing system is outlined. The pulsepasses through the binary mask M and a 1-m focal lengthlens f. The transmission through the mask is approximately15%. At a distance L behind the lens either a filteredCCD-camera for beam profile measurement or the testsample is placed. As shown in Fig. 1b the mask M consistsof 0.75-mm diameter holes arranged in such a way that thecenters build triangles of equal sides. The distances be-tween two neighboring holes are chosen equal to theirdiameter. For the experiments we prepared a mask with 3cm = 3 cm dimension from a copper plate with a thick-ness of 1 mm.

3. Beam profile at the sample position

Figs. 2a–2c show the measured diffraction pattern atthree different distances L. A desired pattern at the loca-tion of the test sample would be an ensemble of Gaussian-like spots with a non-uniform distribution of peak fluences.According to Fig. 2b this is the case at the position Ls87cm behind the lens. As can be seen from Figs. 2a and 2cthe correct positioning of the sample is sensitive only on acm scale.

In order to model this focusing system the spectralmethod of beam propagation was applied. A super-Gaus-sian beam profile was assumed with the waist at the

Fig. 1. Experimental setup for the LIDT measurements: P, Joulemeter; BS, beam splitter; M, binary mask; f, lens with focal length f ; S,sample; CCD, chip of the CCD camera.

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174170

Fig. 2. Measured and calculated diffraction patterns at different distances from the focusing lens. For all measurements: focal length fs100Ž . Ž . Ž . Ž . Ž . Ž . Ž .cm, mask hole diameter ds0.75 mm a , b , c are measured patterns while d , e , f are the corresponding calculated patterns; a and

Ž . Ž . Ž . Ž . Ž .d Ls91 cm, b and e Ls87 cm, c and f Ls82 cm.

position of the mask M. The beam at this position zs0can be described as

2nU r ,0 sexp y rrR , 1Ž . Ž . Ž .Ž .Ž 2 2.1r2where rs x qy , R is the beam radius, and n is the

order of the super-Gaussian. The transfer function of thelens with focal length f is given by

ik2t r sexp r , 2Ž . Ž .f ž /2 f

where ks2prl is the wave number.The transfer function of the mask can be written as

`

< <t r s u ry r ydr2Ž . Ž .ÝM i ji , jsy`

`

< <su rydr2 m d ry r , 3Ž . Ž .Ž .Ý i , ji , jsy`

where r are lattice vectors defined by the center of thei j

holes of the mask, u is the Heaviside function, m denotesthe convolution and d is the Dirac delta function.

Ž .The field U x, y, z can by calculated using the fre-Ž .quency transfer characteristic of the free space H a ,b , z

w x24

A a ,b , zŽ .2 2(H a ,b , z s sexp yikz 1ya yb ,Ž . ž /A a ,b ,0Ž .

4Ž .

where ask rk and bsk rk denote the cosine direc-x y

tions of the k-vector, and

A a ,b ,0 sFT U x , y ,0 , 5Ž . Ž . Ž .Ž .A a ,b , z sFT U x , y , z , 6Ž . Ž . Ž .Ž .where FT denotes the Fourier transformation. Finally, the

Ž .field at a distance z in front of the aperture U x, y, z canbe written in the form

y1U x , y , z sFT H z FT t r t r U x , y ,0 .Ž . Ž . Ž . Ž . Ž .M f

7Ž .

Ž .The implementation of Eq. 7 using the FFT algorithm ona PC delivers a fast tool for evaluating other gratings or

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174 171

modified setups. In Fig. 2d–2f the calculated diffractionpatterns are shown. The resolution of all the calculations is7.8 mm = 7.8 mm, whereas the resolution of the measure-ments with the CCD camera is 24.5 mm = 16.9 mm. Themeasured and the calculated field distributions are seen tobe in excellent agreement.

In Fig. 3 centered vertical and horizontal scans of theŽ . Ž .measured solid curve and calculated dotted curve beam

at the position Ls87 cm are shown. Because of theaberrations of the beam the peak fluence of the measuredbeam slightly differs from the theoretical one. The 1re2-diameter of a single spot near the center is about 100 mm.

The center-to-center separation is about 350 mm in thehorizontal direction while in the vertical direction thecenters of the spots are separated by about 200 mm. The

Ž .profile of a single spot cross symbols near the center isŽ .shown in Fig. 4 and a Gaussian curve is fitted solid line

with a least square algorithm. The agreement is better than90%, indicating that the spots are Gaussian-like. The com-parison of Fig. 4a with Fig. 4b shows that the measuredcurve has a 25% larger diameter than the theoretical one.This is caused by the divergence of the beam which hasbeen neglected in the model. The diameter of a single

Ž .measured spot is about 80 mm FWHM . According to thistwo spots with a size which may be defined by their

Ž .diameter FWHM are separated by a distance of at least120 mm. If the peak fluence of the spots is much higherthan the threshold energy of the mirror the damage causedby the single spots may be very large and interdependencecannot be excluded. In this case the laser energy has to bereduced. Another possibility to overcome this problem isto build up a mask which defines an interference patternwith a larger spot-to-spot separation. For a larger spot sizethe diffraction pattern at the position 76 cm in front of thelens may be considered. At this position again an ensembleof Gaussian-like spots is found but with the spot size of

Ž .about 220 mm FWHM .The most critical part in this measurement is the deter-

mination of the absolute value of the peak fluence of asingle spot. We adopted the method proposed by Smith et

Ž .Fig. 3. Scans through the center of the measured dotted line andŽ . Ž .the calculated solid line diffraction pattern; a horizontal scan,

Ž .b vertical scan.

Fig. 4. Spatial profile of a single spot. Crossed points are mea-Ž .sured while the solid line is a fitted Gaussian curve; a Gaussian

Ž .fit of the measured curve; b Gaussian fit of the calculated curve.

w xal. 25 which consists in measuring the energy of eachshot with an apertured Joulemeter. For the same shot onlythe counts of the pixels on the chip of the CCD cameraover the same aperture are taken into account for thecalculation of the total energy. The calibration constant Cof the CCD camera can then be defined as

EnergyCs , 8Ž .

countsÝa

where only the pixel counts which are inside the aperture aare summarized.

Each shot through the mask M can now be describedby its peak fluence distribution. In Fig. 5a the histogram ofthe peak fluences of a single shot with an energy of 190mJ is shown and for comparison in Fig. 5b the histogramof a calculated shot calibrated to have the same energy ispresented. It is seen in Fig. 5a that with one shot a range ofpeak fluences from approximately 3 Jrcm2 to 20 Jrcm2

can be covered. For the interpretation of the damageprobability it has to be kept in mind that there are only fewshots with peak fluences exceeding 20 Jrcm2. In the caseof large shot-to-shot fluctuation of the laser the experimen-tal setup has to be modified in such a way that theintensity map and the exposure of the sample can be done

w xsimultaneously 16 .

Fig. 5. Number of spots inside a fluence interval versus fluence;Ž . Ž .a experimental histogram of a shot with 190 mJ; b calculatedhistogram corresponding to an energy of 190 mJ.

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174172

4. Experimental results

A comparison between the single-shot method and amultiple-shot method was performed by testing the LIDTof a highly reflecting multi-layer coating for 1060 nm on afused silica substrate produced with commercial methods

Ž .by Guinchard Optical Glass Switzerland . The LIDT ofthis coating was first measured with the conventional1-on-1 method. For this measurement twenty shots werefocused resulting in a beam diameter of about 2 mm at thesample position. In order to prevent conditioning effectsafter each shot the sample was moved by a distance of 3

mm, regardless whether damage occurs or not. A defini-w xtion for a LIDT may be given by 15

1E s E qE 9Ž .Ž .thr maxŽND . minŽD .2

where E is the highest non-damaging fluence andmaxŽND .E is the minimum fluence where damage occurs.minŽD .From this the spread S is calculated by SsE ymaxŽND .E . With this multiple-shot method a LIDT of E 9.8minŽD . thr

Jrcm2 and a spread of 2.3 Jrcm2 was measured.In order to test the reproducibility of the proposed

single-shot method five shots were taken on the sametarget at different positions. From each shot the LIDT isevaluated separately.

Ž . Ž . Ž . Ž . Ž .Fig. 6. Morphology of the damage; a shot energy 235 mJ; b shot energy 170 mJ; c to e increasing the peak fluence; c morphology ofŽ . Ž .the damage near threshold; d and e typical damage morphology for peak fluences above threshold.

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174 173

Fig. 6 shows examples of the morphology of damageon different scales using a scanning electron microscope.Figs. 6a and 6b show an entire damage region. The energyof the shot corresponding to Fig. 6a was 235 mJ while theenergy of the shot shown in Fig. 6b was 170 mJ. Themissing spots on this grid indicate that the correspondingpeak fluences were smaller than the damage threshold ofthis coating.

From Fig. 6c to 6e single damage spots at increasingpeak fluence are shown. Fig. 6c shows a typical pin pointdamage which is caused by a spot with a peak fluence of14.8 Jrcm2. At increasing fluence lower-lying layers ofthe coating are damaged as shown in Figs. 6d and 6e. InFig. 6d the peak fluence of the spot was 16.8 Jrcm2 and inFig. 6e 18.3 Jrcm2, respectively. For a peak fluence muchhigher than the damage threshold the morphology of the

Ž .damage changes from massive pin point damage Fig. 6dŽ .to massive damage Fig. 6e . The occurrence of damage

becomes very reproducible. The diameter of the damage isabout 40 mm, increasing with increasing energy. Nearthreshold there are large fluctuations in the morphology ofthe damage which indicates a dominance of the defect-in-duced damage mechanism. From this point of view it isobvious that single-shot measurements of LIDT whichmiss the statistical aspect of the occurrence of damage aredifficult to be interpreted. Using Nomarski microscopy wefound that all damages were surrounded by a not damagedregion. From this we assume that interdependence can beneglected.

To evaluate the LIDT of the coating first the damage-w xfrequency method 15 was applied on the data resulting

from a single shot. Each single measurement is representedby its fluence histogram shown in Fig. 7. Grey-shadedareas show the number of shots in the same peak fluenceinterval which cause damage on the sample coating. From

Žthis the probability of damage occurrence crosses in Fig.

Fig. 7. Evaluation of a single-shot LIDT measurement. Histogram:peak fluence distribution; grey-shaded area shows the percentageof damage; crosses: measured probability of damage occurrence;solid curve: fitted probability curve of single-shot damage as afunction of the peak fluence.

Table 1Measurements of LIDT on the same coating

Shot E E E Spread Dthr,s thr2 2 2w x w x w x w xno. mJ Jrcm Jrcm Jrcm

1 192 9.1 9.9 1.3 19.4

2 235 9.6 11.0 1.9 11.1

3 170 8.5 10.1 1.6 11.2

4 192 9.9 10.2 0.4 37.1

5 219 8.2 10.4 1.4 7.9

E: the laser energy at the sample position; E : fitted LIDT;thr,sŽ .E , spread: LIDT calculated using Eq. 9 with the data of athr

single shot.

.7 can be calculated by a division of these two numbers foreach peak fluence interval. To fit the measured data a

w xfunction of the form 15

0 EFE° thr ,s

yDr2~ EP E, E , D s 10Ž .Ž .thr ,s1y E)Ethr ,s¢ ž /Ethr ,s

was chosen where E is the peak fluence at the sampleposition and E and D are considered as fit parameters.thr,s

The solid line in Fig. 7 shows the fitted curve representingthe single-shot probability of damage.

Table 1 gives a summary of the results of the experi-ments. In the second column, the laser energy E at theL

sample position is given. E is the damage thresholdthr,s

calculated from the fitted data. The calculated damagethreshold E can be considered as a sort of safe energythr,s

where no damage occurs. As shown in the second columnof Table 1 the pulse energy E has variations caused byL

the amplitude variations of the laser output. Although thepulse energy E has variations up to 35%, the measuredsingle-shot threshold is reproducible with a standard devia-tion of 8%.

In order to compare the results with the LIDT of 9.8Jrc2 measured with the conventional 1-on-1 method, the

Ž .LIDT of the samples have been evaluated using Eq. 9with the data of a single shot. The results are displayed inTable 1, column four. The mean value of the measuredLIDT E is 10.3 Jrcm2 with a standard deviation ofthr

4.1%. This is in excellent agreement with the measuredvalue of 9.8 Jrcm2 using the classical 1-on-1 method. Aninteresting effect is that the spreads have large variations.We think this is caused by the small spot size and thedefect-dominated mechanism of damage in agreement with

w xRef. 14 .

5. Conclusion

In summary, we have presented a single-shot methodfor the measurement of LIDT of thin-film coatings. Abinary mask is used to generate an ensemble of Gaussian-

( )F. Loewenthal et al.rOptics Communications 152 1998 168–174174

like spots with a non-homogeneous peak fluence distribu-tion at the position of the test sample. Comparing thefluence map of the incident beam with the damage it ispossible to determine the LIDT with both the damagefrequency method or the mean-value method with the datafrom a single shot. With this experimental setup it ispossible to measure the LIDT of a thin film with onesingle shot where the corresponding conventional methoduses about 100 shots in order to obtain a comparablestatistical distribution.

In order to evaluate other setups an algorithm is pre-sented to calculate the expected beam profile at the sampleposition. The results of the single-shot method are inexcellent agreement with the LIDT measured with themultiple-shot 1-on-1 method.

This method, as presented here, is limited to perpendic-ular incidence of the beam and further studies are requiredto extend it to non-perpendicular incidence. Smaller valuesof the spread may be obtained if the setup is optimized toget larger 1re2-diameter of the single spots. Here anoptimum between spot size and peak fluence distributioncan be expected.

Acknowledgements

The authors would like to acknowledge the technicalassistance of B. Locher and E. Bigler for the support withthe scanning electron microscope. This work was sup-ported by the Swiss National Science Foundation.

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