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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10151–10164
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Damage morphology change condition and thermal accumulation effect on high-reflection coatings at 1064nm

Zhichao Liu, Jin Luo, Yi Zheng, Ping Ma, Zhe Zhang, Yaowei Wei, Feng Pan, and Songlin Chen  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 10151-10164 (2014)
http://dx.doi.org/10.1364/OE.22.010151


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Abstract

The damage conversion behavior of high-reflection coatings under multiple shot of 1064nm nanosecond pulse laser has been investigated. The mechanism of initiation and evolution law of multi-shot damage has been revealed by use of surface profiler and focus ion beam with SEM. The scald damage tends to become delaminate damage under some certain condition. Huge experiments supports that this morphology change condition has a close connection with scald initial fluence, scald size, subsequent fluence and shot number. The relationship among these factors is for the first time achieved to offer the “safety lines” for components. The thermal accumulation effect on the decline of damage threshold under multi-shot has been studied in theory and verified experimentally. In addition, a theory-based formula is used to fit the experiment data for further prediction of thin film life-time.

© 2014 Optical Society of America

1. Introduction

2. Experiment

Fused silica is chosen as the substrate with the surface roughness of 0.4nm (tested by atom force microscope). The samples are prepared by e-beam evaporation method. Hafnia and silica are the high and low index material, respectively. The deposition temperature is set at 210°C. The deposition rates of hafnia and silica are 0.4nm/sec and 0.5nm/sec, respectively. The designed film stack is (HL) ^15H0.5L2.36H0.7L1.41H0.7L1.29H0.12L. The spectrum of coatings is tested by the spectrophotometer (Lambda 950) with s-pol at 22.5°, and the reflectivity of all samples is over 99.5% at 1064nm.

Damage tests were performed on the small beam damage test bench. The schematic layout of this bench is shown in Fig. 1.
Fig. 1 The layout of the small beam damage test bench.
The repetition rate of the Nd: YAG laser is 30Hz, and the typical pulse length (FWHM) is 10ns. By using of a single lens with focal length of 2m, the laser beam spot has a 1/e2 diameter of about 495μm at the plane of sample surface. Two mirrors with angled variable reflectivity are united as the energy attenuator. The laser energy is measured by a photo diode (PD1). The spatial distribution of beam on the sample surface is recorded by setting a camera (CCD1) at an equivalent position of sample stage. Samples are held by a two-dimension stage in a special chamber to keep air or vacuum environment. A 24-bits true color CCD coupled with a 6 × magnification lens (short for CCD2) is employed to detect visible surface damage, and its resolution is 10μm. Another photo diode (PD2) is added to receive scattered light from surface, and it provides rapid response for slight initial damage.

3. Results and discussion

3.1 Damage classification

Scald and delaminate are the typical damage morphologies under multi-shot in our experiment. Most scalds are the initial damage which occurred with plasma at relatively lower laser fluence. The typical image of scald is shown in Fig. 2.
Fig. 2 Typical images of scald damage, a) under 100 × Nomarski microscope; b) multi-hole structure and sphere clusters under high magnification SEM (up to 150000 × ); c) 3-D image of scald taken by surface profiler; and d) the profile of damaged region.
There is a multi-hole structure on the scald’s surface which is rather rough. And the peak-to-valley value of roughness measured by surface profiler (Dektak 150) is about 250nm (see Fig. 2(c) and Fig. 2(d)). High magnification SEM image indicates that there are also lots of sphere clusters on the damaged surface with the lateral size varied from 150nm to 400nm (see Fig. 2(b)). It seems that the multi-hole structure and sphere clusters are both relative to thermal melting process taking place in a few outer layers of coatings.

The size of delaminate increases in a pulse train. Two different laser beam sizes, with the 1/e2 diameter of 495μm and 1470μm, are used in multi-shot test to determinate the growth rule of delaminate. The results are shown in Fig. 4and Fig. 5.
Fig. 4 The diameter of delaminate increase with pulse number under two different beam spot size of 495μm and 1470μm (1/e2 diameter), respectively. The laser fluence is 72.5J/cm2 and 55J/cm2.
Fig. 5 Growth behavior of final size of delaminate (after 1000 shots) vs. laser fluence.
For both small and big laser beams, once the delaminate forms, its lateral size shows an exponential growth rule in the first few shots, actually about 60 to 80 shots in our experiment. After rapid increasing, the growth rate tends to slow down and the diameter maintains in a stable value. Interesting, this value is a little bigger than the 1/e2 diameter of laser beam. This phenomenon indicates that even at the edge of beam spot, where with relatively low energy density, there still has some contribution to damage expansion. Considering the influence of laser energy, it could find that the final size of delaminate at the end of a pulse train seems to depend on how large laser energy is. By expanding the range of laser energy, the relationship between final sizes of delaminates and laser fluence is achieved, as shown in Fig. 5. Once again the tendency of fluence vs. final size of delaminates for small beam is similar to big beam: The final size appears to be proportional to laser fluence in a certain range. However, when the laser energy exceed the critical point, about 85-90J/cm2 in our experiments, the final size of delaminate tends stabilize at a certain value, about 900μm for small beam and 2200μm for big beam. Along with the size increasing, the morphology of delaminate dramatically changes from single-ring to double-ring and then to several dozen concentric rings. This process has been shown in Figs. 3(a)3(c). After sufficient laser irradiation, the substrate will appear in the center of delaminate and this damaged area will absolutely lose its optical function [29

29. L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, and H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002). [CrossRef]

].

3.2 Morphology change condition

The damage growth process under multi-shots could be summarized into two phases (see Fig. 6): morphology change process (from scald to delaminate) and delaminate expansion.
Fig. 6 The schematic diagram of several phases in damage growth process.
From the discussion in preceding section, it is known that delaminate is an unstable status and the delaminate expansion phase is quite hard to control in real applications. If the damage maintains at the first phase and never change its morphology to delaminate, the life time of thin films could be extended even though with slight damage. Therefore, the key point is that we need to know the damage morphology change condition in advance to predict the tendency of damage growth, and adjust the laser parameters timely avoiding catastrophic damage. However, to our best knowledge, the morphology change condition is rather complicated and depends on many factors, such as laser fluence, beam size, damage size, shot number, native status of surface, etc. In this work, we try to simplify and partly solve this problem with two basic hypotheses. Firstly, we mainly consider these damages which occurred in the region without visible defects, such as nodules. In order to avoid the influence of defects that may induce uncontrollable damage behaviors, we particularly choose the regions without nodule, more accurately, without visible defects. To achieve this purpose, the CCD with 6 × lens and scatter light detector were employed to monitor the sample surface. Any visible defects larger than 10µm, such as nodule and scratch, will be detected and skipped. Another hypothesis is that the morphology change condition mainly depends on scald size, scald initial fluence, subsequent fluence and shot number.

In order to find the relationship among these factors mentioned above, a couple of special designed experiments were performed on HR coatings. The experiments could be briefly described as follow: Firstly, several groups of scalds were artificially created under single-shot with small beam (495μm of 1/e2 diameter) in a certain laser fluence range, especially from 20J/cm2 to 70J/cm2 in our experiment. These scalds are carefully classified according to their initial fluence and lateral size. And then the scalds will be irradiated under multi-shot (up to 1000) with different fluence to check if these damage sites change its morphology to delaminate or not. Finally, by establishing the relationship among the corresponding subsequent fluence, shot number, scald initial fluence and scald size, the morphology change threshold (short for MCT, J/cm2) is finally achieved (see Fig. 7 and Fig. 8).
Fig. 7 The contours of morphology change threshold vs. scald initial fluence under varying shot number.
Fig. 8 The contours of morphology change threshold vs. scald size under varying shot number.

The contours in Fig. 7 and Fig. 8 represent the MCTs vs. scald initial fluence and scald size with different shot number, respectively. The result in Fig. 7 indicated that the MCTs show a decreasing law with scald initial fluence. It means that, within a certain shot number, the scald which initiated by less laser fluence usually requires more energy to change its morphology to delaminate. It also could be found that the more subsequent shots, the less fluence is needed to complete the morphology change process for a certain scald. Similar to scald initial fluence, the result in Fig. 8 represents the influence of scald size in morphology change process. There exists a critical point for scald size on these contours in Fig. 8. When the scald size is smaller than this critical value (about 160μm), the MCTs show a decreasing law with scald size: the smaller size of scald is, the more energy and the more shots needed to trigger the morphology conversion. However, when the scald size exceeds the critical value, it seems that the scald size almost not impact the morphology change process. For example, the scald size of point A (170μm) is smaller than A′ (190μm), but their morphology change condition is nearly the same. Moreover, there is one point in common for Fig. 7 and Fig. 8. The MCT contours appear to be more closed to each other along with shot number increasing, especially while it exceeding 100 shots. That phenomenon implies that MCTs changes dramatically in a relatively small number of shots. And with the shot number increasing, the contribution of shot number to the morphology change process becomes less and less.

From the discussion above it could be concluded that there indeed exists a rule of damage morphology change process. The scald size, scald initial fluence, subsequent fluence and shot number react to each other, and collectively impact the tendency of morphology conversion. These contours in Fig. 7 and Fig. 8 could also be considered as “safety lines”, which means that the scalds would never turn to delaminate with a certain laser fluence or shot number below its corresponding safety lines. Oppositely, some scalds will have a chance to change its morphology from scald to delaminate once the laser fluence or shot number beyond the safety lines. If the subsequent fluence and shot number are set at a proper value, for instance, according to Fig. 7 or Fig. 8, the morphology conversion would not occur at all. Therefore, the novel concept of safety line gives us a chance to avoid the catastrophic damage occurrence in real applications.

The morphology change condition (MCC for short) achieved in this work is based on specific thin film. It’s true that the coating method has significant influence on MCC. It will impact the specific value in MCC, such as, MCT, shot number, scald size, etc. Nevertheless, it is found that the tendency of MCC will not change too much, for instance, MCT decreases along with either scald initial fluence or scald size. The tendency is a common law for different thin films. Therefore, the conclusion of MCC in this work is still referable for other researchers to study the particular morphology changing properties on their custom-made thin films.

Compared with numerous clusters, there also exist small amount of micro-crack in layers which could be observed under larger magnification (see Fig. 9(b2)). The depth of micro-cracks is quite different. Most of them appeared in the first several layers. The micro-cracks may be caused by the internal stress releasing process. The micro-cracks inside layers could play an important role in damage growth owing to the effects of laser field enhancement. In addition, the mechanical strength of the material surrounding micro-cracks may be decreased and become more susceptible to further irradiation. In summary, the numerous haze clusters and small amount of micro-cracks observed by FIB are both the micro-structure changes inside scald damage. The probable important role they played in damage growth process make them should be highlighted in mitigation of delaminates in the future.

3.3 The decline law of damage threshold

The damage probability of scald and delaminate under multi-shot were tested according to the S/1 test standard described in ISO 21254. The testing result is shown in Fig. 10, the solid and dash contour lines represent the different damage behaviors of scald and delaminate, respectively.
Fig. 10 Contours of threshold vs. shot number under varying damage probabilities (from 0% to 100%).
In fact, this contour line map figures out the relationship among laser fluence, damage probability and shot number. It is significantly valuable for damage probability prediction under certain condition. In other words, if the laser fluence and shot number is given, the damage probability of scald and delaminate could be inferred from this contour line map.

The damage thresholds of varied probability decreases exponentially with shot number for both scald and delaminate. The decline law of delaminate is more significant than scald, which means that delaminate seems to be more sensitive to shot number than scald. Further analysis indicates that there exists an overlapping area between the contour lines of scald and delaminate, marking as a shadow area in Fig. 10. Both scalds and survived sites are on the film surface when the test point is below the shadow area. For example, point A in Fig. 10 means that 40% irradiated sites will turn to scald where the laser fluence is 50J/cm2 and the shot number is 25. And the rest of the sites will survive. In this situation, the scald will be rather stable and never change its morphology to delaminate due to either insufficient laser fluence or shot number. If the test point extends beyond the shadow area, none of irradiated sites could be survived, such as point C. It means that no test sites could survive, 60% sites turn to delaminates and the others are scalds, where the laser fluence is 95J/cm2 and the shot number is 50. In this situation, with laser fluence and shot number increasing, delaminate gradually become the main damage morphology. It would lead to the loss of optical performance.

However, if the test point just located in the shadow area (i.e, point B in Fig. 10), the surface status will be composed of survived sites, scalds and delaminates. At point B, there nearly 10% sites turn to delaminate, more than 70% sites are still scald and nearly 20% sites survive, where the laser fluence is 65J/cm2 and the shot number is 45. In this situation, all kinds of defects in coatings are triggered in this region. The site with lower damage resistance defects will turn to delaminate and those with higher damage resistance defects will remain in scald. Meanwhile, the rest of defect-free areas with the highest damage resistance survive. Generally, it offers us a rich sample to understand the damage behavior.

3.4 The thermal accumulation model and life-time prediction

Several thermal simulations on thin films have already been performed elsewhere for varied purposes, such as stack optimization [30

30. H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, and Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007). [CrossRef]

], interfacial effect [31

31. Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, and Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998). [CrossRef]

], influence of nano-defects on damage [3

3. L. J. Shaw-Klein, S. J. Burns, and S. D. Jacobs, “Model for laser damage dependence on thin-film morphology,” Appl. Opt. 32(21), 3925–3929 (1993). [CrossRef] [PubMed]

,32

32. M. Commandré, G. Demésy, X. Fu, and L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010). [CrossRef]

,33

33. B. Wang, H. Zhang, Y. Qin, X. Wang, X. Ni, Z. Shen, and J. Lu, “Temperature field analysis of single layer TiO2 film components induced by long-pulse and short-pulse lasers,” Appl. Opt. 50(20), 3435–3441 (2011). [CrossRef] [PubMed]

], etc. In this work, in order to explain the decline law of laser-induced damage threshold under multi-shot, a thermal accumulation model is built by use of finite element analysis. We assume that the thermal accumulation effect plays a crucial role in multi-shot damage process. And this process can be briefly described as follow: the laser energy is partly absorbed by layers and the temperature in layers will continually rise along with pulse shots. Once the material temperature reaches its melting point, it would start to flow and expand to surrounding area. The physical structure of thin films will be destroyed by the thermal explosion. Finally, the visible damage occurs.

A two-dimensional mathematical model based on the Fourier heat exchange equation (see Eq. (1)) is built, and the boundary conditions are given in Eqs. (2)(4). Each coating layer is divided into dozens of cells (20 to 50 cells for one layer, depending on the thickness of layer) in the z direction and the thickness of each cell is about 5nm. The time step in this calculation is 0.05ns for pulse duration and 165μs for pulse interval. The material parameters are given in Table 1.

Table 1. The material parameters used in simulation

table-icon
View This Table

ρiciTitki(2Tir2+1rTir+2TiZ2)=ηI0αini|E|2
(1)
kTr|r=r0=0
(2)
kTZ|Z=0=h(TET)
(3)
T(r,Z,0)=T0,T0=293K
(4)

In our model, a flat-top beam is used as the laser source. When the laser pulse reaches sample surface, the standing wave field will immediately be formed between layers. The electric field intensity is calculated by solving Maxwell equations using the commercial software TFCALC. It could be found that the laser energy is concentrated in several outer layers and the electric intensity declines rapidly along with layer thickness, as shown in Fig. 11(a).
Fig. 11 The distribution of standing wave field (above) and calculated temperature in a couple of layers under several different numbers of shot, from1 to 1000 (below). The repetition rate is 30Hz, the pulse duration is 10ns and the fluence is 50J/cm2. The thin film stack is (HL) ^15H0.5L2.36H0.7L1.41H0.7L1.29H0.12L /Air, and the substrate is fused silica.
The layers are heated by the electric field from inside and temperature begins to rise along with shots. The thermal distribution of thin film could be achieved by using classic thermal diffusion equations. From the simulation result (see Fig. 11(b)) we could firstly find that there exist some drifts between the peaks of electric field and temperature field. For the first pulse, energy absorption effect dominates the layer heating-up process. The temperature rise rate of SiO2 is faster than HfO2, and the peaks are also located in SiO2 layer. For the following pulses, the cooling down between two pulses and thermal conduction effect offer more and more contributions in heating-up process. The temperature peaks begin to transfer from SiO2 to HfO2 layer in several pulses. After 20 pulses, the heating-up process reaches its balance point and the temperature distribution tends to be stable in each layer.

The tendency of temperature-rise for silica and hafnia is rather similar. Figure 12 shows the general transient thermal distribution in the 2nd HfO2 layer: exponential growing with pulse number at first and then turning to stable.
Fig. 12 The time-variation of temperature in the 2nd layer (HfO2). The dash line shows the tendency of maximum temperature along with pulses.
And after a small drop, the temperature will vibrates with small amplitude at the balance point which could be the result of the reaction between laser energy absorption and thermal diffusion. Coupled with the influence of e-flied distribution, interestingly the maximum temperature appears in the 2nd layer and the second peak appears in the 4th layer after 20 pulses, which are both located in hafnia. It means that the melting process maybe initiate inside the film and spread to surface. Actually, we have already observed some kind of clusters and micro-crack inside film (see Figs. 9(b1) and 9(b2)) for some scald damage, usually occurring in several outer layers, which are probably the traces of internal melting process. There is one point worth noting: the conclusion that damage initiated inside the layers is absolutely based on our film stack. Once the film stack changes, the field density distribution and thermal distribution could be totally different.

After a sufficient number of shots, the temperature of outer layer will reach a relative high value which is the so-called thermal accumulation effect. Furthermore, if assuming that damage occurs while the temperature reaches material melting point, the relationship between 0% probability LIDT of scald and shot number can be obtained in theory. The calculation result is shown in Fig. 13.
Fig. 13 The 0% probability LIDT vs. shot number in theory, the red dash line represent fitting result.

It indicates that the relationship between LIDT and shot number probably follows an exponential decay law. A binomial exponential decay formula (see Eq. (5)), which has also been discussed elsewhere [14

14. F. Y. Génin, C. J. Stolz, and M. R. Kozlowski, “Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings,” Proc. SPIE 2966, 273–282 (1997). [CrossRef]

,18

18. A. Ciapponi, P. Allenspacher, W. Riede, J. Herringer, and J. Arenberg, “S-on-1 testing of AR and HR designs at 1064nm,” Proc. SPIE 7842, 78420J (2010). [CrossRef]

,23

23. L. Gallais, J. Y. Natoli, and C. Amra, “Statistical study of single and multiple pulse laser-induced damage in glass,” Opt. Express 10(25), 1465–1477 (2002). [CrossRef]

25

25. J. Arenberg, W. Riede, A. Ciapponi, P. Allenspacher, and J. Herringer, “An empirical investigation of the laser survivability curve,” Proc. SPIE 7842, 78421B (2010). [CrossRef]

], is used to fit the simulation results. For Eq. (5), F (N) is the 0% probability LIDT for N shots and Pi (i = 1~5) are the fitting parameters. The fitting result shows a pretty good correlation with the R2 of 0.999.

F(N)=P1+P2exp(P3N)+P4exp(P5N)
(5)

4. Conclusion

Three aspects of damage behavior on high-reflection coatings under multiple shot at 1064nm have been studied in this work: damage classification, morphology change condition and resistance decline. The main damage morphologies under multi-shot are scald and delaminate. The typical micro-structures of scald are melting and solidification which indicate that the thermal effect dominates damage formation process. However for delaminate, the thermal stress and stress relief seem to give more contribution in damage growth. The scald tends to change to delaminate under proper condition. The morphology change process may be connected with the micro-structure change inside layers, such as hazy clutters and cracks, which has been observed by focus ion beam with SEM. In this work, it is for the first time to put forward a statistical contour map for HR coating on the morphology change condition which is associated with scald initial fluence, scald size, subsequent fluence and shot number. The results offered so called “safety lines” for components to operate under the safe status without catastrophic damage morphology change. The contours of LIDTs versus shot number were obtained. The result reveals an exponential decay law of LIDTs for both scald and delaminate. By use of finite element analysis method, a thermal accumulation model has been established to simulate the temperature distribution inside layers and LIDT prediction. The simulation results indicated that there exist some drifts among the peaks of electric field and temperature field, and the melting process maybe initiate in the highest temperature point, actually inside the layers for our film stack. In the last section, a binomial exponential decay formula is used to predict coatings life-time which appears good fitting.

Acknowledgment

This work was supported by the National High-tech Research and Development Program.

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C. J. Stolz, L. M. Sheehan, S. M. Maricle, S. Schwartz, and J. Hue, “A study of laser conditioning methods of hafnia silica multilayer mirrors,” Proc. SPIE 3578, 144–153 (1999). [CrossRef]

29.

L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, and H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002). [CrossRef]

30.

H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, and Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007). [CrossRef]

31.

Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, and Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998). [CrossRef]

32.

M. Commandré, G. Demésy, X. Fu, and L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010). [CrossRef]

33.

B. Wang, H. Zhang, Y. Qin, X. Wang, X. Ni, Z. Shen, and J. Lu, “Temperature field analysis of single layer TiO2 film components induced by long-pulse and short-pulse lasers,” Appl. Opt. 50(20), 3435–3441 (2011). [CrossRef] [PubMed]

OCIS Codes
(140.3330) Lasers and laser optics : Laser damage
(310.1620) Thin films : Interference coatings

ToC Category:
Thin Films

History
Original Manuscript: December 30, 2013
Revised Manuscript: February 19, 2014
Manuscript Accepted: April 11, 2014
Published: April 21, 2014

Citation
Zhichao Liu, Jin Luo, Yi Zheng, Ping Ma, Zhe Zhang, Yaowei Wei, Feng Pan, and Songlin Chen, "Damage morphology change condition and thermal accumulation effect on high-reflection coatings at 1064nm," Opt. Express 22, 10151-10164 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10151


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  29. L. Lamaignère, V. Cavarro, C. Allais, D. Bernardino, M. Josse, H. Bercegol, “Time-resolved measurements of reflectivity, plasma formation and damage of Hafnia/Silica multilayers mirrors at 1064nm,” Proc. SPIE 4679, 410–419 (2002). [CrossRef]
  30. H. Qi, K. Yi, H. Yu, Y. Cui, D. Li, Z. Gao, J. Shao, Z. Fan, “Laser induced damage of multilayer high-reflectance coatings for 248nm,” Proc. SPIE 6720, 67200W (2007). [CrossRef]
  31. Q. Zhao, Z. L. Wu, M. Thomsen, Y. Han, Z. Fan, “Interfacial effects on the transient temperature rise of multilayer coatings induced by a short-pulse laser irradiation,” Proc. SPIE 3244, 491–498 (1998). [CrossRef]
  32. M. Commandré, G. Demésy, X. Fu, L. Gallais, “Three-dimensional multiphysical model for the study of photo-induced thermal effects in laser damage phenomena,” Proc. SPIE 7842, 78420Q (2010). [CrossRef]
  33. B. Wang, H. Zhang, Y. Qin, X. Wang, X. Ni, Z. Shen, J. Lu, “Temperature field analysis of single layer TiO2 film components induced by long-pulse and short-pulse lasers,” Appl. Opt. 50(20), 3435–3441 (2011). [CrossRef] [PubMed]

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