Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments
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- Lamaignère, L., Dupuy, G., Bourgeade, A. et al. Appl. Phys. B (2014) 114: 517. doi:10.1007/s00340-013-5555-6
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Up to now, laser damage growth on the exit surface of fused silica optics has been mainly considered as exponential, the growth coefficient depending essentially on fluence. From experiments with large beams carried out at 351 nm under nanosecond pulses, a statistical analysis is conducted leading to a refined representation of the growth. The effect of several parameters has been taken into account to describe precisely the growth phenomenon. The two principal parameters proved to be the mean fluence and the size of the damage sites. Nevertheless, contributions of other parameters have been estimated too: the number of neighbors around the damage site, the shot number, etc. From experimental results, a model smoothed on a statistical approach is developed that permits the description of a complete sequence of growth. To evaluate the relevance of the modeling approach, the occluded area estimated from modeling is compared with the ones experimentally measured. For this purpose, numerical growth methods have been developed too. It is shown that the approach outlined is appropriate for a more precise description of the growth.
In this paper, we report growth experiments that have been performed with centimeter-sized beams. The use of large beams permits first the observation of the growth up to large damage area, secondly the study of numerous damage sites at the same time allowing the development of a statistical approach to describe this phenomenon. The results complete previous observations of Negres et al. [7, 8] and above all permit us to propose a new approach to describe the growth leading to a revisited growth law. The model that has been developed takes into account several parameters: the damage sizes, the local fluences, the shot number (background history of the shot sequence), the number of neighbors (damage sites close to the studied site), the optics thickness and the phase modulations. The influence of each parameter has been evaluated separately. This model will be referred in the following as the multiparameter model. To check the validity of the modeling, we have chosen to compare the occluded areas, measured during the experiments shot after shot and estimated from the modeling. This work has been first realized on subaperture areas in order to correctly measure growth coefficients of isolated damage sites that did not merge. After that, the comparison between experiment and modeling has been realized on the full aperture of the beam. In the modeling part, several numerical growth methods have been tested and qualified too. The choice of the numerical method can affect more or less the final estimation of the occluded area. In Sect. 2 of this paper, we describe how tests are carried out. Section 3 is devoted to experimental results. The modeling part is given in Sect. 4. The comparison between experiments and modeling is discussed in Sect. 5. It is shown that the estimation of the occluded area at the end of the growth run is well comparable to the real occluded area experimentally measured. This approach provides a straightforward means of predicting the growth of an optics illuminated with large and inhomogeneous beams: The two main parameters that have to be precisely measured are the local fluence on the damage and its size.
2 Materials and methods
2.1 Test facility
Due to a contrast inside the beam itself (peak to average) of about 4, a shot at a given average fluence covers a large range of local fluences (see Fig. 2). This makes compulsory the exact correlation between local fluence and local damage size and position.
2.2 Samples and test procedure
For this study the laser damage of synthetic fused silica (HEREAUS S312) windows, superpolished by SESO company, is dealt with. All tested samples were antireflection treated with a sol–gel-based process, as in operational conditions and to limit the SBS effect. One-hundred-millimeter-diameter-size samples have been used: About 12 different sites per sample have been illuminated with several laser experimental configurations, mainly in terms of phase modulations. Sample thicknesses are 10 and 34 mm, the latest being representative of thick component used as LMJ vacuum window of target chamber.
Parameters of the experiments and variables adjusted in the multiparameter model and their influence on damage growth prediction
10 or 34
Phase modulation (GHz)
2; 14; 2 and 14; none
Mean fluence (J/cm2)
0 to 20
Damage area (μm2)
102 to 105
1 to 7
Number of neighbors
1 to 10
3 Experimental results
The whole results go for a more precise description of the growth sequence taking into account the local fluence on the damage site, its size and other parameters identified during the experiments. For instance, it is well known that a ramp of fluence may improve the damage resistance of the optic, and at the opposite, a repeated number of shots may lay to a fatigue effect: The shot sequence is then to consider. The growth phenomenon is mainly characterized by the expansion of cracks which can merge between neighbor sites: The number of neighbors could be a relevant parameter too. A multiparameter model is described in the next paragraph. Modeling results are then compared to experimental ones. Next, the model is applied on the full-aperture beam and again compared to experiments.
4 Multiparameter model
In order to improve the estimate of the single-shot growth rate k defined above, experimental results have been used for a statistical study. We have indeed considered the damage sites and their growth in a zone where the successive laser shots create the less new damage events and where the initial damage sites created by the first laser shot will the less merge.
The important progress in this work is the fact to take into account both the mean fluence and the size of the damage shot after shot. The growth coefficient depends mainly on these two parameters and is then adapted to each individual damage and shot. This approach enables us to tackle the uncertainty observed in growth rate even under identical laser conditions. Other issues have been considered such as the damage neighbors and the shot number, but their contributions are less important. It does not mean that there is no effect of laser exposure history, like a “conditioning” effect observed with a fluence ramp  which creates small damage sites with lower growth coefficients. In this model the influence of the shot number is closely linked to the damage size. The initial size of damage sites is also an important parameter governing the first steps of the growth.
This study demonstrates that the growth coefficient is size dependent in addition to be fluence dependent. Then a correct description of the growth phenomena has to take into account at least these two parameters. This formalism is now implemented in the algorithm used to optics lifetime prediction for Ligne d’Intégration Laser (LIL) and LMJ facilities. It is important to keep in mind that this statistical approach is well adapted to describe the growth statistically in case of numerous events (damage sites and shots) but is not able to predict the exact size of each damage site shot after shot. This approach is reliable in the fluence range presented in this paper, which corresponds to fluences actually obtained on high-power laser facilities, but it has to be tested at higher fluences corresponding to unwanted spatial modulations. In this approach, damage sites are characterized only by their surface, the total ablated volume and the crack lengths under the damage sites should be carefully measured for a better description of the growth. We now have to precisely study the growth of very large damage sites (few millimeters in diameters), an effect of saturation being suspected. Experiments on large damage sites require the use of very large and homogeneous beams with high repetition rate in order to perform statistical tests. The knowledge of the growth of small and large damage sites will allow a complete description of this phenomenon and will permit a precise prediction of the lifetime optics under operation.
The parametric study taking into account both phase modulations and sample thickness will be presented in a paper dealing with fluence amplification due to nonlinear effect in thick components.
The authors thank François Dufour and Marie Chavent (Bordeaux Mathematics Institute—IMB) for their fruitful support on statistical methods.
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