1. Introduction

High peak power lasers are of great importance for many scientific, engineering, and industrial applications [1], including laser machining [2, 3] and laser-driven particle accelerators [4–7]. These systems are limited in output due to laser-induced damage on optical components. For high energy lasers, efforts to understand the cause of laser-induced damage for the National Ignition Facility and other similar facilities have produced great gains in performance of ns laser systems [8–11]. High peak power facilities operate at shorter pulse widths in the fs and ps regime, and face different, but related challenges. They use reflective optics, typically multi-layer dielectric coatings. The high peak powers of laser systems such as the Advanced Radiographic Capability (ARC) on NIF push the fundamental limits of materials [12, 13]. It is necessary to understand what the fundamental material limits are for proper design and operation [14,15]. Of particular interest to ARC is the pulse width regime from 1–60 ps, which is postulated to span the range from more fundamental ablation damage to defect-related damage [16].

Determining whether observed damage is at the fundamental limits for a given material has important practical consequences since damage caused by defects or flaws may be corrected or significantly reduced with improved fabrication techniques and/or post-processing such as laser annealing (or laser conditioning). For nanosecond laser pulses, laser-induced damage is caused by isolated precursors that damage well below the fundamental limits of the material [10,11,17,18]. In contrast, femtosecond laser damage occurs near fundamental limits. In this paper, we study picosecond laser pulses over the transition from fundamental mechanisms to the defect-dominated long-pulse regime. We emphasize that when defects are involved, the concept of a strict laser damage threshold no longer applies. A “damage threshold” implies that the material will remain undamaged below the threshold and will damage 100% of the time above this threshold. For defect-related damage, there are regions that will damage at a certain fluence and other regions which will not. In order to understand defect related damage in a consistent manner independent of beam size, the concept of a density of precursors ρ (Φ) is used, which is the number of precursors which damage up to a certain fluence Φ per unit area [19, 20]. Here, we apply this concept to picosecond laser damage from 1 ps to 60 ps. Although laser-induced damage for much of this pulse width range is often thought to be near fundamental limits, we find that analysis using ρ (Φ) is still critical for 1 ps to 60 ps pulses.

In a companion publication [21], we found morphological evidence that laser-induced damage for picosecond pulses is primarily limited by isolated defects that damage at fluences below fundamental limits. Here, we expand on these observations by varying the beam size of the damaging beam and by analyzing the spatial distribution of the damage sites as a function of pulse width and of fluence. We also compare the damage onset scaling laws to well-known models for ablation. By comparing to these existing models and analyzing fluence dependence, we obtain evidence that there are two classes of defects that contribute to laser-induced damage in the ps pulse width regime. First, there are isolated absorbers which cause thermal runaway and laser-assisted absorption fronts [22] similar to those observed in the ns regime. Second, there are ultra-high densities of defects that damage much closer, but still below the ablation thresholds. These ultra-high density defects may undergo a damage mechanism similar to ablation, however with local enhancements in multi-photon absorption or avalanche ionization.

2. Theory

Models for multi-photon initiated and avalanche ionization driven ablation have been used for many years to explain damage in the femtosecond to low picosecond pulse width regime. The use of rate equations for this model was justified using a Fokker-Planck equation-based derivation [23]. Differences between models seen in the literature include the addition [24–27] or exclusion of a decay timescale for exciton recombination, the inclusion of tunneling effects for very short pulses [28], the inclusion of states within the band gap [29], matching these processes to the defect-dominated regime with a $\sqrt{\tau }$ dependence [16] and exciton recombination that depends on the square of the electron density [30] (τ is the pulse width). In the nanosecond regime, laser assisted absorption fronts have been used to explain the expansion of laser-induced modifications from the original small nanoscale precursors to the much larger 10–100 µm scale observed final sizes [22]. We found evidence for the operation of these mechanisms by examination of the morphology of picosecond laser-induced damage sites. We also propose a third mechanism that may be in effect. Namely, there may be regions that have high enough defect densities that lower the threshold for intrinsic ablation. This mechanism may be in operation at short pulse widths and allows for local variations in damage threshold. We determine here that the scaling laws for these different mechanisms vary considerably with respect to parameters. We use these salient behaviors to provide evidence to help distinguish between the operation of these various mechanisms in these materials.

2.1. Intrinsic ablation

According to the most commonly used model [23,24,27], the ablation process occurs in three primary steps. First, multi-photon ionization creates free carriers in the wide band gap material. Second, avalanche ionization causes an exponential growth in the free carrier density and in the energy deposition. A third factor is the decay of free carriers when they return to the ground state. Each of these processes is a term in a differential equation for the density of free carriers.

For realistic laser pulses, the use of rectangular laser pulse shapes may not be adequate. In order to simplify the equations for a solution, we can replace the terms multiplying the term n with a function $w\left(I\right)=\alpha I-\frac{1}{T}$, obtaining

The second case for which we integrate Eq. (1) is for comparison of results to previously obtained fits, including in [23, 24]. In the third case, we integrate Eq. (3) for comparison of results with the calculations of avalanche ionization rates in [25].

It has been discussed in conjunction with results obtained from pump-probe measurements that the importance of avalanche ionization for short pulses may be over-emphasized [31], and that it is inoperative for longer, ns pulse widths [29]. It is important to take these previous results into account when modeling these processes. In order to explain the laser-induced damage data, it appears that an excited state electron-multiplying process is needed. However, direct attempts to measure the electron avalanches have not succeeded in many cases. There may be alternatives that play a role. For example, excited state absorption in defect states may play a role [32]. This may be an alternative process particularly for silica, where self-trapped excitons (STE) are formed within 150 fs [26], but persist for much longer. These STEs formed during the pulse may provide new defects that provide seeds for further defect formation. Other defect-seeding processes may serve to accomplish the same purpose as avalanche, i.e. the exponential increase in free electrons. For example, a high density of defects may allow for energy transfer upconversion (ETU/APTE) processes [33] to create free electrons.

2.2. Local defects: laser-assisted absorption fronts

Material defects affect the intrinsic pathways for laser-matter interactions and determine, in part, the key mechanisms of laser-induced damage. For instance, there may be defects that allow for single-photon activated processes. Single photon-activated processes would cause increases in temperature that are proportional to the total fluence (or energy) in the laser pulse rather than depending on the intensity for activation as is the case for multiphoton absorption. Any modification or change in the surface that is strictly dependent on fluence would be a signature for single-photon activated processes. In addition to absorption within the defect, such a single photon-activated defect may cause heating of the surrounding material which leads to laser-assisted absorption fronts similar to those who observed at 351 nm [22]. In [21], we found features in the laser-damage morphology that match the above requirements for a single-photon defect process leading to laser-assisted absorption fronts. Additionally, the velocities observed for the laser-assisted absorption fronts match what would be expected by scaling the results from ref [22] to ps pulses. Small nanoscale precursors absorb enough energy that the surrounding non-defective material heats up and begins to be absorptive. Since the absorptive material does not allow propagation of the laser beam (by absorption or reflection), these fronts would propagate laterally rather than into the material as for exit surface damage. However, the underlying physical mechanism would be the same as for ns pulses.

For silica (coatings) and fused silica (bulk) materials, we observed damage sites that were outside the beam peak fluence locations. For both materials, these sites exhibited a unique morphology with a small central pit surrounded by a large smooth shallow circular depression. In addition, the density of these sites is much higher in the deposited silica coatings vs. fused silica. We hypothesize that these pits are formed by the absorption of an initial low-fluence damage precursor followed by a laser-assisted absorption front [22]. These damage sites are not as large as those observed for nanosecond pulses at 351 nm on the exit surfaces of optics since we are using shorter pulses with lower photon energy, and they are on the front surface (so that absorption fronts do not propagate into material).

2.3. Local defects: multi-photon activation

In addition to the defects which are made visible at lower fluences and are not strongly dependent on pulse width, there are higher density pits that form near the ablation threshold for 1 ps pulse width and below, and replace the observation of an ablation threshold for 3 ps pulses and longer. The higher density pits scale more strongly with pulse width τ.

There are several possibilities about how defects can affect or reduce damage thresholds. One scenario is that defects could enhance the intrinsic ablation process itself, either by increasing multi photon ionization coefficient β_m, the avalanche ionization coefficient α, or the relaxation time T.

3. Materials and methods

3.1. Laser system

Laser-induced damage testing was performed using an in-air damage test station developed at Lawrence Livermore National Laboratory (LLNL). This test station is of similar design to the in-vacuum laser damage test station described in [14,34], and is located adjacent to it. Without the physical constraints of the vacuum chamber, this station provides adjustable focal spot size on the sample and additional diagnostics. Laser damage is generated from an Optical Parametric Chirped Pulse Amplification (OPCPA) laser system similar to that described in [35,36]. It delivers λ = 1053 nm pulses with energy up to 6 mJ, at 10 Hz repetition rate. The pulse duration is tunable from ∼ 0.4 ps up to 60 ps by changing the compressor slant distance. Pulse durations below 3 ps are measured with a single-shot frequency-resolved optical gating (FROG) device, while longer pulses are measured using a scanning cross correlator with a transform limited reference pulse. For this work the laser pulses are focused onto the sample, located in an air environment, with a f = 500 mm lens to initiate damage. The energy on target is computer-controlled with a motorized half waveplate located before two thin film polarizers.

3.2. Sample preparation

Corning 7980 fused silica, 2-inch round and 1-cm thick samples, were obtained from CVI-Melles Griot (Rochester, NY). Each optic was prepared using an optimized cleaning + etching process described as AMP3 (advanced mitigation protocol 3) at LLNL [10,11]. This process consistently yields high damage resistant optics. Several of these samples were coated with absentee (1/2-wave) silica coatings tuned for 1053 nm and 0° (362 nm thick) using e-beam and plasma-ion assisted deposition (PIAD) at the Laboratory for Laser Energetics (LLE).

3.3. Calibration procedures

Leakage from a beam splitter provides a reference beam path designed to measure the pulse energy, beam profile and position at an equivalent sample plane on every shot. We varied the z position of the two identical lenses in the main and reference beam paths in order to calibrate these positions carefully, ensuring that the reference beam represented the main beam accurately. Three pairs of focusing lenses were used for varying the beam size: f = 1 m for a 100 µm beam, f = 500 cm for a 50 µm beam, and f = 300 cm for a 30 µ m beam. We also used ablation of thin metallic films to validate the measured beam sizes at the sample position in the actual experiment [37].

The pulse widths were measured using a home-built, multi-shot scanning cross-correlator which combines the main pulse (stretched in time) and a fully compressed, transform-limited reference pulse. For pulse widths 3 ps and shorter, the FROG methodology was also used to measure pulse widths on a single shot basis.

Non-linear effects of beam focusing in air were investigated experimentally and computationally. Experimentally, our system simultaneously images the reference and main beams after proper energy balancing onto a single CCD, side by side. The reference is operational for all tests to monitor the beam profile during tests, whereas the main beam imaging is only used for testing and calibration. Without a sample in place, we found that the beam focusing in air did not modify the beam profile through self-focusing until well above the highest energies (fluences) involved in our experiments (all materials and beam sizes).

3.4. 1/1 Tests

We used the 1/1 test methodology for each pulse width, each beam size on three materials: fused silica, e-beam deposited a silica, and PIAD-deposited silica. Each test covered a 4 × 4 mm² square patch where the fluence was ramped with each successive column. For the 100 µm beam size, there were 13 columns and 13 rows of damage sites for a total of 169 damage tests performed. Each test was duplicated at least one more time on a different day. For the lenses yielding smaller beam sizes, there were 20 columns and 20 rows of damage sites for a total 400 damage tests for each pulse width. The minimum and maximum energies tested were determined beforehand in separate test shots. The damage test was monitored using an in situ camera, where each irradiated site on the sample surface was imaged before and after the damage test. This allowed subtraction of background and very sensitive detection of changes in the surface. These sites were later imaged using atomic force microscopy (AFM), confocal microscopy, and scanning electron microscopy (SEM).

In analyzing these experiments, we account for shot-to-shot beam profile and pulse energy fluctuations to compute the local fluence at the sample plane; we then plot the fraction of sites that damaged as a function of the beam fluence. These corrections for individual pulses improve the accuracy of the 1/1 damage curves. We tested the improvement using a 1/1 damage test for fused silica with 1 ps laser pulses; i.e. the test is close to being deterministic for shorter pulses due to the intrinsic ablation mechanism. The above corrections for each pulse reduced the errors significantly. With full corrections, the probability for 10% of the sites to damage was 4.8 J/cm², and the probability for 90% of the sites to damage was 5.8 J/cm². Without corrections, the corresponding fluences were 4.2 J/cm² and 6.2 J/cm².

3.5. Growth measurements

Not all laser induced modifications in materials are of practical importance. What matters most is if transmission, reflection, and scattering at the wavelengths of interest are affected in such a way that the functionality of the optic is severely curtailed. If the damage covers enough area, the optic will have reduced transmission, reflection, or distortion of the surface figure to render the optic unusable. For pulse widths 10 ps and shorter, the changes observed near the damage threshold affect all areas above the damage onset, making it clear that this observed damage would distort the surface figure. However, for 30 ps pulse widths and longer, there are changes observed in the material which may or may not grow with subsequent pulses, and are not large enough to obviously cause the optic to be unusable. In order to determine the practical importance of the laser induced changes at these pulse widths, we have also performed growth tests (multi-shot experiments) for fused silica and the silica coatings. This series of experiments was performed by exposing each site to 10 shots rather than just one shot. An in situ image was acquired before and after each shot. This allowed us to measure and determine the growth onset levels for these materials as well as the scaling law for damage growth.

3.6. Extracting ρ(Φ)

When discussing laser induced damage of imperfect or defective surfaces, it is very important to think beyond the concept of a laser-induced damage threshold. It is necessary to use the concept of a density of precursors for laser-induced damage, where different regions of the optic will have varying propensities for laser-induced damage. It is not possible to simply plot a threshold value as a function of τ, because this threshold depends on beam size and on the definition of damage.

We use two methods for extracting the density of precursors per unit area ρ(Φ) that will damage as a function of pulse fluence. First, as shown previously [18], varying the beam size distinguishes between isolated precursors and fundamental limits. Beams smaller than the spacing between defects avoid sparsely distributed defects, whereas large beams consistently initiate damage at these defects. Here, we use 3 lenses with varying focal lengths, producing beam waists of 100 µm, 50 µm, and 30 µm. Due to instabilities in the beam focus found with the 250 mm lens along the optical axis, we did not attempt to use smaller beams. By repeating the measurements and calibrations using all beam sizes, we obtain information about damage occurring from isolated precursors as described in [18]. Using the fitting model described, we extract ρ(Φ).

In some cases, the density of defects is too high to measure with the beam sizes available. In these cases, we can extract the density of precursors by matching local fluence in a beam with the location of damage as previously demonstrated with large beam damage tests at 351 nm [19,20]. There are two differences between the current work with ps pulses and the previous work with ns pulses. First, the sizes of the individual damage pits here are much smaller, allowing for the measurements of densities much higher than previously measured. Second, for high enough fluences and short enough pulses τ < 10 ps, fundamental material ablation form craters that are not amenable to analysis based on ρ(Φ). In this case, the concept of precursors no longer applies, since the entire material ablates; ρ(Φ) diverges in these cases.

For high density defects, we are able to extract ρ(Φ) for 1–60 ps pulses by matching the beam image to confocal images. This allows us to match the position of a damaged site with the local fluence to extract ρ(Φ). An example image and the corresponding damage detection map are shown in Fig. 1. Figure 1(a) shows the confocal image for a 31 ps pulse using the 50 µm beam (the image width is 141 µm). The detected damage in Fig. 1(b) is found by filtering the image, and applying a threshold to obtain region, and applying an opening filter to remove noise. These data are translated into the ρ(Φ) plots shown in Figs. 11 and 12.

 

Fig. 1 A. Confocal image of damage test with a single 30 ps pulse at 1053 nm for the e-beam coating. Width of image is 141 µm. B. A processed image showing detected damage regions. For extracting density of precursors ρ(Φ), the centers of each region are matched to the corresponding regions in the fluence map.

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4. Results and discussion

4.1. Modeling results

We can solve Eq. 2 numerically for a large number parameters allowing us to understand the predicted behavior of ablation as a function of τ, α, β_m, and T. Figure 2 helps visualize the effects of each parameter on ablation thresholds. These were calculated for rectangular, or flat-in-time laser pulses, which should be kept in mind when comparing with Gaussian pulses.

 

Fig. 2 We use Eq. (2) to determine the effects of varying the avalanche coefficient α (A), the multiphoton ionization coefficient β_m (B), and the recombination time T (C) on the scaling laws for damage threshold. When comparing fused silica and silica coatings, these curves help guide interpretation of changes as changes in α, β, or T.

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There are four main results of these calculations. First, for τ ≫ T, ablation thresholds scale linearly with τ. Second, as seen in Fig. 2(a), changes in the ablation threshold that uniformly affect the threshold over a large range in τ are more likely to be caused by changes in α than by β_m. Third, as seen in Fig. 2(b), large changes in β_m only modestly affect the damage threshold, typically more for small τ. Fourth, T has a significant effect on ablation thresholds as a function of τ; increasing T lowers damage threshold for large τ, but does not affect the threshold for small τ significantly. We will use these results to aid in the interpretation of subsequent damage threshold scaling results.

As mentioned above, modifications to the multiphoton cross-section must be large in order to significantly modify the damage threshold. On the other hand, adjustments to the avalanche ionization coefficients can rather dramatically affect the damage threshold. We observe later that silica coatings have a lower damage onset for all pulse widths. This suggests that larger avalanche ionization coefficients are the primary reason. This may be due to the fact that the band gap is smaller in the coating materials, or due to a higher density of defects —although these two cases may not be distinguishable.

We emphasize that this model predicts the homogeneous removal of material that depends solely on the intensity and fluence of the laser beam at each point in the material. The concept of a damage threshold applies in this model. The depth of such ablation craters is limited due to plasma shielding, where the energy is either absorbed or reflected so that deeper material is not ablated by the laser. Inhomogeneous appearance of the resulting damage could result from the re-deposition of material or debris from the damage event, but flat, undamaged regions with individual pits or damage are not consistent with this model unless material properties vary with position in some way.

4.2. Damage morphology definitions

As discussed in [21], there are three main damage morphologies observed for pulse widths 1ps ≤ τ ≤ 60ps as shown in Fig. 3. These include smooth ablation craters, high-density individual pits, and smooth, circular depressions with a central pit. The smooth ablation craters at sub-ps pulse widths give way continuously to the high-density pits and rough damage craters with increasing pulse width.

 

Fig. 3 Schematics of damage morphologies found in laser-induced damage for pulse widths 1ps ≤ τ ≤ 60ps. A. Smooth ablation crater. B. High density, individual pits that coalesce to form large damage craters. C. Smooth, circular depressions with a central pit, associated with isolated absorbers.

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Exceptions to homogeneous removal predicted above could include inhomogeneous properties of the material, alternative absorption mechanisms for localized defects, and effects due to speckle in the laser beam. As discussed in [21], there is considerable evidence for inhomogeneous removal, both in the rough, ultra-high density pits observed for τ ≥ 3ps and for the smooth, circular depressions observed in fused silica and silica coatings. The high-density pits and the smooth, circular depressions suggest that defects play a role in laser damage. We expand on this observation here to show how pulse width scaling, beam size changes, and damage precursor density measurements can help understand under what conditions defects play a role, and how to understand what physical mechanisms may be in effect.

4.3. Pulse length dependence for fused silica damage

Experiments using variable beam sizes on fused silica for τ at 31 ps and 59 ps distinguish between laser-induced damage caused by isolated defects and intrinsic material processes [18]. As shown in Fig. 4, the smallest beam is able to avoid lower density precursors, raising the onset of observed damage (solid red line), whereas larger beams are not able to avoid these precursors, and hence lead to damage at lower fluence (solid green and blue lines). Additionally, varying the beam size also changes the sharpness of the damage probability curve observed when damage precursor densities are similar to the beam size. We are able to use the same modeling procedure as described in [18] to provide a measure of the density of precursors for the 31 ps and 59 ps measurements of fused silica. These results are discussed in Section 4.6.

 

Fig. 4 If the spacing between damage precursors is similar to the beam size, then variations in the beam size affect the 1/1 damage curves. The damage curve for a 100 µm beam are shown in blue, the curves for the 50 µm beam are in green, and the curves for the 30 µm beam are in red. The solid lines include all types of damage. The dotted lines include only the high-density pits, and excluded the smooth, circular depression damage sites. The definitions used for damage can affect both the sharpness and value of damage onset.

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The smooth, circular depressions identified in the fused silica damage are the limiting contributor to laser induced damage for τ = 31 ps and longer. In Fig. 4, we plot the probability of damage as a function of fluence for two different definitions of damage for a 31 ps pulse width. First, there are smooth, circular depressions which damage at lower fluences. Second, there are rough, high-density pits that follow the beam profile. If we include all types of damage, we obtain a more gradual transition from no damage to 100% damage as seen in the solid lines. However, if we only include the rough pits, we obtained a sudden transition as seen in the dotted lines. These results are consistent with the isolated nature of precursors leading to the smooth, circular depressions.

In contrast with longer τ, for pulse widths τ < 30ps the damage is limited by the ultra-high density pits rather than the smooth, circular depressions. The smooth circular depressions are observed with τ = 13 ps pulse widths, but the ultra-high density pits appear at similar fluences. Measuring the density of the high-density pits is performed in a later section using analysis of confocal and SEM images.

The scaling of the onset of laser induced damage in fused silica with respect to pulse width τ is shown in Fig. 5. As a function pulse width, we show the fluence at which 50% of the tested sites undergo damage. The 50% probability of damage was chosen since it allows a single number to be assigned even in cases where the damage probability changes more slowly with respect to fluence. There are several damage scaling curves shown that reveal the effects of beam size and multiple shots on the observation of damage. First, the solid lines show the damage scaling for three beam sizes, but only including damage exhibiting ultra-high density pits, excluding the smooth, circular depressions. The dashed lines of the same colors show the scaling when including smooth, circular depressions as well. In this case, increasing the beam size lowers the 50% damage level for τ > 10ps. The dotted magenta line shows the lowering of the 50% damage level when a site is exposed to 10 laser shots of similar fluence. The decrease in the 50% damage level is more pronounced for shorter τ.

 

Fig. 5 Pulse length τ scaling of the onset of laser-induced damage for fused silica surfaces with 1053 nm laser. Fluences shown are the level at which 50% of the tested sites undergo damage. Two definitions of damage are used. For solid lines, only damage exhibiting ablation pits or high-density pits (defined in text) are included. For dashed lines, lower density smooth, circular depressions damage are included. Three beam sizes are used, showing the variation of pulse length scaling with beam size. The dotted magenta line is for a damage test using 10 shots per site. Orange squares are the growth thresholds for observable growth using 100 µm beam, and cyan circles are for large-scale growth using the same beam.

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In the operation of high energy and high power lasers, the most important issue in laser induced damage is whether the damage continues to grow shot to shot. We evaluated the propensity and mode of growth of each site by considering how its morphology evolves over a sequence of laser exposures as shown in Fig. 6. The image pairs are an excerpt from a series of 10 laser exposures. The left image in each pair is taken with an in situ microscope after each laser exposure, with a background image taken prior to laser exposure subtracted. The right hand image is the difference the current and previous image. For example, in Fig. 6(c), the lack of features in the right hand image indicates that the damage site was unchanged by the 25.1 J/cm² laser exposure. Two types of damage are observed in the shot sequence. Figs. 6(a) through 6(c) show the smooth, circular depression damage, illustrated in Fig. 3(c). Starting in Fig. 6(d) we see the addition of substrate fracture which quickly grows in Figs. 6(e) and 6(f). We point out that the most dramatic growth is observed in the final three shots, which have the lowest fluence of the entire sequence of shots. Two onset of growth levels were determined: Growth A indicates where smaller changes were observed, small shifts in size as in Figs. 6(b–c), and Growth B indicates where large changes occur as in Figs. 6(d–f). The onset of growth levels are shown in Fig. 5, labeled Growth A and Growth B. These levels are below the onset of damage level observed for the formation of high-density pits, demonstrating that the smooth, circular depression damage is in fact relevant for growth of damage sites for fused silica.

 

Fig. 6 Growth of smooth, circular depression damage sites with 10 shots. in situ images of damage progression were taken before damage and after each shot. 6 of the 10 shots are shown. For each shot, the cumulative change from no shots is shown on the left, and the change from the previous shot is shown on the right. For example, no change is observed in shot 5, but a significant change is observed in shot 8. The fluence of each shot is noted. After shot 1, the damage is a grouping of damage sites with the “smooth, circular depression” morphology. As this figure shows, smooth, circular depressions can grow into large, fractured craters.

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4.4. Pulse length dependence for silica coating damage

For short pulse (<100 ps) optical components, reflective optics made with multilayer dielectric coatings are primarily used in order to avoid non-linear effects and dispersion that would occur in transmissive optics. The most commonly used materials for reflective optics in ps laser systems are alternating stacks of low and high index of refraction materials, such as silica and hafnia coatings. To this end, the ps laser damage performance of two silica dielectric coatings are compared. The morphology of these damage sites and damage scaling properties in the two coatings were similar. The performance of hafnia coatings are studied in a separate publication.

For the silica coatings tested, the primary modes of damage are due to coalescence and growth of smooth, circular depression sites and coating removal. Coating removal is mostly observed for short pulses (τ ≤ 3 ps). For silica coating, we do not observe any significant changes in the damage onset values as we adjust the beam sizes [Figs. 7 and 8]. This is due to the fact that in the coatings the precursors are at a much higher density, so that the distance between them is significantly less than the beam sizes used. The solid lines in both Figs. 7 and 8 for the silica coatings are for damage that exhibits deep, optically dark pits as measured by the in situ and confocal microscopes. The dashed lines show the 50% damage levels where any change in the site is observed. The lowering of damage levels due to multiple shots is observable (magenta dotted lines), but is less dramatic than for fused silica. The damage precursors do not lead to large sites for entrance surface damage with ps pulses, so beam profile based analysis for extraction of damage precursor density ρ(Φ) is applicable—in general, it is possible to identify the location of each precursor without overlapping with the damage resulting from an adjacent precursor. It is seen that the PIAD silica coatings damage at lower fluences than the corresponding E-beam coatings.

 

Fig. 7 Pulse length τ scaling of the onset of laser-induced damage for E-beam silica coatings with 1053 nm laser pulses. Fluences shown are the level at which 50% of the tested sites undergo damage. Two definitions of damage are used. For solid lines, only damage exhibiting deeper pits are included. For dashed lines, all lower density smooth, circular depression damage is included. Three beam sizes are used, in this case showing no variation of pulse length scaling with beam size. The dotted magenta line is for a damage test using 10 shots per site. Orange squares are the growth thresholds for observable growth using 100 µm beam, and cyan circles are for large-scale growth using the same beam.

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Fig. 8 Pulse length τ scaling of the onset of laser-induced damage for PIAD silica coatings with 1053 nm laser. Fluences shown are the level at which 50% of the tested sites undergo damage. Two definitions of damage are used. For solid lines, only damage exhibiting deeper pits are included. For dashed lines, all lower density smooth, circular depression damage are included. Three beam sizes are used, in this case showing no variation of pulse length scaling with beam size. The dotted magenta line is for a damage test using 10 shots per site. Orange squares are the growth thresholds for observable growth using 100 µm beam, and cyan circles are for large-scale growth using the same beam.

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As for fused silica, the primary practical concern is if laser-induced damage continues to grow once initiated. As shown in Fig. 9, the initial damage observed in silica coatings does grow. This figure is in the same format as Fig. 6. Initial damage is not large in Figs. 9(a–b), but begins to grow dramatically once the dark, central region deepens in Fig. 9(c). It is observed that fractured, large damage sites can begin from smaller, less dramatic damage. These results are shown in the damage scaling curves as the orange squares and cyan circles in Figs. 7 and 8. As before, Growth A refers to growth that creates small, additional features, and Growth B refers to large growth in Figs. 9(c–f).

 

Fig. 9 Growth of smooth, circular depression damage sites for E-beam coating with 10 shots. in situ images of damage progression were taken before damage and after each shot. 6 of the 10 shots are shown. For each shot, the cumulative change from 0 shots is shown on the left, and the change from the previous shot is shown on the right. The fluence of each shot is noted. After shot 1, the damage is a grouping of damage sites with the “smooth, circular depression” morphology. As shown also with the fused silica in Fig. 6, the smooth circular depression damage sites on e-beam coatings can grow into large, fractured craters.

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4.5. Modeling comparisons for fused silica and silica coatings

In works studying damage tests as a function of pulse width τ, it is standard to consider the damage “threshold” changing via a scaling law. As an example for these results, see Fig. 10. We used values for multiphoton ionization, avalanche ionization, and recombination from the noted references. It is to be noted that the simulations following [23] were extended beyond 10 ps pulses here for comparison, and that the model did not include recombination. Our fit to the data results in α = 4.8cm²/J and T = 0.22 ps while fixing β_m to the value from [23]. If we allow all three to vary, the value for β_m drops to an unphysical value 10 orders of magnitude down, even if we exclude the point for τ = 0.9 ps. The curve labeled Arnold et al. used the values for β_m from [23], the value for T from [26], and the values for avalanche ionization rates from [25].

 

Fig. 10 Modeling comparisons for Fused Silica and E-beam silica scaling. Solid lines are averages of data from Figs. 5 and 7. Dashed red line is fit using Eq. (2). Other lines are calculations based on parameters from [23,38] using Eq. (1) and [25] using Eq. (3). These models used Gaussian pulses rather than flat-in-time pulses for the simulations. None of the models adequately fit the data observed for 1 ≤ τ ≤ 60 ps.

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It is possible to fit our experimental data to a certain extent with the models, but there are significant discrepancies. First, none of the models capture the observed decrease in damage threshold from the 0.9 ps to 1.8 ps pulses. This decrease is due to the way we define damage as any observed change, and will be discussed in the following section. Second, for longer pulses (≥ 10 ps), the models predict a steeper scaling law than observed, unless the recombination time is increased well above values observed in other experiments [26]. This discrepancy is most likely due to the fact defects are the most important contributor to damage for pulse widths 10 ps and longer, and that the mechanisms modeled do not match the mechanisms of damage for those defects.

Although pulse length scaling is an efficient and often useful tool to discuss damage processes, there are several problems that occur between 1 and 60 ps. First, the definition of what is considered damage changes the scaling properties of the damage process, as seen in Figs. 5, 7, and 8. Second, changing the beam size used for damage testing can affect the observed scaling properties, depending on whether the density of damage precursors matches the size of the beam. Finally, as the morphological study demonstrates, there are fundamental shifts in mechanisms over the range of 1–60 ps. Simply scaling a single physical model over this range will not likely produce meaningful interpretations of the effects of the damage processes as those processes themselves change.

4.6. Comparing of densities of precursors ρ(Φ)

The measured ρ(Φ) for the e-beam silica coating is shown in Fig. 11. In most of these measurements, the only type of damage observed are “smooth, circular depressions”, which we showed can undergo growth [see Fig. 9]. On the high end of fluences, the ρ(Φ) curves end when the single craters are formed, either by material ablation or the merger of the individual damage sites. For most experiments with τ < 10 ps, the only other damage morphology observed was coating removal. We conjecture that the coating removal is initiated by material ablation that, due to the adhesion properties of the silica coating causes it to be completely removed. For example, in one site with τ = 0.9 ps, the coating lifted somewhat but was not completely removed, and there were high-density pits observed with the density indicated by the dashed blue line in Fig. 11. Smooth, circular depressions were also observed. Similar, high-density pits are observed in fused silica just below the ablation threshold, suggesting that a similar ablation process may occur in the coating which ultimately leads to coating removal. However, in the coating site we also observed the smooth, circular depression damage, so we cannot conclusively say that they do not play a role.

 

Fig. 11 Density of precursors ρ (Φ) for e-beam silica coating as a function of pulse width. Solid lines are for all observed damage, with the same definition of damage to dashed lines in Fig. 7: the smooth, circular depression morphology dominated the damage properties. Dash-Dot lines for 31 and 59 ps are only for sites that are similar to those that undergo growth in other experiments (see orange squares in Fig. 7). Dashed line for 0.9 ps is for high density pits observed in one case: in all other cases the coating was completely removed. The overlapping curves for varying pulse widths show that fluence is the critical parameter, suggesting that single photon absorbing process initiate damage in isolated precursors that lead to smooth, circular depressions.

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It is striking that all of the ρ(Φ) curves in Fig. 11 overlap regardless of pulse width τ. This indicates that the absorption processes depend primarily on the total fluence impinging on the site rather than on intensity. This indicates single photon absorption processes, and along with the morphology of the resulting sites (deeper central pit with a shallow, wide, circular depression), suggests that these sites are due to isolated absorbers. Even though linear absorption processes make these sites visible, intensity of the laser beam does affect the development of these sites into growing damage. This can be seen in the orange and cyan dash-dot lines for τ = 31 ps and τ = 59 ps in Fig. 11. In these cases, higher fluences are required for longer τ to obtain the deeper pits that grow as seen in Fig. 9 or quantified in Fig. 7.

A similar analysis of the fused silica damage tests results in a very different set of curves as seen in Fig. 12. In these measurements, the ρ(Φ) curves are extracted for the “high-density pits” for the solid lines. The ρ(Φ) for the smooth, circular depressions are extracted using an alternate method since they are at too low of densities for the previous analysis. We used the data from the variable beam size experiments as described in a previous publication [18]. We are able to use this analysis to extract the density of damage precursors for τ = 31 ps and τ = 59 ps, but not for the other pulse widths. For fluences between 13 and 25 J/cm², the extracted ρ(Φ) nearly overlap [dashed lines in Fig. 12], as was seen for the case of the e-beam coatings in Fig. 11. They diverge as the 31 ps data reach the onset of the high-density pits. As for Fig. 11, the lines end with the coalescence of the individual pits into a single, large, rough crater or with ablation.

 

Fig. 12 Density of precursors ρ (Φ) for fused silica. Solid lines are for high density pits detected using SEM, with the same definition of damage as for the dashed lines in Fig. 5: high-density pits and ablation limit the damage performance. The dotted lines use the variable beam size experiments and the fitting procedure from [18] to extract ρ(Φ). The dashed lines are analogous to the result for e-beam coatings in Fig. 11, suggesting single-photon activated isolated absorbers for fluences less than 30 J/cm². For the solid lines, the scaling of damage onset observed suggests multi-photon processes play a role in initiating the high-density pits.

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The evolution of the density of initiated pits as the pulse width τ increases is seen in Fig. 12. The width of the individual pits increases in size with τ, affecting the upper limit of densities observable. For example, the maximum ρ(Φ) observed for τ = 31 ps is 2 × 10⁸cm⁻². This corresponds to a feature size of 700 nm, which corresponds well to the size of the pits observed at 31 ps. For τ = 3.6 ps, the maximum ρ(Φ) observed is 2.5 × 10⁹cm⁻², which corresponds to a feature size of 200 nm, which also corresponds well to the feature sizes observed by SEM for these pits.

One interesting observation is that ρ(Φ) is significantly smaller at its peak for τ = 0.9 ps than for τ = 1.8 ps. This is confirmed by comparing the images, and provides an important explanation for the lower observed damage threshold for τ = 1.8 ps. The high density pits observed are larger and easier to detect for longer τ, and trigger our assignment of damage sooner. In Fig. 12, the peaks of the curves for τ = 0.9 ps and τ = 1.8 ps are in the same fluence bin. The decrease in measured ρ(Φ) to the right of the peaks comes from the formation of the ablation crater, which happens at very similar fluences for these two pulse widths. This indicates that the lower measured damage level in Fig. 5 for the longer pulse width is due to the appearance of the high-density pits. It should be noted that, although the effective τ calculated is double the shorter (τ = 1.8 ps vs. τ = 0.9 ps), the peak intensity within the τ = 1.8 ps pulse is 63% of the peak for τ = 0.9 ps. Much of the effective pulse width in this case is due to larger wings on the pulse rather than simple widening. The evolution of the high-density pits toward larger sizes with increasing τ may be related to incubation effects observed with sub-ps pulses. As observed previously [39], we found that damage onsets were lower for multiple pulses [Figs. 5, 7, and 8]. In [39], the damage onset decreased only for the first 100–1000 shots, and then flattened. It may be that this incubation reveals and grows the high-density pits as observed here; once the high-density pits are revealed, there are no lower-fluence precursors that can cause damage for lower fluences.

As seen in Fig. 12, the ρ(Φ) for the high-density pits clearly do not overlap for different pulse widths τ. The processes that initiate these high-density pits are likely more complex than the standard ablation model or linear absorption as described for the isolated absorbers. Since the ρ(Φ) do not overlap, the intensity of the laser, matters for the high-density pits, not just fluence. On the other hand, the fact that the highest intensity 0.9 ps pulses had lower densities of observable high-density pits for the same fluence indicates that time is required for the pits to develop or increase in size. We suggest that multiphoton processes are involved in the formation of the high-density pits. This is in contrast to the energy-driven processes that appear to occur with the smooth, circular depressions. Local modifications of the ablation parameters could cause changes in the local ablation threshold. Changes in T and in α seem more likely based on comparison to the graphs in Fig. 2. It is important to note that none of above ablation models as shown in Fig. 10 capture any of the effects discussed, as they only model homogeneous ablation. This makes it important to use care when applying pulse length scaling concepts to pulse widths in this regime.

High-density pits have been observed previously for silica and hafnia coatings [40–42]. They were also observed in fused silica for increasing pulse widths from 50 fs to 2 ps [43]. We make two contributions to help in the understanding of the high-density pits. First, we extend observation of these pits up to 59 ps, where the sizes of the high-density pits increases with pulse width, while the density observed decreases. Additionally, we believe that the density of precursors extracted here provides important clues to the determination of defects and mechanisms for the high-density of pits.

5. Conclusion

We have performed extensive damage tests on fused silica and silica coatings for pulse widths τ between 1 and 60 ps. For shorter pulse widths, damage on fused silica and silica coatings can be fit within previous models of material ablation with the exception of the detection and characterization of the high density pits that become prominent for τ > 1 ps. The pulse width scaling of these high density pits suggests that multi-photon processes are needed to initiate these pits. For τ ≥ 10 ps, smooth, circular depressions that we believe are caused by isolated absorbers undergoing single photon absorption become the limiting source of laser-induced damage.

From the ρ(Φ) curves in the silica coatings, it is clear that the defects that limit damage for longer pulse widths become visible at lower fluence. The process that causes this damage depends on the fluence primarily, only very weakly on intensity. This indicates a linear absorption process that has often been invoked for ns laser damage processes. This suggests a common mechanism and class of damage precursors for UV ns-scale laser damage on exit surfaces with IR ps laser damage on entrance surfaces. For ns-scale lasers, it is understood that a linear absorber leads to damage that scales with pulse width according to a power law likely because of heat diffusion from the absorber in some complex way. This model may continue to hold for certain classes of precursors well down into the ps regime, only to be overtaken by the high-density pits and ablation for τ ≤ 10 ps. This study suggests that there is range of transition between mechanisms that occurs around 10 ps as the mechanisms become competitive. That isolated absorbers leading to smooth, circular depressions dominate the laser damage of silica coatings down to τ = 10 ps has important implications for how to deal with and mitigate laser-induced damage in coating materials for ps lasers.