1. Introduction

Laser-induced damage on the exit surface of fused silica optics is a topic of considerable study [1–16]. The size of damage initiation sites created by ns pulses is strongly influenced by the pulse duration but ranges from 1 to 30 μm [15]. These sites tend to grow exponentially under subsequent laser irradiation [2–5]. The techniques which have been developed to repair these damage sites generally require treatment before a critical size (typically several hundred microns) is reached [12]. As a result, preventing a single or several damage sites from growing too large for repair may require operating the laser system below its peak potential. Past work in the area of laser-induced damage growth has shown growth rates to be primarily dependent on the laser fluence and wavelength [2–5,7,8]. More recent studies suggest that growth rate, similar to the damage initiation process, is affected by a large number of additional parameters including pulse duration, pulse shape, site size, and internal structure. Hence, single-parameters studies are desirable to advance our fundamental understanding of damage initiation and growth mechanisms as well as form the foundation for accurate predictive models of laser optics performance in regards to optical damages.

In this work, we investigate the effect of pulse duration on exit surface damage growth on fused silica optical components under UV laser irradiation. Our experimental method involves a multi-site parallel damage growth technique using a large aperture laser with flexible pulse shapes, i.e. simultaneously irradiate 40-60 laser-induced damage (LID) sites for multiple shots at fixed fluences and discrete pulse durations from 1 ns up to 15 ns. In Ref. 13, we have presented a preliminary analysis based on single-shot growth coefficients and revealed that growth rate scales with pulse duration (τ) from 1 ns to 15 ns as τ^0.3 (i.e., growth threshold and rate increase with fluence) for sites in the 50-100 μm size range. In particular, we noted the divergence of the growth parameters for 1 ns pulses from the general trend of linear dependence on pulse duration from ~2 ns to 15 ns [13]. In the present study we take a different approach to data analysis and focus on the salient attributes of long-term (i.e., multiple shot) growth behavior with short vs. long pulses, including growth rate and site morphology, leading up to these pulse duration effects.

2. Experimental procedure

All growth experiments presented in this work have been conducted at the Optical Science Laboratory (OSL) at LLNL [17]. The laser characteristics as well as the growth experimental layout have been presented in detail elsewhere [17,13]. In brief, OSL is a Nd:glass amplifier laser system with an adjustable pulse width and shape which can fire a single, 100-J pulse at the third harmonic (351 nm) with high quality beam profile once every 45 minutes. The sample is positioned in an image relay plane of the laser system and is housed in a stainless steel vacuum chamber. The beam diameter at 351 nm on the sample is ~30 mm and is collimated with respect to 1-cm thick samples (f/23 optical system). We take advantage of the large area beam to grow simultaneously a large number of sites. Laser beam diagnostics for the test beam on the part include measurements of the temporal pulse shape, energy and input & output beam near field fluence profiles. All test series were conducted in vacuum and at room temperature.

To investigate the damage growth behavior as a function of pulse duration from 1 ns to 15 ns, we employ the 3-cm beam at fixed fluence and pulse duration to simultaneously irradiate a large number of sites for multiple shots. Moreover, we use pulses with flat-in-time temporal profiles to ensure that any pulse shape effects are removed from these experiments. Fresh samples (with pre-initiated sites) were dedicated to each fluence/pulse duration combination. We take advantage of the ~17% spatial beam contrast in OSL to simultaneously test sites with a range of local fluences which vary within ~2-3 J/cm² around the beam average fluence. The 10% uncertainties in local fluences are primarily due to small uncertainties in registration of the beam to the damage site array. Specific details on sample layout/experimental parameters are listed in Table 1 . We note that growth behaviors with 10 ns and 15 ns pulses were qualitatively very similar; therefore, we do not show in great detail the growth results for the latter case.

Table 1. Sample/experimental parameters at various pulse durations

View Table

The samples were 5-cm diameter and 1-cm thick UV grade Corning 7980 glass windows prepared with high damage resistance surfaces [18]. A table top Nd:YAG laser was then used to induce an array of 40 to 60 similar damage sites on the sample’s exit surface within a 3-cm aperture matching that of the OSL beam with either 4 mm or 3 mm spacing [13]. Alignment beam fiducials are also placed on the same surface using a CO₂ laser technique and aid in the accurate registration of the local fluence to an individual site on every laser shot to within 200 μm. More details on the sample preparation and fluence calibration methods can be found in [13,19].

The growth in the lateral size of the damage sites exposed to a single OSL laser pulse is measured offline (outside the vacuum chamber) using an automated robotic microscope that records backlit images of all sites before and after each laser shot with ~1 μm resolution. In this work, the metric for the individual damage pit size is the effective circular diameter based on image thresholding and the measurement error is on the order of 2 μm (see [13] for a more detailed discussion on the instrument errors).

The ‘multi-site parallel damage growth’ technique outlined above is essentially a shoot-and-look procedure in which a sequence of steps is repeated as follows:

3. Results and discussion

3.1 Pulse duration effects on multi-shot growth behavior

The exit surface damage growth has been generally described by an exponential increase in diameter with the number of shots at fixed fluence [2–5], as follows:

Data analysis outlined above is a multi-shot approach in which the growth coefficient α is used to describe the average growth behavior of damage sites for multiple shots (N~30). For the case of long pulse durations, from 5 ns up to 15 ns, we found that exit surface growth exhibits the classic exponential behavior in most cases, in agreement with previous results by numerous groups [1–5]. Typical multi-shot growth behaviors with 5 ns and 10 ns pulses are illustrated in Fig. 1(a) (top and bottom graphs, respectively) along with the local average fluence on individual shots. Exponential fits to the diameter data based on Eq. (1) are shown by the solid curves. The fitting parameters, i.e. growth coefficient α and R², and the average fluence for the shot sequence, ϕ, are listed in the legends.

 

Fig. 1 Typical multi-shot growth of damage site diameter (left y-axis) vs. shot number under laser irradiation at 351 nm with various pulse durations: (a) Exponential growth with 5 ns and 10 ns pulses and (b) Linear growth with 1 ns and 2 ns pulses. The local average fluences (right y-axis) at the site locations on every shot are also shown. The solid lines represent best fits (exponential or linear) to diameter vs. shot number according to Eqs. (1)-(2) (see text) with the fitting parameters indicated in the legends.

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In contrast, exit surface growth with shorter (1-2 ns) pulses is, in general, very different. We found that site diameter increases linearly with shot number, as illustrated in Fig. 1(b). A multiplicative growth factor as in Eq. (1) is no longer appropriate to describe this linear dependence, but rather is described by an additive term to quantify the incremental growth in diameter with shot number as follows:

Having observed this atypical exit surface damage growth behavior with 1-2 ns pulses, we paid close attention to its occurrence at other pulse durations. Careful analysis of the growth character for all sites/samples indicated that, for the majority of the sites, exponential and linear growth persisted for complete shot sequences (for as many as 35 shots) with long and short pulses, respectively. In other words, the example sites in Fig. 1 depict the general picture of the growth character vs. pulse duration in the 1 ns to 10 ns range. However, a small fraction of the sites exhibited nonconforming behaviors. Namely, the growth character may well change from linear to exponential or vice-versa during the shot sequence. Moreover, the unanticipated growth behavior may also carry on for the entire growth sequence or switch back and forth, as discussed below. Examples of such mixed growth behaviors and the fits to diameter vs. shot number data are illustrated in Fig. 2 for 1 ns, 2 ns and 5 ns pulses (open circles and solid lines, respectively). The fitting parameters, i.e. growth coefficients, either exponential or linear, and the average fluence for the corresponding shot sequences are listed in Fig. 2 using the same color code as the solid line fits. It can be seen that exponential growth occurred even with short pulses at either end of the shot sequence while linear growth with 5 ns pulses persisted for as many as 30 shots. It is important to note that shot-to-shot local fluence fluctuations may be in part responsible for triggering changes in the growth behavior. However, the multi-shot persistence of one behavior vs. the other cannot be solely attributed to sporadic fluence fluctuations. As discussed below in Section 3.2, we found a strong correlation between the growth character and the damage site morphology at the microscopic level. The latter parameter is largely unexplored and may play a key role in advancing our fundamental understanding of damage growth mechanisms.

 

Fig. 2 Examples of mixed behaviors observed during the multi-shot growth sequence with 1 ns, 2 ns, and 5 ns pulses: damage site diameter (open circles) and local fluence (closed squares, not all shots are shown) vs. shot number, respectively. The solid lines represent best fits (exponential or linear) to diameter vs. shot number according to Eqs. (1)-(2) (see text) with the fitting parameters indicated in the legends.

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To better quantify the interplay of linear and exponential growth, we took advantage of the large number of sites and growth shots examined in our experiments to compute the growth behavior statistics as a function of pulse duration. Specifically, for each pulse duration experiment, we derived the fraction of shots involved in one or the other behavior for all growing sites (based on plots similar to those presented in Figs. 1 and 2) with respect to the total number of shots and sites, i.e. ${P_{\text{lin/exp}}|}_{\tau }={\left[no.shot{s}_{\text{lin/exp}}/\left(no.shots\times no.sites\right)\right]|}_{\tau },$where ${P_{\text{lin/exp}}|}_{\tau }$ is the probability to observe a specific growth behavior at pulse duration τ, either linear or exponential. We note that the number of sites and shots, as well as the fluence range, varied between experiments with different pulse durations (see Table 1). For the above calculation, we have examined 35 sites grown with 1 ns and 2 ns pulses at 4-6 J/cm² and 50 sites grown with 5 ns and 10 ns pulses at 6-8 J/cm², respectively.

The probability of observing linear or exponential growth behavior vs. pulse duration (1-10 ns) is illustrated in Fig. 3 . These results suggest that the incidence of linear growth behavior on the exit surface increases significantly for the case of 1-2 ns pulses compared to that at 5 ns pulses. The probabilities observed with 1 ns vs. 2 ns pulses are similar within 10%. While it is difficult to estimate the absolute errors in evaluating these probabilities, we attribute this difference in part to experimental and fitting procedure errors. It is also possible that the trend is real, i.e. higher probability for observing linear growth with 2 ns vs. 1 ns pulses, and warrants additional investigation in future growth studies with better site statistics, shorter pulse durations to reveal the underlying physics as well as improved metrics for discerning between growth behaviors. At this time, we will assume the upper bound for the absolute errors on the probability to be 10%. Hence, results in Fig. 3 indicate that linear growth dominates at about 75% with 1-2 ns pulses while growth behavior is mostly exponential in nature with longer pulses (~75% and 100% with 5 ns and 10 ns pulses, respectively); it then follows that there is a non-negligible (~25%) frequency of the nonconforming behavior with 1-5 ns pulses. Finally, growth is exclusively exponential with 10-15 ns pulses (the latter is not shown here). It is important to recognize that the implications of the pulse duration dependence to the growth behavior are twofold. From a practical point of view, the growth character can drastically alter the accuracy of long-term predictions on optics lifetime. For example, to a first order, it may take 20 shots at 6.5 J/cm² to grow a site from 50 μm to 150 μm using 1 ns pulses versus only 12 shots at the same fluence with 5 ns pulses, i.e. which is a 1.7X difference. Secondly, the mixture of linear and exponential growth behaviors with 1-5 ns pulses demonstrates a shift in the dominant growth mechanisms with pulse duration rather than being site/fluence dependent.

 

Fig. 3 Growth behavior statistics as a function of pulse duration.

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Let us now summarize the multi-shot growth behavior, i.e. average growth coefficients, as a function of fluence and pulse duration for the dominant behaviors discussed above, i.e. linear and exponential growth for short and long pulses, respectively. Previous growth studies at 351 nm were conducted primarily with longer pulses (i.e., 3-10 ns, near Gaussian temporal profiles) and established that the average exponential growth coefficient defined in Eq. (1) increases linearly with 351-nm fluence as follows:

The average growth coefficients vs. fluence are plotted in Fig. 4 for all pulse durations and are separated by growth character. Let us first discuss the dominant growth behaviors. The solid data points represent the average of observed growth coefficients from multiple sites grown at similar fluences within ~0.5 J/cm² with error bars representing the standard deviation upon fluence binning. The solid lines represent best fits to the data according to Eqs. (3)-(4) with the fitting parameters (A, B) and R² listed in each panel. These multi-shot results confirm that A and B coefficients depend on pulse duration, in qualitative agreement with those derived using the single-shot analysis approach described in Ref [13]. Specifically, both the rate of change in growth rate with fluence and the fluence growth threshold increase at longer pulse durations, i.e., A and B coefficients. However, the different meaning of the exponential and linear growth parameters as defined by Eqs. (1)-(2) does not permit a straightforward comparison of the multi-shot (this study) and single-shot analysis results [13]. The latter method assumed an exponential single shot growth coefficient <α> (dimensionless) for all pulse durations, thus all the growth parameters were plotted together and compared to one another (see Fig. 4 in Ref. 13).

 

Fig. 4 Dominant growth behaviors vs. fluence and pulse duration: (a) Exponential growth coefficient from Eq. (1) for 5 ns and 10 ns pulses. (b) Linear growth coefficient from Eq. (2) for 1-2 ns pulses. Solid lines represent best linear fits to growth coefficient vs. fluence according to Eqs. (3) and (4), respectively. Also shown are the growth coefficients for atypical behaviors, i.e. linear growth with 5 ns pulses and exponential growth with 1-2 ns pulses.

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For the case of atypical growth behaviors, we plot the observed growth coefficients from several sites in the relevant category. For example, linear growth coefficients observed with 5 ns pulses are illustrated by open triangles in Fig. 4 (b) to be compared with those from 1 to 2 ns pulses. Similarly, the exponential growth coefficients observed with 1-2 ns pulses are plotted along the 5 ns-data points in Fig. 4 (a), i.e. open squares and circles, respectively. Although data for these atypical growth behaviors is sparse, it appears to follow, in general, the dominant trends discussed above. This observation is yet another confirmation for the gradualshift in the fundamental growth mechanisms due to pulse duration effects in the 1 ns to 5 ns range.

3.2 Pulse duration effects on damage site morphology

In addition to the mixture of multi-shot growth behaviors discussed above, we also observed noticeably different damage morphologies with long vs. short pulses. These differences are apparent under scanning-electron microscope (SEM) examination immediately and become obvious to optical examination when sites reach about 100 μm in diameter during the growth sequence. SEM images of two damage sites exhibiting the dominant growth behavior after multi-shot irradiation with 1 ns and 5 ns pulses at similar fluences are shown in Figs. 5(a) and 5(b), respectively. The lower resolution images to the left hand side illustrate the overall size and microscopic features (also visible with optical inspection). Specifically, the damage sites include a crater (core region) from which most of the material has been ejected earlier in the damage process [20,21]. The crater morphology is quite similar for 1 ns and 5 ns pulses, with clear evidence of re-solidified molten material as a consequence of localized extreme conditions of temperature and pressure created during and shortly after each laser pulse in the growth sequence. In addition, the outside border of the sites contains mechanically damaged material extending out to tens and hundreds of microns. However, the lower spatial resolution images in Fig. 5 are sufficient to draw attention to the noticeable different fracture morphologies in this outer region with 1 ns vs. 5 ns pulses. Namely, growth with long pulses is primarily due to lateral and radial fractures; in contrast, growth with short pulses proceeds with initiations around the periphery, very similar to the input growth morphology [9].

 

Fig. 5 SEM images of typical damage sites grown at ~6-7 J/cm² with (a) 1 ns and (b) 5 ns pulses, respectively. Selected regions located at the periphery and at the center of the damage craters demonstrate the distinct morphological features associated with pulsed duration effects (higher spatial resolution images on the right hand side).

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It has been previously reported that the size of initiated damage sites is strongly dependent on pulse duration [15]. We hypothesize that the crossover between linear and exponential growth is likely due to the size of the initiation centers becoming larger with pulse duration until they begin to interact causing the lateral and radial fractures associated with exponential growth. To better support this interpretation, we refer to the higher resolution SEM images shown to the right hand side of Fig. 5. Selected regions located at the periphery of the damage craters with both 1 ns and 5 ns pulses expose the interplay between re-initiation and fracture contributing to growth in this transitional pulse duration regime. Although the fracture size correlates with pulse duration, there is clear evidence of small fractures at the periphery of the site grown with 1 ns pulses as seen in Fig. 5(a), in addition to the characteristic re-initiation centers (~1 μm in diameter [15], ). Likewise, an isolated damage site (small ‘pansy’, see Ref. 15 for common damage terminology) is observed amidst the lateral fractures brought about with 5 ns pulses, as shown in Fig. 5(b). Hence, the morphology of the sites presented in Fig. 5 reveals evidence of both growth mechanisms and supports our interpretation of pulse duration effects on the multi-shot growth behavior, discussed in detail in the previous section.

4. Conclusion

We have investigated the growth behavior of laser damage sites on the exit surface of fused silica optics as a function of laser pulse duration at 351 nm and found that pulse duration has a strong influence on damage growth. This effect has not been previously documented and has important implications for both long-term predictions on optics lifetime as well as the fundamental understanding of laser damage mechanisms. This study demonstrates that multi-shot damage growth is largely exponential in nature for pulses longer than about 2 ns, while shorter pulses (1-2 ns) produce a dominant linear growth. The latter behavior was unexpected on the exit surface of fused silica. We have examined a large collection of damage sites at each fluence/pulse duration combination and demonstrated a linear fluence dependence of the multi-shot growth coefficients for both exponential and linear growth behaviors. In addition, the rate of change in growth rate with fluence and the fluence growth threshold increase with pulse duration in the 1 ns to 10 ns range, in qualitative agreement with previous results based on single-shot growth analysis [13].

Furthermore, the change in growth character with pulse duration is accompanied by distinct site morphology. Sites grown with longer pulses (i.e., 5-15 ns in duration) appear to have most of the laser energy deposited in the central core, as suggested by the presence of molten material and flaking off large chips on the periphery. This type of growth results in an exponential increase in the site diameter (or surface area) with number of shots. In contrast, for pulses as short as 1 or 2 ns, energy is deposited all across the damage site and growth proceeds by initiation on previously damaged material at the edge of the site. These observations seem to confirm previous reports of localized energy deposition at multiple locations within the site [22,23]. It has also been hypothesized that individual re-initiation sites are less likely to interact across the site during laser energy deposition with shorter pulses. Therefore the difference in exponential vs. linear growth behavior could be due to cooperative effects of localized energy deposition. In the former case, larger levels of stress result in larger fractures (flakes or chips), as observed around the perimeter of the damage site.