We study the dynamics of energy deposition and subsequent material response associated with exit surface damage growth in fused silica using a time resolved microscope system. This system enables acquisition of two transient images per damage event with temporal resolution of 180 ps and spatial resolution on the order of 1 µm. The experimental results address important issues in laser damage growth that include: a) the specific structural features within a damage site where plasma formation initiates; b) the subsequent growth of the plasma regions; c) the formation and expansion of radial and circumferential cracks; d) the kinetics and duration of material ejection; e) the characteristics of the generated shockwave.
©2013 Optical Society of America
Laser systems for Inertial Confinement Fusion (ICF) experimental facilities require large aperture optical components and high output power densities. As a result, these lasers often operate near the laser-induced damage threshold of their optical components, especially those exposed to ultraviolet (UV) laser light. Such laser systems utilize customized temporally shaped pulses ranging from ~3 ns up to ~20 ns in duration to enable the compression of the target. Damage initiation involves formation of voids in the bulk or craters on the surface of the materials with diameters on the order of 1-30 µm. These initiation sites represent optical features that scatter or modulate the laser beam; yet, if stable under exposure to subsequent laser pulses, these features are not of particular concern for a large aperture laser system. However, damage initiation sites often start growing in size under subsequent exposure (commonly referred to as damage growth), thus increasing the beam power loss and modulation effects –eventually, the optic needs to be removed/repaired. A characteristic example is the case of damage sites on the exit (output) surface in fused silica optics located in the section of the laser system that is exposed to the UV laser pulses.
Due to its impact on the operation of ICF class laser systems, the investigation of laser-induced damage growth has intensified in recent years as a number of such large aperture lasers systems are becoming operational [1–10]. The size of the damage sites tends to grow nearly exponentially under subsequent laser irradiation [1,3]. Previous work addressed this issue by systematically mapping the growth behavior, which is quantified by measuring the diameter of the damage site as a function of the laser parameters and initial damage site morphology. It has been shown that damage growth of laser-induced damage sites is affected by a large number of such parameters including the pulse duration, the laser fluence and laser wavelength or combinations of wavelengths [1–6]. Recent work has demonstrated a transition from a mostly linear to an exponential multiple-shot growth behavior at 351 nm as the pulse-length increases from 1 ns to 15 ns . These salient behaviors have been attributed to a shift in the fundamental growth mechanisms. However, these dominant damage growth mechanisms still remain unknown.
The growth rate of the damage sites determines the lifetime of the optic. To resolve this problem, there are two main approaches that are concurrently under development. The first relates to eliminating (or sufficiently reducing) the damage initiation on the surface of the optic by producing a surface that is free of the types of defects that cause the initial coupling of laser energy into the material (damage initiation) . The second method involves the treatment of the damage sites to arrest growth or reduce the growth rate, commonly referred to as damage mitigation. The latter, most successful method currently under development involves the exposure of the site to a CO2 laser beam [12,13].
The morphology of the surface damage sites in fused silica typically involves two distinctly different regions: a) a central “core” typically located at the bottom of the damage crater containing on its surface a highly scattering modified material that is densified and has a large concentration of light absorbing defects while a network of cracks is located below this surface modified layer; b) the edges of the crater appear to be cleaved surfaces of unmodified material or mechanically damaged material containing cracks that radiate towards the surface [14–16].
In this work, we employ a time resolved imaging system to capture the initiation and evolution of damage growth under exposure to 355 nm, 8 ns laser pulses. The objective of this work is two-fold. First, we want to image the locations where the damage growth process begins. We postulate that this information can be directly related to the material features and thus, help better understand the physical mechanisms involved in the damage growth process. The second objective is to measure the material dynamics following exposure to the laser pulse (and initiation of the damage growth process) including the generation of a shockwave, the formation and growth of additional cracks, and the dynamics of the material ejection process leading to the increase of the diameter and depth of the damage crater.
2. Experimental design
A schematic depiction of the experimental system is shown in Fig. 1 . A detailed description of this time-resolve microscope system can be found elsewhere . In brief, the system involved one pump laser used to initiate the damage and three probe lasers used as strobe illuminators to acquire shadowgraphy microscopic images at pre-determined delay times. The pump laser (Quanta-Ray, Newport-Spectra Physics) was operating at 355 nm, 8 ns full width at half maximum intensity (FWHM) and was focused using a 15 cm focal length lens about 2 cm behind the exit surface of 5-cm-round, 1-cm-thick fused silica windows (CVI Melles Griot, laser grade). The fluence at the input surface of the sample was below the damage initiation threshold, but on the exit surface was just above the breakdown threshold (50 J/cm2) covering an estimated diameter of ~1 mm. Upon damage initiation with a first pulse, the laser fluence was reduced to about 18 J/cm2, which was sufficient to induce damage growth of the pre-initiated damage site.
Time-resolved images were acquired using dual-pulse strobe-light illumination in two different configurations that were optimized for imaging: a) material ejection and shockwave propagation in air, and b) kinetics and material modifications at the surface of the sample. The first configuration utilized two probe pulses at 532-nm, ~4.5 ns in duration (FWHM) with orthogonal linear polarization states produced by two separate lasers (Litron Lasers) that were externally triggered and synchronized with the pump laser via pulse delay generators. The second configuration, which required a higher temporal resolution, employed the output of a third probe laser (EKSPLA) operating at 532 nm with pulse duration of about 180 ps (FWHM) as the strobe illumination source, also synchronized with the pump laser; the laser output was split into two components propagating along different beam paths to generate two temporally delayed (with respect to each other) probe pulses that were orthogonally polarized. In both experimental configurations, the dual probe pulses were recombined using polarized beam splitters (PBS in Fig. 1) before the sample to illuminate the target area at predetermined delay times with respect to the pump pulse.
The images were acquired using two microscope systems (as shown in Fig. 1) comprised of a long working distance 5X objective followed by a 5X zoom lens. The image formed by the microscope’s optics was subsequently split using a polarizing beam splitter to separate the two orthogonal polarization image components (one from each probe pulse arriving at different delay times) and were captured using separate charge-coupled devices (CCD). The image field of view was about 700 µm X 500 µm. As a result, the damage sites were grown not larger than about 250 µm in diameter in order to encapsulate all relevant features within each image captured. Raw images were processed via two methods to improve the signal-to-noise ratio. Most artifacts in the raw images–due to spatially non-uniform intensity of the probe beam or other sources, such as surface imperfections (in transmission view) or dust particles in the beam path–were eliminated by dividing each image pixel-by-pixel to the initial static image (of the bare surface or air, prior to pump pulse exposure) . This background correction was applied to all images presented in this work (labeled ‘ORIGINAL’ in Fig. 2 ). To further enhance the image contrast associated with small transient changes captured in transmission view, each transient image can be divided pixel-by-pixel to its preceding static image of the damage site (from the corresponding camera). This image normalization is demonstrated in Fig. 2 (labeled ‘NORMALIZED’) and is particularly useful in monitoring material modifications along the surface (results presented in Section 2.1). The imaging system has a static spatial resolution on the order of 1 µm and a depth of focus of about 40 µm. The delay of each probe pulse was measured for each damage event, defined as the time separation between the peaks of the pump and probe pulses. In this context, negative delays are associated with the probe pulse arriving before the peak of the pump pulse.
3. Experimental results
3.1 Plasma initiation and lateral expansion
Images in Fig. 2 demonstrate the ability of the experimental system to capture the early material modifications associated with the laser energy deposition during the damage growth process. These images were captured in the transmission view geometry using the 180 ps probe laser. Specifically, Figs. 2(a) and 2(d) show the static images of the damage site prior to and after a single-shot exposure to the pump pulse, respectively. The increased size of the damage site after exposure to the pump pulse–damage growth– is due to absorption of energy from the pump pulse. The images in Figs. 2(b) and 2(c) were captured during the pump pulse (at −3.81 ns and −1.16 ns time delays, respectively) and are largely the same as the image of the damage site before exposure (Fig. 2(a)). However, minor modifications at the peripherycan be visualized in one or both of these transient images, as pointed out with arrows and individually identified with numbers in Fig. 2(c).
Image normalization applied to Figs. 2(b) and 2(c) –division by the image in Fig. 2(a)– enhances the contrast of such minor changes in the transient images, as seen in Figs. 2(b1) and 2(c1), respectively: dark areas in the normalized images represent features in the original images that exhibit increased transmission loss compared to the initial image of the damage site (Fig. 2(a)). We will use this image normalization method to display the transient images in the remaining of this work. The same normalization method was applied to the final image as shown in Fig. 2(d1) and allows for better demarcation of the growth of the damage site: the area that was associated with the original damage site appears as a bright object. Figure 2(a1) also shows a ratio of two consecutive static images of the initial damage site. The damage site has almost the same intensity as the surrounding material exhibiting no specific features of higher contrast. As mentioned earlier, the damage sites typically contain a central core region of highly scattering and defect-rich material while a region containing cleaved surfaces and cracks is located at the edges of the crater. The perimeter of the central core region is highlighted in green in Fig. 2(b1) and facilitates a more detailed interpretation of the experimental observations.
The normalized transient image captured at −3.81 ns shows that the “core” region contains a large number of dark features covering its entire area. This suggests that the material modification associated with damage growth has already started within the “core” region at this delay time under the excitation conditions used in this experiment. The outer region (cleaved and cracked surfaces) shows minimal changes identified with arrows 1 and 3. Specifically, the location identified with arrow 3 is a well-defined region of strong transmission loss (‘dark’ site with transmission on the order of a few percent) at the intersection of the cleaved/cracked surface of the damage site with the surface of the optic. For ease of discussion, we define throughout this work this interface as the “Damage Site Perimeter interface”, or “DSP interface”. The site identified with arrow 1 is also located at the DSP interface and appears as a ‘gray’ object, where the transmission is reduced by about 10%. The transmission of this site continues to decrease with time as manifested in the second transient image acquired at −1.16 ns delay–evolution to a ‘dark’ site with larger dimensions.
Similarly, the dark site indicated by arrow 3 has significantly expanded laterally during the time separation of 2.65 ns between the two transient image acquisitions. In addition, a number of other dark features are visible at the DSP interface or even just outside this interface with characteristic example of the latter case identified with arrows 2 and 4. These dark features are assigned to the formation of plasma as a result of energy coupling from the laser pulse to these specific locations within the pre-existing damage site. Comparison of the transient and final images in Fig. 2 suggests that the lateral expansion of the damage site correlates to locations of plasma formation at the DSP interface –for example the larger, early formed dark site at location 3 lead to a significant expansion of the damage site in this region, as best seen in Fig. 2(d1).
The images in Fig. 3 represent a typical example of our experimental observations with the delay time for transient image acquisition slightly advanced compared to the example shown in Fig. 2. Specifically, these transient image shown in Fig. 3(b) and 3(c) were acquired at −0.44 ns and + 2.21 ns, respectively. The outline of the inner “core” region is also highlighted in the initial image of the damage site shown in Fig. 3(a). The evolution of this damage site proceeds similarly to the one discussed in relation to Fig. 2: the core region appears to be highly populated with dark features associated with a high density of locations of plasma formation; isolated sites of plasma formation are observed at the DSP interface of the damage site; the size of these periphery sites significantly increases during the time interval between transient image acquisitions. In addition, the lateral growth of the final damage site, best visualized in the normalized image of the final site shown in Fig. 3(d1), is strongly correlated with the sites of plasma formation at the DSP interface (e.g., expansion in the lower-right and upper-left quadrants vs. no change in the upper-right quadrant).
Experimental results in Figs. 2 and 3 demonstrate another salient behavior: the absence of plasma formation (dark features in the transient images) in the region between the inner core and the DSP interface. This suggests that the cleaved surfaces are not involved at the intensity/fluence levels used in this experiment in the energy coupling from the laser pulse to the damage site; in contrast, the inner core region is strongly involved, as revealed by the high density of plasma initiation sites that expand with time and can merge to a single or a number of large plasma sites. In addition, isolated plasma sites are formed at the DSP interface at a slightly longer delay compared to the plasma formation at the inner core region–the former sites just appear while the latter sites are already visible in Fig. 2(b1). This may suggest that, for the excitation conditions used in this experiment, the threshold for plasma formation in the inner core is somewhat lower than the threshold for plasma formation at the DSP interface.
Transient images acquired at longer delays indicate that upon the termination of the laser pulse, radial and circumferential cracks form and expand for about 30 ns. The transient images shown in Figs. 4(b) and 4(c) were captured at delays of + 21.09 and + 23.74 ns, respectively. Large radial cracks, denoted with numeric 1, have developed at these delays and are clearly visible. The dark appearance of these cracks can be assigned to scattering and/or absorption and is similar to the experimental observations during laser-induced breakdown in the bulk of fused silica . Comparison of the transient and final images suggests that the radial cracks are still visible, but with a much lower contrast, while the outer circumferential cracks are well correlated with the final outline (DSP interface) of the damage site. The shockwave is also visible, denoted with numeric 2, in the transient images. The expansion speed of the shockwave was estimated from the two transient images and found to be on the order of 2 km/s. This speed is lower than the speed of sound in fused silica (≈5.9 km/s), thus it must be related to the shockwave formed in the air. The irregular shape of the outline of the shockwave reflects the merging of multiple shockwaves originating at different locations –where plasma was formed– around the damage site.
The capability of the experimental system to acquire two transient images per event enabled the estimation of the speed of expansion along the surface of the isolated plasma sites formed at the DSP interface. The average radius of each site was inferred by measuring its area in each transient image; the speed of plasma expansion was estimated from the change in the radius between probes 1 and 2 (delayed by 2.65 ns). The estimated speed as a function of probe 1 delay is shown in Fig. 5 (solid circle data points). Each data point represents a measurement of a different plasma site. All sites were measured at delays up to the peak of the pump pulse before the development of large enough radial cracks that could interfere with the measurement. Some of the transient images captured by probe 1 at earlier delays contained no plasma sites, thus the actual speed is larger than the estimated speed due to uncertainty in the time interval for their expansion. The experimental errors on the plasma expansion speed are estimated to be on the order of 0.5 Km/sec.
The results shown in Fig. 5(a) suggest that the plasma expansion speed is highest during the plasma formation and initial expansion phase (at shorter delays). The linear fit (red solid line) to the experimental data shown in Fig. 5(a) better illustrates this trend. It is interesting to note that the plasma expansion at probe-1 delays between −1.5 ns and 0 ns occurred during exposure to the peak pump pulse intensity; yet, the speed of expansion was lower during this time interval than that for the earlier delays (when the intensity was about half of the peakintensity). This may indicate that the plasma expansion is strongly dependent on the hydrodynamics of the process, not just the laser intensity. To further explore this concept, we also plotted the speed of expansion as a function of the initial radius of the plasma region (as captured in the transient image of probe-1). The data points are shown by green solid circles in Fig. 5(b) while the underlying trend is revealed upon averaging the data in discrete radius bins (2 μm from 0 to 14 μm). The latter is shown by solid squares in Fig. 5(b) –average expansion speed value with error bars of ± 1 standard deviation. The first bin contains all data points for which no plasma was visible in the probe-1 image but was subsequently observed in the probe-2 image; the average speed value in this bin is underestimated (discussed above) and highlighted with a blue solid square and arrow. These results suggest that the speed of plasma expansion is higher for the smaller plasma sites (which are in the early phase of their expansion) than that for the larger sites. This observation supports the above hypothesis on hydrodynamic effects in the plasma expansion process (such as the pressure differential with the surrounding material, the boundary conditions, elastic recoil effects, etc.). We will not further expand the discussion on this issue as it is outside the scope of this work.
3.2. Material ejection
The ejection of material clusters was captured using the side-view geometry and the two probe lasers with 4.5 ns duration (see Fig. 1). Figure 6 shows typical images captured from four different damage growth events. The image shown in Fig. 6(a) was acquired at 500 ns delay and shows the jet of small material clusters having speeds up to about 2.5 km/s. The arrow indicates the position of the air shockwave. The image shown in Fig. 6(b) was acquired at 2 µs delay and captures the onset of removal of large material flakes from the surface. We hypothesize that these flakes are associated with the mechanically damaged material that detaches from the surface due to formation of the radial and circumferential cracks as exemplified in Figs. 4(b) and 4(c). An image acquired at 5 µs delay (Fig. 6(c)) shows the propagation of these larger pieces of material along with numerous particles of smaller size; the jet of ejected material remains well defined. This image also shows that the particles behind the larger material flakes (closer to the surface) are generally smaller while the density of ejected particles starts decreasing. This is a typical observation in our experimental results. The termination of the material ejection process is captured in the image shown in Fig. 6(d) acquired at 25 µs delay. The density of observed ejected particles close to the surface becomes very small although there are still numerous particles near the surface, suggesting that theywere detached from the surface shortly before the image acquisition. This image clearly demonstrates the delayed ejection process that will be discussed in more detail next.
The ability to capture two transient images per event allows to accurately estimate the instantaneous speed of the ejected particles (Vest) along with their estimated average speed (Vavg). The Vavg can be computed as the distance traveled from the sample’s surface divided by the time delay of image acquisition. A more accurate estimate of the instantaneous speed of the particles is given by Vest = (S2− S1) / Δτ, where (S2− S1) is the distance traveled by the particle during the time interval Δτ between the transient image acquisitions. This method was previously used to characterize the kinetic properties of the ejected material following damage initiation on the exit surface of fused silica . Figure 3 in Ref. 19 shows the estimated particle speed, Vest, versus size at various time image acquisition delays (color coded). The analogous schematic for the case of damage growth on the exit surface of fused silica is shown in Fig. 7(a) . Comparison of the speed and size distributions for the case of damage initiation (in Ref 19) and damage growth (Fig. 7(a)) indicates an identical behavior. However, as the damage growth events involve larger volumes of material removed, many more particles were observed in each transient image at all delays (this work). In addition, while the jet seems toterminate at about 5 µs delay in damage initiation, this time is extended to more than ≈20 µs in the case of damage growth. Summarizing the results shown in Fig. 7(a), particles with speeds up to 3 km/s and diameters less than 5 µm are observed in the images at earlier delay times. At later delays, particles with diameter up to ≈30 µm can be observed. Particle speed decreases to ≈100 m/s by around 500 ns delay and continues to further decrease to ≈10 m/s for delays on the order 10-30 µs.
Figure 7(b) shows the ratio of average speed Vave to estimated speed Vest vs. delay time for exit surface damage growth in fused silica. This ratio was introduced in Ref. 19 to quantify the delayed ejection of material clusters during damage initiation. Assuming that there is no deceleration of the particles and that all particles were ejected at t = 0, the ratio should remain close to unity independent of the delay time. Each data point in Fig. 7(b) represents the mean value of this ratio for all particles confined within 200 µm from the surface. Error bars indicate one standard deviation from the mean value within the specified time delay group. The results illustrate that the average value of Vave /Vest is close to 1 for delays up to about 500 ns indicating a low loss of kinetic energy and an ejection time close to zero delay. At 1 µs delay, the particles exhibit a ratio significantly larger than 1 suggesting a strong deceleration effect for this group of particles. As shown in Fig. 6(b), there are larger particles (including material flakes) observed at delays longer than about 1 µs for which interaction with the air can cause significant friction and deceleration. However, at delays longer than about 5 µs, this deceleration effect seems to be countered by a different process as the ratio decreases well below 1. We postulate that this effect arises from a delayed ejection of the observed particles, i.e., not at t = 0. This behavior is identical to the observation for damage initiation (see Fig. 4 in Ref. 19). The data point at 30 µs delay indicated a ratio of about 0.3 which in turn means that these particles were ejected at about 20 µs delay. This is in agreement with the observation of ejected particles being very close to the surface in the image captured at 25 µs delay shown in Fig. 6d.
As discussed above, the ejection of particles is continuous, extending up to tens of microseconds delay, while the speed of the ejected particles decreases with time. Figure 8(a) shows the estimated speed of the particles located up to distance of 200 µm from the surface for each image acquisition delay. The solid squares represent the average values of each data set while the upper and lower bars represent the maximum and lower values measured for each delay. Using the ability of our system to acquire two transient images per event, the ejection time can be estimated by subtracting the ratio of the distance traveled by the particles by their instantaneous speed from the delay time of image acquisition. The ensuing results are shown in Fig. 8(b) where the measured speed of the particles is plotted as a function of theirmean ejection time for each image acquisition delay. The results are plotted on a log-log scale and suggest two distinct regimes. Linear fits through the data in Fig. 8(b) correspond to power law dependencies of particle speed vs. ejection time delay. We observed an initial fast decline of the particle speed with ejection time up to about 100 ns delay while a slower decline is observed thereafter. The power low coefficients for these fits are −1.48 and −0.33 for the early and late ejection time delays, respectively.
The estimation of the ejection time at longer delays is affected by two competing sources of experimental errors. First, the estimation of ejection time is based on the instantaneous speed of the ejected particles at image acquisition delays and does not take into account the loss of speed of these particles in the interim. This effect underestimates the actual ejection delay time. On the other hand, we estimate the ejection time using the distance traveled by the particles from the surface of the optic. However, the particles may originate from the top layer at the bottom of the crater, which is located below the surface. As mentioned earlier, the damage sites were grown to diameters up to about 250 µm. It has been previously shown that the aspect ratio of the crater –diameter to depth ratio (the latter is referring to the bottom of the crater, not the top of the crater considered here)– is larger than about 5 . Thus, the top layer of the crater, even for the larger sites used in this experiment, is not more than 50 µm below the optical surface. Considering the data collected using image acquisition delay of 30 µs, the current estimation of average particle ejection delay time is 22.3 µs with an average particle speed of 0.21 km/s. The average time needed by this group of particles to traverse the maximum crater depth is less than about 2.4 µs. This would lead to a maximum error for this group of data of about 2.4 µs leading to an estimated ejection time of about 20 µs. The absolute value of this error would become increasingly smaller as the speed of the particles increases. It becomes apparent that this effect can only cause a small shift (on the order of 10%) of the estimated ejection delay time as plotted in Fig. 8(b); the offset is caused in part by the error in the actual average speed of the particles which is underestimated using the instantaneous speed at the image acquisition delay.
The identical behavior of material ejection kinetic properties and size distributions in damage initiation and growth discussed above may indicate that these processes are similar; the behavior reflects the same material reaction to the energy deposition (and the accompanying localized high temperatures and pressures) rather than the damage re-initiation process and the size of the absorbing zone, which are both different for damage initiation and damage growth. In both cases, a well-defined jet of ejected material clusters is formed within a narrow cone orthogonal to the surface of the optic. However, the amount of energy deposited and material removed are increasingly higher as the damage site grows. Specifically, while damage initiation sites are typically very small, on the order of 10-30 µm, the growth sites captured in some of our experiments were an order of magnitude larger. Subsequently, the area of plasma formation, and thus the energy deposited, is proportionally different; yet, the experimental results in Fig. 7 indicate that this does not affect the ejected particle speed and size distribution suggesting that the kinetics of the ejected material is not governed by the amount of energy deposited but rather by a different process that is still not well understood.
Figure 9 shows the location of the shockwave formed in the air as a function of delay time. The experimental data (shown as solid circles) span over a wide range of distances traveled for each delay. However, data associated with damage initiation and early growth events consistently define the lower bounds of the data spectrum (shorter distances traveled for each image acquisition delay); the growth events of the larger damage sites (diameter on the order of 150 µm or larger) yield data points associated with longer distances traveled. It must be noted that these measurements represent the maximum distance traveled from the surface (normal to it) as the shockwave expands asymmetrically: the radius of the shockwave along the air-surface interface is approximately 0.6 the distance reported in Fig. 9.
Blue lines in Fig. 9 are fits to the lower (dashed line) and upper (solid line) limits of the data –distance traveled vs. delay time– representing the shockwave propagation during initiation and growth, respectively. We use the fitted curves to estimate the corresponding speed of the shockwave as a function of time, shown in Fig. 9 as the red profiles. These results suggest an initial speed of about 1.2 km/s during a damage initiation event (dashed red line) and remains above the speed of sound during the initial 400 ns of expansion. The speed is much larger during the larger damage growth events (solid red line) starting at about 3.5 km/s and subsequently declining to about 1 km/s at 400 ns delay.
This work presents the first detailed study on the dynamics of the damage growth process in a widely used optical material (fused silica). It is anticipated that the laser parameters affect this behavior in ways difficult to predict in detail due to the fact that underlying mechanisms of how the plasma is formed and how the material reacts to the localized high temperature and pressure remain not well understood. However, there are two main observations that reveal some important basic understanding of the damage growth process in fused silica. The first relates to the structural features of the damage site where the coupling of energy takes place. The second relates to the mechanisms that govern the material ejection process. These two issues will be discussed in more detail next.
The transient images capturing the early material modifications exemplified by Figs. 2 and 3 reveal that the energy deposition takes place in two main locations: a) central “core” region and b) isolated locations at the DSP interface. The first observation may not be surprising as previous work demonstrated plasma formation within the damage core region at much lower fluences than those used in our experiments . Namely, a few, isolated plasma sites form at laser fluences as low as ~2 J/cm2 but do not contribute to any measurable change in the morphology (and size) of the damage site; as the fluence increases, more plasma sites are formed and eventually merge to cover most of the core region at fluences similar to the damage growth threshold fluence (~5-10 J/cm2, depending on the laser pulse duration). The present work not only confirms these observations but also shows that for the experimental conditions used in this experiment, the plasma formation at the “core” region takes place slightly earlier than the formation of isolated plasma sites at the DSP interface (see Fig. 2(b1)). As discussed in the previous section, the exact mechanism of energy coupling leading to plasma formation remains unclear. However, the presence of defects in the “core” region can initiate a cascade increase in the conduction band electron population as discussed in Ref. 21. Previous studies have shown that cracks can give rise to plasma formation and subsequent damage initiation . Furthermore, more recently has been postulated that the presence of defects at cracked surfaces is related with damage initiation . Our results clearly demonstrate initiation of plasma formation at the DSP interface. This may be related to the fact that the DSP interface combines the defects of pure surface states  with the pre-existing population of defects or other types of defect structures known to be present on the as polished optical surface [22, 24]. As a result, the combined defects populations create optically weaker regions, thus promoting plasma formation at relatively low fluences during laser exposure.
The circumferential and radial cracks formed during damage growth are due to stresses that are developed by the pressure pulse following the laser energy deposition. The strength of this pressure pulse with distance depends on the amount of laser energy deposited. As most of the plasma is formed in the central “core” region, the size of the “core” determines the amount of energy deposited and ensuing strength of the stress fields, thus the subsequent number and size of the formed cracks. This in turn determines the distance of the DSP interface from the core region. The amount of energy deposited is also dependent on the laser pulse duration. The plasma is formed before or near the peak of the pump pulse, thus the subsequent energy absorbed by the plasma depends on the duration of the pulse. For shorter pulses, this energy deposition process is considerably shortened and as a result, the number and length of cracks formed is limited. This is demonstrated in Fig. 5(a) of Ref. 7 where the damage site grown under exposure to 1 ns laser pulse exhibits mostly the “core” region modified material. In this case, the damage site will grow incrementally as the inner “core” region expands via the plasma formation, without large cracks and exposed cleaved surfaces. This incremental increase may be associated with the linear growth behavior observed for shorter pulses . On the other hand, as the temporal duration of the laser pulse increases, the amount of cracks formed and their size increases and the DSP interface begins to separate from the core region. This effect is also demonstrated in Fig. 5(b) of Ref. 7 where the damage site grown under exposure to 5 ns laser pulses exhibits a well separated DSP interface from the central “core” region. The plasma formed subsequently at the DSP interface causes a rapid migration of the modified material found in the core region away from the center of the crater; this modified material, under subsequent laser exposure, will generate a large amount of plasma at more distant locations. This additional mechanism of generation and migration of modified material from the “core” region to the periphery increases the rate by which the damage site grows and may represent the underlying mechanism behind the exponential growth reported for longer pulse durations .
As discussed in relation to the results shown in Fig. 8(b), the speed of ejected material clusters vs. ejection time declines faster over the initial ≈100 ns and much slower thereafter. In both cases, a power law dependence is observed with best fit coefficients of −1.48 and −0.33 for the early and late ejection time delays, respectively. The fact that the material ejection process continues for tens of microseconds is rather surprising. It is well understood that the energy deposition yields localized temperatures on the order of 1 eV and pressures on the order of 1-10 GPa; this promotes the formation of superheated material that eventually leads to explosive boiling behavior. This rapid release energy mechanism can account for the ejected particles for delays up to 100 ns. The kinetic energy of each ejected particle depletes the internal energy of the heated material and therefore, the speed of the ejected particles continuously decreases with ejection time. After this initial explosive boiling process, melted material and stress fields are still present within the damage site. This is confirmed by the presence of the modified “core” region in the final damage crater. These conditions continue to generate fractures and mechanically damaged detached particles until a thermal equilibrium is reached. However, the exact mechanism providing the kinetic energy to these particles which continue to be ejected at progressively lower speeds for tens of microseconds is not well understood. We propose that this mechanism is associated with spallation generated by the interaction of stress waves with the remaining melted and mechanically damaged material in the damage site. The origin of the stress waves may be associated with either (a) reflections of the original shockwave formed in the material and/or (b) the recoil action of the optic due to the original compressive stress applied during plasma expansion towards the laser beam (inside the bulk) and subsequent ejection of material via explosive boiling. Additional work is needed to resolve this issue.
It must also be noted that damage outside the DSP interface has been also observed in our experiments exemplified by features indentified with numbered arrows 2 and 4 in Fig. 2. Two similar sites can be observed in Fig. 3. Some of these sites may be attributed to small cracks not clearly visible in our images, thus representing a DSP interface plasma initiation process that is identical to what was discussed above. However, we have also observed debris (small material clusters that were ejected following the preceding damage event on that damage site) to give rise to plasma formation and initiation of a new damage site. Often such debris are located very close to the damage crater and their contribution to the formation of new damage initiation sites can be coupled with the damage growth process. Damage initiation and growth by debris will be addressed in future work.
We thank Michael D. Feit for stimulating discussions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
References and links
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