1. Introduction

Laser-induced damage in transparent optical materials under nanosecond laser excitation arises from the coupling of the laser energy to defects located near the surface or in the bulk of the materials. Significant progress has been made during the past 15 years in understanding these processes via experimental investigations of the dynamics involved, characterization of the resulting material modifications, and modeling the initial steps of the energy deposition process. Above a threshold laser fluence, the defect initiates plasma formation that leads to exposure of the material to localized temperatures of the order of 1 eV and initial pressures up to about 10 GPa. This is followed by the onset of an explosive boiling process that involves ejection of superheated material, the launching of a shock wave, and stresses that result in mechanical damage of the surrounding “cold” material. The dynamics and the ensuing relaxation pathway from exposure of the material to these extreme conditions are typically manifested as a microscopic crater on the surface [1] or a microscopic void formed in the bulk of the material [2], depending on the location of damage initiation.

In contrast, laser-induced damage in absorbing dielectric materials under nanosecond laser pulses has received far less attention. Such absorbing materials are typically used as optical filters to attenuate the laser light for various applications including laser safety, sensor protection, and attenuation of stray laser beams. In addition, nominally transparent optical materials (such as glasses) operating in a high-radiation environment can develop color centers, consequently becoming absorbing at the operational wavelength. Early work was suggestive that nonlinear absorption plays an important part in laser-induced damage in absorbing optical glasses [3] and that damage occurred either at the surface or internally [4]. It was also predicted that, at the center of the focal region of the focused beam, a temperature of 1000°C could be reached after the onset of laser radiation. Absorbing glasses are currently used to attenuate stray light in large-aperture laser systems such as the National Ignition Facility (NIF) (Lawrence Livermore National Laboratory, Livermore, CA). Past studies of the damage morphology of such glasses under relevant excitation conditions indicated a typical “melted-surface” morphology [5]. It was reported, however, that such damage morphology was observed for low fluence, where the calculated surface temperature reached during the laser pulse was well below the melting point of the glass. A more-recent study on the damage morphology as a function of the laser beam size indicated that, with decreased size of the laser beam, the melted-surface damage morphology is changing and the laser beam penetrates through the surface of the glass [6]. The above-mentioned salient results indicate that key issues regarding laser-induced damage in absorbing glasses remain unclear, such as the origin of the increased rate of energy deposition and the change in damage morphology as a function of beam size.

This study was designed to investigate the dominant mechanisms of laser-induced damage in absorbing optical materials under irradiation with 355-nm nanosecond pulses. Various diagnostics tools were employed to enable monitoring of the beam propagation inside the material, to quantify changes in the optical properties of the material, and to capture time-resolved transient material modifications with adequate spatial and temporal resolution. The results suggest that, in addition to linear absorption, excited-state absorption is also a key mechanism contributing to enhanced energy deposition. In addition, there are two competing damage-initiation mechanisms: (1) melting of the material as a result of increased temperature; and (2) self-focusing activated by a transient, fluence-dependent change of the index of refraction. Furthermore, the dominant damage-initiating mechanism depends not only on the material’s electronic and thermophysical properties but also on the laser-excitation conditions.

2. Experimental details

While various absorbing filters were tested as part of this work, detailed results were produced and are presented herein on two materials that exhibited opposing behaviors and are of importance in large-aperture laser systems. The first is the “SuperGrey” glass used on the NIF Laser System (and elsewhere) to absorb stray light at different wavelengths [5] while the second is the Ce³⁺-doped silica glass, which absorbs only in the near-ultraviolet region (also referred to as “blue blocker”) [7]. While SuperGrey glass provides broadband absorption in the visible and near-infrared spectra, the Ce-doped glass provides absorption in the ultraviolet (UV) spectral range and remains transparent in the visible and near-infrared spectral regions. These absorption characteristics of Ce-doped glass enable the utilization of time-resolved microscopy to image transient material modifications using a probe laser operating at 532 nm as a strobe light (which is outside the spectral region exhibiting absorption in this material). In addition, Ce³⁺-doped glass exhibits photoluminescence under UV excitation [7], providing a direct method to monitor the relative changes of the electron population on the first excited state as a function of the excitation conditions. All experiments were performed using ns pulses at 355 or 351 nm (depending on the experimental system used). The corresponding absorption coefficients at 355 nm were ≈10.6 cm^–1 and ≈3.9 cm^–1 for SuperGrey glass and Ce³⁺-doped silica, respectively. The lateral dimensions of the samples were about 50 mm × 50 mm, while the thickness varied from 1 mm to 10 mm, depending on the specific requirements of each experiment. More details will be provided during the description of the experimental results.

The three experimental systems used in this work have been previously discussed in detail elsewhere [7–9]. In short, the first system depicted in Fig. 1(a) was used to monitor beam propagation through various absorbing glasses [7]. The laser beam used was the linearly polarized third-harmonic output of a Nd:YAG laser system having a nearly Gaussian temporal shape with duration at full width at half maximum (FWHM) of about 3.3 ns (at 355 nm). The laser pulse energy and repetition rate were adjustable (computer controlled) as needed for the execution of the experiments. The laser beam was focused using 1-m-focal-length (nominal) lens providing an estimated Rayleigh length of 2 cm at the focal region, while the thickness of the samples varied between 1 mm and 4 mm. An uncoated fused-silica window (1 cm thick) was used to divert part of the output beam to an image-relaying system providing 6.5 × magnification and adjustable focus, so that the beam profile can be imaged onto a charge-coupled–device (CCD) detector at any plane within the sample. An identical fused-silica window was positioned before the sample to provide the image of the beam at the equivalent position to the input surface of the sample using an identical-image relaying system. The two cameras also provide information on the beam energy and spatially resolve the changes of the attenuation of the beam propagating through the sample. The input beam spatial profile had a nearly Gaussian shape with a beam radius at 1/e² of peak intensity of about 48 μm. A fiber connected to a spectrograph (not shown) was also used to record the photoluminescence produced by the sample. The temporal separation between successive pump pulses was 10 s to allow sufficient time for the exposed site to cool before exposure to the next pulse.

 

Fig. 1 Schematic layout of two of the experimental systems used in this work. The pump pulse is at 355 nm having a nearly Gaussian temporal profile with a pulse length (FWHM) of (a) 3.3 ns and (b) 8 ns. CCD: charge-coupled device.

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Figure 1(b) provides a depiction of the second experimental system [8] used for the time-resolved imaging of Ce³⁺-doped silica under excitation with linearly polarized 355-nm pulses. The excitation (pump) laser was a Nd:YAG laser having a nearly Gaussian temporal shape with a FWHM of about 8 ns (at 355 nm). The pump beam was incident at 36° with respect to the normal to the sample’s surface (to avoid intercepting the long-working distance objective used) providing an elliptical exposed area on the sample’s surface having a major axis of about 450 μm and minor axis of about 320 μm. The focal plane of the microscope system is parallel to the surface of the sample, and its position can be adjusted to provide optimal imaging at different planes, including inside the bulk of the sample. Time-resolved imaging is achieved using the output pulses of a Nd:YAG probe laser as strobe-light illumination at 532 nm and 180-ps FWHM pulse duration in the geometry depicted in Fig. 1(b). The temporal separation between successive pump pulses was ~2 min.

The third experimental system was used to damage test absorbing glasses using a large-aperture (1-cm-diam), linearly polarized 351-nm laser beam having a nearly rectangular temporal shape with a duration of ~5 ns and nearly uniform intensity distribution within ± 25% of the average value. A detailed description of this system has been provided elsewhere [9]. Following damage testing, the exposed volume of the sample was imaged using a microscope system having submicron lateral resolution at different depths, starting from the input surface and extending down to 3 mm below the surface in steps of 250 μm. Exposure to a single laser pulse per site was used in this set of experiments.

3. Experimental results

Examination of the damage morphology of various absorbing glasses having thicknesses between 1 mm and 3 mm using the small beam experimental system [depicted in Fig. 1(a)] revealed that typically the damage was observed near or at the exit (output) surface of the samples and not on the input surface. This is rather unexpected since the excitation laser beam is strongly attenuated as it propagates through the material. Using the beam profiling system [depicted in Fig. 1(a)], we observed that damage arises from filaments resulting from self-focusing of the laser beam as it propagates through the sample. A typical example of this behavior is demonstrated in Fig. 2, where the beam intensity profiles along the center of the beam as well as the corresponding image of the spatial beam intensity distribution are shown for a 4-mm-thick SuperGrey glass sample for two different locations (2.3 mm and 4 mm below the input surface; the latter corresponding to the output surface of the sample) and two different input laser fluences (2.5 J/cm² and 8.6 J/cm², respectively). At lower peak fluence (≈2.5 J/cm²), the beam profile remains mostly unchanged at 2.3 mm below the input surface (a1), as suggested from comparison to that of the corresponding image at the input surface of the sample (not shown), but a significant narrowing is observed at the sample’s exit surface (a2). For peak fluence of ≈8.6 J/cm², a significant narrowing of the beam is observed at 2.3 mm below the surface (b1); the effect is further increased at the exit surface location (b2). Although interpretation of the spatial beam intensity distribution inside the material (as captured by the camera) is not straightforward (because of nonlinear propagation of the laser light), these results clearly demonstrate a change in the beam propagation pattern with increasing fluence, leading to a self-focusing behavior.

 

Fig. 2 The intensity cross-section profiles along the center of the laser beam obtained via relay imaging for two input laser (peak) fluences of (a) ≈2.5 J/cm² and (b) ≈8.6 J/cm² at different planes: (1) 2.3 mm below the input surface and (2) the output surface of a 4-mm-thick SuperGrey glass sample, i.e., (a1) and (b1), dotted lines, and (a2) and (b2), solid lines, respectively. The corresponding beam profile images are shown as insets.

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The beam focusing is accompanied by a decrease in the transmittance of the laser beam as a function of laser fluence. This behavior was observed in all samples studied and is exemplified in Fig. 3 for the case of 1-mm-thick Ce³⁺-doped silica. Specifically, Fig. 3 shows the transmittance of the laser beam through the sample, normalized to that at low laser fluence (≈0.5 J/cm²), as a function of peak laser fluence. The data points shown with solid (blue) circles represent measurements while the input laser fluence was increasing, whereas square(red) data points represent the measurement while the fluence was decreasing; in addition, all measurements were performed on the same site of the sample. The complete overlap of these two data sets indicated that there is no permanent change in the material properties, such as changes caused by damage initiation on the input surface. Therefore, this behavior is assigned to the change of the effective absorptivity of the material as a function of laser fluence.

 

Fig. 3 The normalized laser beam transmittance through a 1-mm-thick Ce³⁺-doped silica sample as a function of peak input laser fluence. The data points shown with blue circles and red squares represent measurements on a single site of the sample while the fluence was increasing and decreasing, sequentially. The inset shows the integrated emission normalized to the laser fluence itself as a function of the laser peak fluence.

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The origin of this behavior becomes more evident from the results shown in the inset of Fig. 3, where the integrated emission (after it is normalized to the excitation laser fluence) is plotted as a function of the laser fluence. The normalized emission intensity represents the efficiency of the excitation to produce an electron population in the first excited state. The results suggest that the emission efficiency decreases with increasing fluence in a manner similar to that of the transmittance. Simultaneously, the absorptivity of the material increases with increasing fluence; therefore, more photons are absorbed, which, in turn, produces fluorescence at a lower efficiency. The combination of these two observations suggests that excited-state absorption (ESA) is the underlying mechanism for these behaviors. ESA is associated with absorption of electrons occupying the first (or even higher) excited state. Following ESA, the electrons return to the first excited state via nonradiative relaxation without producing emission through the relaxation process.

To further investigate the characteristics of the transient absorption and the mechanisms that govern the modification of beam propagation through the material, we employed the experimental system shown in Fig. 1(b) using a 1-mm-thick Ce³⁺-doped silica sample. The 355-nm, 8-ns pulses of the excitation (pump) laser produce an excitation volume having a diameter of about 320 μm. Time-resolved images of this volume are acquired by the microscope using the 532-nm, 180-ps probe pulse as a strobe-light illumination source. The image shown in Fig. 4(a) was captured at a delay (measured between the peaks of the pump and probe pulses) of 0 ns (Δτ = 0) with the microscope system focused on the input surface of the sample. The elliptical cross section of the pump beam (having a major axis of about 450 μm and a minor axis of 320 μm, respectively) as it enters the sample at 36° with respect to the normal to the sample’s surface is shown as a guide to the eye. The induced transient absorption is manifested as the area of increased absorption that extends to the left side from the entrance point because of the oblique entry of the pump beam. This experiment yielded a number of notable observations.

 

Fig. 4 The transient response of the transmittance of probe pulse at 532 nm as a function of the delay time from the pump pulse on a 1-mm-thick Ce³⁺-doped silica sample. (a) Transient image using the 180-ps probe pulse as a strobe light for delay of 0 ns. (b) A transient image at delay of 0 ns using pump fluence above damage threshold normalized by the corresponding image at fluence just below damage threshold. The microscope is focused ~0.5 mm below the input surface. (c) The transmittance of the probe beam as a function of delay time.

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First, a spatial variation in the intensity of the propagating probe light is observed. Figure 4(a) shows that the intensity of the probe light varies significantly within the region excited by the pump pulse, exhibiting regions of considerably higher and lower intensities compared to the average intensity of the probe beam propagating within the volume of the material that is not excited by the pump beam. We assign this behavior to the breakup of the probe beam because of the transient modulation of the refractive index by the pump beam. Owing to the attenuation of the pump light as it propagates inside the sample, this effect is stronger at the area (volume) where the pump beam enters the sample.

Next, a similar beam breakup affects the propagation of the pump pulse. This is demonstrated in the normalized image shown in Fig. 4(b) that was acquired at Δτ = 0 with the microscope focused about 0.5 mm below the input surface. The image was captured with a pump fluence about 10% above the damage threshold (it therefore contains one damage site) and was normalized by the image of the same site that was obtained earlier at a fluence about 10% below the damage threshold fluence (with no damage). This normalization process largely removes the transient absorption effect from the image [dark area in image of Fig. 4(a)] and captures only the subtler differences between these images. Three main features are observed in Fig. 4(b): First, we note the modulation of the probe light at the location where the pump beam enters the sample, which is observed with better clarity (separated from the transient absorption) compared to the direct image [Fig. 4(a)]. The second observation is the visualization of a filament damage initiated below the input surface of the sample, observed as a dark feature. This is a result of the absorption of the probe light by the plasma formed at this location. This appears as a horizontal line (out of focus on the left side) because of the 36° angle between the image plane and the direction of the filament (direction of propagation of the pump beam). Finally, additional horizontal features originating from the entrance point of the pump beam are observed. Taking into consideration that the pump-beam profile had an intensity nonuniformity (≈ ± 20% from average), we postulate that this observation is related to the pump beam breakup and formation of self-focusing filaments. Damage was initiated along the path of a filament, as indicated by the image shown in Fig. 4(b).

The decay of the observed transient absorption was investigated by varying the delay (Δτ) between the pump and the probe pulses. The results shown in Fig. 4(c) represent the probe-beam transmittance as a function of delay time measured in the area of the front surface exposed to the 355-nm pump pulse (shown in Fig. 4(a) with the elliptical outline) normalized to the measured value in the absence of the pump pulse. Minimum transmittance was observed during the pump pulse (Δτ < 10 ns), which recovers to about 0.9 within about 100 ns. This relaxation time component (denoted by number 1) is identical to the lifetime of the excited state of the Cr³⁺ ions at room temperature [7]. Since this material is nominally transparent at 532 nm, the results suggest that the origin of this transient absorption at 532 nm (probe) arises from ESA. The results shown in Fig. 4(c) demonstrate that there is a second slower component in the decay of the transient absorption (denoted by number 2), extending the decay to about 10 μs. We attribute this second long-time-constant component to color center formation [7].

Damage-initiation experiments were also performed using the 1-cm-diam, 351-nm laser beam (third experimental) system operating with a pulse duration of ~5 ns (flat in time). The first sample used was a 4-mm-thick SuperGrey glass. Figure 5 provides representative examples of scanning electron microscope (SEM) images at different areas on the sample’s input surface following exposure to a single pulse with fluences of [Figs. 5(a) and 5(b)] 8.9 J/cm², [Figs. 5(c) and 5(d)] 15.8 J/cm², and [Figs. 5(e) and 5(f)] 19 J/cm². Contrary to the observations reported above using the small-beam setup, no filamentary damage was observed in the SuperGrey glass sample using the large-area beam. Instead, the damage appears to be a result of surface melting, similar to that discussed previously [2–6], but there are also characteristic features in each case that indicate the involvement of processes occurring below the surface with typical examples shown in Figs. 5(b), 5(d), and 5(f). These three examples demonstrate the presence of overhangs that have the appearance of deflated microballoons. Such microballoons have been reported to form via laser-induced explosive boiling of polymer solutions [10]. In addition, the areas around these microballoons appear to have been subjected to more melting, often involving the presence of cracks, indicative that excessive heating has been extended below the surface.

 

Fig. 5 SEM images of damage at the input surface of a 4-mm thick SuperGrey glass sample under exposure to the large area beam and fluences of about [(a),(b)] 8.9 J/cm², [(c),(d)] 15.8 J/cm², and [(e),(f)] 19 J/cm².

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The large-beam experiments were also performed using 1-cm-thick Ce³⁺-doped silica, where different areas were exposed to single pulses having an average fluence of about 11, 21, and 32 J/cm², respectively. The entire volume of the sample exposed to the laser beam was subsequently imaged at different depths, starting from the input surface and into the bulkin increments of 250 μm. Figure 6(a) shows the image of a section of the sample that was exposed to a fluence of ≈21 J/cm² at a depth of 1.25 mm below the surface. It shows the presence of numerous filament damage sites having a diameter of about 2 to 3 μm located below the surface. The formation of filaments at this fluence is observed starting from a depth about 0.5 mm and extending to a depth of about 1750 μm. This is demonstrated in the image shown in Fig. 6(b). The highest density of filament damage sites is observed at about 1 mm below the surface, presented as an example in the image shown in Fig. 6(c). Examination of individual filaments reveals that their length is about 750 μm.

 

Fig. 6 Images of filamentation-induced damage in a 1-cm-thick Ce³⁺-doped silica sample at depths of (a) 1.25 mm, (b) 0.5 mm, and (c) 1 mm below the input surface under exposure to a fluence ≈21-J/cm², 351-nm, 5-ns flat in time pulses. (d) The density of filament sites versus depth for laser fluences of about (1) 32 J/cm², (2) 21 J/cm² and (3) 11 J/cm², respectively.

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Figure 6(d) shows the density of observed damage sites in the cross-sectional images [see Figs. 6(a)–6(c)] as a function of the depth (of the image plane) inside the material for three different laser fluences (32 ± 3 J/cm², (2) 21 ± 2.5 J/cm² and (3) 11 ± 1.5 J/cm²). Since each damage site is a filament having an average length of the order of 750 μm, the same filamentary damage site is counted between two and three times in the method described above. However, this method allows one to monitor the depth at which filamentation damage starts and terminates (filaments expand toward the input laser beam, therefore the depth of damage initiation is at the filament maximum depth). The results shown in Fig. 6(d) suggest that the density of damage sites is dependent on the laser fluence. Furthermore, for the higher fluence tested (32 J/cm²), filament damage sites are observed to terminate at a smaller depth (between 250 μm and 500 μm) compared to the other two fluences (11 and 21 J/cm²). As discussed earlier (see Fig. 2), we have observed in our experiment that beam narrowing is occurring at a smaller depth with increasing laser fluence. The results suggest, however, that there is a critical depth (of about 2 mm) beyond which no filamentation damage is observed. We postulate that this is caused by the significant attenuation of the propagating light that becomes too weak to support laser damage.

4. Discussion

Localized absorption of light increases the local temperature, which, in turn, can cause a change of the refractive index. For the case of various glasses, the refractive index increases as a function of temperature until it reaches a critical temperature region (about 500°C for borosilicate glass) and thereafter rapidly decreases [11]. For example, silica exhibits an initial average Δn/ΔT of the order of 1.3 × 10⁻⁵ K^–1 at 355 nm [12] that is attributed to the change of the electronic polarizability of the oxygen ions as a result of the temperature-driven increase of the interionic distance and the strong attraction of the electron cloud of oxygen ions by silicon ions [13]. This change of the index of refraction with temperature is a well-understood problem that can cause wavefront distortions such as in high-average-power laser systems [14]. In the context of this work, the nonuniform distribution of the laser energy can give rise to a variation of the amount of energy absorbed and therefore the local temperature. This in turn would lead to a variation in the refractive index that can support a positive lens and focusing of the beam. However, the experiments considered in this work involve exposure to a single nanosecond pulse with no prior preheating of the material by a preceding pulse. At least part of the absorbed energy by the laser pulse is transferred into the lattice via nonradiative relaxation at time scales of the order of 1 to 10 ps. The ensuing reorganization of the material via thermal expansion will occur in the form of a pressure wave that will exhibit a speed lower than the speed of sound in the material. For example, simulation of pressure induced ionic motion in silica indicated a speed of the pressure front of the order of 2 km/s (2 μm/ns) or less [15]. Since the beam size (the diameter of the volume of the material heated by the laser pulse) in all experiments presented in this work is at least one order of magnitude larger than the distance the expansion wave can traverse during the laser pulse, it is likely that only a fraction (maybe insignificant) of the change of the refractive index caused by heating by the laser pulse would manifest itself during the laser pulse.

The transition of electrons to a higher excited state (via absorption of the laser light) can also trigger transient modulation of the refractive index arising from the difference in the polarizability between the ground and excited states of the impurity ions and even transient defects formed during the excitation process. This can introduce a change (positive or negative) of the refractive index [16]. The relaxation time of this change of the refractive index is the same as the lifetime of the excited state; therefore, it can be much longer than the laser pulse. This mechanism has been studied in the context of optical deformation of laser resonators (mostly in Nd-doped laser systems), ion-doped fibers (mainly Er and Yb doped) for fiber lasers and amplifiers, fiber Bragg gratings, all-optical switching for optical communications, and optical computing applications [17–23]. In addition, defects (such as color centers) or transiently generated defects can introduce a change in the refractive index. For example, it has been reported that defects introduced in the material via exposure to high-energy radiation introduce significant change in the refractive index [24]. Transient defects generated during excitation of phosphate glass to 355-nm laser pulses can also introduce a change in the refractive index [25]. We observed (see Fig. 4(c)) that the relaxation of the transient absorption has a slower component (≈10 μs) that has been attributed to the formation of transient defects. Therefore, it is possible that the transient change of the refractive index can extend beyond the relaxation time of the first excited state as a result of the formation and subsequent decay of transient defect species.

The discussion presented above suggests that the transient change of the refraction index may arise either from the formation of a significant excited-state population or from rapid heating of material resulting from nonradiative relaxation of part of the absorbed energy while both processes occurr concurrently. The spatial variation of the intensity of the laser beam, because of either its small size (such as the gradient along a Gaussian beam profile, as used here in the small-beam experiments) or beam intensity nonuniformities (when using larger beams), introduce gradients in the refractive index that can lead to beam self-focusing and/or beam breakup. Although excited-state absorption causes an additional attenuation of the propagating laser beam, this is not sufficient to limit the self-focusing of the beam and ultimately prevent initiation of laser-induced damage under certain conditions.

The depth of the filamentation damage sites observed in Ce³⁺-doped silica using the large laser beam (see Fig. 6) is similar to that observed using the small laser beam, suggesting that the mechanism is similar in both cases. Using the classical formulation of self-focusing [26], we can assume that absorption of the laser light initiates a gradient of refractive-index change as the beam propagates inside the material. The location of damage initiation is related to the distance traveled inside the material before the filament is developed; therefore, it can be used as a first-order approximation to calculate the induced refractive-index change (Δn). Since the filaments initiate at a depth between 1250 μm and 1750 μm below the input surface, it is estimated that refractive-index change is of the order of 1 × 10⁻³. However, this estimation does not take into consideration the strong attenuation of the laser intensity as the laser pulses propagate inside the material (only the input intensity is assumed). Therefore, we hypothesize that the actual Δn is higher in order to compensate for the declining intensity within the bulk of the sample. In addition, the change of the refractive index evolves during the laser pulse, possibly increasing monotonically as a function of the total energy deposited in the material (thereby increasing the transient temperature and also the excited-state population) during the laser pulse. Future work will focus on better resolving the dominant mechanism of the self-focusing behavior. For example, the dynamics of the change of the refractive index may be investigated by using a probe pulse that trails the pump pulse by an adjustable delay time. The lifetime of the change of the refraction index would be associated either to the lifetime of the first exited state or the thermal diffusion parameters, depending on the dominant mechanism.

The morphology of the damage sites using the small-beam and the large-area laser systems suggest that there are two damage-initiating mechanisms activated during exposure of absorbing materials to nanosecond pulses. The first mechanism is associated with the melting of the material near the input surface resulting from the nonradiative relaxation following laser-energy deposition. This can support heating of the material above melting temperature, which will introduce nonreversible material modifications (damage). This was observed in the SuperGrey absorbing glass only when a larger beam spot was used. We can therefore assume that there is a laser-induced–damage threshold associated with the material surface reaching above melting temperature (LIDT_melt). The second mechanism is associated with self-focusing because of laser-induced transient change of the refractive index. Therefore, a corresponding laser fluence for damage via self-focusing (LIDT_focus) can be assumed in each material (and excitation conditions). The experimentally observed damage behavior of a specific material and excitation conditions is governed by the mechanism with the lowest threshold. As a result, materials with a lower melting temperature will have a reduced LIDT_melt value for the same doping ion (although other material and excitation condition parameters are also important). On the other hand, doping ions with a larger difference in polarizability between the ground and excited states will have a lower LIDT_focus value.

Damage initiation in the Ce³⁺-doped silica samples was associated with self-focusing of the beam for both the small-beam and the large-area-beam experimental systems. The depth of filament damage initiation was also practically identical, at about 1750 μm below the input surface. Filamentation-induced damage was also observed in both cases at laser fluences of the order of about 10 J/cm². In contrast, damage initiation in SuperGrey glass was observed to initiate via filament formation when using a small beam. Melting of the surface was apparent, however, in the case of a larger-area beam. The fluence of damage initiation was also lower for damage with a larger-area beam. The change in the damage mechanism with beam size may arise from the thermomechanical properties of the material and the fact that the peak surface temperature can be a function of the laser spot size. For small beams, the flow of energy (such as via heat diffusion and/or electron transport) reduces the peak temperature, thereby increasing the effective LIDT_melt value. On the other hand, for large beams there is no (or not significant) energy flow, which leads to the generation of higher local temperatures for the same laser fluence. Consequently, a larger beam size promotes a higher localized temperature in the material for the same laser fluence. In materials with similar LIDT_melt and LIDT_focus, exposure to different laser beam spot sizes can lead to different observables because of a change in the governing damage-initiation mechanisms. For similar reasons, the local temperature can be a function of the pulse repetition rate. Such behavior has been documented within previous reports [6]. SuperGrey glass may represent an exemplary case of this behavior. SuperGrey glass has a much lower melting temperature compared to silica (T_g 564°C versus 1530°C), yielding a lower LIDT_melt threshold. Arguably, the damage mechanism in Ce³⁺-doped silica remains via self-focusing as a result of its high LIDT_melt because of its high melting temperature, which can remain above the LIDT_focus independent of the beam size (and perhaps the repetition rate).

5 Conclusion

The objective of this work is to advance understanding regarding the propagation of high-power ultraviolet, nanosecond laser pulses and the ensuing laser-induced damage in absorbing optical materials suitable for applications in high-power, large-aperture laser systems. Two materials, “SuperGrey” glass and Ce³⁺-doped silica glass, that exhibited opposing behaviors and are of importance in large-aperture laser systems were studied as case examples. The results revealed two discrete damage-initiation mechanisms involving (1) melting of the surface resulting from an increase of the local temperature following laser-energy deposition and (2) self-focusing arising from a change of refractive index that supports the formation of a graded-index lens. The localized change of the refractive index is attributed to the change of the electronic polarizability of the materials resulting from either the increase of the local temperature during the laser pulse and/or the formation of a high excited-state(s) electron population. The governing damage-initiation mechanism depends on the thermodynamic properties of the host glass and electronic structure characteristics of the doping ion. It was observed that the governing mechanism can change with laser beam size. This is attributed to the dependence of localized peak temperature and/or excited-state electron population on the dimensions of the beam size.