The influence of the wavelength on the morphology of nanosecond laser-induced damage on the exit surface of fused silica is investigated. A combination between the typical features of damage sites initiated at 1064 nm and 355 nm is observed at 532 nm, including ring patterns sporadically exhibited, in good agreement with calculations of the development of an electron avalanche at this wavelength. The associated ring appearance speed scales as the cube root of the laser intensity, and is ~10.5 km/s while it is ~20 km/s when initiated by infrared pulses. The whole set of results sheds light on the different wavelength-dependent mechanisms governing damage formation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In the nanosecond regime, the laser-induced damage (LID) phenomenon in wide band gap materials is known to be closely related to the existence of precursor defects  of various chemical natures . Contrary to ultrashort laser pulses, the nanosecond pulse duration confers to LID a stochastic aspect and statistical studies have been intensively carried out for decades to measure the damage threshold in a wide variety of materials [3–7]. Such studies provide paramount information about the influence of the laser parameters such as the wavelength  and the pulse duration  on LID. Nevertheless, statistical data are generally insufficient for characterizing the damage dynamics and the underlying mechanisms. In order to overcome this limitation, two strategies have been developed for a more phenomenological approach in fused silica (i.e., the most widely used material in optics). The first one consists of time-resolved measurements thanks to pump-probe experiments for imaging the irradiated sites during the breakdown [10, 11]. However, the destructive and non-repeatable character of LID on a pulse-to-pulse basis inherent to the nanosecond regime complicates the interpretation of the results. Alternatively, the second strategy focuses on post-mortem characterizations of the damage morphology, often highlighting the processes leading to the material breakdown. In that way, Carr et al. have demonstrated the existence of three types of damage sites initiated in the ultraviolet (UV) . Among them, the most frequently observed (referred to as “pansy”) is composed of a complex molten core surrounded by a fractured periphery , evidencing the involvement of thermal and hydrodynamic phenomena in LID processes at 355 nm (3ω), in agreement with time-resolved measurements . On the other hand, we have recently discovered a damage morphology consisting of a ring pattern around a central crater initiated by pulses at 1064 nm (1ω) . The appearance chronology of the rings is tightly correlated to the temporal profile of the pulse which is strongly modulated due to the longitudinal mode beating in the laser cavity. This peculiar morphology, which has been also examined by other groups [15–17] originates from the starting of an electron avalanche favored by the infrared (IR) wavelength, followed by a coupling between the expansion of a plasma in air at ~20 km/s and ablation mechanisms in silica. This scenario confirmed by parametric studies has enabled us to rewind the breakdown movie, bringing valuable information about both the damage incubation and expansion phases [18–20]. Although most of the studies dealing with the damage morphology have been conducted at 1ω as well as at 3ω because of the importance of these wavelengths for inertial confinement fusion applications [21, 22], very few of them compare the morphology of damage sites initiated in the IR and the UV with the same laser source . Moreover, to the best of our knowledge, no similar investigation was carried out for the intermediate visible irradiation at 532 nm (2ω) in fused silica. Examining the damage formation at this wavelength is essential for (i) the fundamental comprehension of the mechanisms involved in the material breakdown from the UV to the IR, and (ii) applications to other transparent materials ranging from the amplification of femtosecond pulses by pumping Ti:sapphire crystals  to contactless corneal ablation .
In the present study, the influence of the wavelength on the laser-induced damage morphology on the exit surface of fused silica is investigated in the nanosecond regime. The LID sites initiated at 2ω may exhibit rings similar to the ones observed at 1ω, and/or a pansy morphology inherent to 3ω pulses. Contrary to the 1ω configuration, the proportion of ring patterned craters produced by 2ω irradiations depends on the laser fluence, in agreement with calculations of the energy acquired by electrons, that make possible or not the development of an electron avalanche process. Finally, we evaluate the appearance speed of the systematic, sporadic and extremely rare rings initiated at 1ω, 2ω and 3ω, respectively. For IR and visible irradiations, this speed scaling as the cube root of the laser intensity is higher than the one of the sound in fused silica (~20 km/s at 1ω, and ~10.5 km/s at 2ω), contrary to the UV configuration (~2.6 km/s at 3ω). The physical mechanisms that may explain the ratio between the speed values measured at 1ω and 2ω are discussed.
2. Experimental design
The experiments have been carried out on 10 mm thick fused silica samples super-polished by SESO company. The damage sites are initiated on the exit surface of the sample at normal incidence in ambient air by one single laser pulse delivered by the laser facility detailed in . Briefly, this facility relying on a tripled Nd:YAG laser can be operated at 1ω, 2ω or 3ω. Dichroic mirrors ensure that the sample is irradiated only at one single wavelength. The pulse duration is about 6.0 ± 0.5 ns, and the temporal intensity profile of the pulse in the multiple longitudinal modes (MLM) configuration is systematically recorded by a high-bandwidth (33 GHz) oscilloscope (Tektronix, DSA73304D) connected to a fast photodiode (25 GHz bandwidth at 1ω and 2ω, and 15 GHz at 3ω) which collects the light transmitted through a dielectric mirror. Because of the longitudinal mode beating in the laser cavity, these profiles exhibit strong modulations (called spikes) which are erratically distributed in a Gaussian envelope [14, 23]. This non-repeatable character of the MLM pulses is shown in Fig. 1 where the intensity profile of two different pulses at 2ω is displayed as a function of time. The beam is focused on the sample by means of a lens whose focal length is 4 m. At the focus, the beam is Gaussian-shaped and the diameter at 1/e systematically measured for each pulse with a CCD camera is ~700 µm, ~550 µm and ~450 µm at 1ω, 2ω and 3ω, respectively. At each wavelength, the confocal parameter is much larger than the sample thickness, ensuring that the beam is constant along its propagation through the sample. The energy is adjusted at the focus by means of a half-wave plate and a polarizer. The maximum fluence that can be reached is 120 ± 5 J/cm2 at 1ω, 135 ± 5 J/cm2 at 2ω, and 50 ± 5 J/cm2 at 3ω. In order to determine if a test site is damaged or not, images recorded in situ under white light illumination by means of a long focal microscope connected to a CCD camera, are compared before and after the laser pulse. A site is considered as damaged if the images are different. These conclusions are confirmed by post-mortem inspections employing Nomarski Interference Contrast (NIC) microscopy which also enables us to characterize the damage morphology with a better resolution.
Prior to the investigation of the impact of the wavelength on the damage morphology, we experimentally establish the fluence ranges where damage can be initiated at each wavelength. For this purpose, we have measured the surface damage density  over three orders of magnitude, where is the damage probability (i.e., the ratio between the number of damage sites and the total tested sites at a given fluence), and is the Gaussian beam equivalent area given at 1/e. High values (i.e., cm−2) have been obtained following the 1-on-1 procedure (ISO Standard 21254-1:2011), whereas the rasterscan procedure  has been employed for measuring low values (i.e., cm−2). The evolution of as a function of the fluence is shown in Fig. 2 at 1ω, 2ω and 3ω. As expected, at every wavelength, the damage density increases with the laser fluence. Furthermore, at a same fluence, more damage is initiated at the shortest wavelengths. This result is consistent with similar studies conducted in potassium dihydrogen phosphate crystals and their deuterated analogs, where the damage threshold decreases when the photon energy increases [8, 26]. As emphasized in Fig. 2, this behavior is also observed on the exit surface of fused silica. This suggests that the mechanisms responsible for the incubation phase of LID preceding the expansion one  depend on the wavelength. In the following experiments where the damage expansion phase is studied, we choose to work in fluence ranges where the damage density is higher than cm−2 at the three wavelengths according to Fig. 2.
As an overview of the dependence of the damage morphology on the laser wavelength, NIC micrographs of typical multi-pit damage sites initiated by single pulses in these fluence ranges are displayed in Fig. 3 at 1ω, 2ω and 3ω. At the IR wavelength, the LID sites systematically exhibit concentric rings originating from the expansion of a plasma in air driven by the intensity spikes of the laser pulses . On the other hand, the wide majority of the damage sites initiated at 3ω exhibits a pansy morphology [12, 13], highlighting the role of thermo-mechanical phenomena in the vicinity of subsurface precursor defects. Concerning LID initiated at the visible wavelength, the striking feature is the presence of the two aforementioned morphologies. Indeed, most of the craters initiated at 2ω are very similar to these initiated at 3ω. Nevertheless, one of the craters in Fig. 3 shows a ring pattern analogous to these initiated at 1ω. It is worth noting that the diameter of the rings initiated at 2ω is about half as large as the one produced at 1ω. At 2ω, the combination of the typical damage morphologies initiated in the IR and in the UV suggests a competition between the formation of a shock wave provoked in air at 1ω  on the one hand, and the hydrodynamic phenomena observed in fused silica at 3ω on the other hand  (this will be discussed below).
This assumption is all the more supported by the NIC image of a singular damage site also initiated at 2ω shown in Fig. 4. Three typical features of the pansy morphology initiated at 3ω are observed: (i) the molten and fractured material (dark area indicated by a white arrow), (ii) the large chips (yellow arrow), and (iii) the subsurface cracks (green arrow). All these elements emphasize the involvement of thermal and hydrodynamic phenomena in LID at 2ω. One may also distinguish concentric rings (red arrow) characteristic of the morphology of damage initiated at 1ω which have been partially hidden by the previously described features. Thereby, this mixed-morphology in Fig. 4 illustrates that at 2ω, even on the same crater, a competition occurs between thermo-mechanical phenomena and the processes leading to ring formation. Comparing the timescale of these mechanisms, since the ring patterns are formed during the laser pulse  while thermal and structural events mainly occur after , the rings in Fig. 4 have been erased by the subsequent thermal diffusion and also by the flaking of the material.
The complex morphology of LID sites at 2ω has led us to conduct a statistical analysis of the presence of rings at this wavelength. The results of this study are shown in Fig. 5, where the evolution of the proportion of ring patterned craters retrieved after post-mortem observations is displayed as a function of the surface damage density at 2ω established in Fig. 2 at various fluences. At the lowest fluences, the ring patterns are rarely observed (~12% of the total craters at 90.3 J/cm2), meaning that the predominant morphology of the craters is the pansy one. However, the proportion of ring patterned craters increases with respect to the laser fluence as the surface damage density does. At high fluences where numerous damage sites are detected, ~38% of the craters exhibit a ring pattern. Thereby, from these results, we deduce that the occurrence of rings at 2ω is closely linked to the laser fluence, contrary to the 1ω configuration where this feature is always observed, independently of the fluence. Finally, one may note that, as shown in [18–20], the diameter of the ring patterned damage sites initiated at 1ω strongly differs from one site to another, even initiated by an identical fluence. This is a direct consequence of the link between the LID phenomenon in the nanosecond regime and the randomly distributed precursor defects , implying that the time when the laser-produced plasma is ejected in air may vary from one site to another. A similar dispersion has been observed for LID initiated at 2ω. The diameter of the ring patterned damage sites ranges from ~120 µm to ~300 µm for the LID sites initiated at 1ω, while it does from ~50 µm to ~160 µm for these initiated at 2ω in the selected fluence ranges.
As previously shown, it is possible to correlate the ring patterns initiated at 1ω with the intensity spikes in the temporal profile of the initiating pulses . By dividing the distance between two consecutive rings by the duration between the two corresponding spikes, one can evaluate the ring appearance speed. By repeating this process for all the rings and spikes, we found that this speed (i) scales as the cube root of the laser intensity, and (ii) is around 20 km/s. Such a speed value, more than three times higher than the one of sound in fused silica, cannot originate from any well-known hydrodynamic process supported by fused silica. This phenomenon has been attributed to the development of an electron avalanche leading to the displacement of an ionization front due to the formation of a laser-supported detonation (LSD) wave in air, simultaneously with ablation mechanisms. It is important to distinguish the LSD wave propagating in air which is a particular type of shock wave described in , and the other mechanical waves propagating in fused silica. This theoretical scenario was subsequently validated by experiments at various angles of incidence , and in vacuum .
In order to interpret the dependence of the occurrence of the ring patterns with respect to the laser fluence at 2ω exhibited in Fig. 5, we evaluate the possible formation of such a LSD wave surrounding the plasma ejected in air through open cracks, similarly to the considerations at 1ω. This mechanism can be provoked by an electron avalanche in air, which can take place if the free electron energy reaches the ionization energy of the neutral species in this medium mostly composed of N2 and O2 molecules. The rate of increase of depends on the ponderomotive energy as well as the elastic collisions with neutrals, and reads :29], respectively, and is the electron speed. The evolution of as a function of time is displayed in Fig. 6 at 1ω, 2ω and 3ω, for the minimum and the maximum fluences in the same ranges previously selected (i.e., cm−2 according to Fig. 2). These calculations give the evolution of the energy for a single electron in air at normal temperature and pressure, under the action of the alternating electric field of a light wave. In all the configurations, the electron energy increases with time until the elastic collisions become too important and decrease it. It must be emphasized that Eq. (1) do not account for energy losses due to the absorption of the laser flux by a defect, implying that the energy levels calculated in Fig. 6 overestimate the ones in the experiments. Nevertheless, this approximation is reasonable for examining if the energy of the free electrons can at least reach the ionization energy of neutral species in air (~12 eV). The calculations at 1ω show that this energy of ~12 eV is easily reached even at the lowest fluences close to the damage threshold, meaning that an electron avalanche always develops in the experiments at this wavelength. This phenomenon followed by the formation of a LSD wave driving the expansion of the plasma, and also by the activation of the surface by free electrons enabling the ablation processes driven by the intensity spikes leads to the appearance of rings . This activation mechanism consists of a bombardment of the surface by the free electrons in the plasma formed in air. The inelastic collisions of these electrons with the ones in the fused silica lattice lead to the production of secondary electrons which are subsequently heated by the light wave, resulting in an electron avalanche which starts in fused silica, and thus a strong energy deposition. Hence, the calculations at 1ω in Fig. 6 explain the systematic appearance of rings in the experiments at this wavelength. Conversely, the electron energy remains below 12 eV at 3ω even at the highest fluences, implying that no rings of the same nature as the ones observed at 1ω can be observed at this wavelength, in agreement with the experiments. Interestingly, the ionization energy of neutral species in air can either be reached or not at 2ω depending on the fluence. This partly explains the results in Fig. 5 where the proportion of ring patterned craters increases with the fluence. However, the stochastic character of the ring appearance at this wavelength can only be interpreted accounting for the different absorptivity of the precursor defects. Indeed, as shown in  as well as in Fig. 3, different damage sites even initiated by the same laser pulse may exhibit different number of rings, meaning that the duration of the damage incubation phase varies from one precursor defect to another. The associated incubation fluence (i.e., the one which is necessary for initiating damage) is thereby defect-dependent . One may note that in the calculations in Fig. 6, a Gaussian pulse which is much steadier than the experimental MLM ones has been used. However, additional simulations (not shown here) implementing the experimentally measured pulses reveal very similar results for various MLM pulses, and only slight modulations of the curves which do not change our main conclusions about the wavelength dependence of the starting of an electron avalanche.
Similarly to the 1ω configuration, one can associate the ring appearance speed at 2ω and the one of the LSD wave . According to a model relying on hydrodynamics, this speed is proportional to the cube root of the laser intensity . Thereby, the distance covered by the plasma from the center of the rings can be expressed as:Fig. 7 the intensity profiles as a function of the distance with the ring pattern of the corresponding damage sites initiated at (a) 1ω and (b) 2ω. The parameter is automatically fixed by the relative position of the intensity spikes. The striking feature in Fig. 7 is that every ring is closely associated with a spike, which is very consistent with the assumption that the observed rings constitute footprints of the plasma dynamics in air. At both wavelengths, the experimentally measured LSD wave speed scales as the cube root of the laser intensity, as predicted by the wavelength-independent model in . The value of deduced from Fig. 7 is 21 km/s and 8.8 km/s at 1ω and 2ω, respectively. By repeating this method on different damage sites, the average LSD wave speed value is found to be around 20 km/s and 10.5 km/s at 1ω and 2ω, respectively. These speed values are both much greater than the speed of sound in fused silica (~6 km/s), confirming that the ring patterns initiated by IR and visible radiation are not caused by hydrodynamic processes in silica and likely originate from an electron avalanche process leading to the expansion of the laser-produced plasma as shown in Fig. 6. The speed obtained at 2ω is about half as much as the one found at 1ω, which is consistent with the size difference of the ring patterns produced at each wavelength as shown in Fig. 3. Finally, one should note that the speed of 20 km/s at 1ω was also measured in  employing another similar laser source, highlighting the universal character and the reproducibility of the ring phenomenon at this wavelength. Since the 1ω beam diameter at 1/e in  is ~1.5 mm while in the present study it is ~700 µm, we also conclude that, contrary to the temporal profile, the spatial one has no effect on the ring phenomenon.
The hydrodynamic theory described in  does not predict this dependence of the LSD wave speed on the laser wavelength. This is a consequence of the assumption that the laser beam is totally absorbed in the passage of the shock discontinuity. In order to take into account the influence of the laser wavelength, modeling should consider the local energy deposit in the layer separating plasma and cold gas regions. Although such an approach is beyond the scope of the present study, the impact of the laser wavelength on hydrodynamics can be analyzed on the basis of simple considerations. Noting that the unknowns of hydrodynamic equations are functions of the energy deposit, the LSD wave speed can be written as:30], for a plasma in which the optical index is very close to 1, the absorption coefficient reads:Eq. (1), obtained on the basis of a thermal electron velocity distribution. Let us indicate by means of subscripts 1 and 2 the parameters relative to the laser frequencies 1ω and 2ω, respectively. For the same laser intensity at 1ω and 2ω, the ones which are effectively absorbed are in the ratio of:Fig. 7 showing that .
Although most of the damage sites initiated at 3ω show a pansy morphology, irregular concentric rings at the micrometer-scale can be rarely observed at this wavelength (~2% of the observed craters) when the laser fluence is near the damage threshold of a precursor defect. This peculiar morphology has been observed in  (see Fig. 9, site “t” in this reference) for damage sites irradiated far away from the spatial peak of a Gaussian beam. However, the low number and the small size of the rings make difficult the correlation between these patterns and the erratically distributed intensity spikes of the MLM laser pulses. In order to circumvent this limitation, we have employed phase modulated laser pulses of ~7.0 ns duration which are generated by the tripled Nd:YAG laser source described in  based on the same technology as the one used for all the other results obtained in the present study. As shown in Fig. 8, the pulses show temporal spikes regularly spaced with 540 ps, as a consequence of the few longitudinal modes existing in the laser cavity. This configuration between the purely MLM and the SLM ones thus enables us to easily match the intensity spikes with the associated rings observed in (b). This correspondence allows us to estimate a ring appearance speed of ~2.6 km/s. One may note that we have assumed that the most intense spike marks the beginning of the damage expansion [i.e., this spike corresponds to the time in Eq. (2)], which is not necessarily the case. However thanks to the regular temporal spacing between the spikes, the evaluated ring appearance speed will not change with respect to the chosen spike for expansion starting. This speed at 3ω is lower than the one of sound in fused silica, unlike the supersonic ones measured at 1ω and 2ω. Moreover, the value of 2.6 km/s is very consistent with the expansion speed directly measured optically by Demos et al. . As demonstrated by Carr et al. , LID at 3ω is provoked by the expansion of an absorption front in fused silica upstream toward the laser flux, while at 1ω this absorption front expands in air. Therefore, we conclude that the ring patterns rarely produced at 3ω do not originate from the same mechanisms as the ones governing LID at 1ω and 2ω, in accordance with the calculations shown in Fig. 6 where the UV wavelength is not able to trigger an electron avalanche.
Finally, the main results obtained in this study at the three tested wavelengths are recapitulated in Table 1.
To summarize, investigations of the influence of the wavelength on nanosecond laser-induced damage morphology on the exit surface of fused silica have been carried out in a multiple longitudinal modes (MLM) configuration. The damage morphology at 532 nm (2ω) is a combination between the one at 355 nm (3ω, where thermo-mechanical phenomena are predominant) and at 1064 nm (1ω, where the defect-produced plasma expanding in air leads to the formation of rings). The ring patterned craters represent 10% to 40% of the total ones initiated ones at 2ω, and increases with the laser fluence. This is very consistent with calculations of the possible development of an electron avalanche at this wavelength, which is the prerequisite for the expansion of a plasma in air thanks to a LSD wave. At 2ω as well as at 1ω, the speed of this wave scales as the cube root of the laser intensity, in agreement with theoretical analyses. This speed is evaluated to be ~10.5 km/s at 2ω, i.e., about half as much as at 1ω. The origin of this difference is likely related to the much stronger energy deposit in the IR than in the visible domain, as suggested by the Drude model describing the plasma absorption coefficient. The comparison of damage initiated at various wavelengths reported in this study makes possible to discriminate the fundamental wavelength-dependent mechanisms leading LID in fused silica, thus bringing crucial information for high-power laser facilities.
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