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Influence of vacuum on nanosecond laser-induced surface damage morphology in fused silica at 1064 nm
Applied Surface Science 362 (2016) 290–296
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Influence of vacuum on nanosecond laser-induced surface damage morphology in fused silica at 1064 nm R. Diaz a,b,∗ , M. Chambonneau a,b , P. Grua a , J.-L. Rullier a , J.-Y. Natoli b , L. Lamaignère a a b
CEA CESTA, 15 Avenue des Sablières, 33116 Le Barp Cedex, France Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, UMR 7249, 13013 Marseille, France
a r t i c l e
i n f o
Article history: Received 3 August 2015 Received in revised form 13 October 2015 Accepted 20 November 2015 Available online 2 December 2015 Keywords: Laser-induced surface damage Vacuum environment Fused silica Energy deposition
a b s t r a c t The influence of vacuum on nanosecond laser-induced damage at the exit surface of fused silica components is investigated at 1064 nm. In the present study, as previously observed in air, ring patterns surrounding laser-induced damage sites are systematically observed on a plane surface when initiated by multiple longitudinal modes laser pulses. Compared to air, the printed pattern is clearly more concentrated. The obtained correlation between the damage morphology and the temporal structure of the pulses suggests a laser-driven ablation mechanism resulting in a thorough imprint of energy deposit. The ablation process is assumed to be subsequent to an activation of the surface by hot electrons related to the diffusive expansion of a plasma formed from silica. This interpretation is strongly reinforced with additional experiments performed on an optical grating in vacuum on which damage sites do not show any ring pattern. Qualitatively, in vacuum, the intensity-dependent ring appearance speed V ∝ I1/2 is shown to be different than in air where V ∝ I1/3 . This demonstrates that the mechanisms of formation of ring patterns are different in vacuum than in air. Moreover, the mechanism responsible of the propagation of the activation front in vacuum is shown to be outdone when experiments are performed in air. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Laser-dielectric interaction in vacuum environments has been investigated for several years [1,2]. The observed differences of nanosecond laser-induced damage (LID) between atmospheric and vacuum environments have been studied [3–6]. In this context, LID in fused silica remains a major issue, since it is one of the most widely used optical materials. In the past decades, LID at surfaces of transparent dielectrics has been shown to arise from subsurface defects absorbing the incident laser flux [7]. This interaction results in a surface plasma leading to the formation of a damage site [8]. More recently, studies performed in air environment have shown the growing interest in working with Multiple Longitudinal Modes (MLM) pulses [9–11]. This kind of pulses correlated to the damage morphology can provide a powerful tool to access the chronology of the damage mechanisms from incubation to expansion in the near infrared domain [12,13]. Therefore, we propose to transpose this experimental study so as to investigate LID formation in vacuum environment.
In the present work, ring patterns are systematically observed on damage sites initiated with single MLM pulses at 1064 nm in vacuum on plane surfaces. The removal of material due to an ablation process is subsequent to the activation of the silica surface provided by the diffusive expansion of the plasma at the vicinity of the surface. This hypothesis is confronted to additional experiments performed in vacuum on an optical grating etched in fused silica in order to study the influence of the surface state. The periodical structure of the grating is shown to inhibit the expansion of this plasma; this suggests that the expansion process likely takes place along the sample surface. A model based on a diffusive process related with thermal conduction is thus proposed to interpret such behavior. As a conclusion, a direct comparison is made between LID formation in air and vacuum environments so as to emphasize the differences between the mechanisms responsible for the ring patterns formation. Thanks to our analysis, the estimation of the diameter of a damage site is possible for both environments with the knowledge of the fluence that feeds the mechanism of expansion of the ring pattern. 2. Experimental investigations of the influence of vacuum on LID morphologies
∗ Corresponding author at: Commissariat à l’Energie Atomique, Départements des Lasers de Puissance, 15 avenue des sablières, 33116 Le Barp, Gironde, France. E-mail address: [email protected] (R. Diaz). http://dx.doi.org/10.1016/j.apsusc.2015.11.199 0169-4332/© 2015 Elsevier B.V. All rights reserved.
The laser facility described in Ref. [14] is used at 1064 nm both in Single Longitudinal Mode (SLM) and MLM regimes to perform this
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Fig. 2. Correlation between the morphology of a damage site initiated at the rear surface of a fused silica sample in vacuum and the temporal profile of the corresponding MLM pulse. Fig. 1. NIC images of typical damage sites obtained in air and vacuum environments for both SLM and MLM configurations. The fluence of the four shots is 110 J/cm2 . The scale of the images in vacuum is twice smaller than the scale of the images in air.
study. In the SLM regime, the pulse equivalent duration, defined as the ratio of the energy over the peak power, is 9 ns. The sample is positioned in the focal plane where the spot is Gaussian-shaped and 1 mm in diameter at 1/e. The Rayleigh range of the beam is much longer than the sample thickness. In the MLM regime, the random spectral fluctuations induced by longitudinal mode beating in the laser cavity result in a strong variation of the positions and magnitudes of the spikes in the intensity profiles from pulse to pulse. Therefore, the intensity profiles are recorded for each laser shot with a 25 GHz bandwidth photodiode and a 33 GHz bandwidth oscilloscope (Tektronix DSA73304D). Experiments are performed on fused silica samples of 10 mm thickness that exhibit plane superpolished surfaces. The samples are used as a window for the vacuum chamber in which the test will be performed. The front surface is in air environment whereas the rear surface is in vacuum environment. A turbo-molecular pump permits to reach a pressure level of 10−5 mbar. Each damage site was initiated by a single laser pulse at 1064 nm. Since the beam is collimated during the propagation in the sample, LID systematically occurs on the rear surface. All samples are illuminated during the first hour of their exposition to vacuum even though it might not play a role in our single shot experiments. For both SLM and MLM regimes, the largest damage sites show very similar sizes despite strongly different morphologies. Nomarski Interference Contrast (NIC) micrographs of these damage sites obtained in vacuum are shown in Fig. 1, together with equivalent damage achieved in air environment. The fluences of the shots that initiated the damage sites are 110 J/cm2 in all cases. In both SLM and MLM configurations, the damage sizes are reduced by more than a factor of two once the surrounding air is removed. Thus, the scales are multiplied by a factor of two between the images in air and in vacuum. These observations suggest that the environment strongly influences the damage expansion speed. Moreover, the presence of a ring pattern is again systematically obtained in the MLM configuration in vacuum environment. Each ring pattern observed on damage sites in the case of MLM pulses is closely associated with intensity spikes. As in air environment, we match space and time scales thereby making possible
Fig. 3. Instantaneous ring appearance speed as a function of short-time-average laser intensity for three sites initiated in vacuum by three different MLM pulses. The curves stand for the fits of corresponding data.
the evaluation of ring appearance speed [12]. In Fig. 2, a damage site obtained in vacuum environment is shown with the associated intensity profile of the MLM pulse. The white dashed arrows exhibit the correspondence between spikes and rings showing that inner rings appear before outer ones. The red arrow indicates the time t0 (set to zero on the time scale), associated to the beginning of the formation of the rings. The time t0 is unique by definition and cannot be shifted to another peak. The dilatation as well as the matching of the temporal profile with the rings is also unique. This matching allows us to precisely define the instantaneous ring appearance speed as the ratio of the distance between two successive rings to the time interval separating the two adjacent temporal spikes. Although most intensity spikes can be matched with rings, some dispersion in speed measurement is observed, meaning that ring appearance speed is not constant throughout the pulse. For each speed measurement, we calculate the short-time-average intensity which corresponds to the averaged intensity over the time between the two adjacent spikes (e.g. white dashed arrows in Fig. 2) used to calculate the ring appearance speed. As an example, we have reported in Fig. 3 the ring appearance speed V as a function of short-time-average laser intensity I for three damage sites. The three sites in Fig. 3 show very similar
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Fig. 4. Schematic representation of the optical grating used in the experiments.
Fig. 6. Damage site initiated in air environment with a single MLM pulse at the surface of the fused silica optical grating. The correspondences between ring patterns and intensity profiles as functions of the distance (in red) are shown. The time t0 corresponds to the creation of the surface plasma at the center of the damage site (red arrow); black dashed arrows indicate the spike-ring associations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. NIC images of damage sites initiated with MLM pulses in vacuum environment at 10−5 mbar on the plane surface (a) and on the optical grating (b) for fluences of 65 J/cm2 and 55 J/cm2 , respectively.
results. In order to fit the experimental data a power law V = aIb is proposed, where a and b are fitting parameters. This choice makes possible to impose V = 0 for I = 0. Similar measurements have been carried out on twelve distinct damage sites initiated in vacuum by different MLM pulses and the mean ring appearance speed reads:
V [km/s] = 2.75 I GW/cm2
1/2
.
The ring appearance speed reaches up to 12 km/s. This value is greater than the speed of sound in fused silica (5.9 km/s). The assumed mechanism responsible for the ring pattern formation is linked to the development of a plasma generated by subsurface defects in fused silica and ejected toward vacuum. Classical hydrodynamic processes involved in interaction of lasers with solid materials at intensity levels corresponding to our experiments do not yield such speed values. When air is present, it brings an auxiliary medium able to support plasma expansion speeds in the relevant range. In vacuum, a particular configuration is likely implicated in the generation of a plasma confined at the vicinity of the surface, which is supposed to be “crawling” on the surface of the sample. In order to verify this hypothesis we have studied the influence of the surface state on the expansion of the ring patterns. In order to illustrate this point, we have tested a specific sample of 10 mm thickness which exit surface is an optical grating, made of periodical pillars of 710 nm height and 140 nm width with a regular spacing of 410 nm. The Rayleigh range is always much larger than the sample thickness. This vertical periodical structure, schematically represented in Fig. 4, is supposed to inhibit the expansion of the “crawling” plasma along the surface. In Fig. 5, an example of NIC images of damage sites initiated on both the plane surface and the optical grating in vacuum environment with 1ω MLM pulses are displayed. The fluence of the shots is 65 J/cm2 for the damage site of Fig. 5(a) and 55 J/cm2 for the one of Fig. 5(b) and makes it possible the comparison of the morphologies. A systematic ring-pattern is obtained on damage sites on the
exit surface of the plane surface (Fig. 5(a)) whereas a more fractured damage site without rings is always obtained on the exit surface of the optical grating (Fig. 5(b)). Thus, a major difference of morphology is observed between the damage sites initiated on the optical grating and the plane surface. Several shots at different fluences were performed on each sample and these observations are independent of the laser fluence. The imprinting of the rings in vacuum never takes place on the surface of the optical grating. In this case, the periodical structure at the surface manifestly prevents the expansion of the “crawling plasma”, as assumed earlier. In order to make sure the periodical structure is responsible for the inhibition of the “crawling plasma” expansion in vacuum, additional experiments are performed in air to verify that the formation of a ring pattern still takes place. Thus, the damage sites initiated in air on the surface of the optical grating are compared to those obtained in air on the plane surface. The NIC image of a typical damage sites initiated in air on the exit surface the optical grating is presented in Fig. 6 with the temporal profiles of the MLM pulse that initiated it. In order to verify that the ring appearance speed of a damage site follows the same law on both surfaces in air environment, the formation starting time of the rings t0 and the matching of the rings with intensity spikes have been determined for the damage site of Fig. 6. Then, the instantaneous ring appearance speeds V is supposed to follow the same power law in the ring patterns initiated in air expressed according to Refs. [12,13]:
V [km/s] = 9.3 I GW/cm2
1/3
.
This assumption is directly confronted to the NIC image as we have expressed the laser intensity as a function of the distance for the MLM pulse that initiated the damage sites in Fig. 6. This distance t is written r (t) = t V () d, where the speed V () is taken from 0
the previous relation. Thus, we are able to construct an intensity profile depending on r to be confronted to the NIC image. The good correlation between intensity spikes and the corresponding rings obviously suggests that in air environment, the phase of expansion leading to the formation of the ring pattern does neither depend on the sample surface state nor the type of precursor defect involved, as long as a plasma is generated. As a consequence, the change
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in morphologies obtained in vacuum between the damage sites initiated on the plane surface and those obtained on the optical grating (cf. Fig. 5) can be attributed to the influence of the pillars on the expansion of the “crawling plasma”.
extends beyond the plasma zone (orange toward green area in silica). The zone which becomes absorbent follows a lateral expansion due to electron heat conduction. In addition the plasma is kept hot due to the laser irradiation (variable dashed red lines), and also fed by the initial surface emission (black arrows). In zone 3, the silica surface is heated and an absorption front moves upstream the laser flux (orange area), deeply inside the material, leading to an ablation process (black arrows) similar to mechanisms involved in the technique of laser backside etching [17,18]. Each intensity spike illuminating the absorbent surface will then contribute to ablate the material and form a ring pattern, since the absorption front can start from silica surface only once it has been activated by hot electrons. The mechanisms described above can only take place when the laser flux is high enough to produce an electron avalanche in the medium that expands in vacuum leading to the creation of a strongly ionized plasma. As reported in Ref. [16], when the ionization degree is still low, the energy level of prime electrons cannot exceed the following value, depending on the laser wavelength and on the laser intensity I:
3. Interpretations
Em [eV] ≈ 4.9( [m]) I GW/cm2
Fig. 7. Schematic illustration of a ring pattern forming for silica interfacing with vacuum.
The hypothesis that a “crawling plasma” could be responsible for the activation of material in vacuum environment, and thus for the imprint of the ring patterns, has been strongly reinforced by experiments involving gratings on the exit surface of optical components. Indeed, in this case, the morphology of the damage sites is completely different from the ones observed on a regular surface and does not show any ring pattern in vacuum. Moreover, when ring patterns are obtained on the plane surface in both environments, measurements have shown different scaling of the speed V with respect to laser intensity: V ∝ I1/3 for experiments conducted in air [12,13] and V ∝ I1/2 in vacuum (Fig. 3). The behavior observed in air was attributed to the displacement of an ionization front in the surrounding gas, and a simple hydrodynamic model including the perfect gas approximation has given consistent results for both qualitative and quantitative points of view [9]. A similar hydrodynamic process, inducing an ionization front propagating within the solid material, may occur in experiments performed in vacuum environment. It can be shown that a V ∝ I1/2 scaling is obtained in fused silica with the appropriate choice of equation of state of this material, mainly built on the basis of potential energy and elastic pressure contributions [15,16]. However, although the dependency of speed with respect to laser intensity qualitatively corresponds to experiments, the quantitative results given by this kind of hydrodynamic model for the dense material are out of experimental range (typically lower than 2 km/s). Thus, this is not consistent with the experimental results displayed in Fig. 3. Therefore, any hydrodynamic process occurring in the dense material is not considered here. In that matter, the expansion processes of a high temperature region around the point of damage initiation involving the speeding up of the material must be ruled out. A sine qua non condition is that free electrons may be created in the region of silica expanding toward vacuum, and may participate in the activation of the material surface by thermal conduction. It is this assumption, which will be retained and the corresponding mechanism of silica surface activation is schematically described in Fig. 7. Three different zones are distinguished to describe the mechanisms responsible for the ring pattern formation. In zone 1, the exit surface is transparent because it has not yet been activated by hot electrons. Zone 2 corresponds to the boundary of the plasma domain. It refers to the propagation of the activation front with the speed Va . In this zone hot electrons impacting silica surface are able to activate the material, making it absorbent (green arrows). We note that the activated silica surface
2
As the ionization threshold of the neutral species (Si, O and O2 ) is about 12 eV, the intensity threshold at 1064 nm is about 2.2 GW/cm2 and is easily reached in the experiments presented in this study. In order to interpret the experimental results shown in Fig. 3 and quantify the axis-symmetric two-dimensional mechanism described above, we estimate the velocity of the surface breakdown. This estimation is made along the x axis (from right to left in Fig. 7), parallel to the surface, which is attributed to an infinitesimal portion of the radius of a ring at the vicinity of the activation front between zone 1 and zone 2 in Fig. 7. Thus, we consider a one dimensional model which is representative of the physical process of propagation of the activation front. For that purpose, we consider that the silica surface is activated once the electron temperature in the vicinity of the surface has reached a threshold value. The heated area expands by thermal conduction mainly due to free electrons. Since the expansion velocity is much larger than estimated hydrodynamic velocities related to heavy species, their motion can be neglected as long as quasi neutrality of the medium is conserved. Thus, as we are interested in the fast mechanisms, the energy balance equation of electrons reduces to the heat equation given by
∂Te ∂ Ce = ∂t ∂x
∂Te e ∂x
+ ˛I
(1)
where Ce is the electron specific heat, e the electron thermal conductivity and ˛ the absorptivity. For simplicity, in this energy balance relation several processes have been disregarded, such as electron energy exchange with heavy species or screening of the laser by free electrons and hot silica. We have to keep in mind that these approximations may lead to overestimate the breakdown wave velocity. Looking for a solitary wave as a solution of the heat Eq. (1), it comes Va Ce
∂Te ∂ + ∂s ∂s
e
∂Te ∂s
+ ˛(s) I(s) = 0,
where Va is the velocity of the activation front and s the space variable in the propagation frame defined by s = x − Va t. The s = 0 coordinate corresponds to the border of the plasma region in Fig. 7. Then, if we consider a wave traveling toward s > 0 (noted + ), absorptivity is assumed to verify ˛(s > 0) = 0 and to take a constant value for s ≤ 0 (noted − ). Assuming also Ce to be constant and that e can take two different values, e− (s ≤ 0) and e+ (s > 0), the solution
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reads Te (s) = T0 −
˛I s, Va Ce
for s ≤ 0,
and Te (s) = T0 exp(−
Va s ), De+
for s ≥ 0, where T0 is the threshold temperature and De± = e± /Ce the electron diffusivity. The conservation of heat fluxes through the boundary between hot and warm regions (s = 0) allows us to determine the velocity given by
Va =
De− ˛ I . Ce T0
(2)
The dielectric function of the hot region, where a free electron population of density ne is present, can be described with the help of the Drude model. Hence, the following absorption coefficient is obtained: ˛≈
n e2
ei , 2 nm c ε0 me ω2 + ei
e
where e is the electron charge, me the electron mass, ε0 the vacuum permittivity, c the speed of light, ω the laser angular frequency, nm the optical index of the medium and ei the electron-ion collision frequency. Two other parameters are required to define completely the activation velocity. The first one is the electron diffusivity in the hot region De− =
kB Te , me
where kB is the Boltzmann’s constant, and = ei + ee (ee is the electron-electron collision frequency). The second parameter is the specific heat Ce which will be assumed to be the one of a perfect gas: Ce =
3 kB ne . 2
With the help of the three previous formulas, the velocity Va is finally given by e Va = me
I 2
, 3 nm ε0 c ω2 + 2 1 + ee /ei ei
and shows a very low dependency with respect to the set of parameters involved in the definition of plasma state, since the collision frequency can only be much lower than ω and the optical index close to 1. Numerically, for a laser wavelength of 1064 nm 2 with respect to ω2 , taking n ≈ 1 (ω = 1.79 × 1015 s−1 ), neglecting ei m and ee /ei ≈ 2, the above formula becomes Va
Fig. 8. Maximum (solid line) and minimum (dashed line) ring appearance speed as a function of the short-time-average intensity for both environments, air (blue) and vacuum (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
km s
GW
≈ 2.83
I
cm2
.
This approach reproduces well the I1/2 scaling law of the experimental results and gives a quantification of the thermal wave speed. However, the calculated speed remains lower than the ones found in air environment [12]. 4. Comparison of vacuum and air environments In order to quantify the influence of the environment on the mechanisms responsible for the printing of the ring pattern, the experimental measurements obtained in vacuum and in air (12) are reported in Fig. 8. For each configuration, twelve different ring patterns are correlated with their corresponding temporal profile to measure the evolution of the speed as a function of short-timeaverage intensity. Each result is fitted with a power law which
exponent is set to 1/3 in air (12) and 1/2 in vacuum. In Fig. 8, only minima and maxima fits are displayed. The small difference between minimum and maximum confirms the repeatability of the experiments. The mean values of the remaining fitting parameters are 2.75 in vacuum and 9.3 in air and are representative of the different physical processes involved in the formation of the ring pattern in both environments. We note that the absence of air reduces significantly the measured speed. In air, the propagation of an ionization front is fast enough to outdo the mechanism occurring in vacuum and silica surface is no longer the support of the activation front. The surrounding air thus plays the role of a catalyst of the ring formation mechanism. The use of MLM pulses provides a powerful tool to investigate the chronology of events occurring during the formation of LID at 1064 nm. Indeed, the activation front starting time t0 can be determined for each damage ring pattern. Thus, two damage formation phases can be distinguished. The first phase corresponds to the incubation of the laser flux by a subsurface defect until t0 . The second is related to the damage expansion that only refers to the energy deposit feeding the activation mechanism up to the end of the pulse. Thus, the total fluence Ftot of a laser pulse can be written as:
t0
+∞
I t dt +
Ftot = Fabs + Fexp = 0
I t dt ,
(4)
t0
where Fabs and Fexp are relative to the absorption by the precursor defect and the expansion of the ring pattern, respectively. The damage diameters obtained in vacuum are thus displayed in Fig. 9 as a function of Ftot (empty circles) and Fexp (empty triangles) with the ones previously obtained in air [13]. These results suggest that there is no correlation between the size of a damage site and the fluence Ftot of the pulse whatever the environment. The distribution of the diameters, related to the wide range of t0 , is supposed to arise from the randomness of the precursor characteristics (absorptivity, depth, size) [19]. However, the striking feature is that the diameters are proportional to the fluence of expansion. For a given Ftot , if we approximate that I(t) ≈ Iavg in Eq. (4), we can estimate the final diameter of the ring pattern at the end of the pulse. On the one hand, Eq. (4) becomes: Ftot = ttot Iavg = tabs Iavg + texp Iavg , where ttot = 9 ns is the pulse duration, defined as the equivalent duration of the SLM pulses, tabs refers to the duration of absorption of a precursor defect up to t0 and texp stands for the expansion duration. On the other hand, the ring appearance speed is given by
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Fig. 9. Ring pattern diameters as function of total fluence (full red triangles for air and full blue circles and green squares for vacuum) and as a function of expansion fluence (empty red triangles for air and empty blue circles and green squares for vacuum). The lines correspond to the value of Table 1 calculated with Eq. (5). Data for air are extracted from Ref. [13]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Experimental values of the different parameters for both air and vacuum environments.
a km cm Air Vacuum Vacuum
9.3 2.75 2.75
2b
GW−b s−1
Ftot J/cm2
1/3 1/2 1/2
88.5 63 103
b , where a and b are fitting parameters. Finally, the diameter v = aIavg Ф of a ring pattern can be calculated as:
t 1−b
= 2v texp = 2a
tot
Ftot
Fexp .
b
(5)
As a consequence, the outer diameters are directly proportional to the fluence of expansion at a given Ftot . All the experimental values of the parameters for both air and vacuum environments are reported in Table 1. In order to show the good reliability of Eq. (5), two sets of data are reported for the experiments performed in vacuum that correspond to two different predetermined control fluences. In Fig. 9, the coefficients of Table 1 are used to plot the lines which permit us to compare the predictions of Eq. (5) with experiments. The results of the two single-shot series allow us to observe the dependence of the slope of the calculated straight line with Ftot (cf. Eq. (5)) for a vacuum environment. The good agreement obtained for the three sets of experimental data justifies the approximation I(t) ≈ Iavg . Moreover, Eq. (5) is shown to be reliable for the determination of the final diameter as a function of Fexp in both environments. As suggested in Fig. 1, the diameters are larger in air than in vacuum by a factor of ≥2 for a given Fexp . This observation is consistent with the different interpretations of the ring pattern formation in each environment. In vacuum, the ring pattern is clearly more concentrated than in air environment. Moreover, for a predetermined control fluence, the variation of Ftot around the mean value (triangles) induces a small variation of Fexp (circles) because of the power 1 − b in Eq. (5) that decreases the influence of experimental scatter. Furthermore, for the two experiments performed in vacuum shown in Fig. 9, when Ftot varies from 103 J/cm2 to 63 J/cm2 , the slope of the calculated lines increases. These variations of Ftot induce a change in Iavg for a given ttot . The decrease of the slopes means that the incubation time tabs of the
2a ttot /Ftot
1−b
m cm2 /J
4.05 2.08 1.63
precursors is changing with Iavg , inducing a shift of the lines from right to left with decreasing Ftot . As a consequence of this analysis, we show that it is possible to determine Fexp only from the diameter of the ring pattern. Then, Fabs can be directly determined from the knowledge of Ftot . Hence, this approach can provide information on the precursor reactiveness. 5. Conclusion In this study, the morphology of laser-induced damage sites initiated at the rear surface of fused silica samples in vacuum at 1064 nm has been investigated. In the MLM regime, on a plane surface, all damage sites show a ring pattern that is closely associated with intensity spikes, thereby making possible the evaluation of the speed of appearance of the rings. A power law of laser intensity with an exponent value of 1/2 has been found to fit experimental measurements. These speeds are high enough to necessarily considerate a plasma issued from the bulk of fused silica as a trigger for the printing of the rings. The removal of material due to an ablation process is subsequent to the activation of the silica surface due to the diffusive expansion of the plasma at the vicinity of the surface. For a collimated beam, the same principles cannot be applied for a front side silica surface since the ablation fronts are directed upstream the laser flux toward the interface between vacuum and fused silica, making impossible any etching of the material. These hypotheses are confronted to additional experiments performed in vacuum on an optical grating. The rugged structure of the grating is shown to inhibit the expansion of the “crawling plasma”. A model describing the expansion of the heated area by thermal conduction due to free electrons in the plasma is developed. This theoretical development allows us to interpret the behavior V ∼ I1/2 and also provides the quantification of activation speed magnitude, which is lower than in air. A direct comparison between the results
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obtained in air [12,13] and in vacuum validate the models developed in both environments. Despite the differences in the dynamics of the ring pattern formation, the powerful tool that MLM pulses provide permits the investigation of the chronology of physical processes involved in LID in both environments. As a result, the expansion phase subsequent to the incubation leads to final diameters twice greater in air than in vacuum. Moreover, the estimation of the fluence of expansion from the final diameter only is possible for a given environment thanks to the knowledge of the activation front speeds. References [1] X. Ling, Y.-A. Zhao, D.-W. Li, M. Zhou, J.-D. Shao, Z.-X. Fan, Chin. Phys. Lett. 26 (2009) 074203. [2] S. Xu, X. Zu, X. Jiang, X. Yuan, J. Huang, H. Wang, H. Lv, W. Zheng, Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 2936–2940. [3] P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, Proc. SPIE 5991 (2005) 599128. [4] L. Jensen, M. Jupé, H. Mädebach, H. Ehlers, K. Starke, D. Ristau, W. Riede, P. Allenspacher, H. Schroeder, Proc. SPIE 6403 (2007) 64030U. [5] X. Ling, Appl. Surf. Sci. 257 (2011) 5601–5604.
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Influence of vacuum on nanosecond laser-induced surface damage morphology in fused silica at 1064 nm R. Diaz a,b,∗ , M. Chambonneau a,b , P. Grua a , J.-L. Rullier a , J.-Y. Natoli b , L. Lamaignère a a b
CEA CESTA, 15 Avenue des Sablières, 33116 Le Barp Cedex, France Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, UMR 7249, 13013 Marseille, France
a r t i c l e
i n f o
Article history: Received 3 August 2015 Received in revised form 13 October 2015 Accepted 20 November 2015 Available online 2 December 2015 Keywords: Laser-induced surface damage Vacuum environment Fused silica Energy deposition
a b s t r a c t The influence of vacuum on nanosecond laser-induced damage at the exit surface of fused silica components is investigated at 1064 nm. In the present study, as previously observed in air, ring patterns surrounding laser-induced damage sites are systematically observed on a plane surface when initiated by multiple longitudinal modes laser pulses. Compared to air, the printed pattern is clearly more concentrated. The obtained correlation between the damage morphology and the temporal structure of the pulses suggests a laser-driven ablation mechanism resulting in a thorough imprint of energy deposit. The ablation process is assumed to be subsequent to an activation of the surface by hot electrons related to the diffusive expansion of a plasma formed from silica. This interpretation is strongly reinforced with additional experiments performed on an optical grating in vacuum on which damage sites do not show any ring pattern. Qualitatively, in vacuum, the intensity-dependent ring appearance speed V ∝ I1/2 is shown to be different than in air where V ∝ I1/3 . This demonstrates that the mechanisms of formation of ring patterns are different in vacuum than in air. Moreover, the mechanism responsible of the propagation of the activation front in vacuum is shown to be outdone when experiments are performed in air. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Laser-dielectric interaction in vacuum environments has been investigated for several years [1,2]. The observed differences of nanosecond laser-induced damage (LID) between atmospheric and vacuum environments have been studied [3–6]. In this context, LID in fused silica remains a major issue, since it is one of the most widely used optical materials. In the past decades, LID at surfaces of transparent dielectrics has been shown to arise from subsurface defects absorbing the incident laser flux [7]. This interaction results in a surface plasma leading to the formation of a damage site [8]. More recently, studies performed in air environment have shown the growing interest in working with Multiple Longitudinal Modes (MLM) pulses [9–11]. This kind of pulses correlated to the damage morphology can provide a powerful tool to access the chronology of the damage mechanisms from incubation to expansion in the near infrared domain [12,13]. Therefore, we propose to transpose this experimental study so as to investigate LID formation in vacuum environment.
In the present work, ring patterns are systematically observed on damage sites initiated with single MLM pulses at 1064 nm in vacuum on plane surfaces. The removal of material due to an ablation process is subsequent to the activation of the silica surface provided by the diffusive expansion of the plasma at the vicinity of the surface. This hypothesis is confronted to additional experiments performed in vacuum on an optical grating etched in fused silica in order to study the influence of the surface state. The periodical structure of the grating is shown to inhibit the expansion of this plasma; this suggests that the expansion process likely takes place along the sample surface. A model based on a diffusive process related with thermal conduction is thus proposed to interpret such behavior. As a conclusion, a direct comparison is made between LID formation in air and vacuum environments so as to emphasize the differences between the mechanisms responsible for the ring patterns formation. Thanks to our analysis, the estimation of the diameter of a damage site is possible for both environments with the knowledge of the fluence that feeds the mechanism of expansion of the ring pattern. 2. Experimental investigations of the influence of vacuum on LID morphologies
∗ Corresponding author at: Commissariat à l’Energie Atomique, Départements des Lasers de Puissance, 15 avenue des sablières, 33116 Le Barp, Gironde, France. E-mail address: [email protected] (R. Diaz). http://dx.doi.org/10.1016/j.apsusc.2015.11.199 0169-4332/© 2015 Elsevier B.V. All rights reserved.
The laser facility described in Ref. [14] is used at 1064 nm both in Single Longitudinal Mode (SLM) and MLM regimes to perform this
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Fig. 2. Correlation between the morphology of a damage site initiated at the rear surface of a fused silica sample in vacuum and the temporal profile of the corresponding MLM pulse. Fig. 1. NIC images of typical damage sites obtained in air and vacuum environments for both SLM and MLM configurations. The fluence of the four shots is 110 J/cm2 . The scale of the images in vacuum is twice smaller than the scale of the images in air.
study. In the SLM regime, the pulse equivalent duration, defined as the ratio of the energy over the peak power, is 9 ns. The sample is positioned in the focal plane where the spot is Gaussian-shaped and 1 mm in diameter at 1/e. The Rayleigh range of the beam is much longer than the sample thickness. In the MLM regime, the random spectral fluctuations induced by longitudinal mode beating in the laser cavity result in a strong variation of the positions and magnitudes of the spikes in the intensity profiles from pulse to pulse. Therefore, the intensity profiles are recorded for each laser shot with a 25 GHz bandwidth photodiode and a 33 GHz bandwidth oscilloscope (Tektronix DSA73304D). Experiments are performed on fused silica samples of 10 mm thickness that exhibit plane superpolished surfaces. The samples are used as a window for the vacuum chamber in which the test will be performed. The front surface is in air environment whereas the rear surface is in vacuum environment. A turbo-molecular pump permits to reach a pressure level of 10−5 mbar. Each damage site was initiated by a single laser pulse at 1064 nm. Since the beam is collimated during the propagation in the sample, LID systematically occurs on the rear surface. All samples are illuminated during the first hour of their exposition to vacuum even though it might not play a role in our single shot experiments. For both SLM and MLM regimes, the largest damage sites show very similar sizes despite strongly different morphologies. Nomarski Interference Contrast (NIC) micrographs of these damage sites obtained in vacuum are shown in Fig. 1, together with equivalent damage achieved in air environment. The fluences of the shots that initiated the damage sites are 110 J/cm2 in all cases. In both SLM and MLM configurations, the damage sizes are reduced by more than a factor of two once the surrounding air is removed. Thus, the scales are multiplied by a factor of two between the images in air and in vacuum. These observations suggest that the environment strongly influences the damage expansion speed. Moreover, the presence of a ring pattern is again systematically obtained in the MLM configuration in vacuum environment. Each ring pattern observed on damage sites in the case of MLM pulses is closely associated with intensity spikes. As in air environment, we match space and time scales thereby making possible
Fig. 3. Instantaneous ring appearance speed as a function of short-time-average laser intensity for three sites initiated in vacuum by three different MLM pulses. The curves stand for the fits of corresponding data.
the evaluation of ring appearance speed [12]. In Fig. 2, a damage site obtained in vacuum environment is shown with the associated intensity profile of the MLM pulse. The white dashed arrows exhibit the correspondence between spikes and rings showing that inner rings appear before outer ones. The red arrow indicates the time t0 (set to zero on the time scale), associated to the beginning of the formation of the rings. The time t0 is unique by definition and cannot be shifted to another peak. The dilatation as well as the matching of the temporal profile with the rings is also unique. This matching allows us to precisely define the instantaneous ring appearance speed as the ratio of the distance between two successive rings to the time interval separating the two adjacent temporal spikes. Although most intensity spikes can be matched with rings, some dispersion in speed measurement is observed, meaning that ring appearance speed is not constant throughout the pulse. For each speed measurement, we calculate the short-time-average intensity which corresponds to the averaged intensity over the time between the two adjacent spikes (e.g. white dashed arrows in Fig. 2) used to calculate the ring appearance speed. As an example, we have reported in Fig. 3 the ring appearance speed V as a function of short-time-average laser intensity I for three damage sites. The three sites in Fig. 3 show very similar
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Fig. 4. Schematic representation of the optical grating used in the experiments.
Fig. 6. Damage site initiated in air environment with a single MLM pulse at the surface of the fused silica optical grating. The correspondences between ring patterns and intensity profiles as functions of the distance (in red) are shown. The time t0 corresponds to the creation of the surface plasma at the center of the damage site (red arrow); black dashed arrows indicate the spike-ring associations. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. NIC images of damage sites initiated with MLM pulses in vacuum environment at 10−5 mbar on the plane surface (a) and on the optical grating (b) for fluences of 65 J/cm2 and 55 J/cm2 , respectively.
results. In order to fit the experimental data a power law V = aIb is proposed, where a and b are fitting parameters. This choice makes possible to impose V = 0 for I = 0. Similar measurements have been carried out on twelve distinct damage sites initiated in vacuum by different MLM pulses and the mean ring appearance speed reads:
V [km/s] = 2.75 I GW/cm2
1/2
.
The ring appearance speed reaches up to 12 km/s. This value is greater than the speed of sound in fused silica (5.9 km/s). The assumed mechanism responsible for the ring pattern formation is linked to the development of a plasma generated by subsurface defects in fused silica and ejected toward vacuum. Classical hydrodynamic processes involved in interaction of lasers with solid materials at intensity levels corresponding to our experiments do not yield such speed values. When air is present, it brings an auxiliary medium able to support plasma expansion speeds in the relevant range. In vacuum, a particular configuration is likely implicated in the generation of a plasma confined at the vicinity of the surface, which is supposed to be “crawling” on the surface of the sample. In order to verify this hypothesis we have studied the influence of the surface state on the expansion of the ring patterns. In order to illustrate this point, we have tested a specific sample of 10 mm thickness which exit surface is an optical grating, made of periodical pillars of 710 nm height and 140 nm width with a regular spacing of 410 nm. The Rayleigh range is always much larger than the sample thickness. This vertical periodical structure, schematically represented in Fig. 4, is supposed to inhibit the expansion of the “crawling” plasma along the surface. In Fig. 5, an example of NIC images of damage sites initiated on both the plane surface and the optical grating in vacuum environment with 1ω MLM pulses are displayed. The fluence of the shots is 65 J/cm2 for the damage site of Fig. 5(a) and 55 J/cm2 for the one of Fig. 5(b) and makes it possible the comparison of the morphologies. A systematic ring-pattern is obtained on damage sites on the
exit surface of the plane surface (Fig. 5(a)) whereas a more fractured damage site without rings is always obtained on the exit surface of the optical grating (Fig. 5(b)). Thus, a major difference of morphology is observed between the damage sites initiated on the optical grating and the plane surface. Several shots at different fluences were performed on each sample and these observations are independent of the laser fluence. The imprinting of the rings in vacuum never takes place on the surface of the optical grating. In this case, the periodical structure at the surface manifestly prevents the expansion of the “crawling plasma”, as assumed earlier. In order to make sure the periodical structure is responsible for the inhibition of the “crawling plasma” expansion in vacuum, additional experiments are performed in air to verify that the formation of a ring pattern still takes place. Thus, the damage sites initiated in air on the surface of the optical grating are compared to those obtained in air on the plane surface. The NIC image of a typical damage sites initiated in air on the exit surface the optical grating is presented in Fig. 6 with the temporal profiles of the MLM pulse that initiated it. In order to verify that the ring appearance speed of a damage site follows the same law on both surfaces in air environment, the formation starting time of the rings t0 and the matching of the rings with intensity spikes have been determined for the damage site of Fig. 6. Then, the instantaneous ring appearance speeds V is supposed to follow the same power law in the ring patterns initiated in air expressed according to Refs. [12,13]:
V [km/s] = 9.3 I GW/cm2
1/3
.
This assumption is directly confronted to the NIC image as we have expressed the laser intensity as a function of the distance for the MLM pulse that initiated the damage sites in Fig. 6. This distance t is written r (t) = t V () d, where the speed V () is taken from 0
the previous relation. Thus, we are able to construct an intensity profile depending on r to be confronted to the NIC image. The good correlation between intensity spikes and the corresponding rings obviously suggests that in air environment, the phase of expansion leading to the formation of the ring pattern does neither depend on the sample surface state nor the type of precursor defect involved, as long as a plasma is generated. As a consequence, the change
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in morphologies obtained in vacuum between the damage sites initiated on the plane surface and those obtained on the optical grating (cf. Fig. 5) can be attributed to the influence of the pillars on the expansion of the “crawling plasma”.
extends beyond the plasma zone (orange toward green area in silica). The zone which becomes absorbent follows a lateral expansion due to electron heat conduction. In addition the plasma is kept hot due to the laser irradiation (variable dashed red lines), and also fed by the initial surface emission (black arrows). In zone 3, the silica surface is heated and an absorption front moves upstream the laser flux (orange area), deeply inside the material, leading to an ablation process (black arrows) similar to mechanisms involved in the technique of laser backside etching [17,18]. Each intensity spike illuminating the absorbent surface will then contribute to ablate the material and form a ring pattern, since the absorption front can start from silica surface only once it has been activated by hot electrons. The mechanisms described above can only take place when the laser flux is high enough to produce an electron avalanche in the medium that expands in vacuum leading to the creation of a strongly ionized plasma. As reported in Ref. [16], when the ionization degree is still low, the energy level of prime electrons cannot exceed the following value, depending on the laser wavelength and on the laser intensity I:
3. Interpretations
Em [eV] ≈ 4.9( [m]) I GW/cm2
Fig. 7. Schematic illustration of a ring pattern forming for silica interfacing with vacuum.
The hypothesis that a “crawling plasma” could be responsible for the activation of material in vacuum environment, and thus for the imprint of the ring patterns, has been strongly reinforced by experiments involving gratings on the exit surface of optical components. Indeed, in this case, the morphology of the damage sites is completely different from the ones observed on a regular surface and does not show any ring pattern in vacuum. Moreover, when ring patterns are obtained on the plane surface in both environments, measurements have shown different scaling of the speed V with respect to laser intensity: V ∝ I1/3 for experiments conducted in air [12,13] and V ∝ I1/2 in vacuum (Fig. 3). The behavior observed in air was attributed to the displacement of an ionization front in the surrounding gas, and a simple hydrodynamic model including the perfect gas approximation has given consistent results for both qualitative and quantitative points of view [9]. A similar hydrodynamic process, inducing an ionization front propagating within the solid material, may occur in experiments performed in vacuum environment. It can be shown that a V ∝ I1/2 scaling is obtained in fused silica with the appropriate choice of equation of state of this material, mainly built on the basis of potential energy and elastic pressure contributions [15,16]. However, although the dependency of speed with respect to laser intensity qualitatively corresponds to experiments, the quantitative results given by this kind of hydrodynamic model for the dense material are out of experimental range (typically lower than 2 km/s). Thus, this is not consistent with the experimental results displayed in Fig. 3. Therefore, any hydrodynamic process occurring in the dense material is not considered here. In that matter, the expansion processes of a high temperature region around the point of damage initiation involving the speeding up of the material must be ruled out. A sine qua non condition is that free electrons may be created in the region of silica expanding toward vacuum, and may participate in the activation of the material surface by thermal conduction. It is this assumption, which will be retained and the corresponding mechanism of silica surface activation is schematically described in Fig. 7. Three different zones are distinguished to describe the mechanisms responsible for the ring pattern formation. In zone 1, the exit surface is transparent because it has not yet been activated by hot electrons. Zone 2 corresponds to the boundary of the plasma domain. It refers to the propagation of the activation front with the speed Va . In this zone hot electrons impacting silica surface are able to activate the material, making it absorbent (green arrows). We note that the activated silica surface
2
As the ionization threshold of the neutral species (Si, O and O2 ) is about 12 eV, the intensity threshold at 1064 nm is about 2.2 GW/cm2 and is easily reached in the experiments presented in this study. In order to interpret the experimental results shown in Fig. 3 and quantify the axis-symmetric two-dimensional mechanism described above, we estimate the velocity of the surface breakdown. This estimation is made along the x axis (from right to left in Fig. 7), parallel to the surface, which is attributed to an infinitesimal portion of the radius of a ring at the vicinity of the activation front between zone 1 and zone 2 in Fig. 7. Thus, we consider a one dimensional model which is representative of the physical process of propagation of the activation front. For that purpose, we consider that the silica surface is activated once the electron temperature in the vicinity of the surface has reached a threshold value. The heated area expands by thermal conduction mainly due to free electrons. Since the expansion velocity is much larger than estimated hydrodynamic velocities related to heavy species, their motion can be neglected as long as quasi neutrality of the medium is conserved. Thus, as we are interested in the fast mechanisms, the energy balance equation of electrons reduces to the heat equation given by
∂Te ∂ Ce = ∂t ∂x
∂Te e ∂x
+ ˛I
(1)
where Ce is the electron specific heat, e the electron thermal conductivity and ˛ the absorptivity. For simplicity, in this energy balance relation several processes have been disregarded, such as electron energy exchange with heavy species or screening of the laser by free electrons and hot silica. We have to keep in mind that these approximations may lead to overestimate the breakdown wave velocity. Looking for a solitary wave as a solution of the heat Eq. (1), it comes Va Ce
∂Te ∂ + ∂s ∂s
e
∂Te ∂s
+ ˛(s) I(s) = 0,
where Va is the velocity of the activation front and s the space variable in the propagation frame defined by s = x − Va t. The s = 0 coordinate corresponds to the border of the plasma region in Fig. 7. Then, if we consider a wave traveling toward s > 0 (noted + ), absorptivity is assumed to verify ˛(s > 0) = 0 and to take a constant value for s ≤ 0 (noted − ). Assuming also Ce to be constant and that e can take two different values, e− (s ≤ 0) and e+ (s > 0), the solution
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reads Te (s) = T0 −
˛I s, Va Ce
for s ≤ 0,
and Te (s) = T0 exp(−
Va s ), De+
for s ≥ 0, where T0 is the threshold temperature and De± = e± /Ce the electron diffusivity. The conservation of heat fluxes through the boundary between hot and warm regions (s = 0) allows us to determine the velocity given by
Va =
De− ˛ I . Ce T0
(2)
The dielectric function of the hot region, where a free electron population of density ne is present, can be described with the help of the Drude model. Hence, the following absorption coefficient is obtained: ˛≈
n e2
ei , 2 nm c ε0 me ω2 + ei
e
where e is the electron charge, me the electron mass, ε0 the vacuum permittivity, c the speed of light, ω the laser angular frequency, nm the optical index of the medium and ei the electron-ion collision frequency. Two other parameters are required to define completely the activation velocity. The first one is the electron diffusivity in the hot region De− =
kB Te , me
where kB is the Boltzmann’s constant, and = ei + ee (ee is the electron-electron collision frequency). The second parameter is the specific heat Ce which will be assumed to be the one of a perfect gas: Ce =
3 kB ne . 2
With the help of the three previous formulas, the velocity Va is finally given by e Va = me
I 2
, 3 nm ε0 c ω2 + 2 1 + ee /ei ei
and shows a very low dependency with respect to the set of parameters involved in the definition of plasma state, since the collision frequency can only be much lower than ω and the optical index close to 1. Numerically, for a laser wavelength of 1064 nm 2 with respect to ω2 , taking n ≈ 1 (ω = 1.79 × 1015 s−1 ), neglecting ei m and ee /ei ≈ 2, the above formula becomes Va
Fig. 8. Maximum (solid line) and minimum (dashed line) ring appearance speed as a function of the short-time-average intensity for both environments, air (blue) and vacuum (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
km s
GW
≈ 2.83
I
cm2
.
This approach reproduces well the I1/2 scaling law of the experimental results and gives a quantification of the thermal wave speed. However, the calculated speed remains lower than the ones found in air environment [12]. 4. Comparison of vacuum and air environments In order to quantify the influence of the environment on the mechanisms responsible for the printing of the ring pattern, the experimental measurements obtained in vacuum and in air (12) are reported in Fig. 8. For each configuration, twelve different ring patterns are correlated with their corresponding temporal profile to measure the evolution of the speed as a function of short-timeaverage intensity. Each result is fitted with a power law which
exponent is set to 1/3 in air (12) and 1/2 in vacuum. In Fig. 8, only minima and maxima fits are displayed. The small difference between minimum and maximum confirms the repeatability of the experiments. The mean values of the remaining fitting parameters are 2.75 in vacuum and 9.3 in air and are representative of the different physical processes involved in the formation of the ring pattern in both environments. We note that the absence of air reduces significantly the measured speed. In air, the propagation of an ionization front is fast enough to outdo the mechanism occurring in vacuum and silica surface is no longer the support of the activation front. The surrounding air thus plays the role of a catalyst of the ring formation mechanism. The use of MLM pulses provides a powerful tool to investigate the chronology of events occurring during the formation of LID at 1064 nm. Indeed, the activation front starting time t0 can be determined for each damage ring pattern. Thus, two damage formation phases can be distinguished. The first phase corresponds to the incubation of the laser flux by a subsurface defect until t0 . The second is related to the damage expansion that only refers to the energy deposit feeding the activation mechanism up to the end of the pulse. Thus, the total fluence Ftot of a laser pulse can be written as:
t0
+∞
I t dt +
Ftot = Fabs + Fexp = 0
I t dt ,
(4)
t0
where Fabs and Fexp are relative to the absorption by the precursor defect and the expansion of the ring pattern, respectively. The damage diameters obtained in vacuum are thus displayed in Fig. 9 as a function of Ftot (empty circles) and Fexp (empty triangles) with the ones previously obtained in air [13]. These results suggest that there is no correlation between the size of a damage site and the fluence Ftot of the pulse whatever the environment. The distribution of the diameters, related to the wide range of t0 , is supposed to arise from the randomness of the precursor characteristics (absorptivity, depth, size) [19]. However, the striking feature is that the diameters are proportional to the fluence of expansion. For a given Ftot , if we approximate that I(t) ≈ Iavg in Eq. (4), we can estimate the final diameter of the ring pattern at the end of the pulse. On the one hand, Eq. (4) becomes: Ftot = ttot Iavg = tabs Iavg + texp Iavg , where ttot = 9 ns is the pulse duration, defined as the equivalent duration of the SLM pulses, tabs refers to the duration of absorption of a precursor defect up to t0 and texp stands for the expansion duration. On the other hand, the ring appearance speed is given by
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Fig. 9. Ring pattern diameters as function of total fluence (full red triangles for air and full blue circles and green squares for vacuum) and as a function of expansion fluence (empty red triangles for air and empty blue circles and green squares for vacuum). The lines correspond to the value of Table 1 calculated with Eq. (5). Data for air are extracted from Ref. [13]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Experimental values of the different parameters for both air and vacuum environments.
a km cm Air Vacuum Vacuum
9.3 2.75 2.75
2b
GW−b s−1
Ftot J/cm2
1/3 1/2 1/2
88.5 63 103
b , where a and b are fitting parameters. Finally, the diameter v = aIavg Ф of a ring pattern can be calculated as:
t 1−b
= 2v texp = 2a
tot
Ftot
Fexp .
b
(5)
As a consequence, the outer diameters are directly proportional to the fluence of expansion at a given Ftot . All the experimental values of the parameters for both air and vacuum environments are reported in Table 1. In order to show the good reliability of Eq. (5), two sets of data are reported for the experiments performed in vacuum that correspond to two different predetermined control fluences. In Fig. 9, the coefficients of Table 1 are used to plot the lines which permit us to compare the predictions of Eq. (5) with experiments. The results of the two single-shot series allow us to observe the dependence of the slope of the calculated straight line with Ftot (cf. Eq. (5)) for a vacuum environment. The good agreement obtained for the three sets of experimental data justifies the approximation I(t) ≈ Iavg . Moreover, Eq. (5) is shown to be reliable for the determination of the final diameter as a function of Fexp in both environments. As suggested in Fig. 1, the diameters are larger in air than in vacuum by a factor of ≥2 for a given Fexp . This observation is consistent with the different interpretations of the ring pattern formation in each environment. In vacuum, the ring pattern is clearly more concentrated than in air environment. Moreover, for a predetermined control fluence, the variation of Ftot around the mean value (triangles) induces a small variation of Fexp (circles) because of the power 1 − b in Eq. (5) that decreases the influence of experimental scatter. Furthermore, for the two experiments performed in vacuum shown in Fig. 9, when Ftot varies from 103 J/cm2 to 63 J/cm2 , the slope of the calculated lines increases. These variations of Ftot induce a change in Iavg for a given ttot . The decrease of the slopes means that the incubation time tabs of the
2a ttot /Ftot
1−b
m cm2 /J
4.05 2.08 1.63
precursors is changing with Iavg , inducing a shift of the lines from right to left with decreasing Ftot . As a consequence of this analysis, we show that it is possible to determine Fexp only from the diameter of the ring pattern. Then, Fabs can be directly determined from the knowledge of Ftot . Hence, this approach can provide information on the precursor reactiveness. 5. Conclusion In this study, the morphology of laser-induced damage sites initiated at the rear surface of fused silica samples in vacuum at 1064 nm has been investigated. In the MLM regime, on a plane surface, all damage sites show a ring pattern that is closely associated with intensity spikes, thereby making possible the evaluation of the speed of appearance of the rings. A power law of laser intensity with an exponent value of 1/2 has been found to fit experimental measurements. These speeds are high enough to necessarily considerate a plasma issued from the bulk of fused silica as a trigger for the printing of the rings. The removal of material due to an ablation process is subsequent to the activation of the silica surface due to the diffusive expansion of the plasma at the vicinity of the surface. For a collimated beam, the same principles cannot be applied for a front side silica surface since the ablation fronts are directed upstream the laser flux toward the interface between vacuum and fused silica, making impossible any etching of the material. These hypotheses are confronted to additional experiments performed in vacuum on an optical grating. The rugged structure of the grating is shown to inhibit the expansion of the “crawling plasma”. A model describing the expansion of the heated area by thermal conduction due to free electrons in the plasma is developed. This theoretical development allows us to interpret the behavior V ∼ I1/2 and also provides the quantification of activation speed magnitude, which is lower than in air. A direct comparison between the results
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obtained in air [12,13] and in vacuum validate the models developed in both environments. Despite the differences in the dynamics of the ring pattern formation, the powerful tool that MLM pulses provide permits the investigation of the chronology of physical processes involved in LID in both environments. As a result, the expansion phase subsequent to the incubation leads to final diameters twice greater in air than in vacuum. Moreover, the estimation of the fluence of expansion from the final diameter only is possible for a given environment thanks to the knowledge of the activation front speeds. References [1] X. Ling, Y.-A. Zhao, D.-W. Li, M. Zhou, J.-D. Shao, Z.-X. Fan, Chin. Phys. Lett. 26 (2009) 074203. [2] S. Xu, X. Zu, X. Jiang, X. Yuan, J. Huang, H. Wang, H. Lv, W. Zheng, Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 2936–2940. [3] P. Allenspacher, W. Riede, D. Wernham, A. Capanni, F. Era, Proc. SPIE 5991 (2005) 599128. [4] L. Jensen, M. Jupé, H. Mädebach, H. Ehlers, K. Starke, D. Ristau, W. Riede, P. Allenspacher, H. Schroeder, Proc. SPIE 6403 (2007) 64030U. [5] X. Ling, Appl. Surf. Sci. 257 (2011) 5601–5604.
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