Investigations on laser damage growth in fused silica with simultaneous wavelength irradiation Maxime Chambonneau,1,* Margaux Chanal,1 Stéphane Reyné,1 Guillaume Duchateau,2 Jean-Yves Natoli,3 and Laurent Lamaignère1 1 2
3
CEA CESTA, 15 Avenue des Sablières, CS 60001, 33116 Le Barp Cedex, France
Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications, UMR 5107, 351 Cours de la Libération, F-33405 Talence, France
Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, UMR 7249, 13013 Marseille, France *Corresponding author: [email protected] Received 11 November 2014; revised 19 January 2015; accepted 19 January 2015; posted 20 January 2015 (Doc. ID 226724); published 19 February 2015
The laser-induced damage growth phenomenon is experimentally studied for damage sites on the exit surface of fused silica. The sites are irradiated by nanosecond laser pulses at 1064 and 355 nm separately and also simultaneously. The results in the single wavelength configurations are expressed in terms of the probability of growth and growth coefficient. For growing sites, a fluence correction expression is proposed in order to take into account the millimetric Gaussian profile of the beams. The use of this expression is necessary to obtain results that are consistent with the ones obtained in the existing literature with large homogeneous beams. In the multiple wavelengths configuration, the results are expressed as a function of the laser fluences at each wavelength and are found to be closely related to the parameters determined in the single wavelength experiments. A coupling between the two wavelengths is quantified, and could originate from the formation and the expansion of a plasma produced both in the center and at the periphery of the damage sites. © 2015 Optical Society of America OCIS codes: (140.3330) Laser damage; (160.4670) Optical materials; (160.6030) Silica; (240.6700) Surfaces. http://dx.doi.org/10.1364/AO.54.001463
1. Introduction
Laser-induced damage (LID) is one of the key issues for the success of inertial confinement fusion laser facilities such as the laser megaJoule (LMJ, in France) or the National Ignition Facility (NIF, in the USA) [1]. This phenomenon can give rise to a degradation in the optical function of a component. Moreover, it may induce optical modulation effects on the transmitted laser beam, and damage the downstream components [2]. At the LMJ, nanosecond laser beams at 1053 nm (1ω) are converted to 527 nm (2ω) and 351 nm (3ω) with the use of potassium 1559-128X/15/061463-08$15.00/0 © 2015 Optical Society of America
dihydrogen phosphate (KDP) crystals and their deuterated analogs (DKDP). The 3ω laser beams are then focused on a millimetric target by means of focusing gratings that separate the unconverted 1ω and 2ω beams [3]. Since the conversion efficiency of the crystals is about 50%, the fused silica gratings are irradiated in a multiple wavelengths configuration by the main 3ω beam and also the 1ω and 2ω residual ones. The physical mechanisms involved during LID initiation on the exit surface of fused silica have recently been investigated at 1ω as well as at 3ω on samples polished with the same processes [4]. Studies of LID morphology show that subsurface cracks are located under the molten and fractured initiated craters [5,6]. These subsurface cracks are assumed to absorb the laser flux [7,8]. Hence, 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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successive laser irradiations may induce an increase in the size of the damage sites and a production of subsurface cracks at their periphery. The understanding of this phenomenon (referred to as “LID growth”) enables the development of mitigation techniques [9,10]. Many studies have been conducted in order to determine how LID sites grow at 1ω [11,12], as well as at 3ω [13–16], expressing the growth coefficient as a function of the laser fluence. These studies have been performed using large homogeneous beams > 10 mm2 . However, few studies compare the growth coefficients obtained using large homogeneous and small Gaussian beams [17]. Recent works show that the probability of growth at 3ω is a function of both the initiated damage size and the laser fluence [18,19]. Even if the LID growth phenomenon is well characterized in the single wavelength configurations, few studies have been conducted in a multiple wavelengths configuration [20,21]. These studies show that combining the wavelengths increases the growth coefficient values. However, the probability of growth in this configuration needs to be investigated. Other recent studies show that both LID initiation [22,23] and growth [24] phenomena originate from a plasma formation and expansion in the center and also at the periphery of the damage sites. The simultaneous irradiations of silica at two different wavelengths could significantly impact the dynamics of the produced plasma. In this multiple wavelengths configuration, both the probability of growth and the growth coefficient need to be expressed as a function of the two laser fluences. In the present study, the probability of growth and the growth coefficient are both investigated at 1ω, at 3ω, and also in a configuration combining these two wavelengths, for damage sites on the exit surface of synthetic fused silica samples. Contrary to the linear growth of the damage sites on the entrance surface, the area of the ones located on the exit surface is known to scale exponentially with the number of laser pulses [25], which may originate from the absence of a plasma shielding of the surface from the laser flux [26]. In our experiments, we have used millimetric and Gaussian-shaped laser beams. These spatial characteristics imply that a damage site whose dimensions are close to the diameter of the incident beam is irradiated at an average fluence significantly lower than the maximum one. The spatial profile of the beams is thus taken into account while investigating the damage growth. We propose a fluence correction expression that enables us to compare our results to the ones obtained with large homogeneous beams existing in the literature. The probability of growth is investigated for damage sites with various initial areas. In order to express this probability as a function of the laser fluence only, we have chosen to study the growth of damage sites initiated at 3ω with initial diameter around 60 μm. In the multiple wavelengths configuration, the probability of growth and the growth coefficient are 1464
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experimentally determined and parameterized as a function of the laser fluences at the two wavelengths. In order to interpret the complete set of results in the multiple wavelengths configuration, some physical processes that might be involved in our experiments are proposed. 2. Experimental Setup
The experimental study has been performed on 10 mm thick synthetic fused silica samples superpolished by SESO company. The laser facility described in Ref. [27] has been employed to irradiate the samples. This facility is based on a tripled Nd: YAG laser, giving access to pulses at 1064 nm (1ω) and 355 nm (3ω) irradiating the sample simultaneously (multiple wavelengths configuration) or separately (single wavelength configurations). It operates in multiple longitudinal modes (MLM), and the pulse durations [full width at half maximum (FWHM)] of the Gaussian fits of the temporal profiles are 6.5 and 5.5 ns at 1ω and 3ω, respectively. The 1ω and 3ω pulses are separated by means of a dichroic mirror. Each beam is then focused by means of a lens whose focal length is approximately 4 m. Using another dichroic mirror, at the focus region, the two spots are collinear and Gaussian-shaped, and their diameters at 1/e are 700 and 500 μm at 1ω and 3ω, respectively. The depths of focus are much higher than the sample thickness. As a consequence, both the beams’ diameters are considered constant along their propagation through the sample. The maximum fluences that can be reached in the single wavelength configurations are 130 and 75 J∕cm2 at 1ω and 3ω, respectively. The sample is fixed on a motor-driven stage providing translations in a plane that is perpendicular to the laser beams. The damage sites on the exit surface of the sample are separated by 3 mm in order to prevent the influence of a damage growth session on another one. The exit surface of the sample is illuminated with white light. The size measurement of the damage sites is performed recording their images after each laser pulse by means of a long focal microscope and a CCD camera. In order to protect these two last apparatuses from the incident laser beams, an angle of about 10° is introduced between the microscope and the laser path. Recent studies have shown that LID morphology is strongly related to the associated pulse wavelength [28], particularly when the laser operates in the MLM regime [23]. These differences in morphology could significantly impact the growth behavior of a damage site. In order to obtain results that are independent of the LID morphology, the same initiation wavelength has been chosen in all the studied growth configurations. Since at a given fluence LID density is much higher at 3ω than at 1ω [4], the initiation wavelength has been chosen at 3ω. At high fluences (i.e., for damage initiation probability higher than 80%), the observed initiated damage sites generally show multiple pits. Hence, the damage sites are
P
ng ; ntot
(1)
where ng is the number of growing damage sites among the ntot total tested ones. Since the probability of growth is known to increase for increasing initial damage areas A0 or laser fluences F [19], P has been evaluated for various A0 and F values. The previously developed notion of probability of growth is not sufficient to describe the growth behavior of the damage sites. In the present study, the damage sites are located on the exit surface of silica, and grow exponentially with respect to the number of laser pulses [25]. Thereby, the damage area after n laser pulses (noted An ) can be written as An A0 ek·n : Fig. 1. Confocal micrograph of a damage site initiated at 3ω. The images noted (a) and (b) correspond to side views of the site, and (c) corresponds to its top view.
initiated at 50 J∕cm2 , where the damage initiation probability is around 50%, and the sites are single pit with sizes of about 60 μm. The morphology of a typical LID site initiated at this fluence is shown in Fig. 1. The measurement has been realized employing a confocal microscope in reflective mode operating at 532 nm. This characterization exhibits that subsurface cracks of about 10 μm are distributed under a crater that is about 10 μm deep. This morphology is consistent with the observed one in Refs. [5] and [6] for damage sites initiated at 3ω. Once initiated, the damage sites are irradiated by several laser pulses separated by a few seconds (i.e., single-shot mode) at a constant fluence at 1ω, at 3ω, or simultaneously at 1ω and 3ω. The maximum growth fluences at 1ω and 3ω are 40 and 20 J∕cm2 , respectively. In the case of nongrowing damage sites, the growth sessions are stopped after 200 pulses. In the single wavelength configurations, the sessions are stopped when the damage size reaches the beam diameter at 1/e. Since the beam diameter at 3ω is smaller than at 1ω, the growth sessions in the multiple wavelengths configuration are stopped when the damage size reaches the beam diameter at 3ω.
(2)
The growth coefficient k in Eq. (2) is the mean of the growth coefficients kn defined pulse to pulse as A kn ln n1 ; An
3
where An and An1 are the damage areas after the pulses n and n 1, respectively. Due to the Gaussian shape of the millimetric beam spots used in our experiments, it is worth noting that the average fluence irradiating a damage site strongly depends on its area. Figure 2 schematizes the necessity to take into account the spatial profile of the laser beam while evaluating the fluence irradiating a growing damage site. A site with size close to that of the incident beam at 1/e is irradiated at an average fluence F dam significantly lower than the measured maximum one (noted F max in Fig. 2). It is thus necessary to take into account the increase in damage size while evaluating both the fluence and the growth coefficient after a laser pulse. Demos et al. have shown that plasma is produced both in the center and at the periphery of a damage site during its growth [24,29]. In our experiments performed
3. Data Analysis
In order to quantify the growth behavior, an image of the damage sites is recorded after every irradiation. The images are then converted into binary images using ImageJ software, giving access to the damage area after each pulse. The angle between the camera and the sample is taken into account when evaluating the aspect ratio of the images. The first result directly obtained after a growth session on a damage site is its probability of growth. A damage site has been considered as growing if its final size after N laser pulses (N < 200) is at least twice as large as its initial size. The probability of growth P reads
Fig. 2. Schematic illustration of a damage growth session. The lightest shades of gray represent the earliest stages of the growth session. The ratios f k between the average fluence F dam irradiating the damage site (concentric ellipses) and the maximum laser fluence F max for the shots n, n 1, and n 2 are reported on the vertical axis. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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with small Gaussian beams, the center and the periphery of a damage site are mainly irradiated by the Gaussian peak and the non-Gaussian part (i.e., the wings) of the laser spot, respectively. Hence, the measured maximum fluence can be written as F max F g F w , where F g and F w are the fluences of the Gaussian peak (with area Sg ) and the wings (with area Sw ), respectively. For a laser spot with an equivalent area Seq (at 1/e), the fluences F g and F w have been calculated as follows: Seq − Sw Seq − Sw : ; F F max 1− F g F max Sg − Sw w Sg − Sw On the basis of Fig. 2, we propose that the average fluence F dam irradiating a damage site with area Sdam reads S S Sg Sw − dam − Sdam Sg F dam F g 1−e Fw 1 − e w ; (4) Sdam Sdam where the first and second terms of the sum are the contributions of the Gaussian peak and the wings, respectively. For both of these terms, the exponential decrease of F dam with respect to Sdam is due to the exponential growth of the studied damage sites. For damage sites with areas Sdam that are much lower than Sg and Sw , F dam ≈ F max according to Eq. (4). The ratio between F dam and F max is calculated in Fig. 3 according to Eq. (4) at 1ω and 3ω as a function of the damage diameter. The spatial parameters at each wavelength are issued from two typical measurements of the beams. At both wavelengths, for damage areas from 0 to Seq , the fluence decreases from F max to about 0.6F max . The decrease of the ratio F dam ∕F max is higher at 3ω since the beam at this wavelength is smaller than at 1ω. It is worth
noting that for the typical size of the studied sites (60 μm), F dam ∈ 0.99F max ; F max at each wavelength. Thereby, the probability of growth P given by Eq. (1) can be associated with the fluence F max . However, for growing damage sites, Fig. 3 shows that the growth coefficient kn given by Eq. (3) has to be associated with the fluence F dam . In the multiple wavelengths configuration, F dam is calculated at both wavelengths, considering separately the areas Seq, Sg , and Sw of the two spots. According to the previous expressions of the probability of growth, growth coefficient, and corrected fluence, the results can be expressed in both the single and multiple wavelengths configurations. In each single wavelength configuration, the probability of growth P is calculated according to Eq. (1). We have first investigated the influence of the initial damage size on P at constant 1ω and 3ω fluences. As shown in Ref. [19], the probability of growth for damage sites with a given size increases with respect to the laser fluence F and can be fitted by a sigmoid curve as PF 1 −
1
1
;
p F F 50%
where F 50% is the fluence at which the probability of growth is equal to 50%, and the exponent p determines the shape of the sigmoid curve. The percent error (noted % error) on the probability measurements is given by [19] % error
P1 − P p : P ntot
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(6)
In the multiple wavelengths configuration, the set of probability values P is expressed as a function of both the fluences at 1ω and 3ω. For growing damage sites, the growth coefficient [kn in Eq. (3)] is calculated after each laser pulse and expressed as a function of the corrected fluence [F dam in Eq. (4)]. In the single wavelength configurations, the average growth coefficient values hki are commonly fitted as follows [13,15]: hki CF dam − F th ;
Fig. 3. Evolution of the ratio F dam ∕F max calculated according to 3ω Eq. (4) at 1ω (in red) and 3ω (in blue). The notations S1ω g and Sg indicate the diameters associated with the areas of the Gaussian peaks, experimentally measured at 1ω and 3ω, respectively. The 3ω notations S1ω eq and Seq indicate the diameters associated with the equivalent areas (at 1/e) at 1ω and 3ω, respectively. The diameters associated with the areas of the wings Sw are 1000 and 880 μm at 1ω and 3ω, respectively. At both wavelengths, the fluence contained in the wings corresponds to about 10% of the maximum fluence. The notation A0 indicates the typical initial diameter of the studied damage sites.
(5)
(7)
where C is the rate of increase in the growth coefficient, and F th is the fluence threshold for growth. The parameterization given by Eq. (7) is representative of the experimental results: the damage area exponentially increases after a laser pulse with a fluence higher than a threshold where no growth is observed below. In the multiple wavelengths configuration, the kn values are fitted with a nonlinear least squares Levenberg–Marquardt algorithm [30], assuming a linear superposition as follows: 3ω 1ω 1ω ~ hkF 1ω dam ; F dam i C1ω F dam − F th
~ 3ω F 3ω − F 3ω ; C dam th
(8)
~ 1ω and C ~ 3ω are where the rates of increase in growth C two fitting parameters. The fluence thresholds for 3ω growth F 1ω th and F th at 1ω and 3ω, respectively, are determined by the results obtained in the single wavelength configurations. 4. Results and Discussion A.
LID Growth in Single Wavelength Configurations
The growth behaviors are first determined in both the single wavelength configurations, at 1ω and 3ω separately. We first study the probability of growth as a function of the initial damage size at constant fluences at 1ω and 3ω. Then, for a given damage size, the probability of growth is expressed as a function of the fluence F max . The evolution of the probability of growth for damage sites as a function of their initial diameters is displayed in Fig. 4. The chosen fluences are 34 J∕cm2 at 1ω and 13 J∕cm2 at 3ω, which are higher than the growth thresholds reported in Refs. [11,13,15]. As previously shown in Ref. [19], the probability of growth increases with the initial damage diameter at a constant fluence at 3ω. A similar behavior is obtained at 1ω. The dependence in size of P could originate from the absorbing subsurface fractures, which are larger and more numerous for large craters [6]. As a consequence, a site with a large size more efficiently absorbs the laser energy and its size increases easily. The double dependence (in size and in fluence) of the probability of growth could complicate the interpretation of the results. In order to study the influence of the combination of wavelengths, the size of the studied initiated damage sites has been chosen constant. Hence, all the following experiments have been performed for initiated damage sites with diameters of about 60 μm (10 μm). The evolution of the probability of growth as a function of the fluence at 1ω and 3ω for damage sites with the previously considered size is shown in Fig. 5. The sigmoid fits for the experimental data have been introduced in Eq. (5). The fluence at which the prob 33.5 and ability of growth is equal to 50% is F 50% 1ω 2 15.5 J∕cm at 1ω and 3ω, respectively. At F 50% 3ω both wavelengths the p exponent value is 5. In both
Fig. 4. Probability of growth for damage sites on the exit surface of fused silica as a function of their initial diameter at 1ω (34 J∕cm2 ) and 3ω (13 J∕cm2 ). The error bars stand for % error given by Eq. (6).
Fig. 5. Probability of growth for damage sites with diameters of about 60 μm 10 μm as a function of the fluence at 1ω (red circles) and at 3ω (blue squares). The red and blue dashed sigmoid curves stand for the parameterizations of the results according to Eq. (5) at 1ω and 3ω, respectively. The error bars stand for % error given by Eq. (6).
the single wavelength configurations, the probability of growth increases with the laser fluence for damage sites with similar sizes, in accordance with a previous study conducted at 3ω by Negres et al. [19]. One can note that the parameters p and F 50% associated with the sigmoid fits would have been different for other initial damage diameters [19]. The average growth coefficient hki obtained for different growing damage sites at 1ω among the previously considered ones is reported in Fig. 6 as a function of the corrected fluence F dam and also as a function of the maximum fluence F max . In each case, hki linearly scales the fluence whether it is corrected or not. For fluences around 30 J∕cm2 , hki ≈ 0.32 when the correction described by Eq. (4) is applied, and hki ≈ 0.24 when it is not. This shift is reduced for higher fluences, which corresponds to the beginning of the growth sessions where F dam ≈ F max (Fig. 3). The comparison between the results obtained at 1ω with large homogeneous beam experiments by Razé et al. [11] and the hki values obtained in our study, expressed as a function of F dam and also F max , highlights the necessity of taking into account the damage size when evaluating the fluence during a growth session. Similar results are obtained at 3ω when compared to the ones reported in Ref. [15].
Fig. 6. Evolution of the average growth coefficient hki in the 1ω configuration, expressed as a function of F max (green triangles), and F dam (red circles) calculated according to Eq. (4). The green and red dashed lines stand for the corresponding fits with equations hki 1.77 × 10−2 F max − 13.1 and hki 1.62 × 10−2 F dam − 6.9, respectively. The orange squares are data issued from Ref. [11]. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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Hence, we have expressed hki as a function of F dam in all the configurations reported below. A comparison of the evolution of hki as a function of F dam in the two single wavelength configurations is reported in Fig. 7. As shown in Fig. 6 at 1ω, hki linearly scales with F dam at 3ω. The rates of increase in growth are C1ω 1.62 × 10−2 and C3ω 3.18× 10−2 cm2 ∕J. The deduced values for the fluence 3ω 2 thresholds are F 1ω th 6.9 and F th 3.4 J∕cm . A growth coefficient of 0.40 (corresponding to an area multiplied by 1.5) is reached at 32 and 16 J∕cm2 at 1ω and 3ω, respectively. Thereby, Figs. 5 and 7 show that the LID growth phenomenon is enhanced in the 3ω configuration, by comparison to the 1ω one. This result can qualitatively be explained by the subsurface fractures that more efficiently absorb the photons at 3ω than at 1ω. These two figures and the associated fitting parameters are used as preliminary results for the following multiple wavelengths study. B.
LID Growth in Multiple Wavelengths Configuration
Based on the results obtained in the single wavelength configurations, LID growth has been experimentally studied in the simultaneous multiple wavelengths configuration. In this case, the initial tested damage sites exhibit the same morphology (initiated at 3ω) and size (about 60 μm) as the ones studied in the single wavelength cases. Thereby, the probability of growth and also the growth coefficient mainly depend on the laser fluences at 1ω and at 3ω, as suggested in Refs. [20] and [21]. Figure 8 shows the probability of growth as a function of the 3ω fluence at various additional 1ω fluences. The probability of growth increases with respect to the 3ω fluence at every 1ω fluence. The data obtained at each F 1ω value are compared with the following expression: PF 1ω ; F 3ω 1 −
1
1
F 1ω 50% F 1ω
;
F 3ω p F 50% 3ω
(9)
and F 50% at which the where the fluences F 50% 1ω 3ω probability of growth is 50%, and also the exponent
Fig. 7. Evolution of the average growth coefficient hki as a function of the corrected fluence F dam at 1ω (red circles) and at 3ω (blue squares). Red and blue dashed lines stand for the parameterizations of the results according to Eq. (7) at 1ω and 3ω, respectively. 1468
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Fig. 8. Evolution of the probability of growth for damage sites with diameters of about 60 μm 10 μm in the multiple wavelengths configuration as a function of the fluence at 3ω for various additional 1ω fluences. The experimental data (colored circles) are compared to the parameterizations issued from Eq. (9) at the same 1ω fluences (dashed curves in the same colors). The error bars stand for % error given by Eq. (6).
p 5, are the values determined in the single wavelength configurations. Figure 8 shows that the parameterization of Eq. (9) reproduces fairly well the experimental trends. Moreover, it ensures that both the single wavelength cases are also well fitted. In order to check the validity of Eq. (9), we have tried to fit the results in the multiple wavelengths configuration with other parameterizations. For p ≠ 5 in Eq. (9), the slopes at half maximum of the calculated curves do not enable us to reproduce the experimental trends. Moreover, these cases are not consistent with the results obtained in the single wavelength configurations. In Eq. (9), we have F 3ω ∕F 50% p by also replaced the term F 1ω ∕F 50% 1ω 3ω F 1ω ∕F 50% p F 3ω ∕F 50% p . Although this case is 1ω 3ω consistent with the single wavelength configurations, the results obtained in the multiple wavelengths configuration are underestimated by this parameterization that does not involve the cross terms in F 1ω ∕F 50% F 3ω ∕F 50% p when it is devel1ω 3ω oped. Hence, these results suggest a coupling between the two wavelengths. The increase in the probability of growth in the multiple wavelengths configuration compared to the single wavelength configurations (Fig. 8) could originate from the formation of the plasma in the neighborhood of the absorbing subsurface cracks [7,24,26,29]. Even if such a plasma is easily produced by the 3ω pulse, two mechanisms induced by the 1ω pulse can be evoked in order to explain this coupling. The first one is the field intensification arising from subsurface cracks, which gives rise to plasma formation [7,29]. Combining the wavelengths could enhance this phenomenon. The second mechanism is described by the Drude model [31]. The free electrons provided by the plasma are more easily heated at 1ω than at 3ω [27]. The heat is transferred in silica, leading to an increase in the damage size. As previously done in the single wavelength configurations, the growth coefficients kn have been calculated for the growing damage sites in the multiple wavelengths case. The resulting average growth
Fig. 9. Evolution of the average growth coefficient hki as a func1ω tion of F 3ω dam at various F dam values. The experimental data (colored circles) are compared to the parameterization issued from Eq. (10) at the same 1ω fluences (dashed lines in the same colors).
coefficient hki in this configuration is plotted in Fig. 9 1ω as a function of F 3ω dam at various additional F dam values. A linear increase in hki with respect to the 3ω fluence is reported at every 1ω fluence. Moreover, the hki values increase for increasing 1ω fluence at a constant 3ω fluence. In order to quantify this increase in hki, the complete set of kn values has been parameterized according to Eq. (8), where the fluence thresh3ω 2 olds for growth F 1ω th 6.9 and F th 3.4 J∕cm are extracted from the previous results in the single wavelength configurations, and the growth rates ~ 3ω are two fitting parameters. After optimi~ 1ω and C C ~ 3ω values are 1.70 × 10−2 and ~ 1ω and C zation, the C −2 2 3.23 × 10 cm ∕J, respectively, with standard error around 3%. It is worth noting that the values of the ~ 1ω and C ~ 3ω are close to the two fitting parameters C rates of increase in growth that have been previously obtained in the single wavelength configurations. This result suggests that the average growth coefficient hk1;3 i in the multiple wavelengths case can be written as hk1;3 F 1ω ; F 3ω i hk1 F 1ω i hk3 F 3ω i;
(10)
where hk1 i and hk3 i are the growth coefficients in the single wavelength configurations. A comparison between the parameterization given by Eq. (10) and the experimental data is reported in Fig. 9. Once again, the parameterization issued from Eq. (10) is consistent with the results obtained in the single wavelength configurations. Moreover, it reproduces fairly well the experimental trends, meaning that hk1;3 i essentially depends on the two laser fluences. This agreement holds if hk1;3 i is plotted as a function 3ω of F 1ω dam at various additional F dam values. The small discrepancy between the parameterization given by Eq. (10) and the experimental data could originate from the dependence of the growth coefficient on the size of the damage sites [15,16], which has not been taken into account. In order to interpret the increase in growth coefficient in the multiple wavelength configuration compared to the 3ω one, Lamaignère et al. and Norton et al. have suggested that the plasma produced in the
neighborhood of the subsurface cracks starts absorbing the laser flux at both wavelengths [20,21]. Such a plasma absorbs the 1ω flux after its production by the 3ω pulse. In these multiple wavelengths studies, the growth coefficient linearly scales with the total fluence F 3ω KF 1ω , where K corresponds to the percentage of the 1ω fluence required to fit the results at 3ω only. The values of the K parameter in Refs. [20] and [21] are 0.80 and 0.70, respectively. In our study, according to Eq. (10), this value is fixed by the ratio C1ω ∕C3ω ≈ 0.55. These differences in the K values could result from the temporal shape of the pulses—MLM in our study, and single longitudinal mode (SLM) in Refs. [20] and [21]. The plasma production at 3ω is facilitated for SLM pulses compared with MLM ones [4]. Hence, in our study, the absorption of the 1ω flux by the plasma starts later in the pulse than in Refs. [20] and [21], which can explain the differences in the K values between our experiments and the existing literature. Moreover, recent studies show that plasma dynamics are different at 1ω [23] and at 3ω [22,29]. Hence, the cooperative effect of the two wavelengths concerning the growth coefficient described by Eq. (10) could result from a combination of the growth processes involved at 1ω and 3ω separately. 5. Conclusion
In this experimental study, we have first highlighted the influence of the initial damage size on the growth phenomenon on the exit surface of fused silica. For damage sites of about 60 μm initiated at 3ω, the results have been expressed as a function of the laser fluence only. An expression has been proposed in order to take into account the spatial profiles of the Gaussian-shaped millimetric laser beams while evaluating the fluence irradiating a damage site during a growth session. This fluence correction has allowed us to obtain results that are consistent with large homogeneous beams existing in the literature at 1ω and 3ω. The probability of growth and the growth coefficient scale as a sigmoid and a linear function of the laser fluence, respectively. The results in the multiple wavelengths configuration have been deduced from the parameters obtained at 1ω and 3ω. The probability of growth obtained when combining the two wavelengths is a sigmoid function of the fluences at 1ω and 3ω. The growth coefficient in this configuration can be obtained summing the growth coefficients determined in the single wavelength configurations. The complete set of experimental results suggests a coupling between the two wavelengths that could originate from the formation and the expansion of a plasma produced in the neighborhood of the subsurface cracks. To go further in the comprehension, the same study will be performed for damage sites with different morphologies and sizes in order to evaluate the impact of this last parameter on damage growth in the multiple wavelengths configuration. Investigations on the impact of the polishing process of the optical component on damage 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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growth would also be interesting. These experimental studies on LID growth will also be confronted to hydrodynamic calculations in future investigations. References 1. H. Bercegol, A. Boscheron, J.-M. Di-Nicola, E. Journot, L. Lamaignère, J. Néauport, and G. Razé, “Laser damage phenomena relevant to the design and operation of an ICF laser driver,” J. Phys. Conf. Ser. 112, 032013 (2008). 2. Y. Zheng, P. Ma, H. Li, Z. Liu, and S. Chen, “Studies on transmitted beam modulation effect from laser induced damage on fused silica optics,” Opt. Express 21, 16605–16614 (2013). 3. J. Néauport, E. Journot, G. Gaborit, and P. Bouchut, “Design, optical characterization, and operation of large transmission gratings for the laser integration line and laser megajoule facilities,” Appl. Opt. 44, 3143–3152 (2005). 4. R. Diaz, M. Chambonneau, R. Courchinoux, P. Grua, J. Luce, J.-L. Rullier, J.-Y. Natoli, and L. Lamaignère, “Influence of longitudinal mode beating on laser-induced damage in fused silica,” Opt. Lett. 39, 674–677 (2014). 5. J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355 nm) laser pulses,” J. Non-Cryst. Solids 352, 255–272 (2006). 6. B. Bertussi, P. Cormont, S. Palmier, P. Legros, and J.-L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express 17, 11469–11479 (2009). 7. S. G. Demos, M. R. Kozlowski, M. Staggs, L. L. Chase, A. Burnham, and H. B. Radousky, “Mechanisms to explain damage growth in optical materials,” Proc. SPIE 4347, 277–284 (2001). 8. A. M. Rubenchik and M. D. Feit, “Initiation, growth and mitigation of UV laser induced damage in fused silica,” Proc. SPIE 4679, 79–95 (2002). 9. S. Palmier, L. Gallais, M. Commandré, P. Cormont, R. Courchinoux, L. Lamaignère, J.-L. Rullier, and P. Legros, “Optimization of a laser mitigation process in damaged fused silica,” Appl. Surf. Sci. 255, 5532–5536 (2009). 10. R. N. Raman, R. A. Negres, M. J. Matthews, and C. W. Carr, “Effect of thermal anneal on growth behavior of laser-induced damage sites on the exit surface of fused silica,” Opt. Mater. Express 3, 765–776 (2013). 11. G. Razé, J.-M. Morchain, M. Loiseau, L. Lamaignère, M. Josse, and H. Bercegol, “Parametric study of the growth of damage sites on the rear surface of fused silica windows,” Proc. SPIE 4932, 127–135 (2003). 12. M. A. Norton, E. E. Donohue, W. G. Hollingsworth, M. D. Feit, A. M. Rubenchik, and R. P. Hackel, “Growth of laser initiated damage in fused silica at 1053 nm,” Proc. SPIE 5647, 197–205 (2005). 13. M. A. Norton, L. W. Hrubesh, Z. We, E. E. Donohue, M. D. Feit, M. R. Kozlowski, D. Milam, K. P. Neeb, W. A. Molander, A. M. Rubenchik, W. D. Sell, and P. Wegner, “Growth of laser initiated damage in fused silica at 351 nm,” Proc. SPIE 4347, 468 (2001). 14. R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18, 19966–19976 (2010). 15. L. Lamaignère, G. Dupuy, A. Bourgeade, A. Benoist, A. Roques, and R. Courchinoux, “Damage growth in fused silica optics at 351 nm: refined modeling of large-beam experiments,” Appl. Phys. B 114, 517–526 (2014).
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16. R. A. Negres, D. A. Cross, Z. M. Liao, M. J. Matthews, and C. W. Carr, “Growth model for laser-induced damage on the exit surface of fused silica under UV, ns laser irradiation,” Opt. Express 22, 3824–3844 (2014). 17. R. Courchinoux, G. Razé, C. Sudre, M. Josse, A. Boscheron, C. Lepage, E. Mazataud, E. Bordenave, L. Lamaignère, M. Loiseau, T. Donval, and H. Bercegol, “Laser-induced damage growth with small and large beams. Comparison between laboratory experiments and large-scale laser data,” Proc. SPIE 5273, 99–106 (2004). 18. C. W. Carr, D. A. Cross, M. A. Norton, and R. A. Negres, “The effect of laser pulse shape and duration on the size at which damage sites initiate and the implications to subsequent repair,” Opt. Express 19, A859–A864 (2011). 19. R. A. Negres, G. M. Abdulla, D. A. Cross, Z. M. Liao, and C. W. Carr, “Probability of growth of small damage sites on the exit surface of fused silica optics,” Opt. Express 20, 13030–13039 (2012). 20. L. Lamaignère, S. Reyné, M. Loiseau, J.-C. Poncetta, and H. Bercegol, “Effects of wavelengths combination on initiation and growth of laser-induced surface damage in SiO2,” Proc. SPIE 6720, 67200F (2007). 21. M. A. Norton, A. V. Carr, C. W. Carr, E. E. Donohue, M. D. Feit, W. G. Hollingsworth, Z. Liao, R. A. Negres, A. M. Rubenchik, and P. J. Wegner, “Laser damage growth in fused silica with simultaneous 351 nm and 1053 nm irradiation,” Proc. SPIE 7132, 71321H (2008). 22. S. G. Demos, R. A. Negres, R. N. Raman, A. M. Rubenchik, and M. D. Feit, “Material response during nanosecond laser induced breakdown inside of the exit surface of fused silica,” Laser Photon. Rev. 7, 444–452 (2013). 23. M. Chambonneau, R. Diaz, P. Grua, J.-L. Rullier, G. Duchateau, J.-Y. Natoli, and L. Lamaignère, “Origin of the damage ring pattern in fused silica induced by multiple longitudinal modes laser pulses,” Appl. Phys. Lett. 104, 021121 (2014). 24. S. G. Demos, R. N. Raman, and R. A. Negres, “Time-resolved imaging of processes associated with exit-surface damage growth in fused silica following exposure to nanosecond laser pulses,” Opt. Express 21, 4875–4888 (2013). 25. M. A. Norton, E. E. Donohue, M. D. Feit, R. P. Hackel, W. G. Hollingsworth, A. M. Rubenchik, and M. L. Spaeth, “Growth of laser damage on the input surface of SiO2 at 351 nm,” Proc. SPIE 6403, 64030L (2007). 26. S. Papernov and A. W. Schmid, “Laser-induced surface damage of optical materials: absorption sources, initiation, growth and mitigation,” Proc. SPIE 7132, 71321J (2008). 27. S. Reyné, G. Duchateau, J.-Y. Natoli, and L. Lamaignère, “Competition between ultraviolet and infrared nanosecond laser pulses during the optical breakdown of KH2PO4 crystals,” Appl. Phys. B 109, 695–706 (2012). 28. B. Ma, H. Ma, H. Jiao, X. Cheng, and Z. Wang, “Laser-damage growth characteristics of fused silica under 1064-and 532-nm laser irradiation,” Opt. Eng. 52, 116106 (2013). 29. S. G. Demos, M. Staggs, and M. R. Kozlowski, “Investigation of processes leading to damage growth in optical materials for large-aperture lasers,” Appl. Opt. 41, 3628–3633 (2002). 30. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963). 31. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt College, 1976), Chap. I, pp. 1–27.
3
CEA CESTA, 15 Avenue des Sablières, CS 60001, 33116 Le Barp Cedex, France
Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications, UMR 5107, 351 Cours de la Libération, F-33405 Talence, France
Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel, UMR 7249, 13013 Marseille, France *Corresponding author: [email protected] Received 11 November 2014; revised 19 January 2015; accepted 19 January 2015; posted 20 January 2015 (Doc. ID 226724); published 19 February 2015
The laser-induced damage growth phenomenon is experimentally studied for damage sites on the exit surface of fused silica. The sites are irradiated by nanosecond laser pulses at 1064 and 355 nm separately and also simultaneously. The results in the single wavelength configurations are expressed in terms of the probability of growth and growth coefficient. For growing sites, a fluence correction expression is proposed in order to take into account the millimetric Gaussian profile of the beams. The use of this expression is necessary to obtain results that are consistent with the ones obtained in the existing literature with large homogeneous beams. In the multiple wavelengths configuration, the results are expressed as a function of the laser fluences at each wavelength and are found to be closely related to the parameters determined in the single wavelength experiments. A coupling between the two wavelengths is quantified, and could originate from the formation and the expansion of a plasma produced both in the center and at the periphery of the damage sites. © 2015 Optical Society of America OCIS codes: (140.3330) Laser damage; (160.4670) Optical materials; (160.6030) Silica; (240.6700) Surfaces. http://dx.doi.org/10.1364/AO.54.001463
1. Introduction
Laser-induced damage (LID) is one of the key issues for the success of inertial confinement fusion laser facilities such as the laser megaJoule (LMJ, in France) or the National Ignition Facility (NIF, in the USA) [1]. This phenomenon can give rise to a degradation in the optical function of a component. Moreover, it may induce optical modulation effects on the transmitted laser beam, and damage the downstream components [2]. At the LMJ, nanosecond laser beams at 1053 nm (1ω) are converted to 527 nm (2ω) and 351 nm (3ω) with the use of potassium 1559-128X/15/061463-08$15.00/0 © 2015 Optical Society of America
dihydrogen phosphate (KDP) crystals and their deuterated analogs (DKDP). The 3ω laser beams are then focused on a millimetric target by means of focusing gratings that separate the unconverted 1ω and 2ω beams [3]. Since the conversion efficiency of the crystals is about 50%, the fused silica gratings are irradiated in a multiple wavelengths configuration by the main 3ω beam and also the 1ω and 2ω residual ones. The physical mechanisms involved during LID initiation on the exit surface of fused silica have recently been investigated at 1ω as well as at 3ω on samples polished with the same processes [4]. Studies of LID morphology show that subsurface cracks are located under the molten and fractured initiated craters [5,6]. These subsurface cracks are assumed to absorb the laser flux [7,8]. Hence, 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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successive laser irradiations may induce an increase in the size of the damage sites and a production of subsurface cracks at their periphery. The understanding of this phenomenon (referred to as “LID growth”) enables the development of mitigation techniques [9,10]. Many studies have been conducted in order to determine how LID sites grow at 1ω [11,12], as well as at 3ω [13–16], expressing the growth coefficient as a function of the laser fluence. These studies have been performed using large homogeneous beams > 10 mm2 . However, few studies compare the growth coefficients obtained using large homogeneous and small Gaussian beams [17]. Recent works show that the probability of growth at 3ω is a function of both the initiated damage size and the laser fluence [18,19]. Even if the LID growth phenomenon is well characterized in the single wavelength configurations, few studies have been conducted in a multiple wavelengths configuration [20,21]. These studies show that combining the wavelengths increases the growth coefficient values. However, the probability of growth in this configuration needs to be investigated. Other recent studies show that both LID initiation [22,23] and growth [24] phenomena originate from a plasma formation and expansion in the center and also at the periphery of the damage sites. The simultaneous irradiations of silica at two different wavelengths could significantly impact the dynamics of the produced plasma. In this multiple wavelengths configuration, both the probability of growth and the growth coefficient need to be expressed as a function of the two laser fluences. In the present study, the probability of growth and the growth coefficient are both investigated at 1ω, at 3ω, and also in a configuration combining these two wavelengths, for damage sites on the exit surface of synthetic fused silica samples. Contrary to the linear growth of the damage sites on the entrance surface, the area of the ones located on the exit surface is known to scale exponentially with the number of laser pulses [25], which may originate from the absence of a plasma shielding of the surface from the laser flux [26]. In our experiments, we have used millimetric and Gaussian-shaped laser beams. These spatial characteristics imply that a damage site whose dimensions are close to the diameter of the incident beam is irradiated at an average fluence significantly lower than the maximum one. The spatial profile of the beams is thus taken into account while investigating the damage growth. We propose a fluence correction expression that enables us to compare our results to the ones obtained with large homogeneous beams existing in the literature. The probability of growth is investigated for damage sites with various initial areas. In order to express this probability as a function of the laser fluence only, we have chosen to study the growth of damage sites initiated at 3ω with initial diameter around 60 μm. In the multiple wavelengths configuration, the probability of growth and the growth coefficient are 1464
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experimentally determined and parameterized as a function of the laser fluences at the two wavelengths. In order to interpret the complete set of results in the multiple wavelengths configuration, some physical processes that might be involved in our experiments are proposed. 2. Experimental Setup
The experimental study has been performed on 10 mm thick synthetic fused silica samples superpolished by SESO company. The laser facility described in Ref. [27] has been employed to irradiate the samples. This facility is based on a tripled Nd: YAG laser, giving access to pulses at 1064 nm (1ω) and 355 nm (3ω) irradiating the sample simultaneously (multiple wavelengths configuration) or separately (single wavelength configurations). It operates in multiple longitudinal modes (MLM), and the pulse durations [full width at half maximum (FWHM)] of the Gaussian fits of the temporal profiles are 6.5 and 5.5 ns at 1ω and 3ω, respectively. The 1ω and 3ω pulses are separated by means of a dichroic mirror. Each beam is then focused by means of a lens whose focal length is approximately 4 m. Using another dichroic mirror, at the focus region, the two spots are collinear and Gaussian-shaped, and their diameters at 1/e are 700 and 500 μm at 1ω and 3ω, respectively. The depths of focus are much higher than the sample thickness. As a consequence, both the beams’ diameters are considered constant along their propagation through the sample. The maximum fluences that can be reached in the single wavelength configurations are 130 and 75 J∕cm2 at 1ω and 3ω, respectively. The sample is fixed on a motor-driven stage providing translations in a plane that is perpendicular to the laser beams. The damage sites on the exit surface of the sample are separated by 3 mm in order to prevent the influence of a damage growth session on another one. The exit surface of the sample is illuminated with white light. The size measurement of the damage sites is performed recording their images after each laser pulse by means of a long focal microscope and a CCD camera. In order to protect these two last apparatuses from the incident laser beams, an angle of about 10° is introduced between the microscope and the laser path. Recent studies have shown that LID morphology is strongly related to the associated pulse wavelength [28], particularly when the laser operates in the MLM regime [23]. These differences in morphology could significantly impact the growth behavior of a damage site. In order to obtain results that are independent of the LID morphology, the same initiation wavelength has been chosen in all the studied growth configurations. Since at a given fluence LID density is much higher at 3ω than at 1ω [4], the initiation wavelength has been chosen at 3ω. At high fluences (i.e., for damage initiation probability higher than 80%), the observed initiated damage sites generally show multiple pits. Hence, the damage sites are
P
ng ; ntot
(1)
where ng is the number of growing damage sites among the ntot total tested ones. Since the probability of growth is known to increase for increasing initial damage areas A0 or laser fluences F [19], P has been evaluated for various A0 and F values. The previously developed notion of probability of growth is not sufficient to describe the growth behavior of the damage sites. In the present study, the damage sites are located on the exit surface of silica, and grow exponentially with respect to the number of laser pulses [25]. Thereby, the damage area after n laser pulses (noted An ) can be written as An A0 ek·n : Fig. 1. Confocal micrograph of a damage site initiated at 3ω. The images noted (a) and (b) correspond to side views of the site, and (c) corresponds to its top view.
initiated at 50 J∕cm2 , where the damage initiation probability is around 50%, and the sites are single pit with sizes of about 60 μm. The morphology of a typical LID site initiated at this fluence is shown in Fig. 1. The measurement has been realized employing a confocal microscope in reflective mode operating at 532 nm. This characterization exhibits that subsurface cracks of about 10 μm are distributed under a crater that is about 10 μm deep. This morphology is consistent with the observed one in Refs. [5] and [6] for damage sites initiated at 3ω. Once initiated, the damage sites are irradiated by several laser pulses separated by a few seconds (i.e., single-shot mode) at a constant fluence at 1ω, at 3ω, or simultaneously at 1ω and 3ω. The maximum growth fluences at 1ω and 3ω are 40 and 20 J∕cm2 , respectively. In the case of nongrowing damage sites, the growth sessions are stopped after 200 pulses. In the single wavelength configurations, the sessions are stopped when the damage size reaches the beam diameter at 1/e. Since the beam diameter at 3ω is smaller than at 1ω, the growth sessions in the multiple wavelengths configuration are stopped when the damage size reaches the beam diameter at 3ω.
(2)
The growth coefficient k in Eq. (2) is the mean of the growth coefficients kn defined pulse to pulse as A kn ln n1 ; An
3
where An and An1 are the damage areas after the pulses n and n 1, respectively. Due to the Gaussian shape of the millimetric beam spots used in our experiments, it is worth noting that the average fluence irradiating a damage site strongly depends on its area. Figure 2 schematizes the necessity to take into account the spatial profile of the laser beam while evaluating the fluence irradiating a growing damage site. A site with size close to that of the incident beam at 1/e is irradiated at an average fluence F dam significantly lower than the measured maximum one (noted F max in Fig. 2). It is thus necessary to take into account the increase in damage size while evaluating both the fluence and the growth coefficient after a laser pulse. Demos et al. have shown that plasma is produced both in the center and at the periphery of a damage site during its growth [24,29]. In our experiments performed
3. Data Analysis
In order to quantify the growth behavior, an image of the damage sites is recorded after every irradiation. The images are then converted into binary images using ImageJ software, giving access to the damage area after each pulse. The angle between the camera and the sample is taken into account when evaluating the aspect ratio of the images. The first result directly obtained after a growth session on a damage site is its probability of growth. A damage site has been considered as growing if its final size after N laser pulses (N < 200) is at least twice as large as its initial size. The probability of growth P reads
Fig. 2. Schematic illustration of a damage growth session. The lightest shades of gray represent the earliest stages of the growth session. The ratios f k between the average fluence F dam irradiating the damage site (concentric ellipses) and the maximum laser fluence F max for the shots n, n 1, and n 2 are reported on the vertical axis. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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with small Gaussian beams, the center and the periphery of a damage site are mainly irradiated by the Gaussian peak and the non-Gaussian part (i.e., the wings) of the laser spot, respectively. Hence, the measured maximum fluence can be written as F max F g F w , where F g and F w are the fluences of the Gaussian peak (with area Sg ) and the wings (with area Sw ), respectively. For a laser spot with an equivalent area Seq (at 1/e), the fluences F g and F w have been calculated as follows: Seq − Sw Seq − Sw : ; F F max 1− F g F max Sg − Sw w Sg − Sw On the basis of Fig. 2, we propose that the average fluence F dam irradiating a damage site with area Sdam reads S S Sg Sw − dam − Sdam Sg F dam F g 1−e Fw 1 − e w ; (4) Sdam Sdam where the first and second terms of the sum are the contributions of the Gaussian peak and the wings, respectively. For both of these terms, the exponential decrease of F dam with respect to Sdam is due to the exponential growth of the studied damage sites. For damage sites with areas Sdam that are much lower than Sg and Sw , F dam ≈ F max according to Eq. (4). The ratio between F dam and F max is calculated in Fig. 3 according to Eq. (4) at 1ω and 3ω as a function of the damage diameter. The spatial parameters at each wavelength are issued from two typical measurements of the beams. At both wavelengths, for damage areas from 0 to Seq , the fluence decreases from F max to about 0.6F max . The decrease of the ratio F dam ∕F max is higher at 3ω since the beam at this wavelength is smaller than at 1ω. It is worth
noting that for the typical size of the studied sites (60 μm), F dam ∈ 0.99F max ; F max at each wavelength. Thereby, the probability of growth P given by Eq. (1) can be associated with the fluence F max . However, for growing damage sites, Fig. 3 shows that the growth coefficient kn given by Eq. (3) has to be associated with the fluence F dam . In the multiple wavelengths configuration, F dam is calculated at both wavelengths, considering separately the areas Seq, Sg , and Sw of the two spots. According to the previous expressions of the probability of growth, growth coefficient, and corrected fluence, the results can be expressed in both the single and multiple wavelengths configurations. In each single wavelength configuration, the probability of growth P is calculated according to Eq. (1). We have first investigated the influence of the initial damage size on P at constant 1ω and 3ω fluences. As shown in Ref. [19], the probability of growth for damage sites with a given size increases with respect to the laser fluence F and can be fitted by a sigmoid curve as PF 1 −
1
1
;
p F F 50%
where F 50% is the fluence at which the probability of growth is equal to 50%, and the exponent p determines the shape of the sigmoid curve. The percent error (noted % error) on the probability measurements is given by [19] % error
P1 − P p : P ntot
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(6)
In the multiple wavelengths configuration, the set of probability values P is expressed as a function of both the fluences at 1ω and 3ω. For growing damage sites, the growth coefficient [kn in Eq. (3)] is calculated after each laser pulse and expressed as a function of the corrected fluence [F dam in Eq. (4)]. In the single wavelength configurations, the average growth coefficient values hki are commonly fitted as follows [13,15]: hki CF dam − F th ;
Fig. 3. Evolution of the ratio F dam ∕F max calculated according to 3ω Eq. (4) at 1ω (in red) and 3ω (in blue). The notations S1ω g and Sg indicate the diameters associated with the areas of the Gaussian peaks, experimentally measured at 1ω and 3ω, respectively. The 3ω notations S1ω eq and Seq indicate the diameters associated with the equivalent areas (at 1/e) at 1ω and 3ω, respectively. The diameters associated with the areas of the wings Sw are 1000 and 880 μm at 1ω and 3ω, respectively. At both wavelengths, the fluence contained in the wings corresponds to about 10% of the maximum fluence. The notation A0 indicates the typical initial diameter of the studied damage sites.
(5)
(7)
where C is the rate of increase in the growth coefficient, and F th is the fluence threshold for growth. The parameterization given by Eq. (7) is representative of the experimental results: the damage area exponentially increases after a laser pulse with a fluence higher than a threshold where no growth is observed below. In the multiple wavelengths configuration, the kn values are fitted with a nonlinear least squares Levenberg–Marquardt algorithm [30], assuming a linear superposition as follows: 3ω 1ω 1ω ~ hkF 1ω dam ; F dam i C1ω F dam − F th
~ 3ω F 3ω − F 3ω ; C dam th
(8)
~ 1ω and C ~ 3ω are where the rates of increase in growth C two fitting parameters. The fluence thresholds for 3ω growth F 1ω th and F th at 1ω and 3ω, respectively, are determined by the results obtained in the single wavelength configurations. 4. Results and Discussion A.
LID Growth in Single Wavelength Configurations
The growth behaviors are first determined in both the single wavelength configurations, at 1ω and 3ω separately. We first study the probability of growth as a function of the initial damage size at constant fluences at 1ω and 3ω. Then, for a given damage size, the probability of growth is expressed as a function of the fluence F max . The evolution of the probability of growth for damage sites as a function of their initial diameters is displayed in Fig. 4. The chosen fluences are 34 J∕cm2 at 1ω and 13 J∕cm2 at 3ω, which are higher than the growth thresholds reported in Refs. [11,13,15]. As previously shown in Ref. [19], the probability of growth increases with the initial damage diameter at a constant fluence at 3ω. A similar behavior is obtained at 1ω. The dependence in size of P could originate from the absorbing subsurface fractures, which are larger and more numerous for large craters [6]. As a consequence, a site with a large size more efficiently absorbs the laser energy and its size increases easily. The double dependence (in size and in fluence) of the probability of growth could complicate the interpretation of the results. In order to study the influence of the combination of wavelengths, the size of the studied initiated damage sites has been chosen constant. Hence, all the following experiments have been performed for initiated damage sites with diameters of about 60 μm (10 μm). The evolution of the probability of growth as a function of the fluence at 1ω and 3ω for damage sites with the previously considered size is shown in Fig. 5. The sigmoid fits for the experimental data have been introduced in Eq. (5). The fluence at which the prob 33.5 and ability of growth is equal to 50% is F 50% 1ω 2 15.5 J∕cm at 1ω and 3ω, respectively. At F 50% 3ω both wavelengths the p exponent value is 5. In both
Fig. 4. Probability of growth for damage sites on the exit surface of fused silica as a function of their initial diameter at 1ω (34 J∕cm2 ) and 3ω (13 J∕cm2 ). The error bars stand for % error given by Eq. (6).
Fig. 5. Probability of growth for damage sites with diameters of about 60 μm 10 μm as a function of the fluence at 1ω (red circles) and at 3ω (blue squares). The red and blue dashed sigmoid curves stand for the parameterizations of the results according to Eq. (5) at 1ω and 3ω, respectively. The error bars stand for % error given by Eq. (6).
the single wavelength configurations, the probability of growth increases with the laser fluence for damage sites with similar sizes, in accordance with a previous study conducted at 3ω by Negres et al. [19]. One can note that the parameters p and F 50% associated with the sigmoid fits would have been different for other initial damage diameters [19]. The average growth coefficient hki obtained for different growing damage sites at 1ω among the previously considered ones is reported in Fig. 6 as a function of the corrected fluence F dam and also as a function of the maximum fluence F max . In each case, hki linearly scales the fluence whether it is corrected or not. For fluences around 30 J∕cm2 , hki ≈ 0.32 when the correction described by Eq. (4) is applied, and hki ≈ 0.24 when it is not. This shift is reduced for higher fluences, which corresponds to the beginning of the growth sessions where F dam ≈ F max (Fig. 3). The comparison between the results obtained at 1ω with large homogeneous beam experiments by Razé et al. [11] and the hki values obtained in our study, expressed as a function of F dam and also F max , highlights the necessity of taking into account the damage size when evaluating the fluence during a growth session. Similar results are obtained at 3ω when compared to the ones reported in Ref. [15].
Fig. 6. Evolution of the average growth coefficient hki in the 1ω configuration, expressed as a function of F max (green triangles), and F dam (red circles) calculated according to Eq. (4). The green and red dashed lines stand for the corresponding fits with equations hki 1.77 × 10−2 F max − 13.1 and hki 1.62 × 10−2 F dam − 6.9, respectively. The orange squares are data issued from Ref. [11]. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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Hence, we have expressed hki as a function of F dam in all the configurations reported below. A comparison of the evolution of hki as a function of F dam in the two single wavelength configurations is reported in Fig. 7. As shown in Fig. 6 at 1ω, hki linearly scales with F dam at 3ω. The rates of increase in growth are C1ω 1.62 × 10−2 and C3ω 3.18× 10−2 cm2 ∕J. The deduced values for the fluence 3ω 2 thresholds are F 1ω th 6.9 and F th 3.4 J∕cm . A growth coefficient of 0.40 (corresponding to an area multiplied by 1.5) is reached at 32 and 16 J∕cm2 at 1ω and 3ω, respectively. Thereby, Figs. 5 and 7 show that the LID growth phenomenon is enhanced in the 3ω configuration, by comparison to the 1ω one. This result can qualitatively be explained by the subsurface fractures that more efficiently absorb the photons at 3ω than at 1ω. These two figures and the associated fitting parameters are used as preliminary results for the following multiple wavelengths study. B.
LID Growth in Multiple Wavelengths Configuration
Based on the results obtained in the single wavelength configurations, LID growth has been experimentally studied in the simultaneous multiple wavelengths configuration. In this case, the initial tested damage sites exhibit the same morphology (initiated at 3ω) and size (about 60 μm) as the ones studied in the single wavelength cases. Thereby, the probability of growth and also the growth coefficient mainly depend on the laser fluences at 1ω and at 3ω, as suggested in Refs. [20] and [21]. Figure 8 shows the probability of growth as a function of the 3ω fluence at various additional 1ω fluences. The probability of growth increases with respect to the 3ω fluence at every 1ω fluence. The data obtained at each F 1ω value are compared with the following expression: PF 1ω ; F 3ω 1 −
1
1
F 1ω 50% F 1ω
;
F 3ω p F 50% 3ω
(9)
and F 50% at which the where the fluences F 50% 1ω 3ω probability of growth is 50%, and also the exponent
Fig. 7. Evolution of the average growth coefficient hki as a function of the corrected fluence F dam at 1ω (red circles) and at 3ω (blue squares). Red and blue dashed lines stand for the parameterizations of the results according to Eq. (7) at 1ω and 3ω, respectively. 1468
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Fig. 8. Evolution of the probability of growth for damage sites with diameters of about 60 μm 10 μm in the multiple wavelengths configuration as a function of the fluence at 3ω for various additional 1ω fluences. The experimental data (colored circles) are compared to the parameterizations issued from Eq. (9) at the same 1ω fluences (dashed curves in the same colors). The error bars stand for % error given by Eq. (6).
p 5, are the values determined in the single wavelength configurations. Figure 8 shows that the parameterization of Eq. (9) reproduces fairly well the experimental trends. Moreover, it ensures that both the single wavelength cases are also well fitted. In order to check the validity of Eq. (9), we have tried to fit the results in the multiple wavelengths configuration with other parameterizations. For p ≠ 5 in Eq. (9), the slopes at half maximum of the calculated curves do not enable us to reproduce the experimental trends. Moreover, these cases are not consistent with the results obtained in the single wavelength configurations. In Eq. (9), we have F 3ω ∕F 50% p by also replaced the term F 1ω ∕F 50% 1ω 3ω F 1ω ∕F 50% p F 3ω ∕F 50% p . Although this case is 1ω 3ω consistent with the single wavelength configurations, the results obtained in the multiple wavelengths configuration are underestimated by this parameterization that does not involve the cross terms in F 1ω ∕F 50% F 3ω ∕F 50% p when it is devel1ω 3ω oped. Hence, these results suggest a coupling between the two wavelengths. The increase in the probability of growth in the multiple wavelengths configuration compared to the single wavelength configurations (Fig. 8) could originate from the formation of the plasma in the neighborhood of the absorbing subsurface cracks [7,24,26,29]. Even if such a plasma is easily produced by the 3ω pulse, two mechanisms induced by the 1ω pulse can be evoked in order to explain this coupling. The first one is the field intensification arising from subsurface cracks, which gives rise to plasma formation [7,29]. Combining the wavelengths could enhance this phenomenon. The second mechanism is described by the Drude model [31]. The free electrons provided by the plasma are more easily heated at 1ω than at 3ω [27]. The heat is transferred in silica, leading to an increase in the damage size. As previously done in the single wavelength configurations, the growth coefficients kn have been calculated for the growing damage sites in the multiple wavelengths case. The resulting average growth
Fig. 9. Evolution of the average growth coefficient hki as a func1ω tion of F 3ω dam at various F dam values. The experimental data (colored circles) are compared to the parameterization issued from Eq. (10) at the same 1ω fluences (dashed lines in the same colors).
coefficient hki in this configuration is plotted in Fig. 9 1ω as a function of F 3ω dam at various additional F dam values. A linear increase in hki with respect to the 3ω fluence is reported at every 1ω fluence. Moreover, the hki values increase for increasing 1ω fluence at a constant 3ω fluence. In order to quantify this increase in hki, the complete set of kn values has been parameterized according to Eq. (8), where the fluence thresh3ω 2 olds for growth F 1ω th 6.9 and F th 3.4 J∕cm are extracted from the previous results in the single wavelength configurations, and the growth rates ~ 3ω are two fitting parameters. After optimi~ 1ω and C C ~ 3ω values are 1.70 × 10−2 and ~ 1ω and C zation, the C −2 2 3.23 × 10 cm ∕J, respectively, with standard error around 3%. It is worth noting that the values of the ~ 1ω and C ~ 3ω are close to the two fitting parameters C rates of increase in growth that have been previously obtained in the single wavelength configurations. This result suggests that the average growth coefficient hk1;3 i in the multiple wavelengths case can be written as hk1;3 F 1ω ; F 3ω i hk1 F 1ω i hk3 F 3ω i;
(10)
where hk1 i and hk3 i are the growth coefficients in the single wavelength configurations. A comparison between the parameterization given by Eq. (10) and the experimental data is reported in Fig. 9. Once again, the parameterization issued from Eq. (10) is consistent with the results obtained in the single wavelength configurations. Moreover, it reproduces fairly well the experimental trends, meaning that hk1;3 i essentially depends on the two laser fluences. This agreement holds if hk1;3 i is plotted as a function 3ω of F 1ω dam at various additional F dam values. The small discrepancy between the parameterization given by Eq. (10) and the experimental data could originate from the dependence of the growth coefficient on the size of the damage sites [15,16], which has not been taken into account. In order to interpret the increase in growth coefficient in the multiple wavelength configuration compared to the 3ω one, Lamaignère et al. and Norton et al. have suggested that the plasma produced in the
neighborhood of the subsurface cracks starts absorbing the laser flux at both wavelengths [20,21]. Such a plasma absorbs the 1ω flux after its production by the 3ω pulse. In these multiple wavelengths studies, the growth coefficient linearly scales with the total fluence F 3ω KF 1ω , where K corresponds to the percentage of the 1ω fluence required to fit the results at 3ω only. The values of the K parameter in Refs. [20] and [21] are 0.80 and 0.70, respectively. In our study, according to Eq. (10), this value is fixed by the ratio C1ω ∕C3ω ≈ 0.55. These differences in the K values could result from the temporal shape of the pulses—MLM in our study, and single longitudinal mode (SLM) in Refs. [20] and [21]. The plasma production at 3ω is facilitated for SLM pulses compared with MLM ones [4]. Hence, in our study, the absorption of the 1ω flux by the plasma starts later in the pulse than in Refs. [20] and [21], which can explain the differences in the K values between our experiments and the existing literature. Moreover, recent studies show that plasma dynamics are different at 1ω [23] and at 3ω [22,29]. Hence, the cooperative effect of the two wavelengths concerning the growth coefficient described by Eq. (10) could result from a combination of the growth processes involved at 1ω and 3ω separately. 5. Conclusion
In this experimental study, we have first highlighted the influence of the initial damage size on the growth phenomenon on the exit surface of fused silica. For damage sites of about 60 μm initiated at 3ω, the results have been expressed as a function of the laser fluence only. An expression has been proposed in order to take into account the spatial profiles of the Gaussian-shaped millimetric laser beams while evaluating the fluence irradiating a damage site during a growth session. This fluence correction has allowed us to obtain results that are consistent with large homogeneous beams existing in the literature at 1ω and 3ω. The probability of growth and the growth coefficient scale as a sigmoid and a linear function of the laser fluence, respectively. The results in the multiple wavelengths configuration have been deduced from the parameters obtained at 1ω and 3ω. The probability of growth obtained when combining the two wavelengths is a sigmoid function of the fluences at 1ω and 3ω. The growth coefficient in this configuration can be obtained summing the growth coefficients determined in the single wavelength configurations. The complete set of experimental results suggests a coupling between the two wavelengths that could originate from the formation and the expansion of a plasma produced in the neighborhood of the subsurface cracks. To go further in the comprehension, the same study will be performed for damage sites with different morphologies and sizes in order to evaluate the impact of this last parameter on damage growth in the multiple wavelengths configuration. Investigations on the impact of the polishing process of the optical component on damage 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS
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