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Abstract
Forward pump pulses with nanosecond duration are able to generate an acoustic wave via electrostriction through a few centimeters of bulk silica. Part of the incident energy is then scattered back on this sound wave, creating a backward Stokes pulse. This phenomenon known as stimulated Brillouin scattering (SBS) might induce first energy-loss, variable change of the temporal waveform depending on the location in the spatial profile making accurate metrology impossible, and moreover it might also initiate front surface damage making the optics unusable. Experiments performed on thick fused silica optics at 355 nm with single longitudinal mode pulses allowed us to detect, observe and quantify these backward pulses. Experimental results are first compared to theoretical calculations in order to strengthen our confidence in metrology. On this basis a phase-modulator has been implemented on the continuous-wave seeders of the lasers leading to pulses with a wide spectrum that suppress SBS and do not exhibit temporal overshoots that also reduce Kerr effects. The developed set-ups are used to check the reduction of the backward stimulated Brillouin scattering and they allow measuring with accuracy the rear surface damage of thick fused silica optics.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The Laser-Induced Damage (LID) measurement of fused silica optics irradiated at 355nm in the nanosecond range and very specifically in the case of thick optics is a tricky metrology. This problem is of critical importance in the framework of high power facilities (LMJ, NIF,…) where thick plates as vacuum windows and vacuum lenses are implemented to sustain the pressure between air and vacuum environments. Due to their thicknesses and very high intensity pulses, these optics are highly incline to damage due to nonlinear effects such as Kerr effects [1]. More an additional nonlinear effect appears with narrow band lasers that are used to qualify the LID resistance of fused silica optics: that is the Stimulated Brillouin Scattering (SBS) effect [2]. These two non-linear effects are first prejudicial and secondly they make impossible accurate LID measurements, the transmitted beam becoming unstructured and finally unknown. The motivation of this work is then the suppression of these effects on laser damage benches that operate nanosecond Nd:YAG lasers with a continuous-wave injection seeder delivering pulses that have by nature a narrow spectral bandwidth. To this end, a specific metrology has been first implemented to detect, measure and precisely quantify the SBS beam. Next measurements are compared to numerical simulations to strengthen our understanding of this nonlinear effect. Finally a technological solution, based on a phase-modulator, is presented that allows the suppression of such effects [3]. In that way, damage occurrence of thick optics is considerably reduced; more accurate metrology of LID resistance of thick optics is then possible.
Repeatable and well-characterized laser pulses are mandatory to get accurate and reproducible LID measurements. For that purpose, tests are generally carried out by means of single longitudinal mode (SLM) pulses characterized by smooth bell-shaped temporal profiles that are easy to measure and stable shot to shot [4]. In that way such pulses allow the comparison of rear surface damage densities of fused silica optics irradiated on different facilities working at different pulse durations [5]. However, in the case of testing thick optics, high intensity levels may involve non-linear effects that are prejudicial to the interpretation of the results, such as the Kerr effect [6–10], driven by the instantaneous intensity, and stimulated Brillouin scattering (SBS) [2,11,12] mainly driven by the spectral power density. The use of SLM pulses at low fluences avoids high intensities and thus minimizes the Kerr effect but SBS should be considered. Stimulated scattering always involves the coupling of the incoming laser beam, acting as a pump, and a frequency-shifted scattered wave. In the case of SBS, the pump and the scattered optical waves are coupled by acoustic waves (i.e. acoustic phonons) generating an intense frequency-shifted radiation. Compared with Raman scattering (due to molecular vibrational transitions), Brillouin scattering typically has a larger cross section but a narrower linewidth (the Raman gain is known to be one order lower than the Brillouin one). For this reason, stimulated Brillouin scattering tends to arise at lower intensities for narrow-band (e.g. single-longitudinal-mode) lasers. Thus the stimulated Raman scattering is not considered in this paper [13]. SBS occurs in a large variety of transparent media, from single-mode fibers [14] to fused silica optics employed in large laser facilities devoted to inertial confinement fusion [1,15]. This effect is mainly driven by the electrostriction strain produced by an intense laser pulse with long enough nanosecond durations. This strain excites acoustic waves on which a Stokes wave scatters a significant amount of energy. At a low energy level, Yoshida [16] demonstrated that fused-quartz glass can be used as a mirror with a high-SBS reflectivity of over 95%, without any damage. At a high energy level, for large optical components and large beams [17], the fracture damage in the center of a lens was attributed to an intense acoustical wave brought to focus in the center by reflecting off the circular edge of the optic. The source of this wave was light generated by transverse stimulated Brillouin scattering (TSBS). For large beams and high power lasers, to suppress such damage events, an increase in laser bandwidth reduces the amplification of SBS. It was demonstrated that an average bandwidth of few GHz is sufficient in reducing TSBS to undetectable levels for conditions twice the SBS threshold [15]. Nonetheless, for smaller beams and smaller but thick enough optical components, the Stokes wave direction is preferably in the direction opposite to the pump one: the backward SBS (BSBS) and its intensity increases exponentially with the intensity of the pump beam and the length of the interactive media. Then, for powerful pump beams, the counter-propagating Stokes wave can convey high enough fluence to trigger front surface damage, whereas the damage occurrence of transparent dielectrics is known to appear quasi-systematically on the rear face. Figure 1 reports front surface damage densities (FSDD) measurements we made initiated on fused silica samples of different thickness (6.5; 20; 43mm) at 355 nm and with 3 ns pulse duration. These samples were finished with the same polishing process meaning that damage precursors are supposed to have the same physical properties and the same population density [18]. The thicker the sample, the higher the FSDD: the damage density enhancement with the increase of the thickness is then likely due to BSBS. These results suggest a “threshold-in-thickness effect” for BSBS. In addition, the damage picture presented in Fig. 2, obtained on the 43mm thickness optic, shows a front surface BSBS-induced damage multiple-pit pattern, whereas a unique damage pit is usually obtained on the rear surface at this fluence level, corresponding to the peak fluence of the Gaussian beam. This damage pattern is very similar to the spatial profile pattern numerically calculated [2] reporting a spatially incoherent Stokes wave on the front surface. Then these numerous front surface damage sites are likely due to numerous small ‘hot spots’ (small areas with large energy) due to the loss of spatial coherence of the BSBS wave. Hence with or without front surface damage occurrence, the pump beam depletion renders the rear surface damage measurements complex.
Fig. 1 Front surface damage density, measured by means of rasterscan procedure, as a function of intensity for fused silica samples with different thicknesses (6.5 – 20 – 43 mm) irradiated at 355nm for a linear polarization.
Fig. 2 Front surface damage due to BSBS obtained on a 43 mm-thick fused silica optic irradiated by a 355 nm - 3 ns SLM pulse of 15 J/cm2 (5 GW/cm2).
In order to reduce this effect on laser damage benches that operate nanosecond Nd:YAG lasers with a continuous-wave injection seeder delivering narrow spectral bandwidth pulses, we have developed specific laser set-ups to detect, measure and quantify the BSBS. Next, a phase-modulated injection seeder was used so that the laser delivers pulses having both a large spectral bandwidth and a smooth temporal waveform [3]. The smooth temporal profile is mandatory to avoid non-linear Kerr effect leading to the uncontrolled enhancement of the rear surface damage densities. Due to a large enough spectral bandwidth, such pulses allow for instance suppressing SBS. In that way, such a seeder makes rear surface damage measurements of thick optics possible.
The paper is organized as follows. Section II presents the experimental set-ups that allow for the detection of the BSBS. Brillouin characterization is presented in Sec. III. Experimental results are compared to 1D and 3D time-dependent models that strengthen our understanding of BSBS both experimentally and theoretically. Finally, in Sec. IV, we investigate the reduction of the BSBS by means of a phase-modulated injection seeder and use it to carry out rear surface damage measurements of thick fused silica optics.
2. Experimental set-ups
2.1 Facility
The experimental study was conducted by means of two different laser damage facilities at CEA/CESTA in France. These facilities are all based on tripled Q-switched Nd:YAG lasers providing access to 1064 nm (1ω) or 355 nm (3ω) radiations. A continuous-wave (CW) injection seeder ensures the selection of a single longitudinal mode (SLM) and permits the generation of repeatable near-Gaussian pulses. The equivalent pulse durations (defined as the ratio of the total energy to peak power) are 6.5 ns and 3 ns at 3ω depending on the facility. At the output, the lasers deliver approximately 700 mJ and 200 mJ at 3ω respectively. Energy on the sample is adjusted through a “λ/2-plate-polarizer” system (see Fig. 3). A pyroelectric cell records the energy for each shot, this diagnosis being calibrated with a standard calorimeter before each set of experiments. For each facility, the laser beam is linearly polarized. Each laser beam is then focused on the sample by a plano-convex lens whose focal lengths are approximately 8 m and 3 m, respectively. Thus, the depths of focus are much longer than the sample thickness ensuring that the beam shapes are constant along their propagation through the sample. At the focus region, beam spots are millimetric, Gaussian-shaped and their diameters are about 850 μm and 275 μm at 3ω (given at 1/e for a Gaussian beam). Thus, fluences up to 100 J/cm2 are available on these facilities.
Fig. 3 General experimental set-up dedicated to laser damage experiments (PC: pyroelectric cell ; CCD: charge coupled device camera ; IP: intensity profile). Specific instrumentations have been added to detect and measure the BSBS (diagnostics #1 and #3 were either a spectrometer or a high-speed phototube HSP). The inset in the left corner schematizes pump (Ip) and BSBS (IBSBS) beams for a length of interaction L.
2.2 Damage test procedure
The rasterscan procedure was used to measure laser-induced damage densities (LIDD) on a large fluence range both on front surface and rear surface during the same experiment. A large area was then irradiated. The laser worked at 10 Hz, the sample moved continuously and the shot-to-shot step was chosen to ensure that a large fraction of the surface was scanned. Due to shot-to-shot fluctuations, the main beam parameters, energy, spatial and temporal profiles, and the beam positions on the sample, were recorded for each shot in order to build the corresponding fluence map.
After the rasterscan, a post-mortem observation of the irradiated areas was made to obtain the damage maps on the front and rear surfaces. The use of a long working distance microscope permits the detection of damage sites of a few micrometers. In this study all the detectable damage sites (above about 5 μm) were considered whatever their morphologies. Matching the fluence and damage maps allows one to extract the fluence Fp for each damage site. Damage sites are then gathered in several fluence groups [(Fp-ΔFp/2) to (Fp + ΔFp/2)]. Knowledge of the number of damage sites in each fluence group N(f), the number of shots (or irradiated area) for each group n(f) and the equivalent area of each shot, allows for the obtaining of LIDDs on front and rear surfaces [19].
2.3 Samples
For this study, one-hundred-millimeter-diameter samples, made in synthetic fused silica (HERAUS S312) and superpolished by the SESO company, were used. Their damage densities are typically of the order of 1 to 10 damage.cm-2 in the range of 10 to 15 J.cm-2. Sample thicknesses were 6.5, 20 and 43 mm for the experiments dealing specifically with the measurements of front surface LIDD (Fig. 1), and 34, 43 and 90 mm for the detection and quantification of BSBS.
2.4 Specific diagnosis for BSBS analysis
The set-ups used for laser damage experiments, previously presented [5,19], were up-graded in order to be able to carry out at the same time LIDD measurements and BSBS experiments. Three identical high-speed phototubes (band-pass 7 GHz, Hamamatsu RU435) were added for that purpose (see Fig. 3). Phototube, referenced as #1, records the temporal profile of the pump pulse directly behind a leaky mirror: this is the reference signal. Phototube, referenced as #2, records the transmitted pulse through the sample. Due to the fact that the BSBS pulse is collinear to the pump beam, in a counter-propagating direction, the BSBS temporal profile is recorded on Phototube, referenced as #3, located behind a leaky mirror too. Comparison of these 3 signals allows us to quantify the pump beam depletion due to Brillouin occurrence. The signals on these three phototubes are simultaneously measured. They are plugged on a three-channel oscilloscope that has a 6 GHz bandwidth on each channel (Tektronix DSA73304D).
It was first necessary to check that the backscattered beam corresponds to the Brillouin beam and not to the back-reflected pump one. To this end, instead of phototubes #2 and #3, a spectrometer was also placed in order to measure the wavelengths of the pump beam and the BSBS during infrared (IR) experiments. Let us note that the sample is tilted (angle of incidence around 5° with respect to the component surface) with the pump beam to avoid the specular front reflection of the pump beam towards both the cavity laser and diagnosis #3. In that way, the signal recorded on diagnosis #3 is supposed to correspond to the BSBS signal. Spectrometer #2, which directly collects the transmitted beam through the sample, measures the fundamental wavelength of the pump beam which is 1064.179nm (measured in air environment) whereas spectrometer #3 measures a wavelength of 1064.243nm inducing a shift of about 0.064nm. The difference between the pump and the BSBS wavelengths corresponds to a frequency shift of about ΔνB~17 GHz. This shift is in the range of those currently observed for solid materials pumped with an intense laser beam with very narrow spectral line, between 9 and 19 GHz [20, 21].
3. Brillouin characterizations
In this section, the tests have been carried out on thick fused silica optics (90 mm) without damaging the front face of the samples. To this end, experiments were realized at fluences corresponding to negligible rear and front surface damage event probabilities. It means that the signals collected on diagnostics #3, are not biased by front surface damage occurrence. Brillouin energy as a function of the interaction length is presented. It will first allow a good knowledge of the Brillouin properties in order to be able next to reduce its effects with confidence.
3.1 Temporal measurements
Figure 4 illustrates for experiments realized with the laser working at 6.5 ns the temporal profiles of both the pump and the BSBS pulses collected by phototube#1 and phototube#3, respectively. Signals have been normalized to 1 for the sake of comparison, the intensity of the BSBS wave being much smaller than the pump one. The temporal profile of the BSBS pulse is truncated compared to the pump one; its duration is then systematically shorter than the pump one. This means that BSBS occurrence is triggered by a high enough intensity and that, while the intensity of the pump wave decreases along its propagation direction (z-axis), the intensity of the BSBS wave increases along the –z direction.
Fig. 4 Pump and Brillouin temporal profiles during experiments realized at 355 nm and 6.5 ns. For readability, the two signals are normalized, the BSBS signal being much lower than the pump one. They are also arbitrarily matched on the time scale to illustrate the development of the BSBS wave after few nanoseconds of interaction between the pump beam and the host media.
3.2 Energy measurements: experiments
Experiments have been realized at 355nm – 3 ns at constant intensity for a progressively decreasing length of fused silica. To this end a 90 mm thick optics has been used, its rear surface is corrugated in order to trigger a damage at low intensity. Once the damage is triggered, the pump beam irradiates the damaged site and induces the growth of the damage in the bulk, collinearly to the pump beam. In that way, the length of interaction between the pump wave and the BSBS wave decreases as long as the damage grows in a counter-propagating direction to the pump beam. The inset in Fig. 5 shows the pump and Brillouin intensity profiles with a visualization of the bulk damage in the sample. A complete sequence is given in Visualization 1. This sequence shows that the average peak intensity of the Brillouin signal decreases with the sample thickness decrease (linked to the growth of the damage in the bulk). During this sequence, the pump beam was kept at a constant intensity (4 GW/cm2), its temporal profile is then quite constant all along the sequence, a standard deviation (σ) of less than 2% has been measured on peak intensities; whereas in the meantime, the BSBS temporal profile fluctuates a lot shot-to-shot due to its nonlinear intrinsic behavior. BSBS peak intensities fluctuations are about 10% at 1σ. In order to keep visible the BSBS signal on the oscilloscope screen, the vertical range of the BSBS channel is adapted during the sequence. The sequence is stopped when the BSBS signal is too low to be acquired by the phototube. Nonetheless, it does not mean that there is no BSBS anymore. It corresponds to a length of fused silica about 40mm. In order to quantify the BSBS decrease, Fig. 6 reports the BSBS energy as a function of the fused silica length. This energy, reported in arbitrary unit, is directly obtained integrating the BSBS intensity profile. A decrease over more than four decades is observed on a range of about 50 mm.
Fig. 5 Pump (left) and Brillouin (right) temporal profiles on the left corner during irradiation at I = 4 GW/cm2. The length of interaction (L, corresponding to the fused silica thickness) is 90mm at the beginning of the sequence and it decreases continuously due to the bulk damage occurrence all along this sequence (as schematized in the inset of Fig. 3). See Visualization 1. During the sequence the vertical oscilloscope range of the BSBS is reduced step by step in order to keep the temporal profile visible on the screen (3V [0-35sec.]; 1V [35-65sec.]; 0.5V [65-70sec.]; 0.20 V [70-100sec.]); 0.025 V [100-134sec.]).
Fig. 6 BSBS energy (in arbitrary units) as a function of the fused silica thickness. Experiments have been conducted at 355nm and 2.5ns, and at constant pump intensity (about 4 GW/cm2). Blue diamonds and brown squares correspond to experimental data and 1D calculations, respectively.
3.3 Modeling results
Experimental results are compared to numerical ones using a time dependent model developed by Sajer [3] that takes into account the slow varying envelope approximation. This model allows the computation of the unsteady stimulated Brillouin scattering initiated by noise with pump depletion. The simulations are named 1D when diffraction terms are ignored or 3D on the contrary. In that case a potential self-focusing due to the Kerr effect of the different waves is considered. The parameters needed by the simulations are the steady-state Brillouin gain coefficient (g) and the Brillouin linewidth (Γ: reciprocal of the acoustic phonons lifetime). The results presented elsewhere are obtained with g = 3.1cm/GW, Γ/2π = 330 MHz at λ = 0.355 nm, values which are typical of optical glasses [22].
1D simulations have been performed using the exact experimental values of the tests in terms of spatial beam profile (Gaussian), beam diameter, pulse duration, beam intensity. Simulations have shown that the first half of the laser pulse propagates through the sample without any modification due to a low SBS conversion, and the second half is nearly totally scattered due to a large SBS conversion located near the front surface, see Fig. 5 of [2]. Next, the Stokes energy has been calculated for interaction lengths from 40 to 90 mm. In order to compare modeling results with experimental ones, the first numerical value at 40 mm has been normalized to the experimental one.
The experimental increase of the BSBS energy with the interaction length is well described by the modeling approach over more than four decades. As the model is mainly of interest in the general trends obtained from Fig. 6, it gives confidence in BSBS measurements. That also allows us to estimate the pump beam depletion due to BSBS occurrence (see next paragraph for a comparison with experimental beam depletion measurements). Finally the combination of the modeling approach and the experiments permits to carry out laser-induced damage testing at a very low Brillouin level that gives a higher confidence in our ability to determine rear-surface LIDD, see Section 4.2.
4. Pump beam depletion
4.1 Silica plates with different thicknesses
We tried to quantify the depletion of the pump beam due to BSBS. This depletion is defined as the ratio of the BSBS energy over the pump energy. This estimation was performed from the measurements of the transmitted beam acquired on phototube #2 (this signal is shortened due to the BSBS energy), the BSBS beam acquired on phototube #3; these two measurements were next compared to the energy of the pump beam (measurements acquired on phototube #1 and on the pyroelectric cell). Figure 7 reports the beam depletion as a function of the pump beam intensity for two optical components whose thicknesses are 34 and 43 mm. The pump beam depletion is lower than 1% and increases with the pump intensity. Above 5 GW/cm2, front and rear surface damage occurs and experiments are no longer possible. Around 2 GW/cm2, the pump beam is entirely transmitted through the optics meaning that there is no or few SBS. As expected from the previous results reported in paragraph 3, the thicker the optics the higher the depletion.
Fig. 7 Pump beam depletion as a function of the pump beam intensity, for two sample thicknesses (43 and 34mm, squares and triangles respectively). Experiments have been performed at 355nm and 6.5ns with single longitudinal mode pulses. Full and empty symbols correspond to experimental data and 3D calculations respectively.
3D calculations, based on the formalism described in the previous section, have also been performed. Stokes energies have been calculated as a function of pump intensities from 3 to 4.1 GW/cm2 and from 3 to 5.2 GW/cm2 for 43 and 34 mm interaction lengths respectively. These Stokes energies are compared to pump energies to calculate the pump beam depletion. This depletion increases approximately up to 1.2% as the experimental observations on the same range of pump intensities (Fig. 7). Despite experimental and numerical results are few uneven, the general trends are well reproduced (let us note that the determination of experimental pump intensities considers perfect Gaussian beam, spatially and temporally, that is not the case; a rigorous comparison should consider intensity error bars that are larger than 10% [5]) and the depletion levels are quite the same.
This depletion is low in comparison with the total energy of the pump beam. However, it does not permit first to determine with accuracy the fluence and/or the intensity on the rear face of the optics. The SBS-generated optical wave is a parasitic wave that removes energy from the transmitted wave [23]. Moreover, for intensities larger than 5 GW/cm2, this depletion is large enough to trigger the damage occurrence on the front face which could fracture thick optical windows. Indeed the BSBS energy is only about 1% of the pump energy, but localized on very small areas (see Fig. 2) and temporally set at the end of the pulse: local intensities on the front face could be very high.
4.2 Rear surface damage
It is well known that an increase in laser bandwidth reduces the amplification of SBS. On this basis, Penninckx et al [3] have developed a system allowing for the suppression of the SBS effect occurring in optics irradiated with high laser intensities. It consists of a phase-modulated CW injection seeder in a nanosecond Nd:YAG Q-switched laser with pulses having both a large spectral bandwidth and a smooth temporal waveform [24]. Due to this smooth temporal waveform, such pulses make it possible to avoid strong intensity modulations and then to suppress the Kerr effect and, due to the large spectral bandwidth, to suppress SBS. The frequency of the sinusoidal phase-modulation fm is adjusted to a multiple of the inverse of the round-trip time of the laser cavity and it was shown that the higher the modulation depth, the larger the optical bandwidth. The efficiency of such a system has been checked by the assessment of the pump beam depletion, as reported in the previous paragraph. Figure 8 reports beam depletions as a function of pump intensities with and without the activation of this system for the 43mm thick plate. In this study, the phase-modulation frequency is 1.83 GHz (corresponding to ten times the longitudinal mode spacing of the laser cavity) and the modulation depth is m~1.4 rad. With the phase modulation, on this range of intensities, Fig. 8 shows that the beam depletion is reduced by a factor of 2 meaning that the BSBS is reduced. At this frequency, higher modulation depth should suppress entirely the SBS effect although it was not accessible with the device we had for this measurement. In the meantime, with the same phase modulation, laser damage experiments have been performed on the 34 mm thick plate, and it was possible first to measure laser induced-damage densities on the rear face without the occurrence of any front surface damage, another evidence that the SBS is reduced at a level well below the one leading to front surface damage as reported in Fig. 1. Secondly, Fig. 9 reports that rear surface damage densities measured on this thick plate were equivalent to the ones measured on a thin optics (10 mm, with a quite equivalent polishing process). This experimental result shows that the pump beam was then not depleted. The whole of results is clear evidence that such phase-modulated pulses are mandatory for laser-induced damage testing of thick silica plates.
Fig. 8 Pump beam depletion as a function of the pump beam intensity, for two laser mode configurations (Single longitudinal mode and a phase modulated continuous wave). Experiments have been performed at 355nm and 6.5ns on a 43mm thick sample. The lines are a guide for the eye only.
Fig. 9 Rear surface damage density as a function of the fluence (355 nm – 6.5 ns) determined on the entrance of the optical components. Measurements have been taken with a phase modulated beam in order to reduce SBS.
5. Conclusion
Backward stimulated Brillouin scattering has been measured on fused silica optics irradiated at 355 nm from Q-switch Nd-YAG lasers pulses seeding with a monochromatic continuous-wave making the laser spectrum very narrow. In order to select the optimum phase modulation frequency and modulation depth to suppress BSBS, we have first precisely characterized its properties. The dedicated set-up allowed us to measure these pulses as a function of the pump intensity and the fused silica thickness. The experimental results showed that BSBS in optics sets is roughly well predicted by models reported in literature such as the exponential increase of BSBS with pump intensity and with the interaction media length. The experimental results are also in good agreement with numerical calculations that strengthen our understanding of the phenomenon.
The energy-loss in the pump beam has been precisely quantified, at low intensities in order to avoid front surface damage. Next a phase-modulator has been implemented in the continuous-wave seeders of the lasers leading to pulses with a wide spectrum in order to suppress SBS. The developed set-ups were used to check the reduction of the backward stimulated Brillouin scattering. The measurement of nanosecond laser-induced damage densities at the output surface of thick optical components is then possible without the occurrence of non-linear propagation effects such as Kerr and Brillouin that distort the metrology.
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