Abstract
1 Introduction
Laser-induced damage (LID) is one of the most limiting phenomena for the increase of overall energy and peak power for high-power laser facilities, such as the National Ignition Facility (NIF)[1] or Laser Mégajoule (LMJ)[2]. As far as LMJ is concerned, the resistance of optics to LID is qualified in support laboratories with specific lasers. The latter are not necessarily representative of LMJ pulses as they are often small beams of a few
At NIF and LMJ, the temporal shape may vary from one experiment to another. Indeed, some experiments may require a progressive laser energy deposit on target while other experiments for the study of shocks may require pulses for which the energy is suddenly delivered. Another issue concerning high-power nanosecond lasers is the indirect effect of phase modulations used at NIF and LMJ to tackle the issues of Brillouin scattering[5] and optical smoothing[6]. Such phase modulations have the effect of broadening the optical spectrum of laser pulses. When propagating along the beamline, the optical spectrum of the laser pulse may be distorted by several processes. This induces amplitude modulations (AMs) on an initially temporally smooth laser pulse. This effect is called frequency modulation to amplitude modulation (FM-to-AM) conversion[7,8]. Nowadays, such an effect is not considered to predict laser damage. One can hypothesize a priori that fast power variations induced by FM-to-AM conversion can have a strong impact on the absorption of subsurface damage (SSD) that leads to LID[9]. For instance, previous work[10] showed that multi-longitudinal mode (MLM) laser pulses with high-frequency (HF) power modulation can increase the LID threshold of fused silica at 351 nm, when compared to a temporally smooth monomode laser pulse.
Our goal throughout this paper is to study the impact of power modulations with FM-to-AM conversion characteristics on the LID of fused silica in the ultraviolet (UV) range at 351 nm. Thanks to amplitude modulators that are able to scan a wide amplitude and frequency range, several experiments were done on the MELBA experimental testbed to assess the impact of different temporal profiles of the laser pulse on LID.
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To go further, a 1D Lagrangian hydrodynamic code was used to run simulations and explain the LID discrepancies observed experimentally with different temporal profiles. The aim is to gauge the impact of the power modulations on the absorption of SSD leading to the creation of laser damage.
2 Experimental setup for the study of laser-induced damage
2.1 Description of the MELBA experimental testbed
Reported experiments were carried out on the MELBA[11] experimental testbed located at CEA CESTA (France). Initially, a 1053 nm laser pulse (
Two all-fiber Mach–Zehnder interferometers are used to shape the temporal profile of the laser pulse. The first interferometer outputs the user-defined laser pulse. The second interferometer improves the extinction ratio. The overall extinction ratio at the output of both Mach–Zehnder interferometers is 52 dB. For instance, it is possible to create flat-in-time (FIT) or Gaussian pulses of different pulse durations. In fact, the user can program any laser pulse with a temporal resolution of approximately 100 ps and a maximum pulse duration of approximately 20 ns.
To apply fast temporal modulations to the laser pulse and recreate the impact of FM-to-AM conversion on the temporal profile, an all-fiber electro-optic amplitude modulator with a 40 GHz bandwidth was set up. The amplitude modulator can be coupled to two different radio frequency (RF) drivers:
The expression of the laser power P at the output of the modulator is expressed as follows:
After applying temporal pulse shaping, the laser pulse is amplified through a regenerative amplifier to approximately 10 mJ. Then, a four-pass amplifier followed by two booster amplifiers bring the energy up to 7 J. The laser pulse is converted in the UV range at 351 nm (
Figure 1.MELBA spatial profile on the fused silica sample.
2.2 Studying LID on the MELBA experimental testbed
The MELBA experimental testbed is used to study LID and laser damage growth. The analysis of LID on a given test site is composed of several steps. Firstly, the test site of a superpolished synthetic fused silica sample is irradiated with the
With enough tested sites, we can determine damage densities
Statistical error bars are calculated with the collected damage densities and a histogram[12], for each fluence range
2.3 Characterization of the temporal profile
Damage laws determined with different pulse shapes will be compared to each other, all else being equal. This includes the fact that pulses will have the same pulse duration
For instance, a modulation index of
3 Impact of temporal modulations on laser-induced damage
3.1 Temporal characteristics of LF and HF laser pulses
Due to the spectral broadening of laser pulses, high-power facilities such as LMJ or NIF deliver pulses that may undergo FM-to-AM conversion. This phenomenon is responsible for power modulations of different magnitudes and frequencies. As previously discussed, we can reproduce such modulations on the MELBA testbed thanks to LF and HF modulators. Several AM configurations were used to assess the impact of LF and HF modulations, as follows.
The reference FIT pulse as well as different modulated pulses is presented in Figure 2(a). Power profiles are normalized so that the average power is equal to 1. As several sites are tested for each configuration, the calculated modulation index varies from site to site. The presented modulation index is the average modulation index for all tested sites of a given configuration. Relative standard deviations for all modulated configurations comprise between 5 and 11 percentage points.
Figure 2.(a) Examples of power profiles measured with a 33 GHz-bandwidth oscilloscope and photodiode. From left to right: FIT reference and 2, 10 and 30 GHz pulses. The modulation index is approximately equal to for modulated pulses. Power profiles are normalized so that the average power is equal to 1. (b) The amplitude of the Fourier transform for each power profile shown in (a).
Figure 2(a) shows the amplitude of the Fourier transform of the pulses presented in Figure 2(a). For the 2 GHz configuration, we can detect harmonics up to 8 GHz, but these harmonics are quite low when compared to the fundamental at 2 GHz. The 10 GHz configuration only shows the fundamental at 10 GHz, without any noticeable upper harmonics. Finally, the 30 GHz configuration only shows a distinctive peak at 30 GHz, as the bandwidth is limited to 33 GHz. Complementary measurements with a streak camera at
3.2 Comparison of damage laws for LF and HF modulated pulses
Four different temporal profiles were considered to test the impact of LF modulations on LID: a reference case and three 2 GHz modulated pulses of increasing modulation indices
Figure 3.(a) Damage laws for the FIT reference pulse and three 2 GHz pulses of different modulation indices. (b) Damage laws for the FIT reference case, two 10 GHz pulses with different modulation indices and a 30 GHz pulse.
is. In the worst case, we observe a difference in laser damage density between 10 and 100 times when comparing the reference FIT pulse and the 2 GHz pulse with
In order to assess the impact of the frequency of AMs, tests were performed with HF AMs on another 10 mm thick silica sample polished by THALES-SESO. Again, four different configurations were tested: a smooth reference FIT power profile, two 10 GHz modulated power profiles (
A final test was carried out on a new fused silica sample, which was provided by another vendor, namely the ZYGO company. The thickness of the sample is the same as the THALES-SESO sample, namely 10 mm. A damage law for a reference FIT pulse profile was first determined. Then, we tested for two different modulation amplitudes representative of LF and HF power modulations, namely a 2 GHz modulated pulse (
Figure 4.Damage laws determined on a fused silica sample polished by another vendor (reference FIT pulse, 2 GHz modulation and 10 GHz modulation).
Comparison of the size damage sites for the experiment presented in Figure 4 is shown in Figure 5. The results show no dependence of the temporal profile on damage size. This means that AMs at 2 or 10 GHz do not have an influence on laser damage size, when compared to the unmodulated reference pulse. As far as damage morphology is concerned, we did not find any difference between damage sites originating from different temporal profiles. This is coherent with work from Chambonneau et al.[15] and Diaz et al.[10], which showed no important damage morphology change between unmodulated and modulated
Figure 5.Histogram of the damage site diameter for the reference unmodulated pulse (no mod.) and the two amplitude modulations at 2 and 10 GHz. Data were analyzed from the results of the experiment presented in
Moreover, work from Diaz et al.[10] showed that pulses with AM gave different damage laws at
To explain the tendencies we observed experimentally, a model of laser–matter interaction was developed to assess the impact of AMs on the LID of fused silica at 351 nm. A description of the model and the results are presented in the following section.
4 A model to understand laser-induced damage with Esther code
4.1 Description of the model
Amorphous silica can be modeled with a band structure, with a gap between the conduction and valence bands equal to 8.825 eV. This energy gap is approximately three times the energy of a UV photon at 351 nm (3.52 eV). Yet, laser damage is observed despite the transparency of amorphous silica to UV light. The triggering of laser damage in fused silica is mainly explained by single-photon absorption of the incoming laser energy by SSD. Such defects are most often considered to be either absorbing pollutant particles or micro-cracks originating from the polishing process. In the context of the LMJ facility, the quality of silica optics is such that most absorbing pollutants particles should disappear with an etching process[17]. Thus, we will consider subsurface micro-cracks as being the sole contributor to laser damage. The model was designed similarly to the model used by Diaz et al.[10] and Grua et al.[4]. The outline representing the model is represented in Figure 6.
Figure 6.Outline of the modeling of subsurface micro-cracks. The crack is modeled by a 100 nm void surrounded by amorphous silica. Absorption of the UV laser at the SiO2/void interface is represented by an arbitrary absorbing defect layer.
The crack is modeled by a 100 nm void surrounded by amorphous silica. At the interface, the silica can absorb part of the laser energy due to the presence of an arbitrary absorbing defect layer. Examples of such defects can be found in Ref. [18]. Dimension
with
As the temperature of the fused silica
In the equation above,
The initial temperature increase is exclusively driven by the surface absorptivity of the arbitrary absorbing defect. We chose an imaginary refractive index for the absorbing defect of
The thickness of these layers is 5 nm. This choice is made because such defects are localized at the surface interface of the void and silica, so the thickness must be as low as possible. To optimize the calculation time, the meshing of silica follows a geometric progression that provides a fine meshing close to the micro-crack and a rougher meshing far from it. The temporal step for calculation is adapted to the AM frequency of the tested power profile.
The main output parameters considered to track the laser-induced damage threshold (LIDT) for different temporal configurations are the radial stress reached within the material and the temperature. An example for data output of the Esther code is presented in Figure 7. Criteria for laser damage are chosen when the maximal radial stress exceeds the tensile strength of fused silica, which is equal to
Figure 7.Radial stress and temperature output of the code with respect to time and the 1D parameter .
4.2 How to compare the LIDT and damage laws
On the one hand, simulations carried out with Esther code will give information about the fact that a given defect will lead to LID. The fluence at which damage occurs will be called the LIDT. On the other hand, damage laws determined experimentally give a set of damage densities as a function of fluence. Thus, the comparison of experimental and simulated results requires the possibility of defining an LIDT from a damage law. Given a damage law, the following applies.
Figure 8 represents the method used to associate an LIDT from a given damage law determined experimentally.
Figure 8.Determination of the laser-induced damage threshold (LIDT) from a damage law, given a damage density threshold defined at nb/cm.
4.3 Simulations and comparison to experimental results
Pulses with AMs at 2, 10 and 30 GHz with
Figure 9.Evolution of radial stress with respect to laser fluence for different temporal modulations: 2 GHz with or , 10 GHz with and 30 GHz with . Arrows point to the LIDT obtained for the reference without modulation (no mod.) as well as modulated pulses with .
Firstly, we notice that modulations at 2 GHz (
Concerning the modulated pulse at 10 GHz with
When the modulation frequency is equal to 30 GHz (
To understand the difference in simulated LIDT for modulated pulses, it is interesting to look at the evolution of thermodynamic parameters with respect to time. Figure 10 shows the evolution of temperature reached within the micro-crack for the reference FIT case (no mod.) and two modulated pulses with
Figure 10.Evolution of the maximal temperature reached inside the micro-crack with respect to time for the unmodulated reference pulse and two modulated pulses at 2 and 10 GHz ().
The maximal temperature reached within the micro-crack for a modulation at 2 GHz is higher than the maximal temperature in the unmodulated reference case, whereas it is the same for the 10 GHz modulation. Moreover, for time
4.4 Discussion of the simulated results
The simulations presented in this section are in good agreement with the experimental results presented in Section 2.3, as far as qualitative behavior is concerned. In particular, to this day, it is impossible to conclude the quantitative behavior of the impact of AM on LID.
One of the main limitations is that simulations and experiments do not express LID with the same metric. Indeed, simulations only show how one particular and arbitrary SSD behaves under laser irradiation. However, global LID behavior of the optical component, which is measured as damage densities, is a function of several SSDs of different natures (NBOHC, ODC, color center, residual slurry particles from polishing processes, etc.) and with different sizes and orientation parameters (width and angle of incidence with the beam). The fact that we used a single defect in our model might not be enough to assess the impact of FM-to-AM conversion on the LID of fused silica.
Even though the silica samples that were used to carry out experimental LID tests underwent similar polishing processes, the same experiment realized on a different sample can lead to dissimilar quantitative results. This is in fact what we observed on the samples polished by the THALES-SESO and ZYGO companies. In the case of LF versus HF modulations, the same trends were observed but for different fluence ranges and different magnitudes. It is as if the nature of the SSD between the different samples exhibited a different absorption dynamic to the incident laser pulse.
An extensive study was considered in one of the papers[4] that inspired our model. It was shown that it was possible to simulate an entire damage law for fused silica at 351 nm with initial defects of different characteristics. Although we only wanted to show trends regarding the impact of temporal shapes on a single damage, similar simulations could be implemented with different temporal shapes.
Finally, a more general critique can be expressed as far as the model is concerned. Modeling of LID with our model requires data about fused silica for significant temperature
5 Conclusion
This work describes the impact of the temporal shape of nanosecond laser pulses on LID at 351 nm. Amplitude modulators installed on the MELBA experimental testbed were used to study the impact of FM-to-AM conversion on LID. Experimental data showed that AMs around 2 GHz lead to an increase in damage densities for a large fluence range, when compared to a reference unmodulated FIT pulse. Moreover, this difference in damage densities increases with the peak power of the laser pulse. However, when the modulation frequency is equal to or above 10 GHz, this difference is no longer observed and damage densities are the same as those of the unmodulated pulse, regardless of the peak power.
The 1D Lagrangian hydrodynamic code Esther allowed us to create a model for representing LID originating from a single absorbing defect. The model was validated by comparing our simulations with known experimental and simulated results found in the laser damage scientific literature[10]. Then, the model was used to run LID simulations with pulses like those used experimentally. We showed that the simulation and experiments are in good agreement, as far as qualitative behavior is concerned.
Finally, experiments were recently carried out on the MELBA experimental testbed to assess the impact of FM-to-AM conversion on the LID of thicker silica windows, more representative of the vacuum window found at the LMJ facility. The high peak power reached due to this phenomenon may lead to enhanced nonlinear propagation. The high peak power reached with temporal modulations can increase the Bespalov–Talanov gain for the Kerr effect, which typically leads to a local intensity increase and the enhancement of LID[25]. In the worst case, this increase might lead to the filamentation phenomenon inside the silica optic[26,27].
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