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Abstract
The laser-plasma interactions that occur during the ablation of solid materials by a femtosecond filament superimposed with a lower-intensity nanosecond pulse are investigated. Pulses of 50 fs duration with intensities of ∼1014 W/cm2 centered at 800 nm are combined with 8 ns pulses at 1064 nm with ∼1010 W/cm2 intensity with delays of ±40 ns on crystalline GaAs targets in air. For each delay, the volume of material removed by a single femtosecond-nanosecond dual-pulse is compared to the laser-plasma interactions that are captured with ultrafast shadowgraph imaging of the plasma and shockwave generated by each pulse. Sedov-Taylor analysis of the shockwaves provides insight on the coupling of energy from the second pulse to the plasma. These dynamics are corroborated with radiation-hydrodynamics simulations. The interaction of the secondary pulse with the pre-existent plasma is shown to play a critical role in enhancing the material removal.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Although laser filaments can deliver intensities sufficient to ablate materials to kilometer-range distances [1], the ablation by a single filamenting pulse is fundamentally limited. Filaments generated in air by femtosecond pulses (FSPs) centered at 800 nm consist of a high-intensity (∼1014 W/cm2) core that is 100-200 µm in diameter and surrounded by a lower-intensity peripheral reservoir of laser energy up to ∼10 mm in diameter of [2–4]. This unique structure results from the balance of nonlinear processes: initially, Kerr self-focusing of the beam leading to the generation of a weak air plasma on axis that both defocuses and stabilizes the laser light over distances many times the Rayleigh range. These processes clamp the peak intensity to ∼1014 W/cm2, limiting the ablation by a single pulse [5–7], as additional pulse energy beyond what is required for filamentation is distributed away from the core to the peripheral field or into the formation of additional filaments [8,9]. Material removal by a single pulse in the filamentation regime is therefore inhibited by the clamped intensity of the filament core.
The ablation by a filament can be increased by supplementing the target with additional laser energy. In a previous publication [10], we showed the ablation of Gallium Arsenide (GaAs) by a 50 fs pulse with an intensity of 1014 W/cm2 and 150 µm diameter spot size was enhanced by superimposing an infra-red (IR) nanosecond pulse (NSP). In this experiment by Kerrigan et al, a 1064 nm pulse of 8 ns duration and an intensity of 1010 W/cm2 improved the material removal when it collinearly followed the FSP with a delay up to 1 µs. Particularly, delays between 40 and 200 ns generated ∼3-fold increases in crater volume compared to the FSP alone and more than a 150% increase compared to the combined volume of the craters produced by the individual (non-combined) FSPs and NSPs. Conversely, when the NSP preceded the FSP, the ablation was roughly equal to or less than the total ablation of the non-combined pulses.
Analysis of the resultant single-shot crater shapes and surface features provided insight on the ablation mechanisms occurring for different inter-pulse delays [10]. The craters produced by a single FSP showed signatures of the explosive, mostly non-thermal ablation dynamics associated with FSP ablation while craters generated by a single NSP showed evidence of longer thermal processes due to the longer deposition of energy into the target by the NSP [11]. The craters generated by dual-pulses where the NSP preceded the FSP revealed two distinct craters and evidence of both FSP and NSP ablation, implying each pulse interacted with the sample directly. In contrast, there was a lack of physical signatures from NSP ablation when the FSP preceded it with delays up to ∼50 ns. For delays between ∼100 and 200 ns, evidence of longer thermal ablation processes were observed. The shapes of the craters produced by dual-pulses in the FSP-then-NSP configuration were similar in shape to the craters the generated by only the FSP, but nearly three times deeper. To explain this morphology, Kerrigan et al suggested the NSP energy was deposited in advance of the target surface by interacting with the pre-existing plasma generated by the FSP for delays less up to ∼50 ns. For longer delays, the FSP-modified target surface improved the conversion of NSP laser energy into volume removal.
In the present investigation, we further explore this two-pulse ablation scenario with emphasis on the laser-plasma interaction science. Here, femtosecond and nanosecond pulses are combined colinearly with delays between -40 and +40 ns and focused onto a GaAs target. Negative delays correspond to the NSP striking the target first while positive delays indicate the FSP reached the target first. For each delay, ultrafast shadowgraphy of the expanding plasma and shockwave captures the laser-plasma interaction. During ablation with ultrashort pulses in air, the rapid heating of the substrate and ejection of material in the form of plasma generate a shockwave that changes the refractive index in front of the target surface. These index changes can be observed with fine temporal resolution through shadowgraphy with a femtosecond probe. With this technique, we capture the interaction (or lack thereof) of the secondary pulse with the shockwave/plasma generated by the previous pulse. In some cases, the expansion of the shockwave is used to determine the amount of laser energy that contributed to the explosion through Sedov-Taylor analysis [12], providing insight on the coupling of laser energy to the plasma and target. Simulations with the plasma hydrodynamic code FLASH [13,14] further elucidate these laser-plasma dynamics. The laser-target and laser-plasma interactions are compared with the ablation crater volumes generated by each dual-pulse combination to evaluate the effect of secondary pulse coupling on material removal.
2. Experimental details
A schematic of the experimental setup is shown in Fig. 1. Femtosecond pulses were provided by a Titanium:Sapphire chirped pulse amplification system at the Multi-Terawatt Femtosecond Laser (MTFL) facility [15]. Pulses of 50 fs centered at 800 nm and generated at a rate of 10 Hz with 15% shot-to-shot energy stability were split with a 90/10 beam splitter (BS) to provide the FSP and ultrafast probe. Pulses with 3.9 mJ of energy were focused onto the sample with a 1.5 m lens (L1) to a ∼150 µm diameter spot, yielding an intensity of ∼1014 W/cm2. Nanosecond pulses were focused with a 1 m lens (L2) and combined collinearly with the FSP at a shallow angle of 2°. A Nd:YAG laser (Quantel CFR200) provided 8 ns pulses at 1064 nm with 15 mJ per pulse at a rate of 10 Hz with 1.5% shot-to-shot energy stability. These conditions produced a ∼90 µm diameter spot at the sample with an intensity of ∼1010 W/cm2. The delay of the NSP relative to the FSP (Δtfsns) was controlled by triggering the Nd:YAG laser from MTFL, delaying the Nd:YAG laser output with a digital delay generator, and monitoring the temporal spacing with a fast germanium photodiode. In this regime, the timing of the FSP defines time 0 ns, so a negative delay (Δtfsns<0) corresponds to the NSP reaching the target first. A shutter was inserted in the path of the ablating pulses to only allow a single pulse from each laser through to the crystalline GaAs target at a time. The sample was moved between shots so every interaction occurred on a clean part of the sample.
Fig. 1. Experimental setup showing the beam lines of the FSP, NSP, and probe. A timing schematic of the pulses is shown in the top right.
The low-energy pickoff of the femtosecond beam provided the ultrafast probe for shadowgraphy [16]. To capture the shockwave expansion, the probe was delayed from the FSP by more than 60 ns by reflecting the probe many times between two large silver mirrors separated by ∼2 m. The timing of the probe was roughly controlled by changing the distance between the mirrors and number of passes between them. An additional delay arm on an adjustable stage provided finer temporal control of the probe between 0 and 3 ns. The delay between the FSP and the probe (Δtpr) was monitored at the target with a silicon fast photodiode. Second harmonic generation (SHG) of the probe was achieved with a beta barium borate (BBO) crystal inserted before propagation to the target surface into the imaging system, which blocked the IR light with blue-passing filters. A 10x objective imaged the shockwave onto a charge-coupled device (CCD, Imaging Source).
3. Ablation
The sizes of the resultant dual-pulse craters were measured to evaluate the effect of laser-plasma interaction on material removal. The crater volumes were determined with a white-light interferometer (Zygo NewView 6300). Figure 2 shows the average volumes of ∼10 single-shot craters as a function of inter-pulse delay and compares them to the craters produced by only an FSP or NSP (red dash and blue dot line), which generated volumes of ∼5,500 and ∼4,000 µm3, respectively. The craters produced by dual pulses are also compared to the sum of the volumes generated by the individual (non-combined) FSPs and NSPs (green dash-dot line). The volumes in Fig. 2 follow a similar trend to those obtained by Kerrigan et al [10]: negative delays (NSP first) produced craters with volumes less than or approximately equal to the sum of those produced by individual pulses while positive delays (FSP first) enhanced material removal, generating craters with volumes 150-175% larger than the sum of the single-pulse craters. A delay of +40 ns removed the most volume, corresponding to a ∼3-fold increase compared to the FSP-only crater. The least amount of material was removed by dual-pulses with delays of -10 or -20 ns, corresponding to 85% of the single-pulse crater volume sum. From the previous study [10], which employed similar pulse parameters, enhanced volume removal is expected to continue for longer positive delays up to ∼1 µs as a result better coupling of the NSP to the modified GaAs surface. It is also anticipated that longer negative delays would produce craters with volumes approximately equal to the summed volumes of the non-combined pulses, similarly to the case of -40 ns here. The relationship between crater size and dual-pulse timing is related to how to the energy of the second pulse is coupled to the sample, which is explored here by examining the laser-plasma interaction.
Fig. 2. Crater volume as a function of inter-pulse delay. Error bars denote the standard deviation from the mean.
4. Laser-plasma interaction science
4.1 Shadowgraphy
Ultrafast shadowgraphy of the expanding plasma and shockwave was carried out for the individual FSPs and NSPs and for the combined pulses with delays between -40 and +40 ns. The plasma and shockwaves produced by the single pulses (Fig. 3(a) and 3(b)) are compared to those produced by the combined pulses (Fig. 3(c)-(i)) at the various probe delays indicated at the bottom right of each shadowgraph. The probe delays are given relative to the ablating FSP (see Fig. 1). For each dual-pulse combination, the plasma expansion was captured for at least 20 ns after incidence of the second pulse.
Fig. 3. Shadowgraph images of the shockwave generated by (a) the individual FSP, (b) the individual NSP, and by FSP-NSP combinations of (c) -40 ns, (d) -20 ns, (e) -10 ns, (f), 0 ns, (g) +10 ns, (h) +20 ns, and (i) +40 ns. The delay of the probe is given in the lower right of each image. For (a) and (c-i) the probe time is relative to the FSP. For (b) the probe time is relative to the peak of the NSP.
The shockwaves produced by the individual FSPs and NSPs (Fig. 3(a) and 3(b)) exhibit the structure of typical laser-generated shockwaves [12]. These shockwaves generally expand spherically from the laser-target interaction zone, appearing as a semicircle when viewed perpendicularly to the incident laser direction. Several features within the shockwave can be distinguished: a bright region in the center that is the plasma, the plasma front at the outer edge of the bright region, a dark region of compressed air ahead of the expanding plasma, and finally the shockwave front at the outer edge of this dark region. Different structures appear in the plasma and shockwave when the FSPs and NSPs are combined with different delays (Fig. 3(c)-(i)).
For longer negative inter-pulse delays of -40 and -20 ns (Fig. 3(c) and 3(d)), the secondary FSP penetrates the shockwave/plasma generated by the NSP and directly interacts with the target surface. This is evidenced in both Fig. 3(c) and 3(d) by the appearance of a second shockwave at the surface at the time the FSP strikes the target. The second shockwave that appears inside the initial shockwave is most clearly visible in the shadowgraphs taken 7 ns after incidence of the FSP in Fig. 3(c) and 3(d). The lack of interaction between the two pulses is consistent with the crater volume generated by -40 ns delay, which was approximately the sum of the individual pulse volumes with no enhancement to the ablation (Fig. 2). The reduced volume with delays of -20 ns imply some of the FSP energy may be shielded by the NSP plasma. At -10 ns delay (Fig. 3(e)), interaction of the FSP with the plasma is suggested by the distorted shape of the shockwave compared to the single ns case. This distortion takes form of a protrusion from the plasma front that is most visible at 7 and 10 ns in Fig. 3(e). The crater volume produced by this pulse combination was less than the sum of the individual cases, implying the NSP plasma shielded FSP energy from the target.
At 0 ns delay (Fig. 3(f)) the pulses strike the target at the same time as if the target was irradiated by a slowly increasing NSP with a sharp spike in maximum intensity at its peak. Some distortion in the plasma front is visible compared to the single NSP and FSP shockwaves, particularly at 7 and 10 ns. It is surmised that some absorption of the FSP by the plasma produced by the leading part of the NSP occurs followed by plasma absorption of the trialing part of the NSP. As this interaction occurs very close to the sample surface at early times, the distortion washes out as the shockwave expands, taking on the form of a single shockwave with a shape between that of the single FSP and NSP shockwaves. A combination of plasma shielding and enhanced coupling of laser energy is likely occurring, ultimately producing a crater with a volume approximately equal to the sum of FSP and NSP-only craters.
Shadowgraphs of the positive delay laser-target interactions also exhibit shockwave distortions compared the single FSP case. For delays of +10, +20, and +40 ns (Fig. 3(g)-(i)), there is no distinct secondary shockwave formed at the sample surface, implying the majority of the secondary NSP energy does not directly interact with the target. These pulse combinations yielded the formation of a secondary shockwave originating at the edge of the pre-existent plasma, implying the NSP energy was absorbed by the ejected plasma rather than the sample surface. These delays all significantly enhanced material removal by at least 150% compared to the sum of the single-pulse FSP and NSP craters. The absorption of the NSP by the plasma therefore works to improve the transfer of energy from the NSP to sample. The inter-pulse delay corresponding to the most removed material was +40 ns.
4.2 Sedov-Taylor analysis
Sedov-Taylor analysis of the expanding shockwaves was used to determine the shockwave energies. The laser energy incident on a target will mainly be reflected, converted into kinetic energy in the plasma and shockwave, or conducted into the bulk of the target. The absorption and conversion of laser energy depends on the characteristics of the laser pulse (intensity, wavelength, and pulse duration) and the optical and thermal properties of the target. In this experiment, similar amounts of the FSP and NSP are reflected by the un-ablated target as reflectance of solid GaAs is just over 30% for 800 nm and 1064 nm light [17]. The distribution of the remaining laser energy in each pulse depends mainly on the pulse duration. In ablation with FSPs, the pulse duration is shorter than the electron cooling time, so the majority of laser energy is absorbed in a confined region before heat can be conducted away from the interaction zone [11]. In this regime, a significant amount of the laser energy goes into hydrodynamic expansion of the plasma generated in the interaction zone. In NSP ablation, slower thermal processes lead to material removal as a result of the longer pulse duration [11]. Additionally, some of the NSP energy can interact with the plasma generated by the leading part of the pulse [11,18]. Changes to the optical properties of the target surface also occur while energy is being deposited due changes in the temperature and phase of the target [18,19]. The different ways in which the FSPs and NSPs interact with the target lead to differences in the crater morphologies [10] and subtle differences in the shape of their respective shockwaves. The explosive action induced by the FSP causes the shockwave to initially expand more quickly in the direction perpendicular to the surface, giving it a slightly elliptical shape [20].
In Sedov-Taylor theory [12,21,22], the radius R of the shockwave is related to the energy E of the explosion through:
where $\xi$ is unitless and approximately equal to 1, $\rho$ is the density of the background air and approximately 1.2 kg/m3, and t is time. The radial expansions of shockwaves generated by individual FSPs and NSPs are shown in Fig. 4(a). Figure 4 also indicates how the shockwave radii were measured with arrows overlaid on exemplary shadowgraphs. The error bars in Fig. 4 represent the standard deviation of radii measurements from ∼10 shadowgraphs. Sedov-Taylor theory was used to derive the energy of each shockwave by fitting Eq. (1) to each expansion. The error was determined from the quality of the fit to the data. This revealed detonation energies of 2.9 ± 1.4 mJ and 3.0 ± 1.3 mJ for the FSP and NSP blast waves, respectively. The analysis assumes the blast wave originates from a single point in time and space, so small adjustments to t and R were tolerated to obtain the best fit. For the NSP-generated shockwaves, the temporal data, provided by the timing of the probe relative to the peak of the 8 ns pulse, was shifted by ∼4 ns. For both the FSPs and NSPs, < 40 µm adjustments were made to R.Fig. 4. Expansion of the shockwave radius and Sedov-Taylor fit for (a) the individual ns and FSPs and (b) the NSP at various inter-pulse delay and the NSP alone for comparison. The images in the lower right corner of each of plot indicate how the shockwave radius was measured.
In Fig. 4(b), the expansion of the shockwave generated by the single NSP is compared to the shockwave generated by the NSP when combined with the FSP with delays of -40, -20, -10, and +40 ns. Sedov-Taylor analysis was not performed for any other delay combinations because the secondary shockwave front is too difficult to discern. The secondary shockwaves produced at the target surface by the FSP in the case of negative delays experience a changing pressure gradient as they expand behind the shockwave produced by the NSP, complicating the analysis beyond the scope of this investigation. To evaluate the interaction of the FSP with the plasma and shockwave generated by the NSP in the case of negative delays, the radii of the outer NSP shockwaves were measured after the FSP irradiated the target and compared to the shockwaves produced by the NSPs individually. For an inter-pulse delay of -40 ns, the ns blast wave was essentially unchanged with an energy of 3.1 ± 1.6 mJ, implying the FSP did not interact with the plasma. Delays of -20 and -10 ns yielded NSP shockwaves that expanded more rapidly with energies of 4.0 ± 1.8 mJ and 5.3 ± 2.6 mJ, respectively. The more energetic shockwaves after the incidence of the FSP suggest some of the FSP energy was absorbed by the pre-existent plasma. For -20 and -10 ns delays, the changes in ns shockwave energy due to the absorption of the FSP equate to ∼35% and ∼80% of the energy in the shockwave generated by the FSP alone on the target. Better coupling of the FSP energy is thus achieved by directly irradiating the target than irradiating a pre-existent plasma produced by the NSP. The NSP, conversely, produces a secondary shockwave on the FSP plasma front that is more energetic than the shockwave generated on the solid target by the NSP alone. The shockwave produced by the NSP at +40 ns had a detonation energy of 10.0 ± 5.4 mJ, more than a 3-fold increase compared to the shockwave in Fig. 4(a), implying improved coupling of the NSP energy in the presence of the FSP plasma.
5. Discussion
5.1 Absorption of laser light by the plasma
The shadowgraphs and Sedov-Taylor analysis reveal enhanced absorption of the NSP by the plasma generated by the leading FSP for delays as long as +40 ns. The FSP energy, conversely, penetrates the NSP plasma in the reverse case of -40 ns delay or is coupled into the NSP plasma by a reduced amount compared to direct interaction with the sample surface for shorter inter-pulse delays. The absorption of laser light by plasma depends both on the characteristics of the plasma as well as the incident the laser light. For IR laser light, the main mechanism of absorption by plasma is inverse bremsstrahlung absorption (IBA) [12]. The absorption coefficient for IBA is given by [12]:
The plasma produced by the NSP is sufficiently dense to shield a portion of the 800 nm light from the sample for negative delays ≤20 ns, but expansion and recombination reduce the plasma density such that the FSP fully penetrates the plasma at later times as indicated by unchanged NSP shockwave energy for -40 ns delays. Also contributing to the reduced absorption of the FSP, as per Eq. (2), is the higher temperature of the NSP plasma as a result of NSP energy heating the plasma during its formation [20,26] and the shorter wavelength of the FSP. The initially denser plasma produced by the FSP stays sufficiently dense out to +40 ns, the maximum inter-pulse delay in this experiment, such that it efficiently absorbs the NSP. While the shockwave energy from NSP interaction with the plasma at earlier delays was not evaluated, the higher density of the FSP plasma at earlier times in its expansion suggests that at least as much energy of NSP was absorbed. The lower-temperature of the FSP plasma [20,26] combined with the longer wavelength of the NSP also increase the probability of IBA, as per Eq. (2), compared to the FSP interacting with the NSP plasma. Differences in the plasma profiles produced by each pulse and the pulse parameters therefore lead significant differences in the laser-plasma interactions that affect the material removal.
5.2 Simulations with FLASH
The plasma dynamics and shock wave propagation into the air initiated by FSP-NSP dual-pulses were further investigated using the radiation-hydrodynamics code, FLASH [13,14]. The FLASH code is a three temperature (electron, ion, and radiation) state-of-the-art radiation-hydrodynamics solver. It includes models for thermal conduction, multi-group radiation diffusion, tabulated equation-of-state (EOS), and laser ray-tracing. Here, the code is employed to qualitatively investigate the plasma dynamics for the case of a flat crystalline GaAs target (density of ρ∼5.32 g cm-3) in air irradiated by single and combined laser pulses corresponding to those used in the experiment. In the simulation model, the laser beams illuminate the flat target in the radius-Z (R-Z) cylindrical geometry with a Gaussian spatial intensity distribution across the laser focal spot. Approximately the same pulse durations, spot sizes, and intensities reported in Sec. 2 are used to simulate each pulse. The EOS for the target and air are constructed using a non-local-thermodynamic equilibrium (non-LTE) population kinetics model, i.e. the collisional-radiative (CR) solver [27], which includes excited states in a detailed-level accounting approach. The necessary atomic data for the CR solver is calculated using a relativistic configuration-interaction, flexible atomic code (FAC) [28]. The non-LTE EOS databases consist the spectral emissivity and the spectral absorption coefficients on a density-temperature grid. It should be mentioned that to construct the EOS for the air, it is assumed that (i) the air consists of 78% nitrogen and 22% oxygen and (ii) any possible molecular effect on the EOS is negligible due to limitations of the CR atomic solver. The standard atmospheric condition for the density (ρ∼1.33×10−3 g cm-3) and temperature (∼0.025 eV) of the air is assumed.
Figure 5 shows the simulated evolutions of the electron densities for several pulse configurations investigated in the experiment. The non-combined FSP and NSP interactions with the target are shown in Fig. 5(a) and 5(b) and correspond to the shadowgraphs in Fig. 3(a) and 3(b). The dual-pulse cases with delays of -40, 0, and +40 ns, corresponding to the shadowgraphs in Fig. 3(c), 3(f), and 3(i), are shown in Fig. 5(c), 5(f), and 5(i). The contour maps show the electron density, Ne, from 3×1017 to 3×1021 cm-3 at different times after the incidence of the pulses The time elapsed since the peak of the NSP in Fig. 5(b) or the incidence of the FSP in Fig. 5(a), 5(c), 5(f), and 5(i) is indicated at the bottom right of each contour map, approximately corresponding to the probe delays in Fig. 3. Each simulation was carried out to approximately 80 ns.
Fig. 5. Simulated contour map of the electron density (Ne) for different moments corresponding to the shadowgraph images in Figs. 3(a), 3(b), 3(c), 3(f), and 3(i). Following the Fig. 3, FSP-ns combinations are: (c) -40 ns, (f) 0 ns, and (i) + 40 ns. The simulation space (Radius ≤ 400 µm and Z ≤ 700 µm) shows approximately half of the shadowgraph images in Fig. 3.The probe time in the bottom right of each contour map is relative to the incidence of the FSP with the exception of (b), which is relative to the peak of the NSP. The laser beams propagate along the Z-direction, from the bottom to the top.
The simulated electron density evolutions exhibit the typical features of laser-based plasma expansion. That is, during the laser-target interaction, a crater with high-density plasma is formed. The high-temperature dense plasma plume expands rapidly outwards from the crater and the shock front pushes into the stationary cold background air causing its compression to a thin high-density region. Comparison among the shadowgraph images (Fig. 3) and the simulated electron densities (Fig. 5) shows the calculations approximately represent the main features of the experiment, with the exception of the of the expansion rate of the shockwave created by the single FSP. At a probe time of 58 ns, the simulated plasma has a radius normal to surface that is approximately 100 µm smaller than the corresponding shadowgraph image, indicating that the model underestimates the rate of plasma expansion in the case of the FSP. To test the validity of employing FLASH in the case of ultrashort (50 fs) laser interactions with solid targets, the FLASH results were compared to simulations generated with a 1D radiation-hydrodynamics code that is better suited for ultrashort pulses, Multi-fs [29]. The Multi-fs code solves radiation-hydrodynamics coupled to Maxwell’s equations to handle the steep density gradients associated with FSPs. Our case study (not shown here) revealed that the calculations for a 50 fs pulse with an intensity of ∼4×1014 W/cm2 incident on solid aluminum in vacuum are approximately the same with both models. That is, the effect of laser resonance absorption on the electron temperature is negligible compared to IBA for the computational conditions considered in this work. Additionally, the absorption of the FSP by the air background was found to be small and, consequently, has no significant role in direct laser target heating. It should be pointed out that the air background gas crucially decelerates the expansion compared to vacuum conditions as expected. In Fig. 5(a), the FLASH estimates a maximum electron temperature of ∼6 eV and a maximum normal (in the Z-direction) plasma expansion velocity of ∼4×105 cm/s, which is approximately an order of magnitude less than the measured peak velocity in the experiment.
The simulated electron density maps for the single NSP are shown in Fig. 5(b). The FLASH code estimates a maximum electron temperature of ∼28 eV. This hot plasma expands in the Z-direction with a maximum plasma velocity of ∼4.5×106 cm/s, which is in approximate agreement with the shadowgraphs. The calculated radius in the normal direction is somewhat larger than in the shadowgraphs, which may be due to a slightly higher calculated maximum expansion velocity in addition to a high rate of expansion being reached at later time relative to the peak of the pulse. Further computational investigations are needed to refine the model for more accurate simulations of the complex interaction physics, which occur over many timescales, with respect to each pulse. The general laser-plasma dynamics depicted in the calculations, however, are sound and provide valuable insight into the physics of combined FSP and NSP dual-pulses on solid targets.
The FLASH simulations confirm interactions between the secondary laser pulses and plasmas created by the first pulses. Figure 5(c), corresponding to a -40 ns delay, shows strong absorption of the FSP in the vicinity of target surface. Before incidence of the secondary FSP, the electron temperature is ∼1 eV and ∼6 eV in the vicinity of the target surface and plasma corona, respectively. The FSP significantly raises the electron temperature in the dense plasma core adjacent to the target surface to ∼150-200 eV and to a lesser extent, the electron temperature in the low-density corona region to ∼30-50 eV. These temperature ranges rapidly decrease in a few picoseconds time scale to ∼50 and ∼10 eV, respectively. The production of electrons in the vicinity of the surface that later expand into the pre-existing density wave is consistent with the observation of a second shockwave produced on the target surface after incidence of the FSP in the experiment (Fig. 3(c)). Some absorption of the FSP in the corona region is indicated by the protrusion on the front of the electron density wave appearing at ∼1 ns after incidence of the FSP as well, which was observed clearly in the experiment for -20 and -10 ns delays.
In Fig. 5(f), both pulses strike the target at the same time making it difficult to distinguish a plume generated by each pulse, similarly to Fig. 3(f). An average electron temperature over a few nanoseconds is ∼52 eV, which occurs when the peak intensities of the two pulses are overlapped. However, the FSP heats efficiently the dense region close to the target and raises the electron temperature range to ∼150-200 eV that lasts a few picoseconds. The plasma temperature in this case exceeds the temperatures produced by both pulses individually, indicating additional heating of the plasma due in the vicinity of the target surface. The high-density plasma produced above the target reaches the critical frequency for 1 µm light (∼1021 cm-3). Thus, the plasma both shields laser energy from the target and transfers energy to the target via heat conduction and plasma radiation.
In Fig. 5(i), the secondary NSP generates a high electron density (∼1021 cm-3) ∼100 µm from the surface, on the front of the expanding density wave generated by the FSP. A double-plume structure indicative of plasma absorption of the NSP is visible at ∼1 ns after the NSP, as observed experimentally in Fig. 3(i). The maximum electron temperature occurs when the NSP encounters FSP-produced plasma, reaching a value of ∼34 eV. As the second plume expands, high electron densities remain in the vicinity of the target surface for tens of nanoseconds. The high electron densities could be sustained by heat and pressure from the portion of the shockwave produced on the plasma front propagating in the direction of target surface. The confinement of this plasma close to the target surface can transfer energy to the target via heat conduction and radiation. The calculations show the same maximum plasma radiation temperature of ∼6 eV for both conditions relevant to Figs. 5(f) and 5(i), implying conduction plays a significant role in transferring energy to the surface in this scenario.
The calculations by FLASH reveal that the enhancement of plasma temperature (electron, ion and radiation) and electron density close to the target surface play an important role in transferring the energy of the secondary laser pulse to the target surface. However, investigations are underway to improve the model so that the non-combined FSP and NSP plasmas better match the experiment. The rates of expansion of the plasmas and shockwaves generated by the individual FSPs and NSPs were nearly identical in the experiment (Fig. 4(a)) but differed by an order of magnitude in the simulation. This will likely be achieved through improvements to the EOS of the air background and GaAs target, which has complex semiconductor physics that affect the absorption of two pulses used in this experiment. Additionally, the experiment should be repeated on a target with a well-defined EOS.
5.3 Ablation enhancement
The laser-plasma interactions observed in the shadowgraphs and FLASH simulations can be divided into approximately four scenarios that result in different amounts of material removal. The observed interactions include: (i) no laser-plasma interaction at -40 ns delay leading to no enhancements nor reductions in ablation efficiency, (ii) some coupling of the FSP into the NSP plasma at -20 and -10 delays that inhibit ablation, (iii) a combination of effects at 0 ns delay that neither enhance nor inhibit ablation, and (iv) strong absorption of the NSP by the FSP plasma at positive delays that enhance ablation. In the first scenario, the NSP plasma at delays of -40 ns is not sufficiently dense to absorb a significant portion the FSP. The FSP thus directly interacts with the target surface which has been heated by the NSP. The residual temperature effects seen by the FSP do not improve the ablation as phase explosion, a dominant mechanism in FSP ablation, is not temperature dependent for high-intensity FSPs [30,31].
For shorter delays of -20 and -10 ns, plasma shielding is observed, which occurs when laser energy is reflected or absorbed by the plasma but is not coupled to the bulk target [18,32]. While more energy of the FSP was absorbed by the plasma at -10 ns than -20 ns, the crater volumes in each case were similar. The closer proximity of the plasma to the bulk surface at -10 ns may have allowed some of the energy of the FSP absorbed by the plasma to be coupled to the surface. One way of transferring energy to the target is through black-body radiation from the plasma which emits light in the visible and ultraviolet that is better absorbed by the GaAs target than IR [17,33,34]. Another means is through heating of particles that then transfer energy to the surface via conduction [35]. Additionally, energizing the particles could prevent them from cooling, coalescing, and being redistributed in and around the sample [35,36].
In the complex scenario at 0 ns delay, heating of the sample surface and plasma generation by the leading part of the NSP is followed by a large spike in intensity that interacts with the plasma but also transfers energy to the target due to the close proximity of the plasma relative to the bulk surface. The loss of laser energy by the plasma absorption is balanced by transfer of energy from the plasma to the surface and enhanced thermal conduction at the sample surface [10], yielding a crater volume approximately equal the sum of those produced by the individual pulses.
In the regime of positive delays, ablation is enhanced by a number of processes. Firstly, the NSP energy is more efficiently absorbed by the plasma than the bulk GaAs surface. This is evidenced by the ∼3x more energetic shockwave generated on the plasma front compared to the bulk surface. We suspect at least as much absorption of NSP energy for shorter delays due to the higher density of plasma at earlier times before it expands. As mentioned in the -10 ns case, the energized plasma can improve ablation through black-body radiation of wavelengths better absorbed by GaAs than 1064 nm [17,33,34], hot particles that conduct energy to the target [35], and energizing and dispersing particles away from the crater [35,36]. The enhancement to ablation is greater for longer delays, implying another mechanism is at play when the NSP interacts with the plasma further from the surface. At delays of +20 and +40 ns, the NSP clearly forms a secondary shockwave that expands spherically into the ambient air as well as backwards towards the target. The backwards propagating shockwave, which is moving towards the surface of the target faster than the initial pressure wave flows away from the surface, exerts high pressures above the target surface, expelling molten material and confining high temperatures to the bulk [12]. The additional expansion of the plasma achieved before incidence of the secondary NSP increases the area on the target receiving the energy via the plasma or secondary shockwave beyond the laser spot size. The role of modified surface properties and the specific ablation processes occurring can be determined by examining the topology of the resultant craters as described by Kerrigan et al [10].
6. Summary
The role of laser-plasma interactions in the enhancement of ablation by different combinations of femtosecond and nanosecond pulses was investigated. The FSP following the NSP by 40 ns (-40 ns delay) yielded crater a volume approximately equal to the total volume generated by the FSPs and NSPs separately. In this case, little to no FSP energy is absorbed by the NSP-generated plasma and directly interacts with the target, depositing approximately the same energy into the target as if it were the only pulse. At shorter negative delays of -20 and -10 ns, some of the FSP energy is shielded by pre-existent plasma, reducing the ablation to 85% of the total volume produced by the non-combined pulses. When the pulses are overlapped with 0 ns delay, a combination of plasma shielding and plasma-mediated transfer of energy to the target generate craters with no enhancement nor reduction in ablation efficiency. Propagating the NSP second significantly enhanced the coupling of secondary pulse energy to the target in all cases, enhancing the ablation to yield volumes 150-175% larger than the sum of the single-pulse craters. Enhanced coupling of the NSP energy occurs as a result of improved absorption by the FSP plasma compared to the solid target. The most volume was removed with a delay of +40 ns, where the NSP forms a secondary shockwave on the initial plasma front that is ∼3x more energetic than the shockwave produced by the NSP directly on the target. Here, absorption of laser energy by the plasma aids in material removal by the action of the backwards propagating shockwave that expels molten GaAs and the confinement of high temperatures and pressures to the surface. These results provide a framework for using lower-intensity auxiliary laser energy as means of enhancing remote filament ablation.
Funding
Air Force Office of Scientific Research (100000181); Army Research Office (100000183).
Acknowledgment
The authors acknowledge Daniel Webber, Daniel Thul, Danielle Reyes, and Nathan Bodnar for their assistance in this research and the management of MTFL. The authors would also like to thank the FLASH Center for Computational Science at the University of Chicago for making the FLASH code publicly available. The ARO MURI “Light Filamentation Science”, HEL/JTO and AFOSR MRI “Fundamental studies of filament interaction”, and the State of Florida are acknowledged for their support in this research.
Disclosures
The authors declare no conflict of interest.
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