1. Introduction

Laser ablation is a well known phenomenon [1–5] in which focusing of intense laser radiation on a surface spot leads to rapid heating of the irradiated material followed by the formation and expansion of a cloud of plasma and condensed matter which is accompanied by light emission [3] and a characteristic pop sound, the sonic wave derived from the initial supersonic expansion [4]. Since the early days of laser ablation [5], the propagation of the associated shock wave has been studied using the Sedov-Taylor scaling (S-T) for a point explosion [6–8]. The self-similar solution relates the position, R, of the shock front to the energy released, E, the density, ρ, of the ambient gas and the time, t, since the release of E.

In the present work, we aim to gain a better insight on the physical processes causing such divergences which, ultimately, distinguish laser ablation from other blast phenomena. Three different irradiation scenarios have been investigated using Schlieren photography in combination with Rayleigh and Mie scattering, optical emission spectrometry, and optical transmission measurements. By time-resolving these measurements, not only the shock front evolution could be studied but also, its connections to the formation of the plasma plume and the condensation of the vapor into nanoparticles and sub-micron particles.

2. Experimental section

A schematic of the experimental arrangement is shown in Fig. 1. The fundamental output of a Q-switched Nd:YAG laser (Quantel Brilliant B) with a maximum energy of 850 mJ per 6-ns pulse was directed and focused with an AR-coated BK7 positive aspheric lens (f = 150 mm) at a normal direction onto the surface of a Cu sample. The optical emission from the laser-induced plume was collected with a fused silica lens (f = 250 mm, d = 75 mm) which focused the light to the entrance slit of a f/3.6, 163 mm focal length Czerny-Turner spectrograph (Andor SR163i) fitted with a 1200 line/mm grating and a 2048x512 pixel ICCD detector (Andor iStar DH720-18F-03). Synchronization of the laser source and detection was carried out with a digital delay and pulse generator (Stanford Research Systems DG535) in combination with the internal delay generator of the ICCD. A separate Nd:YAG laser doubled at 532 nm was guided with a fiber optic cable, then focused to a 25 μm slit, collimated and directed through the ablation plume induced by the first laser. The emerging beam was focused to a knife edge and projected to a screen from which a rolling shutter CMOS camera (UI-1240SE-M-GL, IDS) captured Schlieren images of the plume. Alternatively, the 532-nm beam was directed to a polarizer and through the plume and a narrow <10-nm band of the scattered radiation was captured using a CMOS camera. The energy stability of the lasers was 0.4% and 2% RMS, at 1064 and 532 nm, respectively. The combined jitter measured with two fast photodiodes and a 1 GHz digital oscilloscope was below 1 ns.

 

Fig. 1 Experimental setup: 1,2 Nd:YAG laser sources, 3 spectrograph, 4 iCCD, 5 digital delay generator, 6 second harmonic generator, 7 sample holder, 8 fiber optic cable, 9 screen, 10 CMOS cameras, 11 oscilloscope, BE1, BE2 beam expander components, BS beam splitter, FM folding mirror, IF interference filter, KE knife edge, L lens, P polarizer, PF polarizing filter, PD fast photodiode, SL 25 μm slit, SM swing-away mirror.

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3. Results and discussion

Figure 2 shows three sequences of Schlieren images illustrating the post-interaction phenomena initiated by focusing a nanosecond laser pulse on a copper sample under different irradiation conditions (see Fig. caption). Figure 2(a) corresponds to a 100 J·cm⁻² fluence and Figs. 2(b) and 2(c) have been obtained at 10 J·cm⁻². The first nanoseconds of the three series in Fig. 2 show a plume of material emerging form the sample surface. The expansion of such material to a few millimeters above the surface pushes the surrounding 1 atm air creating a supersonic shock wave. Once the plasma stops expanding, the wave of shocked air propagates freely until it becomes sonic (only the nearly-sonic shock front in Fig. 2(b) at 20 μs is shown). Despite the said resemblances, formation, expansion velocity and morphology throughout the plasma lifespan are directly related to the irradiation conditions. While the same spot size influences the similar plasma morphology in 2(a) and 2(b), the higher pulse energy used in 2(a) and 2(c) results in an apparently faster shock wave propagation. Conversely, the same fluence leads to very different results if 2(b) and 2(c) are compared.

 

Fig. 2 Sequences of Schlieren images obtained after the irradiation of a copper sample with a 6 ns laser pulse and (a) 500 mJ, 0.8 mm spot, (b) 50 mJ, 0.8 mm spot and (c) 500 mJ, 2.5 mm spot. The images have been digitally processed to enhance the contrast. The horizontal pattern in the background is a coherent artifact related to the illumination source.

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In Fig. 3, the distance from the sample to the shock wave front has been plotted versus time for the three cases above. The experimental data was fitted (no weighing) to a power function, yielding exponent values of 0.62, 0.65 and 0.55 for series 3(a), 3(b) and 3(c), respectively. While these values are close to β = 1 or β = 2 in Eq. (1) and the correlation coefficients obtained are between 0.986 and 0.99, the fittings have slight deviations, of up to ~10%, from the experimental data (bottom of Fig. 3). Note that this is much larger than the 0.4% energy stability and that the behavior is similar for the three cases. Initially, the shock front travels faster than predicted by the model and then decelerates. The accelerated propagation phase displays initial velocities of 5.04 x 10⁴ and 2.88 x 10⁴ m·s⁻¹ for 3(a) and 3(b), respectively with maxima at 100 ns for both series. In the third case, 3(c), the maximum appears approximately at 1 μs and the initial velocity of 3.6 x 10³ m·s⁻¹ increases to 8.4 x 10³ m·s⁻¹.

 

Fig. 3 Top: distance measured in perpendicular from the sample surface to the shock front. The line shows the fitting to a power function. Bottom: residuals between the experimental data and the fitting. Experimental conditions for (a), (b) and (c) as in Fig. 2.

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As pointed out before, the S-T scaling assumes that R_SW is larger than the spot size, which is true for 3(a) and 3(b) from the first point on but is not fulfilled by 3(c) before 500 ns. This is a further indication of the influence of the focusing geometry on the plume expansion. The Gaussian energy profile of the beam, reproduced by the focusing lens on a 2.5 mm spot at the sample surface, translates into the formation of a plasma which propagates predominantly in parallel to the sample surface versus perpendicularly from the surface. The theoretical energies estimated using Eq. (1) at large times were 331, 33, and 318 mJ for 3(a), 3(b) and 3(c), respectively. The three estimates fall between a 33% and a 36% below the actual pulse energy which could be explained by reflection and conduction losses and by the ablation of micron-sized particles due to phase explosion [2,12]. However, the initial acceleration and subsequent deceleration of the shock front as compared to the model remains unexplained. In fact, Eq. (1) produces exceedingly large values for the energy at short and medium times.

In order both to further investigate this issue and to contrast the above results, the optical emission of the plasma in the 200-800 nm range was spatially resolved along the plasma z-axis. The results for the first microsecond of the plasma life have been plotted in Fig. 4(a) and 4(b). A similar graph in the experimental conditions of 3(c) was not representative owing to clipping of the wider plasma image. The plots at t = 0 in Figs. 4(a) and 4(b) show the plume of material expanding to stopping distances of ~5 and ~4 mm, respectively. The plasma position and integrated optical emission are plotted versus time in Fig. 5. The initial velocities calculated from these graphs were 5.72 x 10⁴, 2.29 x 10⁴ and 3.5 x 10³ m·s⁻¹, respectively, and are in good agreement with those observed with the Schlieren measurements. It is remarkable that, the initial velocity in 4(a) is only ~2.5 times that in 4(b) despite the laser pulse being 10 times more energetic for 4(a). In fact, the ratio of the total signal integrated over the first 100 ns was found to be ~3, which is indicative that shielding of the pulse energy by the plasma is significant in 4(a). The energy of the incoming pulse is absorbed via inverse bremsstrahlung both into: (i) the thin layer of highly-compressed air on top of the plasma as illustrated by the shoulder at 4-6 mm of the t = 0 plot, and (ii) the plasma itself, whose temperature and electron density raise, becoming optically thick. This aspect was verified by measuring the plasma transmission at 1064 nm [12] and by examining the spectral emission which was accordingly characterized by an intense continuum and broadened line emission. Oppositely, the spectra acquired for (b) showed a rapidly decreasing continuum background followed by thin line emission with low self-absorption.

 

Fig. 4 (a) and (b): Optical emission registered along the plasma z-axis in the 200-800 nm range at several delay times (in ns) from the laser pulse. (c) From top to bottom, spectral emission at 1, 5 (5x) and 20 μs (25x) after the laser pulse. Conditions for (a), (b) and (c) as in Fig. 2.

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Fig. 5 Plasma plume temporal evolution: (■) distance, z, from target surface to the point of maximum intensity of the plasma, and (●) total plasma integrated emission in the 200-800 nm range. The signal in (c) is abnormally low owing to clipping of the plasma image. Experimental conditions for (a), (b) and (c) as in Fig. 2.

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The spectral emission in Fig. 4(c), featured a long-lasting strong continuum contribution in addition to self-absorbed and self-reversed lines, indicative of temperature inhomogeneities along the line of sight in the plasma. The initial expansion velocity is one order of magnitude lower than those in 4(a) and 4(b), what makes sense since the plasma expands from a large spot size and drag by the surrounding air can be significant. The data in Fig. 4 was fitted to a drag function in the form z(t) = z_sd[1-exp(ξ·t)] [14,15]. The fitting slowing coefficients, ξ, are 2.39 x 10⁻⁷, 4.39 x 10⁻⁸ and 2.71 x 10⁻⁷ s⁻¹ for Figs. 5(a) to 5(c), respectively.

As with the initial velocities, these values support the discussion for Figs. 2 and 3. The expansion represented by the z-coordinate plots in Fig. 5 accounts for a substantial fraction of the plasma internal energy decrease owing to the work exerted in displacing the ambient gas. On the other side, bremsstrahlung, recombination and other decay processes in the plasma emit radiation subtracting energy otherwise available to propel the plume expansion. The integrated intensity curves in Fig. 5 account for most of these plasma radiative losses which span tens of microseconds. the lower expansion rate and emission intensity in 5(b) are in good agreement with the slower, less energetic shock wave observed in 3(b). In the case of 5(c) with a similar stopping distance to that of 5(b) and despite the much slower initial velocity, the propagation of the shock wave in 3(c) gradually approaches that of 3(a) to eventually match it after 500 ns. Significantly, the velocities calculated from 3(a) and 3(b) follow an identical monotonically decreasing behavior during the whole time interval plotted with 3(b) below 3(a) whereas that of 3(c) has a maximum at 20 ns and becomes the highest of the three from 100 ns onwards and then matches 3(a). While a 2.5-mm Gaussian spot -(c)- results in an heterogeneous plasma with slow onset and initial propagation speed, being optically-thinner than 3(a), the extra mass ablated in 3(c) might store more energy to be released at later times.

Figure 6 shows two series of scattering images of the plume between 0 and 20 μs for the sample irradiated with the 2.5 mm spot. The series of Rayleigh scattering images show the early formation of small nanoparticles, approximately <27 nm, fading until approximately 20 μs from the pulse arrival. The sequence at the top of Fig. 6 reveals a similar behavior for the growth of larger nanoparticles and submicron particles reaching a plateau at about 20 μs. No significant increase of the scattering signal was observed after that point it time.

 

Fig. 6 Time-resolved Mie and Debye (top) and Rayleigh (bottom) scattering images of the plume illustrating particle formation. Time scale in μs. Experimental conditions as in Fig. 2(c).

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Laser ablation can be modeled as an adiabatic expansion process of a mass of sample following a sudden isochoric temperature increase beyond the critical point [16]. In a temperature vs density phase diagram, the affected mass subsequently undergoes an adiabatic expansion resulting in different condensation products whose composition depends both on the temperature reached and on the expansion velocity. It is, thus, feasible that the expansion path of the plasma in Fig. 6 intercept the saturation binodal between vapor and liquid, leading to the observed aerosol of nanoparticles and molten material which eventually solidifies [3]. However, this ideal approach assumes all species are initially neutral and neglects radiative losses. Moreover, in the present case, the nanosecond pulse tail interacts with the expanding material as illustrated in previous sections. Therefore, far from time- and spatially-localized phase transitions, Fig. 6 shows a plasma cloud in which the condensation processes described take place heterogeneously and spreading the release of the phase transition enthalpies continuously in the microsecond time scale. The mass evaporated under such conditions was 0.7 μg·pulse⁻¹ which would release 3-4 mJ into the plume during its expansion. Even though this energy is a small fraction of the 318 mJ initially coupled, it certainly contributes to the deviations observed in Fig. 3.

4. Conclusion

The deviations of the S-T scaling have been investigated with a combination of time-resolved optical techniques at three different laser ablation regimes. In the three cases, the time evolution of the shock front has been confirmed to be determined by the formation, expansion and properties of the plasma. Both, the time scale of the different radiative processes, as well as the time span for vapor condensation into nanoparticles and sub-micron particles are compatible with the divergences between the model and experimental data. Although very different among themselves, the three scenarios described show the first stages of plume expansion as a self-regulated process in which the laser pulse energy is coupled to the sample or to the plasma, depending on the fluence. Whether it is a larger amount of mass ablated or a higher ionization degree, the outcome is an increase of the expansion velocity.