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We report on the effect of pulse to pulse interactions during percussion drilling of steel using high power ps-laser radiation with repetition rates of up to 10 MHz and high average powers up to 80 W. The ablation rate per pulse is measured as a function of the pulse repetition rate for four fluences ranging from 500 mJ/cm2 up to 1500 mJ/cm2. For every investigated fluence an abrupt increase of the ablation rate per pulse is observed at a distinctive repetition rate. The onset repetition rate for this effect is strongly dependent on the applied pulse fluence. The origin of the increase of the ablation rate is attributed to the emergence of a melt based ablation processes, as Laser Scanning Microscopy (LSM) images show the occurrence of melt ejected material surrounding the drilling holes. A semi empirical model based on classical heat conduction including heat accumulation as well as pulse-particle interactions is applied to enable quantitative conclusions on the origin of the observed data. In agreement with previous studies, the acquired data confirm the relevance of these two effects for the fundamental description of materials processing with ultra-short pulsed laser radiation at high repetition rates and high average power.
© 2014 Optical Society of America
1. Introduction
Ultrafast lasers with pulse durations shorter than several picoseconds have gained increasing interest in the last years as they enable high-precision processing for a wide range of various materials with negligible thermal load [1–3]. Ablation and in particular percussion drilling of metals have been investigated in several studies, underlining the potential of ultra-short pulsed laser radiation for materials processing [4–9].
Although achievable processing quality is excellent, the limited processing speed is an obstacle to industrial applications in many cases. However, with the development of ultra-short pulsed lasers with average output powers of several 100 W in the last years [10–12], the laser sources might now reach industrial demands not only in terms of processing quality but also in terms of productivity. As the pulse fluence is usually limited to a few J/cm2 for highly precise and efficient materials processing [2], the upscaling of ultrafast laser ablation to higher average power is accompanied by an upscaling of the repetition rate [13]. With the use of high repetition rates of more than a few hundred kHz, pulse to pulse interactions have to be taken into account, as they have a strong influence on the precision, the productivity and the thermal load during materials processing [4,5,14–16].
Basically, pulse to pulse interactions can be divided into heat accumulation on the one hand and optical interaction of the laser pulse with plasma, vapor or particles induced by the previous pulse on the other. In the first case a certain amount of the deposited energy does not contribute to the ablation process, remains in the workpiece [17, 18] and leads to significant thermal load due to heat accumulation if the temporal time separation between subsequent laser pulses is smaller than the time needed for the energy dissipation into the bulk of the workpiece. In the second case, the laser pulse interacts with already ablated material in form of particles, vapor or plasma by being scattered, reflected or absorbed. In the following, these processes will be summarized as pulse-particle interactions. The effects of these interactions on the heat input during ultra-short pulse materials processing are determined by the dynamics and the composition of the induced ablation plumes. Ablation plumes induced by ultra-short pulsed laser radiation have been analyzed in several studies using time resolved microscopy techniques [14, 19–23] as well as optical transmission measurements [23, 24]. However, most of these experimental works are carried out at processing conditions that differ significantly from those applied in this study, using an order of magnitude higher fluences, different pulse durations, other materials or focusing on different time scales [14, 19, 21–23]. In the work with the most similar processing conditions [20], the ablation plume subsequent to laser ablation of aluminum with a single laser pulse of 100 fs pulse duration and with a fluence of 1.8 J/cm2 is investigated. In that work, the authors identify three characteristic time regions regarding the ablation dynamics. Within the first 200 ns after the irradiation, the observations include the emission of vapor, the formation and the expansion of highly pressured material as well as the formation of shockwaves. In the time frame between 200 ns and 700 ns after the laser pulse the authors observe the ejection of droplets and material particles with diameters of approx. 1-3 µm and attribute this characteristic emission to ablation induced by phase explosion [25, 26]. For time delays longer than 700 ns a jet of molten material is observed, which has also been observed for the irradiation of thin gold films [27, 28].
In good agreement with these results, two minima of the optical transmission of the ablation plume at the surface of a steel sample have been observed in time-resolved transmission measurements [24]. Up to about 30 ns a strong absorption is measured and attributed to optical absorption in a dense plasma. In the range of 50 to 200 ns, another decrease of the transmission is observed and identified with absorption by vapor and droplets. This shielding effect can last up to several microseconds depending on the fluence of the ablating pulse. Thus, for repetition rates of more than a few hundred kHz optical pulse to pulse interactions can be expected. In drilling experiments using a fs fiber-laser with a repetition rate up to 1000 kHz the effect of these processes on percussion drilling has been experimentally validated [4,5].
In this work we report on the effect of high repetition rates up to 10 MHz on heat accumulation and pulse-particle interactions during percussion drilling of steel using high power ps-laser radiation with an average power up to 80 W. The observed correlation of repetition rate and ablation rate is analyzed by comparing the experimental results with a semi empirical model that considers heat accumulation as well as pulse-particle interactions. The theoretical model shows that only a combination of these two effects is capable to explain the observed experimental data. A comparison of the relevant time scales with results regarding plume dynamics after single pulse laser ablation [20, 24], allows for a reasonable assumption about the underlying physical phenomena. The experimental results and the theoretical description of the ablation rate in dependence of the repetition rate give a fundamental basis for the understanding of the influence of heat accumulation and pulse-particle interactions on ablation processes using ultra-short pulsed laser radiation with high average power.
2. Experimental setup and procedure
An f-theta objective with a focal length of 80 mm is used to focus the laser radiation of an EdgeWave PX picosecond Nd-YAG slab laser onto a 10 mm thick steel (1.4301) sample resulting in a focus diameter of about 30 µm. The laser system emits laser pulses with a pulse duration of τ = 10 ps at a central wavelength of λ = 1064 nm and repetition rates adjustable between frep = 0.2 and 10 MHz. The maximum average power of the laser system is between 30 and 80 W depending on the repetition rate chosen.
Percussion drilling of the steel sample is performed by using different pulse fluences and repetition rates, while other processing parameters are kept constant as shown in Table 1. The number of pulses is adjusted to N = 400 for all experiments using an electro-optic switch that is integrated in the laser system and allows fast modulation of the laser output.
Table 1. Summary of Processing Parameters Used in the Experiments
The ablation depth and the morphology of the drilled holes is measured using laser scanning microscopy (LSM).
3. Experimental results
In Fig. 1, the ablation depth per pulse as a function of the applied repetition rate is shown for different pulse fluences between F = 500 and 1500 mJ/cm2. The characteristic dependency of the ablation depth per pulse on the repetition rate is comparable for all examined pulse fluences. For repetition rates smaller than a certain value, the ablation rate remains nearly constant, whereas for slightly higher repetition rates, a significant increase of the ablation rate is observed. The maximum obtained ablation rate is approx. 10 times higher than the initial ablation rate for small pulse repetition rates.
Fig. 1 Ablation rate in depth per pulse as a function of the applied repetition rate for different pulse fluences ranging from F = 500 to 1500 mJ/cm2. The ablation depth per pulse is calculated by dividing the total depth of a crater by the number of laser pulses N = 400.
In Fig. 2, holes drilled with a fluence of F = 750 mJ/cm2 for different repetition rates are shown. With increasing repetition rate an increasing amount of molten material is observed at the drilling entrance. At 2.5 MHz significant recast of molten and ejected material is visible, explaining the drastic increase of the ablation rate above 2 MHz as shown in Fig. 1. Thus, the increase of the ablation rate is related to a progressively melting based ablation process leading to higher ablation rates but simultaneously to poor quality due to significant recast formation. Simultaneously, the crater diameter increases from 36.5 µm for a repetition rate of 1 MHz up to 49.5 µm for an applied repetition rate of 10 MHz. However, the impact on the crater diameter is with an increase of 40% small compared to the impact on the ablation depth per pulse that increases by a factor of 10. Hence, radial energy transport can be neglected contrary to the dominant heat transport directed perpendicular to the workpiece surface. With decreasing pulse fluences the threshold of the repetition rate, at which progressive melt formation has a relevant impact on the ablation rate, shifts to higher values.
Fig. 2 LSM images of ablation craters for different pulse repetition rates. For repetition rates of more than 2 MHz a distinctive ejection of molten material is observed (F = 750mJ/cm2, N = 400). The crater diameter increases from 36.5 µm for the use of 1 MHz up to 49,5 µm for the use of 10 MHz.
A decrease of the ablation rate for repetition rates in the range of 0.2 to 0.3 MHz due to shielding effects as reported by Ancona et al. [5] cannot be resolved in these experiments. This is probably caused by be the smaller experimental resolution regarding the repetition rates below 1 MHz and the more than 10 times smaller fluences used in this study. The results for higher repetition rates are in good agreement with the investigations obtained in [5], extending the knowledge of the influence of high repetition rates on the achieved ablation rate to smaller pulse fluences and much higher repetition rates.
4. Modelling
As the origin of the observed increase in ablation rate is identified with an ablation process dominated by melt ejection, the ablation depth within the following theoretical approach is described by calculating the melt depth, based on classical heat conduction. Generally, heat accumulation as well as pulse-particle interactions have to be considered to cause the observed behavior. At first, the effect of heat accumulation is being examined. Afterwards, the effect of interaction of the laser pulses with material ablated by the previous pulse is discussed and finally the two effects are combined to describe the experimentally observed correlation between ablation depth per pulse and applied repetition rate.
4.1 Heat accumulation
The theoretical approach to calculate the effect of heat accumulation is based on the following assumptions:
- • The applied model is reduced to 1-dimensional heat conduction directed perpendicular to the workpiece surface. Heat conduction radial to the drilling direction is neglected, as the effect on the crater diameter is small compared to the effect on the ablation depth per pulse. Moreover, the temperature gradient in lateral direction is much smaller due to the energy input by the spatial Gaussian intensity distribution of the applied laser radiation.
- • A certain amount AHA of the absorbed fluence remains in the workpiece and contributes to heat accumulation. The other part is reflected or contributes to the initial ablation process inducing plasma or evaporation and does not remain in the sample. Since we measure the depth at the center of the crater, the crater depth is mainly determined by the peak-fluence. The peak-fluence F0 = 2 F is the fluence in the center of the Gaussian fluence distribution and equals two times the pulse energy divided by the focus area. It is assumed that a certain fraction AHA of the peak fluence F0 is deposited uniformly in a depth Δ = 10 nm respectively Δ = 100 nm. This are the energy penetration depths determined for picosecond laser processing of steel for the low and the high fluence regime, respectively. Thereby, the threshold between those two regimes has been estimated to 1100 mJ/cm2 [29].
- • The following thermo-physical values are assumed to be constant: density ρ = 7.9 g/cm3, heat capacity cv = 0.510 J/gK, and thermal diffusivity α = 0.06 cm2/s [30].
- • There is no heat flow through the surface of the workpiece.
- • The ablation depth is the depth, where the deposited energy equals the sum of the energy that is needed to exceed the melting temperature of the stainless steel of Tmelt = 1600 K and the melting enthalpy LM = 281 J/g [30].
- • The energy deposition is assumed to be instantaneous. Thus, the temperature distribution is given by superposition of the solutions for an instantaneous point source.
Based on these assumptions, the temperature-rise due to the amount AHA of a single pulse with a peak-fluence F0 = 2 F is given by the superposition of instantaneous point sources along the drilling direction z:
In this equation, the definition of the limits of integration from -Δz to Δz, is equivalent with introducing heat sources above the workpiece surface, applied to realize a vanishing heat flux through the workpiece surface. The value of Δz depends on the applied fluence and equals the energy penetration depth of the low and the high fluence regime, respectively. Based on Eq. (1), the temperature-rise after N pulses at a certain repetition rate frep is given by the superposition of the temperature rise induced by N single pulses:
, with Θ representing the Heaviside function.Based on this expression, the temperature rise at z = 1 µm below the surface of stainless steel as a function of time for different repetition rates is shown in Fig. 3. The term F0 ∙ AHA is 80 mJ/cm2 in the presented case. With increasing repetition rate the temperature rise between two subsequent laser pulses increases due to a reduced time for energy dissipation. In consequence, accumulation of heat within the workpiece becomes continuously more relevant. However, the effect of heat accumulation on its own cannot explain the observed correlation of the ablation depth per pulse and applied repetition rate. Therefore, in the following section the theoretical approach is extended by considering pulse-particle interactions.
Fig. 3 Temperature rise as a function of time for z = 1 µm below the workpiece surface for different pulse repetition rates. With increasing repetition rate the temperature rise between two subsequent laser pulses increases due to less time for energy dissipation. The absorbed laser peak-fluence F0 ∙ AHA is 80 mJ/cm2 in this case.
4.2 Pulse- particle interactions
To extent the theoretical approach, pulse-particle interactions are considered by introducing a dependency of AHA on the time difference between subsequent laser pulses and the laser peak-fluence F0. This means that we assume that absorption or scattering of the laser pulses by particles or vapor inside the drilling hole has a significant impact on AHA and can lead to an enhanced or reduced heat input into the workpiece. We state a linear dependence of AHA on the temporal pulse to pulse separation Δt, which can be derived on basis of plume transmission measurements at the workpiece surface during laser ablation performed by König et. al. [24]. If the temporal pulse to pulse separation exceeds a certain value, pulse-particle interactions do not occur, because the time difference between subsequent laser pulses is longer than the presence of ablation products in the drilling hole. In this case there is no interaction of the applied laser pulses with ablated particles.
Based on the assumed linear dependence, AHA is described by:
Here a, b and c are empirical factors that can be interpreted as follows: The temporal time separation with the value –a/b is equivalent to the point in time when pulse-particle interactions begin to have an impact on AHA. The value c corresponds to the amount of the applied fluence that contributes to heat accumulation without any pulse-particle interactions. The parameter a is the maximum increase of AHA due to pulse-particle interactions that would be in effect for a vanishing temporal pulse to pulse separation. The temporal relaxation of AHA due to reduced effects of pulse-particle interactions with increasing temporal pulse to pulse separation is described by the parameter b.
However, in this context we want to point out that the approach of a simple increase of the absorbed laser fluence F0 on its own, cannot explain the experimentally observed behavior. Due to the restricted energy penetration depth and the logarithmic dependence of the ablation depth per pulse from the applied fluence, an increased absorption cannot cause the high ablation depth per pulse observed in the experiments.
4.3 Combination of heat accumulation and pulse-particle interactions
In the following section, the combination of heat accumulation and pulse-particle interaction is applied to describe the observed correlation between repetition rate and ablation depth per pulse. The parameters a, b and c are chosen to obtain the best agreement of the semi empirical model with the measured data for each pulse fluence F. The resulting parameters for the different pulse fluences are shown in Table 2.
Table 2. Summary of the Values for AHA(Δt,F) Used as Empirical Factors in the Simulation
The parameter a, which describes the maximum amount of applied energy that would remain in the workpiece for a vanishing temporal pulse to pulse separation decreases with increasing pulse fluence. One possible explanation for this behavior is that for higher applied fluences shielding effects that avoid the heat transfer to the sample play a major role, although the total amount of energy contributing to heat accumulation is higher for higher pulse fluences. On the other hand the parameter b, which describes the temporal relaxation of the effect of pulse-particle interactions decreases with decreasing pulse fluence from F = 1500 mJ/cm2 to 500 mJ/cm2. These results are in qualitatively good agreement with the experimental data obtained in other studies [20, 24]: For the ablation of steel using a pulse fluence of 400 mJ/cm2, a reduction of more than 10% of transmission of the ablation plume is observed [24]. This drop in the plume transmission can be measured up to about 0.45 µs after the ablating laser pulse, what corresponds to the value of –a/b that represents the timescale on that pulse-particle interactions become relevant. A comparison of this result with characteristic time scales presented in [20], allows for a discussion of the physical phenomena responsible for the increase of the absorption: The value of approx. 0.5 µs for the temporal delay after which pulse-particle interactions begin to have a relevant influence on the ablation process is in good agreement with the characteristic time frame between 0.2 µs and 0.7 µs for the ejection of aforementioned droplets and material particles observed in [20]. Therefore, it is assumed that the incident laser radiation is scattered by those droplets, which exhibit diameters in the range of the laser wavelength (Mie-scattering). Inside the drilling hole, the scattering leads to an enhanced heat transfer into the workpiece. In combination with the effect of heat accumulation, the enhanced heat input leads to the extensive increase of the ablation rate. Based on the observation of a dense jet of molten material [20] for time delays longer than 700 ns, an extensive pulse-particle interaction could be expected for even lower repetition rates. However those jets of molten material have only been observed for aluminum and gold. The authors attribute that behavior to the small electron-phonon coupling for gold and aluminum that favors melt formation [20]. Consistent with this argumentation, a considerably stronger electron-phonon coupling for steel inhibits the formation of that characteristic feature within the ablation dynamics. In consequence, we do not observe an interaction on this time scale.
The estimated values of –a/b, shift to smaller values for higher pulse fluences. At higher pulse fluences more material is ablated leading to temporal extended effects of pulse-particle interactions. With these empirical factors and the assumptions mentioned above the model reproduces the experimental results as shown in Fig. 4. The calculated ablation depth per pulse as a function of the repetition rate is in rather good agreement with the measured one. Thus, the characteristic dependence of the repetition rate on the ablation depth per pulse can be described by the introduced model that includes a combination of heat accumulation and effects of pulse-particle interactions. The good quantitative agreement between the theoretical approach and the measured data is achieved by a semi-empirical approach for AHA, which has been chosen to coincide with the measured data.
Fig. 4 Measured and modeled ablation depth per pulse as a function of repetition rate. The increase is caused by the superposition of heat accumulation and increasing energy input due to pulse-particle interactions.
5. Conclusion and outlook
The effects of heat accumulation and pulse-particle interaction during ultra-short pulse percussion drilling of steel are investigated. With increasing repetition rate a significant increase of the ablation depth per pulse up to a factor of 10 is observed. However, an isolated consideration of heat accumulation or increased absorption as a consequence of pulse-particle interactions cannot explain the observed strong increase of melt formation and ablation rate. Therefore, the observed behavior is described by a model that takes both heat accumulation as well as pulse-particle interactions into account. Thereby pulse-particle interactions lead to an enhanced heat transfer within the drilling hole that amplifies the effect of heat accumulation. The quantity of the enhanced heat input is described by introducing semi-empirical factors which have been chosen to give the best agreement with the experimental results. Thereby the obtained factors are in qualitatively good agreement with previous results [20, 24]. A comparison of the corresponding time scales with results from plume analysis by means of time resolved shadowgraphy [20], enables the assumption that scattering of the incident laser pulses with particles with diameters in the range of the laser wavelength (Mie scattering) plays the major role for the increased energy transfer into the workpiece. The increased energy transfer leads, in combination with heat accumulation, to an extensive increase of the ablation rate. Based on the presented study, pulse to pulse interactions play an essential role for percussion drilling of steel with ultra-short pulsed laser radiation for repetition rates exceeding 2 MHz at an applied pulse fluence of F = 1500 mJ/cm2 or exceeding 3 MHz for applied pulse fluences of 500 mJ/cm2.
Further research will concentrate on the role of heat accumulation and pulse-particle interactions during high power ultra-short pulse laser ablation with moving laser focus. However, not only the used pulse fluence and the repetition rate but especially the spatial pulse to pulse separation will determine the influence of heat accumulation and pulse-particle interactions.
Acknowledgments
The authors would like to thank the European Regional Development Fund for funding this work within the Innovation Cluster “AdaM”. Furthermore, they would like to thank EdgeWave GmbH for the possibility to use the EdgeWave PX picosecond laser for this study.
References and links
1. B. N. Chichkov, C. Momma, S. Nolte, F. Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys., A Mater. Sci. Process. 63(2), 109–115 (1996). [CrossRef]
2. C. Momma, B. N. Chichkov, S. Nolte, F. von Alvensleben, A. Tünnermann, H. Welling, and B. Wellegehausen, “Short-pulse laser ablation of solid targets,” Opt. Commun. 129(1-2), 134–142 (1996). [CrossRef]
3. S. Nolte, C. Momma, H. Jacobs, A. Tünnermann, B. N. Chichkov, B. Wellegehausen, and H. Welling, “Ablation of metals by ultrashort laser pulses,” J. Opt. Soc. Am. B 14(10), 2716 (1997). [CrossRef]
4. A. Ancona, S. Döring, C. Jauregui, F. Röser, J. Limpert, S. Nolte, and A. Tünnermann, “Femtosecond and picosecond laser drilling of metals at high repetition rates and average powers,” Opt. Lett. 34(21), 3304–3306 (2009). [CrossRef] [PubMed]
5. A. Ancona, F. Röser, K. Rademaker, J. Limpert, S. Nolte, and A. Tünnermann, “High speed laser drilling of metals using a high repetition rate, high average power ultrafast fiber CPA system,” Opt. Express 16(12), 8958–8968 (2008). [CrossRef] [PubMed]
6. P. S. Banks, M. D. Feit, A. M. Rubenchik, B. C. Stuart, and M. D. Perry, “Material effects in ultra-short pulse laser drilling of metals,” Appl. Phys., A Mater. Sci. Process. 69(7), S377–S380 (1999). [CrossRef]
7. S. Döring, S. Richter, S. Nolte, and A. Tünnermann, “In situ imaging of hole shape evolution in ultrashort pulse laser drilling,” Opt. Express 18(19), 20395–20400 (2010). [CrossRef] [PubMed]
8. G. Kamlage, T. Bauer, A. Ostendorf, and B. N. Chichkov, “Deep drilling of metals by femtosecond laser pulses,” Appl. Phys. A 77, 307–310 (2003).
9. G. Dumitru, V. Romano, H. P. Weber, M. Sentis, J. Hermann, S. Bruneau, W. Marine, H. Haefke, and Y. Gerbig, “Metallographical analysis of steel and hard metal substrates after deep-drilling with femtosecond laser pulses,” Appl. Surf. Sci. 208–209, 181–188 (2003). [CrossRef]
10. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010). [CrossRef] [PubMed]
11. J. Limpert, F. Roser, T. Schreiber, and A. Tunnermann, “High-power ultrafast fiber laser systems,” IEEE J. Sel. Top. Quantum Electron. 12(2), 233–244 (2006). [CrossRef]
12. P. Russbueldt, T. Mans, G. Rotarius, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “400W Yb:YAG Innoslab fs-Amplifier,” Opt. Express 17(15), 12230–12245 (2009). [CrossRef] [PubMed]
13. B. Neuenschwander, B. Jaeggi, M. Schmid, V. Rouffiange, and P.-E. Martin, “Optimization of the volume ablation rate for metals at different laser pulse-durations from ps to fs,” Proc. SPIE 8243, 824307 (2012). [CrossRef]
14. D. Breitling, A. Ruf, and F. Dausinger, “Fundamental aspects in machining of metals with short and ultrashort laser pulses,” Proc. SPIE 5339, 49–63 (2004). [CrossRef]
15. J. Finger, M. Weinand, and D. Wortmann, “Investigations on processing of carbon fiber reinforced plastics using ultrashort pulsed laser radiation with high average power,” Proceedings of ICALEO, #1905 (2013).
16. J. Schille, R. Ebert, U. Loeschner, P. Scully, N. Goddard, and H. Exner, “High repetition rate femtosecond laser processing of metals,” Proc. SPIE 7589, 758915 (2010). [CrossRef]
17. A. Y. Vorobyev, V. M. Kuzmichev, N. G. Kokody, P. Kohns, J. Dai, and C. Guo, “Residual thermal effects in Al following single ns- and fs-laser pulse ablation,” Appl. Phys., A Mater. Sci. Process. 82(2), 357–362 (2006). [CrossRef]
18. A. Y. Vorobyev and C. Guo, “Enhanced energy coupling in femtosecond laser-metal interactions at high intensities,” Opt. Express 14(26), 13113–13119 (2006). [CrossRef] [PubMed]
19. N. Zhang, X. Zhu, J. Yang, X. Wang, and M. Wang, “Time-resolved shadowgraphs of material ejection in intense femtosecond laser ablation of aluminum,” Phys. Rev. Lett. 99(16), 167602 (2007). [CrossRef] [PubMed]
20. I. Mingareev and A. Horn, “Time-resolved investigations of plasma and melt ejections in metals by pump-probe shadowgrpahy,” Appl. Phys., A Mater. Sci. Process. 92(4), 917–920 (2008). [CrossRef]
21. R. E. Russo, X. L. Mao, H. C. Liu, J. H. Yoo, and S. S. Mao, “Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation,” Appl. Phys., A Mater. Sci. Process. 69(7), S887–S894 (1999). [CrossRef]
22. C. Y. Liu, X. L. Mao, R. Greif, and R. E. Russo, “Time Resolved Shadowgraph Images of Silicon during Laser Ablation: Shockwaves and Particle Generation,” J. Phys. Conf. Ser. 59, 338–342 (2007). [CrossRef]
23. S. H. Jeong, R. Greif, and R. E. Russo, “Shock wave and material vapour plume propagation during excimer laser ablation of aluminium samples,” J. Phys. D Appl. Phys. 32(19), 2578–2585 (1999). [CrossRef]
24. J. König, S. Nolte, and A. Tünnermann, “Plasma evolution during metal ablation with ultrashort laser pulses,” Opt. Express 13(26), 10597–10607 (2005). [CrossRef] [PubMed]
25. L. V. Zhigilei, Z. Lin, and D. S. Ivanov, “Atomistic modeling of short pulse laser ablation of metals: connections between melting, spallation, and phase explosion†,” J. Phys. Chem. C 113(27), 11892–11906 (2009). [CrossRef]
26. A. Miotello and R. Kelly, “Laser-induced phase explosion: new physical problems when a condensed phase approaches the thermodynamic critical temperature,” Appl. Phys., A Mater. Sci. Process. 69(S1), S67–S73 (1999). [CrossRef]
27. F. Korte, J. Koch, and B. N. Chichkov, “Formation of microbumps and nanojets on gold targets by femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 879–881 (2004). [CrossRef]
28. C. Unger, J. Koch, L. Overmeyer, and B. N. Chichkov, “Time-resolved studies of femtosecond-laser induced melt dynamics,” Opt. Express 20(22), 24864–24872 (2012). [CrossRef] [PubMed]
29. R. Le Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249(1-4), 322–331 (2005). [CrossRef]
30. H. Treusch, P. Schäfer, and H. Junge, Abtragen, Bohren und Trennen mit Festkörperlasern (VDI-Technologiezentrum Physikalische Technologien, 1997).
