Fig 4 - uploaded by Jan Winter
Content may be subject to copyright.
Electron heat conductivity coefficient of copper as a function of electron temperature in dependence on ion temperature in solid and liquid phase in comparison to commonly used Anisimov model [60]. 

Electron heat conductivity coefficient of copper as a function of electron temperature in dependence on ion temperature in solid and liquid phase in comparison to commonly used Anisimov model [60]. 

Source publication
Article
Full-text available
In this paper, we present ultrafast measurements of the complex refractive index for copper up to a time delay of 20 ps with an accuracy <1% at laser fluences in the vicinity of the ablation threshold. The measured refractive index n and extinction coefficient k are supported by a simulation including the two - temperature model with an accurate de...

Contexts in source publication

Context 1
... for the electron- ion contribution over the wide electron temperature range. Thus, the effect of the density change under compression or stretch- ing conditions for electron-electron and electron-ion collisions are relatively weak in contrast to the influence of the electron temper- ature and can be considered as independent of the density [58]. Fig. 4 indicate the electronic heat conductivity as a function of the electron temperature in the non-equilibrium 2T-state for ion temperatures in solid and liquid phase compared with commonly used Anisimov model [60]. At low electron temperatures the non- monotonic prediction of the electron heat conductivity coefficient in the solid phase ...
Context 2
... with commonly used Anisimov model [60]. At low electron temperatures the non- monotonic prediction of the electron heat conductivity coefficient in the solid phase is dominated by the effective electron-ion col- lision frequency from the thermal resistance in comparison to the relatively weaker contribution of electron-electron collisions (see Fig. 4, solid curves at 2 kK). In contrast, at higher electron temper- atures above ∼15 kK the growth of heat conductivity is due to a significant increase of the effective electron-electron collision fre- quency connected with continuing raise in the heat capacity of s-electrons and its average electron ...

Citations

... Even though a part of electrons is excited and accelerated to velocities beyond the Fermi velocity ( ∼ 10 6 m / s in Mo [16] ) during the laser excitation, a local thermal equilibrium is assumed at each time instant. Although the complete equilibrium within the electronic subsystem may not be immediately achieved after the pulse termination [18] , the TTM is considered sufficiently accurate for describing the energy absorption and transport of electrons in metals upon laser pulse irradiation, particularly when the pulse fluence is close to the damage threshold [19][20][21][22] . ...
Article
Energy relaxation in a thin molybdenum film exposed to a single laser pulse (wavelength 400 nm, pulse duration 200 fs at FWHM) has been investigated numerically. For this purpose, a two-temperature model was used accounting for the optical and thermodynamical properties of molybdenum deposited on a selection of substrates. The effect of the substrate on laser-induced film heating has been studied for the cases of fused silica, silicon, soda-lime glass as well as for a free-standing film. For a fused silica substrate, the calculated melting threshold fluence is in a good agreement with thickness-dependent experimental data available in literature. It has been found that, for Mo films with the thickness <107 nm, the softening point of the fused silica substrate is exceeded already at the Mo melting threshold fluence. This suggests the possibility of substrate damage related to glass deformation. The melting dynamics of the Mo film and the effects of energy transfer from the irradiated film to the substrate are discussed based on the modeling results.
... A deep insight into fundamental aspects of the electron gas behavior under non-equilibrium laser heating conditions can be obtained based on the Boltzmann equation [11,12], which, however, is difficult to use for practical application in view of the large computer resources required. There are many attempts to improve the TTM description using more sophisticated dependences of the free electron gas properties [8,9,[13][14][15][16], in particular, utilizing parameters calculated based on the density of states theory developed in [17] under the assumption of equilibrium conditions. However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast-laser action [18]. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast-laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast-laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
Article
Full-text available
The ultrafast-laser-induced solid–liquid phase transition in metals is still not clearly understood and its accurate quantitative description remains a challenge. Here, we systematically investigated, both experimentally and theoretically, the melting of gold by single femto- and picosecond near-infrared laser pulses. Two laser systems with wavelengths of 800 and 1030 nm and pulse durations ranging from 124 fs to 7 ps were used, and the damage and ablation thresholds were determined for each irradiation condition. The theoretical analysis was based on two-temperature modeling. Different expressions for the electron–lattice coupling rate and contribution of ballistic electrons were examined. In addition, the number of free electrons involved in the optical response is suggested to be dependent on the laser intensity and the influence of the fraction of involved electrons on the damage threshold was investigated. Only one combination of modelling parameters was able to describe consistently all the measured damage thresholds. Physical arguments are presented to explain the modeling results.
... A deep insight into fundamental aspects of the electron gas behavior under non-equilibrium laser heating conditions can be obtained based on the Boltzmann equation [11,12], which however is difficult to use for practical application in view of the large computer resources required. There are many attempts to improve the TTM description using more sophisticated dependences of the free electron gas properties [8,9,[13][14][15][16], in particular, utilizing parameters calculated based on the density of states theory developed in [17] under the assumption of equilibrium conditions. However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
Preprint
Full-text available
The ultrafast laser-induced solid-liquid phase transition in metals is still not clearly understood and its accurate quantitative description remains a challenge. Here we systematically investigated, both experimentally and theoretically, the melting of gold by single femto-and picosecond near-infrared laser pulses. Two laser systems with wavelengths of 800 and 1030 nm and pulse durations ranging from 124 fs to 7 ps were used and the damage and ablation thresholds were determined for each irradiation condition. The theoretical analysis was based on two-temperature modeling. Different expressions for the electron-lattice coupling rate and contribution of ballistic electrons were examined. In addition, the number of free electrons involved in the optical response is suggested to be dependent on the laser intensity and the influence of the fraction of involved electrons on the damage threshold was investigated. Only one combination of modelling parameters was able to describe consistently all the measured damage thresholds. Physical arguments are presented to explain the modeling results.
... A deep insight into fundamental aspects of the electron gas behavior under non-equilibrium laser heating conditions can be obtained based on the Boltzmann equation [11,12], which however is difficult to use for practical application in view of the large computer resources required. There are many attempts to improve the TTM description using more sophisticated dependences of the free electron gas properties [8,9,[13][14][15][16], in particular, utilizing parameters calculated based on the density of states theory developed in [17] under the assumption of equilibrium conditions. However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
... However, the actual parameters of the free electron gas in metals are expected to lie in between the two extremes, resulting in a more complicated behavior under the highly non-equilibrium conditions obtained under ultrafast laser action [18]. Taking into account the additional complexity of a theoretical description connected with a dynamic change of the optical properties [9,15], a fraction of free electrons involved in the optical response of metals [15,19], and a possible role of ballistic electrons in heat transfer [4,20], the TTM allows several degrees of freedom to adjust modeling results to experimental data. ...
Preprint
The ultrafast laser-induced solid-liquid phase transition in metals is still not clearly understood and its accurate quantitative description remains a challenge. Here we systematically investigated, both experimentally and theoretically, the melting of gold by single femto- and picosecond near-infrared laser pulses. Two laser systems with wavelengths of 800 and 1030 nm and pulse durations ranging from 124 fs to 7 ps were used and the damage and ablation thresholds were determined for each irradiation condition. The theoretical analysis was based on two-temperature modeling. Different expressions for the electron-lattice coupling rate and contribution of ballistic electrons were examined. In addition, the number of free electrons involved in the optical response is suggested to be dependent on the laser intensity and the influence of the fraction of involved electrons on the damage threshold was investigated. Only one combination of modelling parameters was able to describe consistently all the measured damage thresholds. Physical arguments are presented to explain the modeling results.
... First, the physics that governs ultrafast laser ablation is still unclear and is a subject of intense debate 3-19 . The strong electric fields of laser pulses, which are comparable to the electric field inside an atom, drive target materials into states that are strongly out of equilibrium 3,11,15,19 . This situation contrasts with the case of material removal using much longer pulses, in which thermal effects, e.g., melting or vaporization, dominate the process 20 . ...
Article
Full-text available
Laser-based material removal, or ablation, using ultrafast pulses enables precision micro-scale processing of almost any material for a wide range of applications and is likely to play a pivotal role in providing mass customization capabilities in future manufacturing. However, optimization of the processing parameters can currently take several weeks because of the absence of an appropriate simulator. The difficulties in realizing such a simulator lie in the multi-scale nature of the relevant processes and the high nonlinearity and irreversibility of these processes, which can differ substantially depending on the target material. Here we show that an ultrafast laser ablation simulator can be realized using deep neural networks. The simulator can calculate the three-dimensional structure after irradiation by multiple laser pulses at arbitrary positions and with arbitrary pulse energies, and we applied the simulator to a variety of materials, including dielectrics, semiconductors, and an organic polymer. The simulator successfully predicted their depth profiles after irradiation by a number of pulses, even though the neural networks were trained using single-shot datasets. Our results indicate that deep neural networks trained with single-shot experiments are able to address physics with irreversibility and chaoticity that cannot be accessed using conventional repetitive experiments.
... Laser micro-machining of metals using ultrashort pulse (USP) lasers has gained exceptional industrial relevance as well as scientific attention. Besides theoretical explanations [1][2][3][4], quality optimization and efficiency increase [5][6][7][8][9][10] remains a central topic of investigation. In general, micro-machining using USP laser, typically in the sub to few ps range, beats corresponding nanosecond systems, mainly in terms of surface quality and precision [11,12]. ...
... This situation is called fulfillment of stress confinement, written as max { τ ep , τ p } ≤ τ mech [26,27], where for transition metals τ mech is in the range of 3 ps to 5 ps [17]. The resulting pressure amplitude with values up to tens of GPa [1,2,25] propagates into the material as well towards the surface, where it is partially reflected and due to the impedance mismatch transformed to a rarefaction wave [25,28]. This rarefaction causes the material surface to expand already after some ps, known as early mechanical motion δ disp [29,30]. ...
... This rarefaction causes the material surface to expand already after some ps, known as early mechanical motion δ disp [29,30]. Experimental observations using pump-probe interferometry [30] or pump-probe ellipsometry [2,29] reveal velocities of around 1 km/s [30] and a density decrease of 30 -40 % [29]. Exceeding the spall-strength of the already liquefied metal, material fracture may be induced [27]. ...
Article
Full-text available
In the context of current state of the art, understanding the laser ablation efficiency decrease for pulse durations exceeding the mechanical relaxation time of a few ps remains a pending research question. A heuristic approach may be used to reveal the role of effective penetration depth on ablation efficiency. Extending familiar contributions of this quantity by a term related to the mechanical surface expansion during pulse irradiation, the relation of ablation efficiency and pulse duration is deciphered. Thus, longer pulses are coupled into an expanded surface, revealing a direct link to the violation of stress confinement. To best demonstrate this hypothesis, a material with high electron-phonon coupling as well as low thermal conductivity, i.e., strong electron localization, is required. These properties are accomplished by high-entropy alloys, and the CrMnFeCoNi alloy serves as prime candidate. We report on single-pulse ablation efficiency experiments of the CrMnFeCoNi alloy which are support by our proposed model.
... Dans le régime WDM hors équilibre, une augmentation d'environ 50% de l'indice optique du cuivre a été observée juste après des impulsions laser 1,4 J cm 2 de ∼500 fs FWHM [163], diminuant fortement la profondeur de pénétration du laser dans les premiers instants du chauffage. Ce changement brusque serait dû au fait que les électrons de conduction de la bande 3d sont très sensibles à une augmentation de température et leurs états se chevauchent avec ceux de la bande 4s, ce qui augmente la densité de charge dans cette dernière [164]. ...
Thesis
L’irradiation de matériaux par un faisceau laser infra-rouge de durée femtoseconde permet de porter la matière dans le régime dense et tiède, frontière entre la physique du solide et la physique des plasmas. Á une échelle de temps aussi courte, on provoque une situation hors-équilibre thermique, où une grande quantité d’énergie est déposée dans les électrons tandis que les ions restent froids. Ce fort déséquilibre peut alors provoquer de grandes modifications des propriétés de la matière. L’étude présentée ici se penche sur deux métaux différents dans le régime dense et tiède hors-équilibre, le cuivre et le molybdène. Ces métaux ont été étudiés expérimentalement en utilisant la spectroscopie d’absorption des rayons X près des seuils (XANES) résolue en temps, ainsi que des simulations numériques dites ab initio et hydrodynamiques. Ces dernières permettent respectivement d’étudier la matière à l’échelle atomique au travers des structures électronique et ionique, et à l’échelle macroscopique en décrivant le comportement des électrons et des ions suite à un dépôt d’énergie. En utilisant ces trois outils (parmi d’autres), le cuivre a beaucoup été étudié dans le régime dense et tiède hors-équilibre. Notamment, un diagnostic quantitatif de la température des électrons dans le cuivre a été développé dans le passé, basé sur la spectroscopie XANES au seuil L3 et des simulations ab initio. Dans la continuité de ce résultat, nous avons étudié le transport de l’énergie électronique dans le cuivre chauffé par laser à l’échelle femtoseconde, et mis en évidence que, au delà d’un certain flux laser, ce transport est dominé par la diffusion thermique plutôt que par le transport d’électrons balistiques. Ensuite, nous avons transposé la méthodologie d’étude de la matière dense et tiède sur le molybdène, choisi en tant que prototype de métal de transition pour les études dans ce régime. Des simulations hydrodynamiques nous ont permis d’estimer les conditions thermodynamiques caractéristiques du molybdène à la suite d’un chauffage par une impulsion laser femtoseconde. Ensuite, une batterie de simulations ab initio ont été conduites. Elles ont permis d’identifier des motifs spécifiques dans les spectres XANES au seuil L3 du molybdène, ses liens avec les structures électronique et atomique, et comment cela change dans le régime dense et tiède en fonction de la température et de la densité. Enfin, une expérience préliminaire de spectroscopie XANES sur le molybdène dense et tiède nous a montré que le spectre froid du molybdène expérimental est en très bon accord avec les résultats des simulations ab initio. De plus, cette expérience a aussi montré qu’il était possible d’observer expérimentalement les changements du spectre XANES attendus par les simulations sur le molybdène.
... Both, the local reflectivity minimum and the subsequent reflectivity increase in air and water are understood to be a consequence of thermal excitation of electrons by the pump-pulse and subsequent modulated absorption/reflection of the probe pulse as illustrated in previous studies 28,29 . ...
Article
Full-text available
Laser ablation in liquids is a highly interdisciplinary method at the intersection of physics and chemistry that offers the unique opportunity to generate surfactant-free and stable nanoparticles from virtually any material. Over the last decades, numerous experimental and computational studies aimed to reveal the transient processes governing laser ablation in liquids. Most experimental studies investigated the involved processes on timescales ranging from nanoseconds to microseconds. However, the ablation dynamics occurring on a sub-nanosecond timescale are of fundamental importance, as the conditions under which nanoparticles are generated are established within this timeframe. Furthermore, experimental investigations of the early timescales are required to test computational predictions. We visualize the complete spatiotemporal picosecond laser-induced ablation dynamics of gold immersed in air and water using ultrafast pump-probe microscopy. Transient reflectivity measurements reveal that the water confinement layer significantly influences the ablation dynamics on the entire investigated timescale from picoseconds to microseconds. The influence of the water confinement layer includes the electron injection and subsequent formation of a dense plasma on a picosecond timescale, the confinement of ablation products within hundreds of picoseconds, and the generation of a cavitation bubble on a nanosecond timescale. Moreover, we are able to locate the temporal appearance of secondary nanoparticles at about 600 ps after pulse impact. The results support computational predictions and provide valuable insight into the early-stage ablation dynamics governing laser ablation in liquids. Ultrafast dynamics of laser ablation of gold in water revealed by pump-probe microscopy on a picosecond to microsecond timescale.
... [2] In the field of multi-pulsed laser ablation, researchers often use experimental methods to study the changes of hole depth and hole morphology with incident laser parameters. Winter [9] et al. used the experimental method to ultra-fast measurement of the refractive index of copper. At the same time, the TTM and thermo-mechanical model with precise description of thermal and optical properties were used as theoretical support to explore the refractive index n and the extinction coefficient k in different time ranges. ...
Article
Full-text available
Ultrafast laser has an undeniable advantage in laser processing due to its extremely small pulse width and high peak energy. While the interaction of ultrafast laser and solid materials is an extremely non-equilibrium process in which the material undergoes phase transformation and even ablation in an extremely short time range. This is the coupling of the thermos elastic effect caused by the pressure wave and the superheated melting of the material lattice. To further explore the mechanism of the action of ultrafast laser and metal materials, the two-temperature model coupling with molecular dynamics method was used to simulate the interaction of the copper and laser energy. Firstly, the interaction of single-pulsed laser and copper film was reproduced, and the calculated two-temperature curve and the visualized atomic snapshots were used to investigate the influence of laser parameters on the ablation result. Then, by changing the size of the atomic system, the curve of ablation depth as a function of laser fluence was obtained. In this paper, the interaction of multi-pulsed laser and copper was calculated. Two-temperature curve and temperature contour of copper film after the irradiation of double-pulsed and multi-pulsed laser were obtained. And the factors which can make a difference to the incubation effect were analyzed. By calculating the ablation depth under the action of multi-pulsed laser, the influence of the incubation effect on ablation results was further explored. Finally, a more accurate numerical model of laser machining metal is established and verified by an ultra-short laser processing experiment, which provides a new calculation method and theoretical basis for ultra-fast laser machining of air film holes in aviation turbine blades, and has certain practical guiding significance for laser machining.
... The observed material reflectivity and thus the amount of laser energy absorbed in the skin depth is defined by the collective electronic response to the laser field through intraband and interband transitions in sub-bands of the crystal state [8][9][10][11][12]. The time-resolved complex refractive index of the laser-irradiated surface has been previously reported by a dual-angle reflectometry technique, which was applied to study the optical dynamics of d-band electrons in transition metals near the threshold fluence [13][14][15][16]. To better determine the refractive index without Fresnel equations, a direct measurement of optical properties has been recently proposed by an ultrafast pump-probe method combining ellipsometry with reflectometry [17,18]. ...
... In this case, the intraband contribution was considered as a sum of the zero-and first-order oscillators. It is generally believed that for a strong laser excitation, equivalent to a high electron temperature in our case, the interband oscillators change their relative strength f j (becoming stronger or weaker) and width Γ j , whereas the central frequency ω j remains constant [16]. We can see, however, in Figure 5 that the position of the oscillator maxima changes too. ...
Article
Full-text available
Evaluating the optical properties of matter under the action of ultrafast light is crucial in modeling laser–surface interaction and interpreting laser processing experiments. We report optimized coefficients for the Drude–Lorentz model describing the permittivity of several transition metals (Cr, W, Ti, Fe, Au, and Ni) under electron–phonon nonequilibrium, with electrons heated up to 30,000 K and the lattice staying cold at 300 K. A Basin-hopping algorithm is used to fit the Drude–Lorentz model to the nonequilibrium permittivity calculated using ab initio methods. The fitting coefficients are provided and can be easily inserted into any calculation requiring the optical response of the metals during ultrafast irradiation. Moreover, our results shed light on the electronic structure modifications and the relative contributions of intraband and interband optical transitions at high electron temperatures corresponding to the laser excitation fluence used for surface nanostructuring.