Laser excitation and non-thermal processes

The energy of a short laser pulse couples mainly to electrons of the irradiated material. In metals, the presence of conduction-band electrons enables the direct absorption of laser energy by electrons undergoing collisions with nuclei (i.e., by inverse bremsstrahlung). In semiconductors and dielectrics, electrons have to be excited across the bandgap before they can directly absorb photons. ^{Reference Stuart, Feit, Herman, Rubenchik, Shore and Perry27,Reference van Driel28} The electronic excitation in materials with a bandgap may strongly modify the interatomic bonding and can lead to ultrafast phase transitions, including ultrafast melting ^{Reference Rousse, Rischel, Fourmaux, Uschmann, Sebban, Grillon, Balcou, Förster, Geindre, Audebert, Gauthier and Hulin5} and solid–solid phase transformations. ^{Reference Hase, Fons, Mitrofanov, Kolobov and Tominaga6} Such phase transitions are referred to as “non-thermal,” as they are directly stimulated by the laser excitation, take place in the electronically excited state on the sub-picosecond (ps) time scale, and require no electron–phonon equilibration and lattice heating.

In wide bandgap dielectrics, the main mechanisms involved in the generation of free electrons by photons having lower energy than the bandgap are multiphoton and avalanche ionizations, which are highly nonlinear processes. ^{Reference Stuart, Feit, Herman, Rubenchik, Shore and Perry27} Multiphoton excitation (i.e., simultaneous absorption of several photons) is sensitive to the laser intensity as its probability exhibits a power law dependence on the laser intensity, which, in effect, makes the absorption process deterministic. It becomes effective for ultrashort laser pulses whose intensities are greatly increased due to the reduction of the pulse duration τ_p. At high laser intensities, the potential barrier for the escape of electrons from the atoms is distorted, and ionization by electron tunneling through the reduced barrier can dominate over multiphoton ionization. ^{Reference Keldysh29} Once the electrons are excited to the conduction band, they absorb laser energy via inverse bremsstrahlung and can produce a sequence of electron–hole pairs through collisions with valence-band electrons. This process leads to avalanche multiplication of the density of conduction-band electrons.

The competition between these two mechanisms of free carrier generation is responsible for considerable improvement of machining quality with the use of ultrashort laser pulses, as illustrated in Figure 2a. Absorption of ultrashort laser pulses with durations of tens of femtoseconds (fs) and peak intensities above 10¹⁵ W/cm² is mostly governed by the photoionization mechanisms (multiphoton or tunneling), whereas for free electrons the laser pulse is too short to trigger the avalanche process. In this case, the dependence of the lateral extension parameter q, which relates the characteristic size of a generated structure divided by the illuminated area to the incident laser fluence, is logarithmic for a Gaussian beam profile. Therefore, laser-generated cavities can be fabricated with sub-10 nm lateral and vertical precision. ^{Reference Lenzner, Krausz, Krüger and Kautek30} For τ_p > 100 fs, the value of q strongly deviates from the logarithmic dependence, and the modified zone has a rugged splintered morphology, suggesting collateral damage outside the area where the laser fluence exceeds the damage threshold. This is likely to be conditioned by the “stochastic” avalanche process, which becomes efficient at longer τ_p. ^{Reference Rethfeld31}

Figure 2. (a) The dependence of the lateral extension parameter q = ln(F ₀/F _th)/2 on laser fluence F ₀ for the ablation of fused silica in air. The green region highlights values of theoretically predicted q for fluence threshold F _th = 1.4 J cm^–2 (τ_p = 5 fs) and F _th = 1.9 J cm^–2 (τ_p = 12 fs). Inserts below show scanning electron micrographs of cavities generated at different laser pulse durations. ^{Reference Lenzner, Krausz, Krüger and Kautek30} Predominance of the multiphoton excitation mechanism for short laser pulses makes the absorption deterministic, increasing the quality of the material processing. (b) Measured transmission of a fs laser beam (800 nm, 45 fs, NA = 0.25) through a fused silica sample demonstrating the important role of self-trapped excitons (STEs) in light absorption (irregular lines). The results of a simplified modeling accounting for multiphoton and avalanche ionization and free electron trapping are shown by smooth black lines. The up-down arrow underlines the enhancement of absorption by introducing a 70-nJ prepulse in advance of the laser pulse actions. Adapted with permission from Reference Reference Grojo, Gertsvolf, Lei, Barillot, Rayner and Corkum35. © 2010 American Physical Society. (c) Schematics of the formation of defects in a-SiO₂ that are responsible for accumulation effects in laser-irradiation experiments: (i) intrinsic fused silica structure; (ii) STE state (blue color shows the regions with distributed excess charges); (iii) E′-center, and non-bridged oxygen hole centers (unpaired electrons are shown by blue arrows). (d) The map of absorbed energy density predicted for laser beam propagation through fused silica in the pump-probe regime in simulations based on Maxwell’s equations. ^{Reference Bulgakova, Zhukov, Meshcheryakov, Gemini, Brajer, Rostohar and Mocek38} Modeling reveals formation of a defect-mediated umbrella-like shield before the geometrical focus. Note: τ_p, pulse duration; NA, numerical aperture; a-Si, amorphous silicon; E _abs, absorbed laser energy per unit volume; fs, femtosecond; ps, picosecond.

The defects that introduce intra-bandgap states also play an important role in laser excitation/absorption of wide-bandgap dielectric materials. Much work has been done on identifying the kinds of laser-generated defects in optical materials, especially in fused silica glass (bandgap of ∼9 eV), ^{Reference Itoh and Stoneham32,Reference Pacchioni, Skuja and Griscom33} and their roles in laser-induced ionization processes. The pump-probe method, where an excitation pulse is followed by another incoming pulse with an adjustable time delay to probe the transient changes in reflection or transmission within the irradiated spot, is one of the most informative experimental techniques for such studies. ^{Reference Martin, Guizard, Daguzan, Petite, D’Oliveira, Meynadier and Perdrix34,Reference Grojo, Gertsvolf, Lei, Barillot, Rayner and Corkum35}

In particular, the characteristic lifetimes of free electrons ^{Reference Martin, Guizard, Daguzan, Petite, D’Oliveira, Meynadier and Perdrix34} and self-trapped excitons (STEs) ^{Reference Grojo, Gertsvolf, Lei, Barillot, Rayner and Corkum35} (∼150 fs and >30 ps, respectively) have been determined for fused silica by varying time delay between the pump and probe pulses. Figure 2b ³⁵ demonstrates that absorption of energy from a laser beam tightly focused inside the bulk glass can be considerably enhanced by a prepulse, which couples to the sample only 3 ps in advance of the probe pulse and forms a population of STEs. The most important defects produced in fused silica by laser irradiation are schematically presented in Figure 2c. Free electrons created by the pump pulse through ionization of intrinsic glass structure are swiftly trapped into STE states. At the ps time scale, the STEs recombine with ∼0.1% of STEs evolving into permanent defects, ^{Reference Petite, Guizard, Martin and Quéré36} E′-centers (undercoordinated silicon atom), and non-bridged oxygen hole centers (oxygen atoms bonded to one silicon atom with one unpaired electron each) with the absorption peak of 5.8 eV. ^{Reference Pacchioni, Skuja and Griscom33} Accumulation of permanent defects is one of the key factors that affects the quality of laser processing of wide-bandgap dielectrics. ^{Reference Mao, Quéré, Guizard, Mao, Russo, Petite and Martin37}

An example of the strong effects of laser-generated defects on laser beam propagation is provided in Figure 2d, where the results of simulations based on Maxwell’s equations supplemented by hydrodynamic-type equations for free electrons oscillating in the laser field ^{Reference Bulgakova, Zhukov, Meshcheryakov, Gemini, Brajer, Rostohar and Mocek38} are shown for pump-probe irradiation conditions with laser energy in each pulse of 0.2 μJ, τ_p = 150 fs, and time separation between the pulses of ∼3 ps. The simulations, which take into account the formation of STEs and their re-excitation by the probe pulse, predict the formation of a defect-mediated umbrella-like shield and explain the enhancement of light absorption in the pump-probe experiments. ^{Reference Grojo, Gertsvolf, Lei, Barillot, Rayner and Corkum35}

As demonstrated in a recent work on high-impact polystyrene ^{Reference Naghilou, Armbruster, Kitzler and Kautek39} (see Figure 3 ), defect-mediated laser absorption can lead to the reduction of the threshold fluence for material modification with an increase in the laser beam radius, w, and the number of laser pulses applied to the same spot on the surface, N. The darkening of the modified surface in Figure 3a is due to ablation and phase separation, as illustrated by the scanning electron microscope image of the surface topography. The reduction of the threshold for large beam radii (w >> Ω^–0.5, where Ω is the areal density of active low-density defects [LDDs], within the absorption volume), shown in Figure 3b, is ascribed to LDDs embedded in the matrix material and schematically illustrated in Figure 3c. ^{Reference Naghilou, Armbruster, Kitzler and Kautek39} These defects act as donors of free electrons that can initiate an electron avalanche and, as discussed, increase laser absorption. At small beam radii (w << Ω^–0.5), the laser radiation interacts mainly with the matrix material. Accumulation and incubation of LDDs upon repetitive laser irradiation significantly reduces the damage threshold (Figure 3b). This reduction is due to the generation and accumulation of optically active high-density defects (Figure 3c) with a separation distance that is smaller than the irradiation wavelength.

Figure 3. (a) Combination of a scanning electron micrograph (lower right) and of a reflected-light optical micrograph (upper left) of a modification site (N = 1 pulse, beam radius w = 50 ± 5 µm, fluence F ₀ = 11 ± 2 J cm^–2). The modified material, which appears darkened in the optical micrograph, can be correlated to the onset of morphological changes as revealed by the scanning electron micrograph. (b) The dependence of the threshold fluence F _th on the laser beam radius, w, and number of pulses, N, overlain with the best fit of the extended defect model. (c) A schematic sketch of the extended defect model illustrating the presence of high-density and low-density defects. ^{Reference Naghilou, Armbruster, Kitzler and Kautek39} Here, the red laser light is focused on the sample, and the green features represent low density defects, such as voids, cracks, and scratches. The black mesh in the absorption volume depicts high density defects.

Laser-induced structural and phase transformations

The initial non-thermal material response to the ultrafast laser excitation is quickly, within picoseconds, followed by the onset of thermal processes induced by the energy transfer from the excited electrons to atomic vibrations, commonly described as electron–phonon coupling. Rapid electron–phonon equilibration can produce ultrafast heating rates exceeding 10¹⁴ K/s, opening unique opportunities for investigating the kinetic limits of achievable superheating of solid phases. A combination of time-resolved optical, x-ray, and electron diffraction probing of short pulse laser melting ^{Reference Lin and Elsayed-Ali40–Reference Sokolowski-Tinten, Blome, Blums, Cavalleri, Dietrich, Tarasevich, Uschmann, Förster, Kammler, Horn-von-Hoegen and von der Linde42} with theoretical analysis ^{Reference Rethfeld, Sokolowski-Tinten, von der Linde and Anisimov8} and molecular dynamics (MD) simulations ^{Reference Ivanov and Zhigilei9,Reference Ivanov and Zhigilei43,Reference Lin, Leveugle, Bringa and Zhigilei44} have provided important information on the time scales and mechanisms of the melting process occurring under conditions of strong superheating.

However, the short pulse laser irradiation may not only cause rapid heating and melting of localized surface or internal regions of the target, but also produce sharp temperature gradients leading to rapid quenching of the transiently melted material. In strongly absorbing materials such as metals or semiconductors, a combination of shallow depth of the laser energy deposition with high thermal conductivity of the irradiated material can lead to cooling rates approaching and even exceeding 10¹² K/s. ^{Reference Lin, Spaepen and Turnbull22,Reference Wu, Christensen, Savolainen, Balling and Zhigilei23} The cooling rates can be even higher, in excess of 10¹³ K/s, ^{Reference Ivanov, Lin, Rethfeld, O’Connor, Glynn and Zhigilei45} when the laser energy deposition is confined not only within the thin surface layer of the irradiated target, but also in the lateral dimensions, creating conditions for even faster two- or three-dimensional heat transfer from the absorption region. The laterally localized laser energy deposition can be achieved by using tightly focused laser beams ^{Reference Pronko, Dutta, Squier, Rudd, Du and Mourou46,Reference Koch, Korte, Bauer, Fallnich, Ostendorf and Chichkov47} or taking advantage of the local field enhancement in the vicinity of a tip of a scanning probe microscope. ^{Reference Hwang, Ryu, Misra, Jeon and Grigoropoulos48,Reference Huber, Trügler, Hohenester, Prior and Kautek49}

The ultrahigh rates of laser-induced cooling and the resulting resolidification, combined with the generation and relaxation of strong compressive stresses generated by the fast laser heating of the absorption region, ^{Reference Paltauf and Dyer17,Reference Leveugle, Ivanov and Zhigilei18} create conditions for the formation of unusual metastable phases and unique material microstructures that are difficult if not impossible to produce by any other processing methods. In particular, metallic glass formation in systems not previously considered as glass formers has been demonstrated in ns- and ps-pulse laser quenching. ^{Reference Lin, Spaepen and Turnbull22,Reference Alonso and Lopez26} Recent examples of exotic phases produced by lasers include a dense body-centered-cubic Al phase ^{Reference Vailionis, Gamaly, Mizeikis, Yang, Rode and Juodkazis11} and new tetragonal polymorphs of silicon ^{Reference Rapp, Haberl, Pickard, Bradby, Gamaly, Williams and Rode12} formed through ultrafast confined microexplosions generated by fs laser pulses tightly focused inside a sapphire (α-Al₂O₃) crystal and at the interface between a transparent amorphous silicon dioxide layer (SiO₂) and an opaque crystalline Si substrate, respectively. An unusual amorphous carbon phase featuring a large fraction of sp ³-bonded carbon and a propensity for nano-/microdiamond nucleation has been generated by nanosecond laser treatment of amorphous carbon films. ^{Reference Narayan and Bhaumik13}

The laser-induced processes responsible for the generation of complex surface microstructures featuring ultrahigh densities of crystal defects are illustrated in Figure 4 , where the results of large-scale MD simulations (Figure 4a–d) and experimental transmission electron microscopy characterization of the surface modified by fs laser irradiation (Figure 4e) are shown. The snapshots presented in Figure 4a illustrate how a complex interplay of fast laser melting, rapid cooling, resolidification, and the dynamic relaxation of laser-induced stresses in the surface region of a Ag target irradiated by a 100 fs laser pulse result in the formation of a subsurface porous region covered by a nanocrystalline surface layer. ^{Reference Wu, Christensen, Savolainen, Balling and Zhigilei23} The nanocrystalline layer with ultrafine grains (see distribution in Figure 4b) is produced by massive nucleation of crystallites triggered by a deep undercooling of the melted surface region down to ≤ 0.7T _m (T _m is the melting temperature) and features random crystallographic orientation of the nanograins (Figure 4b).

Figure 4. Short pulse laser-induced generation of complex surface microstructure (a–d) predicted in atomistic simulations and (e) observed in experiments: (a–b) Surface “swelling” and nanocrystallization of a Ag target irradiated by a 100 fs laser pulse below the spallation threshold; ^{Reference Wu, Christensen, Savolainen, Balling and Zhigilei23} (c) formation of polyicosahedral structure of a frozen nanospike generated in the same system at higher laser fluence, in the spallation regime; ^{Reference Wu and Zhigilei24} (d) growth twinning predicted for Ni(111) targets irradiated by 50 fs laser pulses in the simulations and (e) confirmed experimentally. ^{Reference Sedao, Shugaev, Wu, Douillard, Esnouf, Maurice, Reynaud, Pigeon, Garrelie, Zhigilei and Colombier25} In (a), the atoms are colored by their potential energies, such that the crystalline part of the target is blue, the melted part is green, and free surfaces are red. In (b), the grain sizes are expressed in units of radii of spherical grains with equivalent volumes; (inset) the grains are colored according to their crystallographic orientation, and the atoms in the atomic view of the structure are colored such that the single and double green layers on a light blue background correspond to twin boundaries and stacking faults in the face-centered-cubic (fcc) structure. In (c), the atoms are colored such that the fcc atoms are yellow, stacking faults and twin boundaries are red, and other defects are purple. In (d), the coherent and incoherent twin boundaries generated within the top 30 nm region of the irradiated target are shown as green atomic layers and red regions within the blue fcc crystal, respectively. In (e), superimposed transmission electron microscope images highlighting the epilayers (blue) and twinned domains (green) in the laser-processed surface region of a Ni(111) target, and the results of the selected-area electron diffraction (SAED) analysis confirming the presence of twinned domains are shown. Note: fs, femtosecond; ps, picosecond.

The enlarged atomic-scale view of the surface microstructure shown for one of the nanograins in Figure 4b reveals a high density of stacking faults, twins, and nanoscale-twinned structural elements with fivefold symmetry. The formation of similar pentagonal structural elements has also been observed in frozen nanospikes generated in a MD simulation performed at a higher laser fluence, in the spallation regime discussed in the next section. ^{Reference Wu and Zhigilei24} Structural analysis of the Ag nanospike generated in the MD simulation (Figure 4c), reveals a remarkable variability of the structural motifs coexisting in the nanospike, including a region of continuous network of pentagonal twinned structural elements arranged into a polyicosahedral structure. ^{Reference Wu and Zhigilei24}

The computational prediction of the formation of a thin nanocrystalline layer with high density of twins suggests that short pulse laser processing is a viable alternative to the severe plastic deformation ^{Reference Valiev, Islamgaliev and Alexandrov50} or pulsed electrodeposition ^{Reference Bufford, Wang, Liu and Lu51} techniques that are currently employed to yield maximum structural refinement and high strength of metallic materials. Moreover, the localization of the nanocrystalline structure within a thin surface layer of the target and the prominent presence of twin boundaries and pentagonal structural elements are two factors that may also increase the ductility of the laser-modified layer, ^{Reference Fang, Li, Tao and Lu52–Reference Li, Dao, Eberl, Hodge and Gao54} a property that is generally incompatible with high strength.

Another example of unusual laser-generated defect configurations is the recent observation of nanoscale lamellar structures of interlaying twinned domains and epilayers in the surface regions of Ni(111) targets transiently melted and resolidified following exposure to fs laser pulses (Figure 4e). ^{Reference Sedao, Shugaev, Wu, Douillard, Esnouf, Maurice, Reynaud, Pigeon, Garrelie, Zhigilei and Colombier25} The results have been explained by atomistic- and continuum-level simulations performed for the same system (Figure 4d). The simulations predict the onset of growth twinning at the resolidification front when the temperature drops below a certain critical level (0.87T _m for the simulated Ni). The results of this study indicate that growth twinning can be used as a sensitive measure of the level of undercooling achieved in the transient laser-induced melting and resolidification of face-centered-cubic metal targets/grains with {111} surface orientation. In the absence of growth twinning, the structural signatures of the transient melting and resolidification (e.g., generation of a high vacancy concentration), ^{Reference Lin, Johnson and Zhigilei55} may be too weak to be detected by ex situ experimental characterization methods. In addition, the formation of a thin layer with high density of growth twins drastically increases the strength of the surface region. ^{Reference Zhang, Misra, Wang, Nastasi, Embury, Mitchell, Hoagland and Hirth56}

Laser ablation: From photomechanical spallation to phase and Coulomb explosions

The process of laser-induced removal of material from an irradiated target, commonly called laser ablation, is at the core of many practical laser-enabled applications, including high-precision cutting and drilling, surface nanostructuring, pulsed laser deposition of films and coatings, and generation of nanoparticles with narrow size distributions and well-controlled compositions. Several mechanisms driving the collective ejection of material from the irradiated target are briefly outlined in the next section.

As mentioned, the fast rate of energy deposition by short laser pulses may lead to the generation of compressive stresses. The laser-generated stresses are particularly high in the regime of stress confinement, ^{Reference Paltauf and Dyer17,Reference Leveugle, Ivanov and Zhigilei18} when the time of the laser heating (defined by the laser pulse duration, τ_p, or the time of the electron–phonon equilibration, τ_e–ph, whichever is longer) is shorter than the time required for the mechanical relaxation (expansion) of the heated volume, in other words, max{τ_p , τ_e–ph} ≤ L _p /C _s, where C _s is the speed of sound in the target material and L _p is the effective depth of the laser energy deposition (optical penetration depth or, in the case of metals, the depth of diffusive/ballistic energy transport during the time of the electron–phonon equilibration). ^{Reference Leveugle, Ivanov and Zhigilei18}

The interaction of the laser-induced compressive stresses with the free surface of the irradiated sample can result in the generation of a tensile wave sufficiently intense to cause the formation subsurface voids (Figure 4a). The growth and percolation of the voids may lead to the separation and ejection of a top layer from the target. Analogous to the term “spallation,” commonly used to describe the dynamic fracture that results from the reflection of a shock wave from the back surface of a sample, material ejection driven by the relaxation of laser-induced stresses is commonly referred to as photomechanical spallation (admittedly, “cavitation” would be a more appropriate term when the photomechanical processes take place in the melted part of the target).

Further increase in the laser fluence above the spallation threshold results in the separation and ejection of thinner layers and/or multiple droplets from the target, and, at a sufficiently high laser fluence, induces a transition to a different ablation regime commonly referred to as “phase explosion” or “explosive boiling.” In this regime, the melted surface region of the irradiated target is overheated above the limit of thermodynamic stability of the liquid phase, ^{Reference Martynyuk19–Reference Bulgakova and Bulgakov21} leading to a rapid decomposition of the overheated melted material into a mixture of vapor and liquid droplets. The transition from photomechanical spallation to phase explosion is signified by a sharp (threshold-like) increase in the amount of the vapor-phase atoms in the ejected plume, ^{Reference Wu and Zhigilei57,Reference Zhigilei and Garrison58} which reflects the difference in the physical mechanisms responsible for the material ejection in these two regimes. An explosive release of vapor, rather than the relaxation of photomechanical stresses, provides the main driving force for the collective ejection of the overheated surface region of the target in the regime of phase explosion. In the case of ablation by longer laser pulses, in the absence of stress confinement, spallation is not activated and explosive boiling is the mechanism responsible for the direct transition from the regime of surface melting and evaporation to the phase explosion. ^{Reference Bulgakova and Bulgakov21,Reference Zhigilei and Garrison58}

Due to the spatial variation of laser intensity within laser beams that often have Gaussian profiles, photomechanical spallation and phase explosion may coexist and jointly contribute to the material ejection induced by the same laser pulse. This is illustrated by Figure 5a, where a “mosaic approach” combining the results of simulations performed at different local laser fluences is used for representation of the laser-induced processes at the scale of the whole laser spot. ^{Reference Wu and Zhigilei57} Two distinct sections can be easily identified within the laser spot: the central area, where the overheated top part of the surface region undergoes an explosive decomposition into vapor and liquid droplets, and the periphery of the spot, where spallation of well-defined liquid layers connected to the bulk of the target by transient foamy structures of interconnected liquid regions is observed. Although the liquid layers observed in individual simulations are flattened by the application of periodic boundary conditions, the integral picture of ablation by the Gaussian laser beam is likely to involve the peel off of a continuous liquid layer with its thickness decreasing toward the center of the laser spot, as shown schematically in Figure 5a by gray stripes and directly observed in Figure 5d, where a snapshot from a simulation of Au surface nanostructuring by periodically modulated energy deposition realized in two-beam interference experiments is shown. ^{Reference Ivanov, Lipp, Blumenstein, Kleinwort, Veiko, Yakovlev, Roddatis, Garcia, Rethfeld, Ihlemann and Simon59}

Figure 5. (a) Visualization of laser ablation obtained in a series of molecular dynamics (MD) simulations of an Al target irradiated by a 100 fs laser pulse. ^{Reference Wu and Zhigilei57} The laser beam has a Gaussian spatial profile with the standard deviation σ and a peak absorbed laser fluence of 2050 J/m². The snapshots are taken at the same time of 150 ps after the laser pulse and are aligned with locations within the laser spot that correspond to the values of local fluence used in the simulations, as shown in the lower part of the panel. The atoms in the snapshots are colored by their potential energy, from blue for low energy atoms in the bulk of the target to red for the vapor-phase atoms. The red dots connected by the red line mark the location of the liquid–crystal interface. (b) Optical micrograph taken at 800 ps after irradiation of a GaAs target by a 110 fs laser pulse. ^{Reference Ionin, Kudryashov, Seleznev and Sinitsyn60} (c) Scanning electron microscope image of surface morphology generated on a Au target irradiated by two 60 fs laser pulses. ^{Reference Vorobyev and Guo14} (d) Result of MD simulation of surface nanostructuring by the two-beam interference technique. ^{Reference Ivanov, Lipp, Blumenstein, Kleinwort, Veiko, Yakovlev, Roddatis, Garcia, Rethfeld, Ihlemann and Simon59} The snapshot is taken at 800 ps after the laser pulse and colored such that the crystalline and melted parts of the target are blue and green, respectively. Note: fs, femtoseconds; ps, picoseconds.

Both spallation and phase explosion provide channels for effective transformation of the energy deposited by the laser irradiation into material disintegration and vaporization, thus creating conditions for rapid cooling and freezing of the transient liquid structures generated in laser spallation or ablation. ^{Reference Wu and Zhigilei24,Reference Wu and Zhigilei57} Indeed, the temperature of the liquid–crystal interface, shown in Figure 5a by the red line connecting red dots, drops down to the melting temperature of Al by ∼600 ps, and the interface starts to move up, toward the surface. One can expect that the solidification process will freeze (either by epitaxial regrowth of the substrate or by rapid homogeneous nucleation of the solid phase under strong undercooling conditions) some of the evolving liquid structures, leading to the formation of a complex surface nanostructure, ^{Reference Vorobyev and Guo14–Reference Oboňa, Ocelík, Rao, Skolski, Römer, Huis in ‘t Veld and De Hosson16} such as the one shown in Figure 5c.

The occurrence of both spallation and phase explosion processes within the same laser spot can also be related to the results of pump-probe experiments, ^{Reference Sokolowski-Tinten, Bialkowski, Cavalleri, von der Linde, Oparin, Meyer-ter-Vehn and Anisimov10,Reference Ionin, Kudryashov, Seleznev and Sinitsyn60,Reference Agranat, Anisimov, Ashitkov, Zhakhovskii, Inogamov, Nishihara, Petrov, Fortov and Khokhlov61} where the observation of optical interference patterns (Newton’s rings) can be explained by the spallation of a thin liquid layer from the irradiated target and the absence of interference fringes in the central part of the laser spot (Figure 5b) can be attributed to the transition to the phase explosion regime.

Another possible ablation mechanism intimately connected to the conditions of electronic nonequilibrium, discussed at the beginning of this article, is the electrostatic disintegration of a superficial layer of irradiated material caused by effective photo- and thermionic emission of electrons and associated positive charging of the material surface, the so-called Coulomb explosion (CE). ^{Reference Bulgakova, Stoian, Rosenfeld, Hertel and Campbell7} This mechanism of ablation, which manifests itself as highly energetic ion emission, has been widely debated for different materials. ^{Reference Stoian, Ashkenasi, Rosenfeld and Campbell62–Reference Kaplan, Lenner and Palmer65} The main feature of CE is the momentum scaling of differently charged ions and ions of different species in time-of-flight signals ^{Reference Stoian, Ashkenasi, Rosenfeld and Campbell62} that suggests their emission and acceleration by the electric field.

The occurrence of CE is defined by the competition between the laser-induced electron photoemission leaving behind a positively charged surface layer of the material and the neutralization of the positive charge by the free electron current from the material bulk. It was proven theoretically that at fluences slightly above the ablation threshold, CE can be realized in wide-bandgap dielectrics while, in semiconductors and metals, high mobilities of charge carriers prevent accumulation of the positive charge up to the level sufficient for disintegration of a surface layer by electrostatic repulsive forces. ^{Reference Bulgakova, Stoian, Rosenfeld, Hertel and Campbell7} When CE does occur, the exploded material leaves behind a smooth undamaged surface ^{Reference Stoian, Ashkenasi, Rosenfeld and Campbell62} that makes this ablation mode highly attractive for nanoscale applications (e.g., ultrafine material polishing). There are indications of the possibility of CE in semiconductors at laser fluences above the plasma formation level. ^{Reference Roeterdink, Juurlink, Vaughan, Dura Diez, Bonn and Kleyn63} However, at such conditions, the ions originating from the CE constitute a small fraction of the ablation products and are masked by the thermal ablation ions, including those accelerated by the plume double layer (two oppositely charged parallel layers created in the front of expanding plasmas due to faster electrons running ahead of slower ions). ^{Reference Roeterdink, Juurlink, Vaughan, Dura Diez, Bonn and Kleyn63,Reference Bulgakova, Bulgakov, Zhukov, Marine, Vorobyev and Guo66} In thin metal wires exposed to ultraintense laser pulses, a substantial fraction of electrons is carried away from the wire by the laser field, resulting in electrostatic disintegration of the ionic lattice left behind. ^{Reference Borghesi, Romagnani, Schiavi, Campbell, Haines, Willi, Mackinnon, Galimberti, Gizzi, Clarke and Hawkes67}

Concluding remarks

Rapid expansion of practical applications of ultrashort pulse lasers into new areas where precise nanoscale control of material modification is required can only be sustained with an improved fundamental understanding of laser–materials interactions. The ability to achieve high spatial resolution in material modification and microstructure engineering usually relies on fast and highly localized energy deposition that, unavoidably, creates conditions of strong electronic, thermodynamic, and mechanical nonequilibrium.

Theoretical and computational description of the materials behavior far from equilibrium is challenging and requires the revision of existing (or the development of new) theoretical models and computational approaches. In particular, the intricate connections between the ultrafast material response to laser excitation, generation of crystal defects, phase transformations, and mass transfer occurring under highly nonequilibrium conditions can only be accounted for by combining the research expertise and theoretical approaches from different disciplines. Close interdisciplinary collaborations and innovative design of new multiscale approaches incorporating dissimilar physical concepts and operating at different time and length scales are needed for disruptive progress in the theoretical and computational description of laser–materials interactions.

On the experimental side, the development of advanced imaging techniques capable of providing time-resolved information on the ultrafast structural and phase transformations is crucial for gaining fundamental understanding of laser-induced processes. Not unlike the theoretical efforts, the imaging/probing of different laser-induced processes requires a combination of optical pump-probe techniques with variable delay and temporal pulse-shaping, advanced diffractive imaging of transient atomic dynamics and ultrafast structural transformations, as well as the imaging/probing of ablation plume dynamics capable of tracking the spatial distribution and physical characteristics of different plume components.

Overall, investigations of ultrafast laser–materials interactions are expanding the limits of the fundamental understanding of material behavior under extreme conditions and providing opportunities for the generation of new material phases and microstructures.