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A finite-difference scheme is presented for the solution of the problem on the interaction of a femtosecond laser pulse with glass in the approximation of nonlinear Maxwell equations supplemented by equations of the hydrodynamic type for conduction electrons. The model takes into account all the basic physical processes involved in this interaction. An axially symmetric problem is considered. The construction of the scheme allows for the specifics of the problem, which ensures the efficiency of the developed method. The use of the scheme is illustrated by the results of modeling the interaction between glass and femtosecond laser pulses of an ordinary Gaussian shape with linear polarization and doughnut pulses with radial and azimuthal polarization. Significant differences in the dynamics of the interaction between glass and these three types of pulses are revealed.

Theoretical and experimental studies have demonstrated that bi-chromatic laser action on bandgap materials can result in highly enhanced efficiency of local energy coupling at properly chosen combinations of wavelengths and energies.

The paper presents an application of the Boltzmann kinetic equation to the simultaneous modeling of multi-dimensional processes. This equation defines the evolution of the distribution of the probability density in a given phase space. In the case of a grinding process, the considered phase space is defined by the Cartesian coordinates of particle position, the components of particle velocity and the particle size. The theory of Markov processes is used in the paper to solve the Boltzmann equation for the multi-dimensional space of system states. In order to verify the presented model, research into the simultaneous comminution and movement of material in a drum ball mill was performed. The methodology developed to solve the Boltzmann equation significantly reduces the computational time, which is particularly important in the solution of multi-dimensional problems.

The interaction of short and ultrashort pulse laser radiation with glass materials is addressed. Particular attention is paid to regimes which are important in industrial applications such as laser cutting, drilling, functionalization of material surfaces, etc. Different factors influencing the ablation efficiency and quality are summarized and their importance is illustrated experimentally. The effects of ambient gas ionization in front of the irradiated target are also analyzed. A possibility to enhance laser coupling with transparent solids by bi-wavelength irradiation is discussed.

Computer simulations and theoretical analysis of laser-materials interactions are playing an increasingly important role in the advancement of modern laser technologies and broadening the range of laser applications. In this chapter, we first provide an overview of the current understanding of the laser coupling and transient variation of optical properties in metals, semiconductors and dielectrics, with the focus on the practical implications on the energy deposition and distribution in the irradiated targets. The continuum-level modeling of the dynamic evolution of laser-induced stresses, nonequilibrium phase transformations, and material redistribution within the laser spot are then discussed, and the need for the physical insights into the mechanisms and kinetics of highly nonequilibrium processes triggered by the laser excitation is highlighted. The physical insights can be provided by atomistic modeling, and several examples are discussed where large-scale molecular dynamics simulations are used for investigation of the mechanisms of the generation of crystal defects (vacancies, interstitials, dislocations, and twin boundaries) and the material redistribution responsible for the formation of laser-induced periodic surface structures in the single-pulse ablative regime. The need for the integrated computational approach fully accounting for the strong coupling between processes occurring at different time- and length-scales is highlighted.

Sophisticated modeling of propagation of ultrashort laser pulses with spatio-temporal coupling through transparent medium has enabled reproducing the effect of directional asymmetry in direct laser writing and gaining a deep insight into the underlying physics.

Ultrashort laser pulses are usually described in terms of temporal and spatial dependences of their electric field, assuming that the spatial dependence is separable from time dependence. However, in most situations this assumption is incorrect as generation of ultrashort pulses and their manipulation lead to couplings between spatial and temporal coordinates resulting in various effects such as pulse front tilt and spatial chirp. One of the most intriguing spatiotemporal coupling effects is the so-called “lighthouse effect”, the phase front rotation with the beam propagation distance [Akturk et al., Opt. Express 13, 8642 (2005)]. The interaction of spatiotemporally coupled laser pulses with transparent materials have interesting peculiarities, such as the effect of nonreciprocal writing, which can be used to facilitate microfabrication of photonic structures inside optical glasses. In this work, we make an attempt to numerically investigate the influence of the pulse front tilt and the lighthouse effect on the absorption of laser energy inside fused silica glass. The model, which is based on nonlinear Maxwell’s equations supplemented by the hydrodynamic equations for free electron plasma, is applied. As three-dimensional solution of such a problem would require huge computational resources, a simplified two-dimensional model has been proposed. It has enabled to gain a qualitative insight into the features of propagation of ultrashort laser pulses with the tilted front in the regimes of volumetric laser modification of transparent materials, including directional asymmetry upon direct laser writing in glass materials.

Interaction of femtosecond laser pulses with a bulk glass (fused silica as an example) has been studied numerically based on non-linear Maxwell’s equations supplemented by the hydrodynamics-type equations for free electron plasma for the cases of Gaussian linearly-polarized and doughnut-shaped radially-polarized laser beams. For Gaussian pulses focused inside glass (800 nm wavelength, 45 fs duration, numerical aperture of 0.25), the free electron density in the laser-excited region remains subcritical while the locally absorbed energy density does not exceed ~2000 J/cm3 in the range of pulse energies of 200 nJ – 2 μJ. For doughnut-shaped pulses, the initial high-intensity ring of light is shrinking upon focusing. Upon reaching a certain ionization level on its way, the light ring splits into two branches, one of which shrinks swiftly toward the beam axis well before the geometrical focus, leading to generation of supercritical free electron density. The second branch represents the laser light scattered by the electron plasma away from the beam axis. The final laserexcited volume represents a tube of 0.5–1 μm in radius and 10-15 μm long. The local maximum of absorbed energy can be more than 10 times higher compared to the case of Gaussian beams of the same energy. The corresponding pressure levels have been evaluated. It is anticipated that, in the case of doughnut-shaped pulses, the tube-like shape of the deposited energy should lead to implosion of material that can be used for improving the direct writing of high-refractive index optical structures inside glass or for achieving extreme thermodynamic states of matter.

In spite of the fact that more than five decades have passed since the invention of laser, some topics of laser-matter interaction still remain incompletely studied. One of such topics is plasma impact on the overall phenomenon of the interaction and its particular features, including influence of the laser-excited plasma re-radiation, back flux of energetic plasma species, and massive material redeposition, on the surface quality and processing efficiency. In this paper, we analyze different plasma aspects, which go beyond a simple consideration of the well-known effect of plasma shielding of laser radiation. The following effects are considered: ambient gas ionization above the target on material processing with formation of a “plasma pipe”, back heating of the target by both laser-driven ambient and ablation plasmas through conductive and radiative heat transfer, plasma chemical effects on surface processing including microstructure growth on liquid metals, complicated dynamics of the ablation plasma flow interacting with an ambient gas that can result in substantial redeposition of material around the ablation spot. Together with a review summarizing our main to-date achievements and outlining research directions, we present new results underlining importance of laser plasma dynamics and photoionization of the gas environment upon laser processing of materials.

Numerous experimental studies in recent years have revealed intriguing symmetry breakings during non-linear interaction of ultrashort laser pulses with materials. Dependence of the formed structures on the direction of laser scanning and polarization, an effect known as non-reciprocal writing, is one of the most commonly observed asymmetries. These observations are generally attributed to spatio-temporal couplings (primarily pulse-front tilt) in the laser pulses. Even though such couplings indeed break the spatial symmetry of the light–matter interactions, a detailed understanding of ongoing phenomena in the microscopic level is still lacking. In this work, we present our theoretical results, which, to the best of our knowledge, constitute the first demonstration of the physical mechanisms behind non-reciprocal writing and related effects in transparent media. Our model is based on non-linear Maxwell’s equations supplemented by the hydrodynamic equations for free electron plasma, and rate equations for the evolution of defects inside the material. It has enabled us to gain a qualitative insight into the features of propagation of ultrashort laser pulses with tilted pulse fronts, in the regimes of volumetric laser modification of transparent materials.

Results of experimental studies of heat-and-mass transfer and hydrodynamic processes at distillation on a regular packing are presented. The mixture of freons R114–R21 at the pressure of 0.3 MPa was used as a working mixture. The mixture was separated on the Mellapak 350Y structured packing with the diameter of 0.9 m under the conditions of complete reflux ( L/V = 1) at different packing heights. A specially designed liquid distributor with a possibility to change the density and pattern of drip points was used to irrigate the packing. The experimental data on the efficiency of mixture separation (height of transfer unit HTU ) and distribution of the local flow rate density over the column cross-section were compared. It is shown that an increase in the height of the structured packing from 2.1 m to 4.0 m leads to a significant decrease in the efficiency of mixture separation in the distillation column.

Interaction of ultrashort laser pulses with transparent materials is a powerful technique of modification of material properties for various technological applications. The physics behind laser-induced modification phenomenon is rich and still far from complete understanding. We present an overview of our models developed to describe processes induced by ultrashort laser pulses inside and on the surface of bulk glass. The most sophisticated model consists of two parts. The first part solves Maxwell’s equations supplemented by the rate and hydrodynamics equations for free electrons. The model resolves spatiotemporal dynamics of free-electron population and yields the absorbed energy map. The latter serves as an initial condition for thermoelastoplastic simulations of material redistribution. The simulations performed for a wide range of irradiation conditions have allowed to clarify timescales at which modification occurs after single laser pulses. Simulations of spectrum of laser light scattered by laser-generated plasma revealed considerable blueshifting which increases with pulse energy. To gain insight into temperature evolution of a glass material under the surface irradiation conditions, we employ a model based on the rate equation describing free electron generation coupled with the energy equations for electrons and lattice. Swift heating of electron and lattice subsystems to extremely high temperatures at fs timescale has been found at laser fluences exceeding the threshold fluence by 2-3 times that can result in efficient bremsstrahlung emission from the irradiation spot. The mechanisms of glass ablation with ultrashort laser pulses are discussed by comparing with the experimental data. Finally, a model is outlined, developed for multi-pulse irradiation regimes, which enables gaining insight into the roles of defects and heat accumulation.

Transmission measurements for femtosecond laser pulses focused in air with spectral analysis of emission from the focal region have been carried out for various pulse energies and air pressures. The air breakdown threshold and pulse attenuation due to plasma absorption are evaluated and compared with calculations based on the multiphoton ionization model. The plasma absorption is found to depend on the pulse repetition rate and is considerably stronger at 1 kHz than at 1-10 Hz. This suggests that accumulation of metastable states of air molecules plays an important role in initiation of air breakdown, enhancing the ionization efficiency at high repetition rates. Possible channels of metastable-state-assisted air ionization and the role of the observed accumulation effect in laser material processing are discussed.

We report a model of nanosecond laser ablation of compound semiconductors taking into account stoichiometry loss as a result of different volatilities of the material components. The model is based on the heat-flow equation for the bulk material and the diffusion equation for its atomic constituents and takes into account variations of material properties as functions of temperature and composition. Changing the optical response which results from stoichiometry violation is described within the concept of an effective medium and a multi-layer reflection model is applied. For cadmium telluride, as an example, the processes of ablation, melting, and resolidification under the action of a KrF laser have been studied in dynamics for particular experimental conditions in a wide range of laser fluences from the ablation threshold to the plasma shielding regimes described by the effective plasma plume representation. Multi-shot irradiation regimes have been investigated and the mechanism of the irradiation-controlled stoichiometry reversal has been elucidated.

In this work we consider an experimentally observed effect of significant increasing of the residual heat in metal targets at their irradiation with femtosecond laser pulses in an ambient gas in respect to the vacuum conditions. Numerical modelling of heating of a platinum target by femtosecond laser pulses in argon under normal conditions has been performed taking into account gas breakdown in the focussing region of the laser beam in front of the target. The applied model is based on a combination of a thermal model describing heating and phase transitions in irradiated samples and a hydrodynamic model to describe motion of the ambient gas perturbed by laser irradiation as a result of multiphoton ionization. The hot ambient gas is shown to heat efficiently the irradiated sample. The hydrodynamic processes in the ambient gas play an important role in heating.

To describe the effect of significant enhancement in thermal energy retained in metal targets following femtosecond laser ablation in a gas environment, we develop a combined model based on both 2D thermal modeling of laser-induced target heating and dynamics of the ambient gas perturbed by multiphoton absorption of laser energy in close proximity to the target. Using our model, we find that thermal energy coupling to the sample is significantly enhanced due to laser-induced gas-dynamic motion in plasma. Another finding is that total thermal energy coupled to the sample due to gas-dynamic energy transfer and thermal energy conduction is close to that measured in our experiment.

The penetration of the rotating magnetic field of the dynamic ergodic divertor (DED) into the TEXTOR tokamak plasma has been investigated, using a two-dimensional reduced magnetohydrodynamics model and taking into account the effects of plasma-neutral interaction and neoclassical viscosity. The real three-dimensional structure of the DED coils design results in a mixture of several spatial Fourier modes which rotate at different phase velocities. It is shown that the field penetration is accompanied by poloidal acceleration of the plasma, which plays a crucial role in the process. For the DED TEXTOR parameters, the plasma-neutral interaction and the neoclassical viscosity allow for a distribution of the perturbed magnetic field close to vacuum one. If the mixture of harmonics is taken into account, the acceleration of the plasma in poloidal direction does not provide a complete penetration of the perturbation.

The relaxation of a magnetic field perturbation periodic in two directions is studied in the electron magnetohydrodynamic approximation. It is shown that the relaxation is accompanied by the coalescence of magnetic cells. When transport coefficients are sufficiently low, the nonlinear stage of the coalescence process is independent of their values. This effect may help to explain why the duration of the crash phase of sawtooth oscillations in tokamaks is anomalously short.

This paper compares models based on nonlinear Maxwell’s and Schrodinger equations developed for modeling typical experiments involving the three-dimensional modification of glasses (using fused quartz as an example) under the action of femtosecond laser pulses. It is shown that the results can be appreciably different when the Maxwell’s and Schrodinger equations are used. A substantial role in this case is played not only by the equations themselves, but also by the form of the boundary condition that describes the focused laser pulse at the input to the region of calculation.

Non-Gaussian laser beams can open new opportunities for microfabrication, including ultrashort laser direct writing. Using a model based on Maxwell’s equations, we have investigated the dynamics of doughnut-shaped laser beams focused inside fused silica glass, in comparison with Gaussian pulses of the same energy. The laser propagation dynamics reveals intriguing features of beam splitting and sudden collapse toward the beam axis, overcoming the intensity clamping effect. The resulting structure of light absorption represents a very hot, hollow nanocylinder, which can lead to an implosion process that brings matter to extreme thermodynamic states. Monitoring the simulations of the laser beam scattering has shown a considerable difference in both the blueshift and the angular distribution of scattered light for different laser energies, suggesting that investigations of the spectra of scattered radiation can be used as a diagnostic of laser-produced electron plasmas in transparent materials.

Based on experiments and a theoretical analysis, we raise questions on two fundamental mechanisms of femtosecond laser desorption/ablation of solids, namely Coulomb explosion (CE) and plasma etching. The effects of laser-induced ionization and surface charging are analyzed which can be responsible for ultrafast ions observed in time-of-flight mass-spectra under ultrashort laser irradiation of solids. The importance of surface charging in formation of velocity distributions of desorbed/ablated species has been revealed for conditions when the CE mechanism is inhibited. The influence of ambient plasma formation on the dynamics of heating of metallic targets by femtosecond laser pulses is studied based on 2D modeling of laser-induced target heating and dynamics of the ambient plasma. The calculations show an intriguing picture of the laser-induced ambient gas motion. We propose a model of laser-induced breakdown of an ambient gas in a region in front of the irradiated target and analyze plasma-chemical processes which can affect laser processing of surfaces in the presence of air or highly reactive media.

A comprehensive analysis of laser-induced modification of bulk glass by single ultrashort laser pulses is presented which is based on combination of optical Maxwell-based modeling with thermoelastoplastic simulations of post-irradiation behavior of matter. A controversial question on free electron density generated inside bulk glass by ultrashort laser pulses in modification regimes is addressed on energy balance grounds. Spatiotemporal dynamics of laser beam propagation in fused silica have been elucidated for the regimes used for direct laser writing in bulk glass. 3D thermoelastoplastic modeling of material relocation dynamics under laser-induced stresses has been performed up to the microsecond timescale when all motions in the material decay. The final modification structure is found to be imprinted into material matrix already at sub-nanosecond timescale. Modeling results agree well with available experimental data on laser light transmission through the sample and the final modification structure.

Numerical simulations based on Maxwell’s equations have been performed for gaining deep insight into the processes governing laser light absorption in transparent dielectrics in the regimes typical for laser direct writing of various optical structures inside bulk glasses such as waveguides, nanoplanes, and voids. Numerical simulations have been performed for fused silica glass irradiated by femtosecond laser pulses at 800 nm wavelength. The geometry of laser energy absorption is compared for two pulse durations and energies from 0.1 to 1 μJ. The effect of the numerical aperture of the laser energy deposition is studied. Double-pulse irradiation has been modeled to gain insight into “exciton-seeded multiphoton ionization” [Phys. Rev. B81, 212301 (2010).PRBMDO1098-0121]. Furthermore, several consecutive laser pulses have been modeled to gain a better understanding of the qualitative tendency of memory effects related to defect accumulation. Features of laser energy coupling into bulk glass such as asymmetry of absorption for the cylindrically symmetric linearly polarized beam and formation of a defect shield developing in multipulse irradiation regimes have been revealed.