Lattice deformation from interaction with electrons heated by an ultrashort laser pulse

We propose a model describing the destruction of metals under ultrashort intense laser pulses when heated electrons affect the lattice through the direct electron-phonon interaction. The metal consists of hot electrons and a cool lattice. The lattice deformation is estimated immediately after the laser pulse up to the electron temperature relaxation time. The hot electrons are described with help of the Boltzmann and heat conduction equations. We use an equation of motion for the lattice displacements with the electron force included. Estimates of the lattice deformation show that the ablation regime can be achieved. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 195–199 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Thermal analysis of intense femtosecond laser ablation of aluminum

This paper numerically simulates the process of ablation of an aluminum target by an intense femtosecond laser with a fluence of 40 J/cm 2 based on the two-temperature equation,and obtains the evolution of the free electron temperature and lattice temperature over a large temporal and depth range,for the first time. By investigating the temporal evolution curves of the free electron temperature and lattice temperature at three representative depths of 0,100 nm and 500 nm,it reveals different characteristics and mechanisms of the free electron temperature evolution at different depths. The results show that,in the intense femtosecond laser ablation of aluminum,the material ablation is mainly induced by the thermal conduction of free electrons,instead of the direct absorption of the laser energy; in addition,the thermal conduction of free electrons and the coupling effect between electrons and lattice will induce the temperature of free electrons deep inside the target to experience a process from increase to decrease and finally to increase again.     

数值模拟飞秒激光加热金属的热电子发射

研究了超短超强激光脉冲与薄膜靶相互作用中产生的电子热发射.当超短激光脉冲与薄膜靶相互作用时,首先入射超短脉冲激光对吸收深度内的自由电子进行热激发,接下来热激发电子将能量传递到附近的晶格,再通过电子和晶格二体系的热传导,以及电子晶格间的热耦合,将能量传递到材料的内部.因此,电子在皮秒级甚至更短的时间内不能与晶格进行能量耦合,使电子温度超出晶格温度很多,电子热发射就变得非常明显了.用双温方程联合Richardson-Dushman方程的方法对飞秒脉冲激光照射金属靶的电子热发射进行了研究,结果发现电子热发射对飞     

Electric quadrupole interactions and the γ–α phase transition in Ce: the role of conduction electrons

We present a theoretical model of the “isostructural" - phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. The latter are treated in tight-binding approximation. The - transition is described as an orientational ordering of quadrupolar electronic densities in a structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the - transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the structure. Received 21 September 1999 and Received in final form 2 May 2000     

Electron Spectrum of Nonlinear Cold Emission from a Metal under the Action of a Laser Shot

The nonlinear emission of electrons from a metal under the action of a femtosecond moderate-intensity laser pulse (laser shot) has been studied. A theoretical model of the process has been constructed based on the 1D nonstationary Schrödinger equation in the vacuum half-space with given boundary conditions for the electron wavefunction. This equation has been solved using the Laplace transformation. It has been assumed that the states of free electrons in a metal, which are described by the Sommerfeld theory of metals, are insignificantly influenced by the laser field. The energy spectrum of emitted electrons has been obtained, and its dependence on the parameters of the lased shot has been found. The calculated spectrum of nonlinear electron emission from a tungsten nanotip under the action of a 6.5-fs-long laser shot generating a field of 9.26 V/nm agrees with the experimental data.     

Self-consistent modelling of X-ray preionized XeCl-laser discharges

In this theoretical work a 0-D model for a self-sustained X-ray preionized XeCl-laser discharge is presented. The model is self-consistent in the sense that it simultaneously solves, contrarily to the usual decoupling procedure, the Boltzmann equation for electrons, the kinetic equations for excited and ionic species, the equations for the electrical circuit and the laser photon density. It includes a rather complete kinetics of HCl(v) vibrational excitation, dissociation and dissociative attachment. The influence of electron collisions with excited species and of e-e Coulomb collisions on the plasma parameters and transport coefficients is discussed. Some evidence of the non-stationary equilibrium between the electron distribution and the reduced electric field E/N is given. Results of the model are compared with experimental ones corresponding to a XeCl-laser discharge driven by a L-C inversion circuit. The model predicts well the main trends for the variation of the laser energy in a large range of experimental conditions. The discrepancy between experiment and model for absolute values of the laser energy is discussed.     

Nonlinear diffraction in inhomogeneous superlattice

We considered the propagation of laser monochromatic radiation in a superlattice that contains regions with an elevated concentration of carriers. The model of the energy spectrum of electrons is chosen in the strong coupling approximation. The electromagnetic field is described quasiclassically with Maxwell equations, which, as applied to the problem under study, are reduced to a non-one-dimensional sine-Gordon wave equation for the vector-potential. We analyzed the wave equation in the approximation of slowly varying amplitudes and phases and obtained and numerically solved an effective equation that describes the electromagnetic field in the superlattice. We studied different regimes of propagation of laser radiation, analyzed diffraction by regions with an elevated electron concentration.     

Scattering of relativistic electrons by high-power laser light tightly focused

We obtain an approximate solution for the drift and oscillatory components of the motion of relativistic electrons in the field of temporally extended high-power laser light under strong focusing of the light (the size of the focal region is of the order of the light wavelength). This makes it possible to start numerically integrating the equations of electron motion near the focal region. We estimate the impact parameters of the electrons when they are still efficiently accelerated in the focal region. Zh. éksp. Teor. Fiz. 111, 1554–1562 (May 1997)     

Nonlinear diffraction of super-gaussian laser beams in an array of quantum-dot chains with coulomb interaction taken into account

We consider the propagation of super-Gaussian monochromatic laser beams in a three-dimensional array of quantum dots coupled by the tunneling effect along one axis. The electron energy spectrum of the system corresponds to the Hubbard model, where the Coulomb interaction of electrons in quantum dots is taken into account. The field of the laser beam is described by the Maxwell equations, from which a nonhomogeneous wave equation for the vector potential is obtained. In the approximation of slowly varying amplitudes and phases, the wave equation is reduced to a phenomenological equation describing the electromagnetic field in an array of chains of quantum dots. We study the influence of the system parameters and the frequency of the laser-beam field on the propagation in the medium by solving numerically the phenomenological equation. We obtain the dependence of the factor characterizing the diffraction blooming of the beam in an array of chains of quantum dots on the parameters of the system’s electron energy spectrum.     

New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma

Abstract

The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas–Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.     

偏振对飞秒激光辐照LiF晶体的影响

飞秒激光聚焦到LiF晶体内部, 晶体的加工形貌随偏振改变. 实验表明, 偏振方向平行于<110> 晶向时, 加工起点到表面的距离是<100>偏振下的1.08 倍; 而<110>偏振下加工终点到表面的距离是<100> 偏振下的1.01 倍. 为了解释加工形貌的偏振依赖, 建立了逆韧致辐射、雪崩电离和无辐射跃迁的模型, 首先, 价带电子通过强场电离和雪崩电离, 从激光中吸收能量跃迁到导带, 该过程用电子密度演化方程和傍轴非线性薛定谔方程描述, 求解方程得到导带电子密度; 其次, 导带电子通过无辐射跃迁过程释放能量给晶格, 由能量守恒计算出晶格温度沿激光传播方向的分布; 最后, 晶格温度超过熔点以上的区域被加工. 模拟结果显示, <110>偏振下加工起点到表面的距离是<100> 偏振下的1.03倍, 而<110>偏振下加工终点到表面的距离是<100>偏振下的0.981 倍, 与实验结果基本一致. 虽然Z扫描技术测量的非线性折射率随偏振方向变化, 但是非线性折射率的变化趋势与实验结果相反. 模拟和实验证明逆韧致辐射导致加工形貌随偏振变化.     

The homogeneity of a stabilized discharge-pumped XeCl* laser

* laser arrangement. The special pumping technique of this laser discharge is based on the additional use of a stabilizing low-current preliminary discharge. The model takes into account the time-dependent electron Boltzmann equation including electron–electron interaction for the determination of the electron kinetics, an extensive reaction kinetics involving various heavy particles and photons, and the relevant electrical circuit equations. The study has shown that density perturbations of preionization electrons lead to the inhomogeneity of the discharge plasma and the laser output. Furthermore, the impact of the spatial distribution of preionization electrons, of the HCl portion of the gas mixture, and of a low-current preliminary discharge for the discharge operation is discussed. Received: 10 September 1996/Revised version: 21 July 1997     

Scattering of relativistic electrons by a focused laser pulse

The problem of the motion of a classical relativistic electron in a focused high-intensity laser pulse is solved. A new three-dimensional model of the electromagnetic field, which is an exact solution of Maxwell’s equations, is proposed to describe a stationary laser beam. An extension of the model is proposed. This extension describes a laser pulse of finite duration and is an approximate solution of Maxwell’s equations. The equations for the average motion of an electron in the field of a laser pulse, described by our model, are derived assuming weak spatial and temporal nonuniformities of the field. It is shown that, to a first approximation in the parameters of the nonuniformities, the average (ponderomotive) force acting on a particle is described by the gradient of the ponderomotive potential, but it loses its potential character even in second order. It is found that the three-dimensional ponderomotive potential is asymmetric. The trajectories of relativistic electrons moving in a laser field are obtained and the cross sections for scattering of electrons by a stationary laser beam are calculated. It is shown that reflection of electrons from the laser pulse and the surfing effect are present in the model studied. It is found that for certain impact parameters of the incident electrons the asymmetic ponderomotive potential can manifest itself effectively as an attractive potential. It is also shown that even in the case of a symmetric potential the scattering cross section contains singularities, known as rainbow scattering. The results are applicable for fields characterized by large (compared to 1) values of the dimensionless parameter η² = e ²〈E ²〉/m ²ω² and arbitrary electron energies.     

Femtosecond laser ablation of aluminium

We investigate femtosecond laser ablation of aluminium using a hybrid simulation scheme. Two equations are solved simultaneously: one for the electronic system, which accounts for laser energy absorption and heat conduction, the other for the dynamics of the lattice where the ablation process takes place. For the electron-temperature a generalized heat-conduction equation is solved by applying a finite difference scheme. For the lattice properties, e.g. pressure, density or temperature, we use common molecular dynamics. Energy transfer between the subsystems is allowed by introducing an electron-phonon coupling term. This combined treatment of the electronic and atomic systems is an extension of the well known two-temperature model [Anisimov, Kapeliovich, Perel’man, Electron emission from metal surfaces exposed to ultra short laser pulses, JETP Lett. 39 (2)].     

The kinetics of low-temperature electron-phonon relaxation in a metallic film following instantaneous heating of the electrons

The theoretical analysis of experiments on pulsed laser irradiation of metallic films sputtered on insulating supports is usually based on semiphenomenological dynamical equations for the electron and phonon temperatures, an approach that ignores the nonuniformity and the nonthermal nature of the phonon distribution function. In this paper we discuss a microscopic model that describes the dynamics of the electron-phonon system in terms of kinetic equations for the electron and phonon distribution functions. Such a model provides a microscopic picture of the nonlinear energy relaxation of the electron-phonon system of a rapidly heated film. We find that in a relatively thick film the energy relaxation of electrons consists of three stages: the emission of nonequilibrium phonons by “hot” electrons, the thermalization of electrons and phonons due to phonon reabsorption, and finally the cooling of the thermalized electron-phonon system as a result of phonon exchange between film and substrate. In thin films, where there is no reabsorption of nonequilibrium phonons, the energy relaxation consists of only one stage, the first. The relaxation dynamics of an experimentally observable quantity, the phonon contribution to the electrical conductivity of the cooling film, is directly related to the dynamics of the electron temperature, which makes it possible to use the data of experiments on the relaxation of voltage across films to establish the electron-phonon and phonon-electron collision times and the average time of phonon escape from film to substrate. Zh. éksp. Teor. Fiz. 111, 2106–2133 (June 1997)     

Nonlinear soliton-like excitations in two-dimensional lattices and charge transport

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.     

Femtosecond laser-induced heating of electron gas in aluminium

The distribution function of free electrons in metal is calculated for irradiation of aluminium with an ultrashort laser pulse of moderate intensity. We consider inverse Bremsstrahlung absorption, electron-electron and electron-phonon interaction. Our theoretical model is based on Boltzmann equations and describes each considered process by a corresponding collision integral. The results show the excitation and relaxation of the free electron gas. Energy transfer to the phonon gas is calculated. Our model predicts linear absorption for intensities up to damage threshold. The calculated absorbed energy compares very well with known absorption characteristics.