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Over the past three decades numerous numerical methods for solving the time-dependent Schr\"odinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having the proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.

We introduce an approximation for strong-laser-field-induced ionization of atoms, which we call atom-Volkov strong-field approximation (aV SFA). For the final state, instead of a plane wave (used in the standard well-known SFA) or a Coulomb wave (used in the Coulomb-Volkov SFA), in the aV SFA we use the exact atom-specific scattering states. We first introduce the aV SFA as an ansatz and show that it yields results that are closer to the exact results than those obtained using the SFA. After that, we systematically derive an iterative theory whose zeroth order is equal to the introduced aV SFA. We analyze its first-order correction, which corresponds to electron rescattering off the parent ion and show that, in the case of forward scattering, this correction leads to the low-energy structures in the photoelectron spectra which are observed in the experiments.

We investigate laser-assisted electron-ion recombination (LAR), high-order harmonic generation (HHG) and above-threshold ionization (ATI) of argon atoms by a bicircular laser field, which consists of two coplanar counter-rotating circularly polarized fields of frequencies r? and s?. The energy of soft x rays generated in the LAR process is analyzed as a function of the incident electron angle and numerical results of direct recombination of electrons with Ar+ ions are presented. We also present the results of HHG by a bicircular field and confirm the selection rules derived earlier for inert-gas atoms in a p ground state. We show that the photoelectron spectra in the ATI process, presented in the momentum plane, as well as the LAR spectra exhibit the same discrete rotational symmetry as the applied field.

In this Letter, we propose a novel laser-induced inelastic diffraction (LIID) scheme based on the intense-field-driven atomic nonsequential double ionization (NSDI) process and demonstrate that, with this LIID approach, the doubly differential cross sections (DDCSs) of the target ions, e.g., ${\mathrm{Ar}}^{+}$ and ${\mathrm{Xe}}^{+}$, can be accurately extracted from the two-dimensional photoelectron momentum distributions in the NSDI process of the corresponding atoms. The extracted DDCSs exhibit a strong dependence on both the target and the laser intensity, in good agreement with calculated DDCSs from the scattering of free electrons. The LIID scheme may be extended to molecular systems and provides a promising approach for imaging of the gas-phase molecular dynamics induced by a strong laser field with unprecedented spatial and temporal resolution.

Quantum interference plays an important role in various intense-laser-driven atomic phenomena, e.g., above-threshold ionization and high-order-harmonic generation, and provides a useful tool in ultrafast imaging of atomic and molecular structure and dynamics. However, it has eluded observation in nonsequential double ionization (NSDI), which serves as an ideal prototype to study electron-electron correlation. Thus far, NSDI usually could be well understood from a semiclassical perspective, where all quantum aspects have been ignored after the first electron has tunneled. Here we perform coincidence measurements for NSDI of xenon subject to laser pulses at 2400 nm. It is found that the intensity dependence of the asymmetry parameter between the yields in the second and fourth quadrants and those in the first and third quadrants of the electron-momentum-correlation distributions exhibits a peculiar fast oscillatory structure, which is beyond the scope of the semiclassical picture. Our theoretical analysis indicates that this oscillation can be attributed to interference between the contributions of different excited states in the recollision-excitation-with-subsequent-ionization channel. Our work demonstrates the significant role of quantum interference in NSDI and may create an additional pathway towards manipulation and imaging of the ultrafast atomic and molecular dynamics in intense laser fields.

Experimental and theoretical investigations of the wavelength dependence of the nonsequential double ionization (NSDI) process of the xenon atom in intense laser fields are reported. The observed wavelength dependence of the ratio Xe2+/Xe+ deviates significantly from the prediction of the three-step model of ionization (sometimes called the "simple-man" model), both in the slope of the overall decrease with increasing wavelength and in the existence of some pronounced humps. A semiclassical model calculation reproduces the changing slope of the overall decrease, which is due to the interplay of wave-packet diffusion, Coulomb focusing, and a closely related Coulomb defocusing effect of the liberated electron. The hump is beyond the scope of the semiclassical model.

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

Strong-field ionization in two-color circularly polarized fields is studied, where both experimental measurements and theoretical analyses suggest that the production of high-energy electrons from electron-ion rescattering is optimized in counterrotating fields, and when the ponderomotive energies of the two laser fields are equal.

We investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by a few-cycle laser pulse. In order to describe molecular HATI in ultrashort laser pulses we have modified our molecular improved strong-field approximation (MISFA), which was developed for long laser pulses and in which the rescattering of the ionized electron off the parent ion was described using the first-order Born approximation (1BA). Now, we introduce the so-called molecular low-frequency approximation (MLFA) in which the elastic rescattering amplitude is calculated exactly. The angle-resolved electron energy spectra for HATI of N2 and O2 obtained using the MLFA are compared with those obtained within the MISFA. The difference between these spectra becomes significant for larger (re)scattering angles. This is due to the fact that the exact scattering amplitude, used in the MLFA, has minima for some values of the rescattering angles that are absent in the 1BA. Also, the rescattering plateau is lower for the MLFA spectra. We investigate the influence of the carrier-envelope phase on the high-energy part of the molecular HATI spectra. As in the atomic case, the left-right (backward-forward) asymmetry is also observed in the molecular case.

The molecular strong-field approximation is applied to calculate angle-resolved photoelectron spectra in the process of high-order above-threshold ionization of carbon-monoxide molecules by an elliptically polarized laser field. The theory is formulated to include the Stark shift of the initial bound state of the valence electron. It is shown that the angle-resolved photoelectron spectra of aligned CO molecules exhibit pronounced minima which can be explained by destructive interference of two partial T-matrix contributions. The dependence of contributing partial amplitudes on the laser field ellipticity is analyzed in detail.

Ionization of atoms by an intense bicircular laser field is considered, which consists of two coplanar corotating or counterrotating circularly polarized field components with frequencies that are integer multiples of a fundamental frequency. Emphasis is on the effect of a reversal of the helicities of the two field components on the photoelectron spectra. The velocity maps of the liberated electrons are calculated using the direct strong-field approximation (SFA) and its improved version (ISFA), which takes into account rescattering off the parent ion. Under the SFA all symmetries of the driving field are preserved in the velocity map while the ISFA violates certain reflection symmetries. This allows one to assess the significance of rescattering in actual data obtained from an experiment or a numerical simulation.

The low-frequency approximation (LFA) for high-order above-threshold ionization is presented. A factorization formula for the differential ionization rate is derived and its range of validity is analyzed. The theory developed is illustrated using the example of Ar atoms. Details of the modeling of the ground state and the rescattering potential for Ar are given. In particular, it is shown, by solving the stationary Schrodinger equation, that our rescattering potential reproduces the Hartree—Fock-type ground-state wave function that we used for the LFA. Electron momentum distributions for ionization of the Ar atom by a linearly polarized laser field having intensity 2.3 × 1014 W/cm2 and wavelength 800 nm are shown. The results obtained using the improved strong-field approximation on the one hand and the LFA on the other are compared.

A brief discussion of gauge invariance in nonrelativistic quantum mechanics is presented. The strong-field approximation for ionization of an atom by a laser field is rederived in such a way that the resulting ionization amplitude comes out identical in any gauge. This result agrees with the usual length-gauge form.

Numerical results obtained applying the strong-field approximation to atomic and molecular processes in intense laser fields are presented. In particular, the forward-backward asymmetry in high-order above-threshold ionization (HATI) of Ar atoms by a few-cycle laser pulse is considered. It is shown that the resonantlike enhancements observed in the focal-averaged spectra disappear with the decreasing laser pulse duration. For HATI and high-order harmonic generation (HHG) by molecular systems, we present new results for diatomic molecules. The choice of gauge and the problem of dressing of the initial bound state are discussed. The appearance of the interference minima in molecular HATI and HHG spectra and their role in the characterization of the molecular structure are considered using the example of the Ar2 molecule.

Recently performed above-threshold ionization (ATI) experiments with noble gases allow the determination of the complete energy and angular distribution of the emitted photoelectrons. In order to simulate such experiments, we have generalized our numerical code for the calculation of ATI spectra in order to achieve a realistic simulation of ATI of the noble gases He, Ne, Ar, Kr, and Xe. Our method is based on an improved version of the strong-field approximation and includes focal averaging. A semiclassical analysis of the dependence of the cutoff law on the photoelectron emission angle is presented. The effects of channel closings on the high-energy spectra are analyzed.

Direct ionization of hydrogen atoms by laser irradiation is investigated as a potential new scheme to generate proton beams without stripping foils. The time-dependent Schrödinger equation describing the atom-radiation interaction is numerically solved obtaining accurate ionization cross-sections for a broad range of laser wavelengths, durations and energies. Parameters are identified where the Doppler frequency up-shift of radiation colliding with relativistic particles can lead to efficient ionization over large volumes and broad bandwidths using currently available lasers.

Nonsequential multiple ionization of atoms in intense laser fields is initiated by a recollision between an electron, freed by tunneling, and its parent ion. Following recollision, the initial electron shares its energy with several bound electrons. We use a classical model based on rapid electron thermalization to interpret recent experiments. For neon, good agreement with the available data is obtained with an upper bound of 460 attoseconds for the thermalization time., 5 pages revtex and 4 figures (eps files)

The theoretical description and the experimental methods and results for above-threshold ionization (ATI) by few-cycle pulses are reviewed. A pulse is referred to as a few-cycle pulse if its detailed shape, parametrized by its carrier-envelope phase, affects its interaction with matter. Angular-resolved ATI spectra are analysed with the customary strong-field approximation (SFA) as well as the numerical solution of the time-dependent Schrodinger equation (TDSE). After a general discussion of the characteristics and the description of few-cycle pulses, the behaviour of the ATI spectrum under spatial inversion is related to the shape of the laser field. The ATI spectrum both for the direct and for the rescattered electrons in the context of the SFA is evaluated by numerical integration and by the method of steepest descent (saddle-point integration), and the results are compared. The saddle-point method is modified to avoid the singularity of the dipole transition matrix element at the steepest-descent times. With the help of the saddle-point method and its classical limit, namely the simple-man model, the various features of the ATI spectrum, their behaviour under inversion, the cut-offs and the presence or absence of ATI peaks are analysed as a function of the carrier-envelope phase of the few-cycle laser field. All features observed in the spectra can be explained in terms of a few quantum orbits and their superposition. The validity of the SFA and the concept of quantum orbits are established by comparing the ATI spectra with those obtained numerically from the ab initio solution of the TDSE.

The quantum-orbit formalism of high-order atomic processes in a strong laser field is presented starting from the strong-field approximation generalized to include higher-order effects. It is shown how to apply the quantum-orbit theory to various processes such as high-order above-threshold ionization and detachment, high-order harmonic generation, laser-assisted X-ray–atom scattering, laser-assisted electron–ion recombination, laser-assisted electron–atom scattering and non-sequential double ionization. Particular attention is devoted to high-order above-threshold ionization by few-cycle laser pulses. The results obtained using the strong-field approximation and the theory of quantum orbits are compared with the ab initio solution of the time-dependent Schrodinger equation. It is shown that Coulomb effects are important for low-energy electron spectra.

The S-matrix element for non-sequential double ionization of an atom irradiated by a high-intensity near-infrared laser field via the recollision–impact-ionization scenario is investigated with particular emphasis on a certain classical limit where classical kinematics govern throughout and wave-packet spreading is ignored. The resulting classical model is applied to the calculation of the one-electron energy spectrum in coincidence with double ionization. Various assumptions are made for the interaction by which the returning electron frees the second, up to this time inactive, electron and its initial wave function. The resulting momentum correlations of the two emitted electrons are investigated just above and below the threshold intensity, for which the maximal energy of the recolliding electron equals the ionization energy of the singly charged ion, and the quantum-mechanical amplitude and the classical approximation are compared. The classical model is extended to intensities below this threshold by...

We consider the nonlinear collective electron dynamics inside a large cluster irradiated by a strong linearly polarized short (0.1 ?ps) laser pulse. The equation of the centre-of-mass motion of the electron cloud driven by the strong laser field is derived using the approximation of an incompressible medium. The analysis of this equation demonstrates the presence of odd harmonics of the fundamental frequency in the cluster dipole moment, and in both the internal and the scattered electric field. Both neutral and ionized clusters are considered. For clusters with radii R 100?? irradiated by a femtosecond titanium?sapphire laser with a peak intensity of I 1016?W?cm?2, the internal electric field strength near the tripled fundamental frequency is shown to be of the same order as the field of the fundamental. The reason is that both for metallic and for laser-ionized van der Waals clusters the Mie surface-plasmon energy ?M is around 5 eV, which is close to three times the energy of a titanium?sapphire laser-field quantum. On the other hand, the condition for first-order resonance with the Mie frequency is not met during the presence of the main laser pulse, but only temporarily, either at the first onset of inner ionization on the leading edge of the pulse (for van der Waals clusters) or during the subsequent Coulomb explosion. In both cases, the ion density is reduced. The presence of a strong third harmonic leads, in particular, to the enhanced production of multiply charged ions in clusters irradiated by a strong laser field, as compared with isolated atoms. This point is discussed in the light of recent experimental results on the production of multiply charged ions in laser?cluster experiments. Third-harmonic generation by a cluster in a strong laser field, as a function of both the cluster and the laser-field parameters, is also considered.

The S matrix for processes induced by intense lasers in atoms can be expanded in terms of the contributions of quantum orbits which are the trajectories of electrons that enter the continuum through ionization and subsequently propagate in the laser field, in order finally to recombine with the atom or to rescatter. The quantum orbits are complex as a consequence of their origin by tunneling. Their superposition in the S-matrix element results in various effects such as constructive and destructive interference and may simulate resonant behavior.

The S matrix for processes induced by intense lasers in atoms can be expanded in terms of the contributions of quantum orbits which are the trajectories of electrons that enter the continuum through ionization and subsequently propagate in the laser field, in order finally to recombine with the atom or to rescatter. The quantum orbits are complex as a consequence of their origin by tunnelling. Their superposition in the S -matrix element results in various eiects such as constructive and destructive interference and may simulate resonant behaviour. Processes considered include above-threshold ionization, high-order harmonic generation and non-sequential double ionization.

Above-threshold ionization (ATI) of atoms by a strong bicircular laser field is investigated using the strong-field approximation and the quantum-orbit theory. The bicircular field consists of two coplanar counterrotating circularly polarized fields with a frequency ratio of 2:1. The velocity map of the angle-resolved ATI spectra, both for direct and rescattered electrons, reflects the shape of a parametric plot of the bicircular field and its symmetries. It is shown that the main characteristics of the ATI spectra can be explained using only a few quantum orbits having short travel times. We also analyze a recently discovered [Phys. Rev. A 93, 052402(R) (2016)] bicircular-field-induced spin asymmetry of the ATI electrons and show that the momentum dependence of the spin-asymmetry parameter is stronger for longer wavelengths.

The velocity map of the above-threshold ionization electron spectrum at long laser wavelength exhibits a characteristic structure normal to the laser polarization, which has the appearance of a trident or a three-pronged fork. The forklike structure vanishes for few-cycle laser pulses. It is explained in terms of the classical-electron-trajectories model of strong-field ionization augmented so as to allow for rescattering. The analysis reveals its relation to the so-called low-energy structure, which was recently observed for very small transverse momenta.

Amplification of high harmonics generated by atoms irradiated by a high-power laser is considered. The general expression for the gain is obtained as a function of the atomic target and the laser parameters. For high-harmonic generation in a fiber, the gain may be substantial. An experiment for the gain measurement is discussed.

We investigate the quantum mechanical process of two-electron tunneling in strong external electric fields. Numerical solution of a two-electron s-wave model reveals the existence of collective tunneling ionization in a mode where both electrons stay at equal distance from the nucleus. Otherwise the lagging electron is immediately recaptured. The corresponding double ionization rate fails to explain nonsequential multiple ionization in strong-field laser experiments. However, an empirically modified version of the analytical one-electron tunneling rate of Ammosov, Delone, and Krainov agrees with the experiments to a surprising accuracy. The reason for this agreement is presently unknown.

We investigate high-order above-threshold ionization of diatomic molecules and their companion atoms by linearly polarized strong laser field using improved molecular (atomic) strong-field approximation. The most noticeable feature of the molecular spectra is the existence of minima that are absent in atomic case. We have derived an analytical formula for their position which is independent of the molecular symmetry.

A generalization of the Keldysh ionization amplitude derived previously which incorporates rescattering is used to calculate above-threshold ionization spectra for medium-high intensity (~1014 W cm-2). Quantum interferences are identified and shown to be capable of causing above-threshold ionization peaks to rise and fall by an order of magnitude when the laser intensity changes by only a few per cent. The calculations are carried out for a zero-range binding potential. Comparison with available three-dimensional accurate calculations for a Coulomb potential shows sufficient agreement suggesting that predictions based on the zero-range potential are qualitatively reliable.

So far, nonsequential double ionization (NSDI) of atoms can be well understood within a semiclassical or even classical picture. No quantum effect appears to be required to explain the data observed. We theoretically study electron correlation resulting from NSDI of argon in a low-intensity laser field using a quantum-mechanical S-matrix theory. We show that quantum interference between the contributions of different intermediate excited states of the singly charged argon ion produces a transition from back-to-back to side-by-side emission with increasing laser intensity, which is in close agreement with the experimental data. For higher intensities, this transition is enhanced by the consequences of depletion of the excited states.

A compact generalization of the Keldysh ionization amplitude is derived that includes rescattering. It is used for calculations of above-threshold ionization spectra with respect to energy for various emission angles for tunneling ionization of helium at high intensity, for the simple case of a zero-range potential as the binding potential. Most of the essential features of recent measurements are reproduced, that is, the onset, the extent, and the relative height of the plateau, which makes up the major part of the observed spectrum.

Molecular above-threshold ionization by a circularly polarized laser field is investigated. Our theoretical approach is based on the modified molecular strong-field approximation. Various gauge-dependent versions of this approximation are considered and homonuclear and heteronuclear molecular species characterized by different symmetries are used as targets. As in the case of a linearly polarized field, the imprint of the molecular multicenter structure can be observed in the above-threshold ionization spectra. It manifests itself as minima in the rate of the ionized electrons as a function of their energy. The locations of these minima are strongly influenced by the symmetry of the corresponding highest occupied molecular orbital as well as the internuclear separation. Analyzing the interference structures of the electron spectra one can obtain information about the molecular symmetry.

We demonstrate the significant role of long quantum orbits in strong-field atomic processes by investigating experimentally and theoretically the above-threshold ionization spectra of noble gases in intense elliptically polarized laser pulses. With increasing laser ellipticity, the yields of different energy regions of the measured electron spectrum in high-order above-threshold ionization drop at different rates. The experimental features can be reproduced by a theoretical simulation based on quantum-orbit theory, revealing that increasing ellipticity favors the contributions of the long quantum orbits in the high-order above-threshold ionization process. DOI: 10.1103/PhysRevLett.110.043002

Rescattering effects in above-threshold ionization such that the electron is driven back to the ionic core by the laser field and rescatters are considered in a completely classical framework, for a laser field consisting of a linearly polarized monochromatic fundamental and its second harmonic, as a function of their relative phase. Several features appear, owing to the two-color field: the energies of the rescattered electrons extend up to 21${\mathit{U}}_{\mathit{p}}$, with ${\mathit{U}}_{\mathit{p}}$ the ponderomotive potential of the entire field; the angular distributions of the rescattered electrons are no longer symmetric with respect to an interchange of the backward and forward direction and more than one ring or side lobe may appear in either direction; the importance of rescattering can be deduced from the violation of a certain symmetry of the total above-threshold ionization rates for fixed energy with respect to the phase between the two fields; the spectra of the rescattered electrons change dramatically when the field intensity is raised from the multiphoton into the tunneling regime.

Recent experimental progress has led to an improved understanding of the role of quasi-free electron propagation in intense-field laser-atom physics. A brief review is given of crucial experiments, such as high-harmonic generation, high-energy effects in above-threshold ionization (plateau and anomalous angular distributions) and nonsequential double ionization, and their interpretation in terms of two- and three-step models is discussed. These models consider the initial 'creation' of the electron in the continuum, the subsequent propagation in the field, and the eventual return of the electron to the ionic core as more or less separate steps. The propagation of the electron in the laser field is treated in terms of the path-integral representation of the propagator. This fully quantum mechanical formulation pinpoints the decisive role of particular classical closed orbits, those that start from and return to the centre of the atomic binding potential, in the above-mentioned phenomena and allows for setting up an exact framework for the formal derivation of the multi-step models. High-harmonic generation and the rescattering effects in above-threshold ionization are given special attention, along with the significance of the polarization of the irradiating laser field.

A calculation of the second-order (rescattering) term in the S-matrix expansion of above-threshold ionization is presented for the case when the binding potential is the unscreened Coulomb potential. Technical problems related to the divergence of the Coulomb scattering amplitude are avoided in the theory by considering the depletion of the atomic ground state due to the applied laser field, which is well defined and does not require the introduction of a screening constant. We focus on the low-energy structure, which was observed in recent experiments with a midinfrared wavelength laser field. Both the spectra and, in particular, the observed scaling versus the Keldysh parameter and the ponderomotive energy are reproduced. The theory provides evidence that the origin of the structure lies in the long-range Coulomb interaction.

Recent experimental investigations of the high-order above-threshold ionization peaks near the onset of the plateau have exhibited anomalous angular distributions of the emitted photoelectrons with pronounced side lobes surrounding emission in the direction of the laser electric field. It is shown that the existence and angular position of these side lobes are consequences of the classical kinematics of electrons in laser fields.

A model is investigated that includes the effects of rescattering on above-threshold ionization in the simplest possible situation. A delta function source injects electrons in the lowest possible continuum state. The electrons propagate from there on in the presence of the laser field, rescatter off a delta function potential and propagate in the field again. Spectra and angular distributions for the electrons are calculated and compared with recent experimental data.

The molecular strong-field approximation (MSFA), which includes dressing of the molecular bound state, is introduced and applied to above-threshold ionization of heteronuclear diatomic molecules. Expressions for the laser-induced molecular dipole and polarizability as functions of the laser parameters (intensity and frequency) and molecular parameters [molecular orientation, dipole, and parallel and perpendicular polarizabilities of the highest occupied molecular orbital (HOMO)] are presented. Our previous MSFA theory, which incorporates the rescattering effects, is generalized from homonuclear to heteronuclear diatomic molecules. Angle- and energy-resolved high-order above-threshold ionization spectra of oriented heteronuclear diatomic molecules, exemplified by the carbon monoxide (CO) molecule, exhibit pronounced minima, which can be related to the shape of their HOMO-electron-density distribution. For the CO molecule we have found an analytical condition for the positions of these minima. We have also shown that the effect of the dressing of the HOMO is twofold: (i) the laser-induced Stark shift decreases the ionization yield and (ii) the laser-induced time-dependent dipole and polarizability change the oscillatory structure of the spectra.

We present experimental and theoretical results on photodetachment of ${\mathrm{Br}}^{\ensuremath{-}}$ and ${\mathrm{F}}^{\ensuremath{-}}$ in a strong infrared laser field. The observed photoelectron spectra of ${\mathrm{Br}}^{\ensuremath{-}}$ exhibit a high-energy plateau along the laser polarization direction, which is identified as being due to the rescattering effect. The shape and the extension of the plateau is found to be influenced by the depletion of negative ions during the interaction with the laser pulse. Our findings represent the first observation of electron rescattering in above-threshold photodetachment of an atomic system with a short-range potential.

The collective collisionless dynamics of the electron gas in free-electron nanofilms irradiated by an obliquely incident p-polarized laser wave are considered in the classical hydrodynamic and jellium-model approximations. The two cases of cold metallic nanofilms and hot free-electron nanofilms laser ionized and laser heated by a pump-laser prepulse are investigated with proper electron statistics. Both linear and nonlinear properties of the plasma resonance excitation in the nanofilms are studied in detail for different film parameters (film thickness, thickness of the diffuse film boundary, outer-ionization degree for hot laser-ionized/heated films, etc.). The significant role of the diffuse film boundaries for both linear absorption of the laser field and third-harmonic generation is demonstrated. For this goal, we do not use the standard dielectric-permittivity approach with boundary conditions between two different media but solve continuously over all space the full set of hydrodynamic and electrodynamic equations in nonrelativistic one-dimensional approximation. It is shown that collisionless edge absorption may be dominant in thin nanofilms, while in cold metal nanofilms it results in the appearance of several linear-absorption resonances below the bulk-plasma resonance frequency. For hot nanofilms, drastic broadening of the linear-plasma-resonance profile is obtained in calculations when the film thickness is reduced. In ourmore » model, the third-harmonic generation is determined by the density gradient in the diffuse film edges. Additional resonances in third-harmonic generation as a function of laser frequency are obtained for cold metal nanofilms. They differ from the standard third-order nonlinear resonance, which is located at one third of the plasma resonance frequency. The important role of the outer-ionization degree in forming the third-order nonlinear response of the hot laser-ionized film is also analyzed and discussed.« less

The strong-field approximation for ionization of diatomic molecules by an intense laser field is generalized to include rescattering of the ionized electron off the various centers of its molecular parent ion. The resulting spectrum and its interference structure strongly depend on the symmetry of the ground state molecular orbital. For ${\mathrm{N}}_{2}$, if the laser polarization is perpendicular to the molecular axis, we observe a distinct minimum in the emission spectrum, which survives focal averaging and allows determination of, e.g., the internuclear separation. In contrast, for ${\mathrm{O}}_{2}$, rescattering is absent in the same situation.

A recently developed unified description of low-order above-threshold ionization (Becker et al 2014 J. Phys. B: At. Mol. Opt. Phys. 47 204022; 2015 J. Phys. B: At. Mol. Opt. Phys. 48 151001) is revisited and extended. By considering the rescattering electron energies and angles at the classical cutoffs and the contributions of particular quantum-orbit solutions, it is shown that summing both the backward- and the forward-scattering contributions, within the low-frequency approximation, it is possible to reproduce the observed features of the ATI spectra both for low and high energies and both on and off the laser-polarization axis in the momentum plane.

In the customary formulation of the strong-field approximation (SFA) for laser-induced ionization, the initial bound state is taken as field-free. In the formulation of a length-gauge SFA for ionization of a molecule described by a two-center binding potential with sufficiently large internuclear separation, we argue that the initial state has to be dressed in order to account for the different scalar potentials at the various centers. We propose a ``dressed-state'' SFA to this end.

We discuss the feasibility of measuring the temporal variation of the electric-field strength of a few-cycle laser pulse with arbitrary polarization using the attosecond streaking method. It is shown that a full characterization of the field requires measuring the photoelectron momenta in two opposite directions in the laser polarization plane for various delays of the extreme ultraviolet burst with respect to the probed laser pulse.

Laser-induced double and multiple ionization of atoms may proceed either sequentially or nonsequentially in one coherent process. For near-infrared lasers of moderate intensity (1014 to 1015 W/cm2), the physical mechanism of the coherent process is inelastic rescattering of a first-ionized electron off its parent ion. The quantum-mechanical S-matrix description of this process is reviewed. Momentum distributions of the ejected electrons and the doubly charged ion are calculated and compared with the experimental data. Their shape is found to be determined by the effective electron-electron interaction, by which the recolliding first electron ejects the up to this time bound second electron. The significance of the finalstate electron-electron interaction is assessed. The underlying classical dynamics are elucidated. Recent experiments with ultra-short phase-stabilized laser pulses are discussed. Nonsequential multiple ionization is modeled by assuming that the returning electron thermalizes with a certain number of bound electrons, and the corresponding thermalization time is estimated.

The force due to the transverse magnetic field of a laser beam drives an electron in the direction of laser propagation, thereby impeding the recollision mechanism for high-order harmonic generation. The longitudinal electric field component of a tightly focused Gaussian beam can sufficiently counteract the magnetic force to enhance the harmonic yield substantially. For tight focusing and a laser intensity of 10(18) W/cm2, it can raise the harmonic yield by several orders of magnitude.

High-order above-threshold ionization by few-cycle laser pulses is analyzed in terms of quantum orbits. For a given carrier-envelope phase, the number of contributing orbits and their ionization and rescattering times determine the shape of the angle-resolved spectrum in all detail. Conversely, analysis of a given spectrum reveals the carrier-envelope phase and the various interfering pathways from which the electron could choose.

The emission of x rays by clusters of moderate to large size ${(10}^{4}--{10}^{6}$ constituents) irradiated by an intense laser pulse ${(10}^{16}--{10}^{19}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ is considered. Over-the-barrier ionization of the constituent cluster atoms generates multicharged ions and electrons. For increasing cluster size, more and more of the electrons remain trapped inside the cluster. X rays are generated in the interaction of the trapped electrons with the cluster ions. Three such radiative processes are considered in detail: direct photorecombination of free electrons and ions, dielectronic recombination, and excitation of ions by electron impact followed by recombination. The main contribution to x-ray emission under the above conditions comes from electron impact excitation, while dielectronic recombination is less important, and photorecombination hardly plays any role. The excitation is created before the cluster explodes, whereas emission of x rays continues thereafter.

Nonsequential double ionization of rare-gas atoms by a low-frequency high-intensity laser field is dominated by the recollision mechanism. The pertinent S-matrix diagram is identified and evaluated under various assumptions for the electron-electron interaction and compared with the data.