Electron-atom scattering in a strong laser field is analyzed using the strong-field approximation and modeling elastic scattering of electrons by atoms with a realistic analytical potential derived from an independent-particle model. The results that include both direct scattering and scattering with a repeated scattering (rescattering) are presented. In the latter case, in the intermediate step of the process, the electron can absorb the energy from the laser field and additional plateau structures appear. The features of these plateaus and their cutoffs are analyzed for various incident electron energies and scattering angles, for different laser intensities, and for various atomic gases. The boundaries of these plateaus are compared with classical estimates.

The influence of the carrier-envelope phase (``absolute phase'') of a few-cycle pulse on the left-right asymmetry of the photoelectron spectrum of high-order above-threshold ionization is analyzed. Energy spectra are calculated for opposite detectors along the polarization axis of a linearly polarized four-cycle laser pulse. The results obtained allow us to determine the value of the absolute phase in a given experiment by comparison with the theoretical spectra. A classical analysis of the calculated spectra is presented, and the corresponding electron trajectories are analyzed. Emission of high-energy electrons is found to occur in one or two ultrashort subfemtosecond bursts.

The evolution of the electric field of laser pulses consisting of a few optical cycles depends on the so-called absolute phase. Strong-field photoionization not only provides means to measure the absolute phase. Rather phase-controlled few-cycle pulses allow investigating photoionization on the attosecond time scale as the sub-cycle ionization dynamics becomes manifest in the photoelectron spectra. Few-cycle pulses thus can serve as a time-domain microscope for investigation of electronic transitions.

Classical cutoffs for the momenta of electrons ejected in laser-induced nonsequential double ionization are derived for the recollision-impact-ionization scenario. Such simple cutoff laws can aid in the interpretation of the observed electron spectra.

A Keldysh-type theory of above-threshold detachment of electrons from negative ions is developed that includes the rescattering of the detached electron on the parent atom. The rescattering potential is the sum of the polarization potential and the static potential. The low-energy part of the spectra obtained reproduces the earlier results of Gribakin and Kuchiev. It is strongly dependent on the parity of the ground state, in contrast to the rescattering-induced high-energy part, whose shape is almost independent of the ground state as well as the rescattering potential. However, its height strongly depends on the latter, that is, on the respective ion (or atom). We relate our results to the recent experiment on photodetachment of F - [I. Yu. Kiyan and H. Helm

In a recent 'stereo above-threshold ionization experiment, the influence of the absolute phase (the phase of the carrier wave with respect to the laser-pulse envelope) on the left-right asymmetry of the emitted photoelectrons ionized by a few-cycle pulse was analyzed. Two detectors were used, positioned opposite each other in a plane perpendicular to the propagation direction of the laser beam. Depending on the value of the absolute phase, one detector registers more electrons than the other. Applying the Keldysh theory of above-threshold ionization, adjusted to the case of few-cycle pulses, we explore this left-right asymmetry in more detail. We investigate the absolute-phase dependence of the differential ionization probabilities and explain it using the saddle-point method. A theoretical analysis of the experiment, based on a correlation technique, is presented. The time dependence of the laser-field intensity of a few-cycle laser pulse is analyzed both for circular and for linear polarization.

Angle-resolved energy spectra of high-order above-threshold ionization are calculated in the direction of the laser polarization for a linearly polarized four-cycle laser pulse (two cycles FWHM) as a function of the carrier-envelope relative phase (absolute phase). The spectra exhibit a characteristic left-right (backward-forward) asymmetry, which should allow one to determine the value of the absolute phase in a given experiment by comparison with the theoretical spectra. A classical analysis of the spectra calculated is presented. High-energy electron emission is found to occur in one or two ultrashort (< inverted exclamation mark<< 0.7 fs) bursts. In the latter case, the spectra display a peak structure whose analysis reveals a time-domain image of electron emission.

Abstract We investigate laser-assisted electron-ion recombination with an emphasis on the spectrum of the emitted high-energy photons. A theory that includes the modification of this spectrum due to the recollision of the incident electron and the ion is presented. Numerical results for the soft X-ray differential power spectra both for a monochromatic and a bichromatic laser field are presented and explained using a semi-classical model. For the bichromatic field with frequencies ω and 2ω, the emitted X-ray spectrum is analysed as a function of the relative phase and the possibility of the coherent phase control is shown. We also show that the laser-assisted electron-ion recombination, which includes the rescattering of the electron at the ion before the recombination, is a process complementary to the well-known processes of high-harmonic generation and high-order above-threshold ionization. For low incoming electron energies, the cut-off of the emitted soft X-ray photon energies, including the process of rescattering, is higher than in the case of the direct recombination process. The results obtained are explained using the semi-classical analysis and the three-step scenario.

Abstract A relativistic generalization of the strong-field-approximation theory of high-order harmonic generation is presented. Numerical results for the harmonic spectra obtained by shining a strong laser pulse on multiply charged ions are analysed. Harmonic generation is explained using the tunnelling-propagation-recombination model. Relativistic effects are important in the intermediate phase of this process and lead to a suppression of both low-order and ultrahigh-order harmonic generation due to the magnetic-field-induced drift, which prevents the return of the electron to the nucleus. For higher laser frequencies and ionization potentials the non-tunnelling mechanism of generation of high harmonics with energies below the ionization potential becomes important. These harmonics are due to inner-atom dynamics, they are emitted with a much higher efficiency, and relativistic effects are less important. We analyse the difference between the plateau heights of the tunnelling and nontunnelling harmonic spectra as a function of the ionization potential and the laser intensity.

Single-atom high-order harmonic generation is considered in the strong-field approximation, as formulated in the Lewenstein model, and analyzed in terms of quantum orbits. Orbits are classified according to the solutions of the saddle-point equations. The results of a numerical integration are compared with the saddle-point approximation and the uniform approximation. Approximate analytical solutions for long orbits are presented. The formalism developed is used to analyze the enhancement of high-order harmonic generation near channel closings. The enhancements exactly at the channel closings are extremely narrow and built up by the constructive interference of a very large number of quantum orbits. Additional broader enhancements occur slightly below channel closings. They are generated by the interplay of a medium number of orbits.

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.