M. V. Frolov

Analytic formulae for high harmonic generation

Analytic formulae describing harmonic generation by a weakly bound electron are derived quantum mechanically in the tunnelling limit. The formulae confirm the classical three-step model and provide an analytic explanation for oscillatory structures on the harmonic generation plateau.

Interaction of laser radiation with a negative ion in the presence of a strong static electric field

This paper provides a general theoretical description of a weakly bound atomic system (a negative ion) interacting simultaneously with two (generally strong) fields, a static electric field and a monochromatic laser field having an arbitrary elliptical polarization. The zero-range δ-potential is used to model the interaction of a bound electron in a negative ion as well as the interaction of a detached electron with the residual atom. Our treatment combines the quasistationary (complex energy) and quasienergy (Floquet) approaches. This quasistationary, quasienergy state (QQES) formalism is the most appropriate one for analysing a decaying quantum system under the influence of a periodic external perturbation. Existing QQES theory is reviewed and some new results are discussed: the Hellmann-Feynman theorem and the normalization procedure for QQES, and the definition of the dipole moment and the dynamic polarizability for a decaying atomic system (in strong static electric and/or laser fields). These results are illustrated using analytical formulae obtained from an exact solution of the QQES problem for a δ-model potential in two strong fields. Finally, from the imaginary part of the dynamic polarizability we obtain analytic results (to first order in the laser-field intensity) for the photodetachment cross section. Our results are then compared with those of previous theoretical studies.

Harmonic generation spectroscopy with a two-colour laser field having orthogonal linear polarizations

The interpretation of many high-order harmonic generation (HHG) experiments is based on the assumption that the HHG yield of an atom can be factorized into (i) a laser-dependent ‘electron wave packet’ with rather simple properties, including a nearly universal shape, and (ii) an atomic photorecombination cross section. We show that this factorization is restricted to linearly polarized laser fields and fails in two-colour laser fields with orthogonal polarizations. At the same time, we show how two-colour HHG spectroscopy using orthogonally polarized intense fundamental and relatively weak second harmonic fields makes a complete experiment possible that enables the retrieval of the angle-resolved photorecombination cross sections for atomic p states.

Potential barrier effects in high-order harmonic generation by transition-metal ions

The experimental finding of significant enhancement or suppression of particular harmonics generated by the ionic component of laser-produced plasmas of transition-metal atoms is explained theoretically in terms of the standard three-step scenario for strong-field harmonic generation, taking into account the potential barrier effects that lead to a strong 3p{yields}3d electric dipole transition that dominates the photoionization cross sections of the outer subshells of those ions.

High-order harmonic generation by atoms in a few-cycle laser pulse: Carrier-envelope phase and many-electron effects

Analytic formulas describing high-order harmonic generation (HHG) by atoms in a short laser pulse are obtained quantum mechanically in the tunneling limit. These results provide analytic expressions of the three-step HHG scenario, as well as of the returning electron wave packet, in a few-cycle pulse. Our results agree well with those of numerical solutions of the time-dependent Schroedinger equation for the H atom, while for Xe they predict many-electron atomic dynamics features in few-cycle HHG spectra and significant dependence of these features on the carrier-envelope phase of a laser pulse.

Analytic description of the high-energy plateau in laser-assisted electron–atom scattering

A closed-form analytic formula describing plateau features in laser-assisted electron–atom scattering (LAES) is derived quantum mechanically in the low-frequency limit. The presented formula confirms the classical rescattering scenario for LAES and provides an analytic explanation for oscillatory structures in the high-energy part of LAES spectra.

An analytical quantum model for intense field processes : quantum origin of rescattering plateaus

After a brief comparison of two basic quantum approaches for the analytic treatment of strong laser field phenomena, we analyse the spatial and temporal dependences of the quasistationary, quasienergy state wavefunction Φ(r, t) of a weakly bound level in a strong laser field. We find from this analysis that the characteristic high-energy plateau structures in the spectra of laser–atom processes originate from similar plateau features in the spectra of the Fourier-harmonic components, Φn(r), of Φ(r, t). Together with a quantum interpretation of the well-known rescattering scenario in terms of these wavefunctions, the results of this analysis provide an explanation for the drastic difference between HHG and ATI/ATD in the sensitivity of plateau structures to binding potential effects.

Stabilization of Bound State Decay in an Intense Monochromatic High-Frequency Field

The formalism of complex quasienergies is used for exact calculation of the field-dependent decay rate for a weakly bound particle (in the model of a three-dimensional zero-range potential) in a strong monochromatic laser field. It is shown that the adiabatic (quasistationary) stabilization regime in this model occurs at frequencies ω exceeding the binding energy and only in a limited intensity range. A simple estimate is obtained for the critical field of stabilization breakdown. The effect may be observed for the decay of H− ions in the field of a neodymium laser of femtosecond duration.

Rescattering effects in laser-assisted electron–atom bremsstrahlung

Rescattering effects in nonresonant spontaneous laser-assisted electron-atom bremsstrahlung (LABrS) are analyzed within the framework of time-dependent effective-range (TDER) theory. It is shown that high energy LABrS spectra exhibit rescattering plateau structures that are similar to those that are well-known in strong field laser-induced processes as well as those that have been predicted theoretically in laser-assisted collision processes. In the limit of a low-frequency laser field, an analytic description of LABrS is obtained from a rigorous quantum analysis of the exact TDER results for the LABrS amplitude. This amplitude is represented as a sum of factorized terms involving three factors, each having a clear physical meaning. The first two factors are the exact field-free amplitudes for electron-atom bremsstrahlung and for electron-atom scattering, and the third factor describes free electron motion in the laser field along a closed trajectory between the first (scattering) and second (rescattering) collision events. Finally, a generalization of these TDER results to the case of LABrS in a Coulomb field is discussed.

Static-electric-field behaviour in negative ion detachment by an intense, high-frequency laser field

Based upon the exact numerical solution of the complex quasienergy problem for a 3-dimensional short-range potential as well as upon analytical evaluations, we demonstrate for any finite frequency ω that the action of an ultra-intense laser field (with electric vector F(ωt)) on a weakly bound atomic system may be described by the cycle-averaging of results for an instantaneous static electric field of strength |F(ωt)|.