Nondipole effects in processes assisted by a THz field having the strength of a few MV/cm can be significant due to its long wavelength. We illustrate this for strong-laser-field-induced ionization assisted by a THz field. To this end, we generalize our strong-field-approximation theory so that it includes the first-order term in a 1/c expansion of the vector potential. We show that in this case, in addition to a shift of the maximum of the photoelectron momentum distribution, the differential ionization probability as well as the cutoff energy can be significantly increased. For an explanation of these unexpected results we use the saddle-point method adjusted to include nondipole effects.

We address ionization of a diatomic molecule by a bichromatic elliptically polarized field with co-rotating components. Using the strong-field approximation we investigate symmetry properties of the photoelectron momentum distribution and explore the minima which appear in the photoelectron spectra. We distinguish two types of minima: (i) two-center interference minima which appear due to the destructive interference of the contributions of two electron wave packets emitted from the two centers of the diatomic molecule and (ii) the one-center minima which are caused by the interference of the parts of the wave packet emitted from the same atomic center at different times. The position of the two-center interference minima depends on the molecular orientation. When a molecular orbital is modelled using the atomic orbitals of a specific parity, the position of the two-center interference minima does not depend on the ellipticity of our driving field. However, when a molecular orbital consists of both odd and even atomic orbitals the interference of their contributions and the position of the minima depend on the ellipticity. The position of the interference minima in the photoelectron momentum plane is confirmed using the saddle-point method. The position and the number of the one-center minima do not depend on the molecular orientation, but they strongly depend on the ellipticity of the field components. Finally, comparing the photoelectron spectra of the CO molecule with the spectra of homonuclear molecules and the NO molecule we show that the electron probability density distribution plays a significant role for the high-energy rescattered electrons.

A macroscopic theory of high-order harmonic generation (HHG) is presented, which applies a focal-averaging method based on the integral solution of the wave equation. The macroscopic high-harmonic yield is the coherent superposition of the single-atom contributions of all atoms of the generating medium, which are positioned at different spatial points of the laser focus and exposed to the space-time-dependent laser pulse. The HHG spectrum obtained in our macroscopic simulations is qualitatively different from the one obtained using the microscopic or single-atom theory of HHG. Coherent intensity focal averaging, the simpler and more approximate of two methods we introduced, gives the spectrum which forms a declining plateau with the same cutoff position as that of the microscopic spectrum. The second, more precise method, which we call coherent spatio-temporal focal averaging, shows that it is possible, changing the macroscopic conditions, to obtain an observable peak in the harmonic spectrum at an energy much lower than the microscopic cutoff energy. Generally, the high-harmonic yield appears to be dominated by the contributions of laser-pulse spatio-temporal regions with lower intensities as well as by interference, so that the high-energy plateau and its sharp cutoff are quenched in the theoretical simulation and, presumably, in the experiment. The height and position of this peak strongly depend on the macroscopic conditions. We confirmed these findings by applying our macroscopic theory to simulate two recent experiments with mid-infrared laser fields, one with a linearly polarized field and the other one with a bicircular field.

The differential ionization rate for strong-field ionization by tailored laser fields of atomic systems averaged over the magnetic quantum number satisfies particular inversion and reflection symmetries. The symmetries of the elliptic-dichroism parameter, which is related to the change of sign of the ellipticity of the laser field, are considered in detail, with particular emphasis on high-order above-threshold ionization. The general results are illustrated by the examples of an elliptically polarized laser field and a bi-elliptical orthogonally polarized two-color (BEOTC) field. For the BEOTC field the differential ionization rate and the elliptic-dichroism parameter are investigated for the ω-2ω and ω-3ω field combinations and for various relative phases between the laser-field components. The inversion and reflection symmetries of the photoelectron momentum distribution in the polarization plane of the field depend on the parities of r and s in the rω--sω BEOTC field combination and on the relative phase between the field components. We suggest that, by analyzing the symmetry properties of the measured momentum distribution of the elliptic-dichroism parameter, one can identify the mechanism of strong-field ionization. If the rescattering mechanism is dominant one can use these distributions to obtain information about the atomic and molecular structure and dynamics.

Extreme terahertz (THz) pulses can be generated via interaction of strong infrared ultrashort laser pulses with a suitable target. Inverting this scheme, we propose to use such THz pulses to control strong-laser-field-driven processes. In particular, we show that for THz-pulse-assisted strong-laser-field ionization the electron yield can be increased by one order of magnitude for some energies, and that the maximal emitted photoelectron energy can be a few times higher than that realized with the laser field alone. This can be achieved with the THz field intensity many orders of magnitude lower than that of the ionizing laser field. The only requirement is that the vector potential amplitude of the THz field, which governs the electron dynamics after the ionization by the laser field, be comparable with that of the used laser field. An important control parameter is the time delay between the THz pulse and the laser pulse. Strong-field ionization of Cs atoms is used for an illustration. The numerical results are obtained applying the improved strong-field approximation. For a physical explanation, we use quantum-orbit theory supported by the modified saddle-point method, as well as a classical model.

Generation of an elliptically polarized attosecond pulse train by an orthogonally polarized two-color (OTC) laser field is investigated theoretically and simulated numerically. The OTC field consists of two linearly polarized fields with orthogonal polarizations and frequencies that are integer multiples of the fundamental frequency ω. For the ω−3ω OTC field, the emitted harmonics are elliptically polarized so that they may form an elliptically polarized attosecond pulse train provided that a group of harmonics is phase-locked. This is the case if only one quantum orbit generates the corresponding part of the harmonic spectrum. If so, then two attosecond pulses are emitted per optical cycle due to the dynamical symmetry of the ω−3ω OTC field. Atomic targets with an s ground state only generate attosecond pulses with almost linear polarization. Using, however, targets with a p ground state, attosecond pulses with substantial ellipticity can be produced because ground states with opposite magnetic quantum numbers m=+1 and m=−1 produce harmonics with opposite helicities at different rates. In this case, the harmonic intensity and harmonic ellipticity are different for the ground states with the magnetic quantum number m=±1. These differences are the source of the attosecond pulse ellipticity and can be controlled using the relative phase as a control parameter. In addition, by choosing a particular group of harmonics, one can select the desired ellipticity of the attosecond pulse train.

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

Scattering of electrons off diatomic molecules in a bichromatic elliptically polarised laser field is considered by applying the S-matrix theory within the second Born approximation. Two characteristic plateaus appear in the energy spectrum of scattered electrons. The higher plateau is observed in the low-energy part of the spectrum and describes the single scattering, while the lower plateau extends to the high-energy part of the spectrum and describes the double scattering. Scattering and rescattering of electrons off molecular targets may occur at any molecular centre and in any order. Interference of contributions results in increasing/decreasing the differential cross section in particular regions of the energy spectrum of scattered electrons. Two contributions for single scattering and four contributions for double scattering exist in the case of diatomic molecules. For some molecular orientations, a sequence of declining maxima may be observed instead of the plateaus in the electron energy spectrum. We have also observed parabolic structures in the angle-resolved energy spectra. Analytical formulas that explain these structures have been provided. We have also explored the impact of the laser-field ellipticity on the scattered-electron energy spectra. The bichromatic ω– and ω– laser fields have been considered. GRAPHICAL ABSTRACT

The molecular strong-field approximation is employed to study high-order harmonic generation by linear and planar polyatomic molecules exposed to an orthogonally polarized two-color laser field, which consists of two orthogonal linearly polarized components with commensurable frequencies. For such a driving field, we find that the harmonic emission rate and the shape of the spectrum strongly depend on the laser-field parameters including the relative phase and the ratio of the intensities of the two components. The values of the relative phase that correspond to the optimal harmonic emission rate, as well as the cutoff position, can be assessed using a classical model. The possible production of an isolated attosecond pulse is investigated. For suitable symmetry of the laser field an attosecond pulse train with only one attosecond pulse per cycle can be generated. Depending on the frequencies of the two field components, the molecular symmetry properties and the orientation of the molecule with respect to the field, the even harmonics can be absent from the spectrum, which can be used to determine the molecular orientation. The emitted harmonics are elliptically polarized and their ellipticity depends on the molecular orientation.