Nonlinear quantum-mechanical phenomena in strong laser fields, such as high-order harmonic generation (HHG) and above-threshold ionization (ATI) are significantly modified if the applied laser field is bichromatic and/or elliptically polarized. Numerical results obtained within the strong-field approximation are presented for two special cases. We show results for HHG by plasma ablation in a bichromatic linearly polarized laser field. We also consider the ATI process in bicircular field which consists of two coplanar counter-rotating circularly polarized fields.

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 rω and sω. 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.

Processes of above-threshold ionization (ATI) and high-order harmonic generation (HHG) for heteronuclear diatomic molecules are investigated. By analyzing the HHG and ATI spectra for different molecular orientation with respect to the main laser polarization axis and for different values of the photon energies and electron energies and emission angle, we are able to draw some conclusions about the molecular structure. The partial elliptic dichroism effect in HHG spectra is also analyzed. Regarding the ATI spectra, two-center interference minima are visible, even for a circularly polarized laser field. The positions of the minima depend on the internuclear distance, on the relative contributions of the atomic orbitals to the highest occupied molecular orbital and on the laser field parameters.

S-matrix theory is used to analyze different atomic and molecular processes in a linearly polarized few-cycle laser field. The energy spectra of high-order above-threshold ionization (HATI) are presented. Electron-atom potential scattering assisted by a few-cycle laser pulse is also analyzed. It is shown that the plateau structures in the energy spectra of the electron-atom potential scattering are dependent on the carrier-envelope phase (CEP) of the laser pulse, so that the cutoff positions of the plateaus can be controlled by changing the CEP. Regarding our analysis of the molecular HATI process, the angle-resolved spectra, obtained by different theoretical approaches, are also presented.

A theory of high-order harmonic generation by heteronuclear diatomic molecules exposed to an elliptically polarized laser field is presented. This theory is based on the molecular strong-field approximation, which takes into account the dressing of the initial and final molecular bound states caused by the laser field. The laser-field-caused Stark shift of the effective ionization potential of the highest occupied molecular orbital changes the structure of the harmonic spectra. Both the even and odd harmonics appear in the harmonic spectra due to the broken inversion symmetry of the heteronuclear diatomic molecule. An interference minima condition that is valid for arbitrary heteronuclear diatomic molecules is derived. Our results are illustrated using examples of CO and NO molecules.

In this paper, we present a quantum-mechanical theory in order to describe laser-induced and laser-assisted atomic and molecular processes with an emphasis on an elliptically polarized strong laser field. The features of the high-energy regions of spectra and their cutoffs are analyzed in detail for different values of ellipticity, laser intensities and various atomic and molecular species. Our theoretical study is focused on the ellipticity dependence of the plateau structures that appear in the energy spectra of atomic and molecular processes in strong laser fields.

In our recent paper (2010 Phys. Rev. A 82 023412) we introduced a theory of high-order harmonic generation by diatomic molecules exposed to an elliptically polarized laser field and have shown that the nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we now develop a theoretical approach for calculating ellipticity and the offset angle of high harmonics. We show that the emitted harmonics generated by aligned molecules are elliptically polarized even if the applied field is linearly polarized. Using examples of N2, O2 and Ar2 molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment and explain them by the destructive two-centre interference. Taking into account that the aligned molecules are an anisotropic medium for high harmonic generation, we introduce elliptic dichroism as a measure of this anisotropy, for both components of the T-matrix element. We propose that the measurement of the elliptic dichroism may reveal further information about the molecular structure.

We present a theory of high-order harmonic generation by diatomic molecules exposed to an elliptically polarized laser field. This theory is based on the molecular strong-field approximation with the laser-field-dressed initial bound state and the undressed final state. The interference minima, observed for linear polarization, are blurred with the increase of the laser-field ellipticity. The $n$th harmonic emission rate has contributions of the components of the $T$-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. We analyze the destructive interference condition for this perpendicular component. Taking into account that the aligned molecules are an anisotropic medium for high-harmonic generation, we introduce elliptic dichroism as a measure of this anisotropy and discuss possibilities of its use for determining the molecular structure.

The multiple-slit type destructive interference in molecular high-order harmonic generation (HHG) leads to the minima in the harmonic yield for particular molecular orientation angle θL and the harmonic order n. For the case of homonuclear diatomic molecules, we have found a condition for this destructive interference in the form of a nonlinear equation over n and θL. This condition strongly depends on the molecular symmetry, on the atomic orbitals of which a particular highest occupied molecular orbital (HOMO) consists and on the internuclear distance R. Therefore, one can learn about the molecular structure and dynamics analysing the HHG spectra of aligned molecules. Using the example of an Ar2 molecule, having 5σu HOMO, for various internuclear distances, we analyse this interference condition and show that, in the (n, θL) plane, it manifests in the form of one or several continuous curves. Furthermore, in the (Rcos θL, λmin) plane, where λmin is an effective de Broglie wavelength of the recombining electron, this condition leads to a set of lines which are positioned between the limiting cases of molecular orbitals consisting of only one type (even or odd) of atomic orbitals (s and p in the Ar2 case).

The multiple-slit type destructive interference in molecular high-order harmonic generation (HHG) leads to the minima in the harmonic yield for particular molecular orientation angle θL and the harmonic order n. For the case of homonuclear diatomic molecules, we have found a condition for this destructive interference in the form of a nonlinear equation over n and θL. This condition strongly depends on the molecular symmetry, on the atomic orbitals of which a particular highest occupied molecular orbital (HOMO) consists and on the internuclear distance R. Therefore, one can learn about the molecular structure and dynamics analysing the HHG spectra of aligned molecules. Using the example of an Ar2 molecule, having 5σu HOMO, for various internuclear distances, we analyse this interference condition and show that, in the (n, θL) plane, it manifests in the form of one or several continuous curves. Furthermore, in the (Rcos θL, λmin) plane, where λmin is an effective de Broglie wavelength of the recombining electron, this condition leads to a set of lines which are positioned between the limiting cases of molecular orbitals consisting of only one type (even or odd) of atomic orbitals (s and p in the Ar2 case).

A theory of high-order harmonic generation by diatomic molecules is introduced. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are investigated. Using examples of homonuclear diatomic molecules such as ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$, it is shown that clear two-center interference minima in the harmonic spectra as a function of the molecular orientation appear only if the final molecular state is undressed. For ${\mathrm{H}}_{2}$ the positions of these minima are in agreement with the ab initio numerical results. Physically, the returned electron wave packet recombines into a molecular orbital, which is a linear combination of the atomic orbitals having different parities. The interference minima in the harmonic spectrum are caused by the destructive interference of the corresponding partial recombination amplitudes. In accordance with this, we have derived an interference minima condition which is valid for arbitrary homonuclear diatomic molecules.