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.

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.

Using our theory which is based on the strong-field approximation we analyze high-order above-threshold ionization and high-order harmonic generation processes for the case of the homonuclear diatomic molecules exposed to an orthogonally polarized two-color (OTC) laser field. The OTC field represents a superposition of two linearly polarized fields with mutually orthogonal polarizations and different frequencies. We analyze the photoelectron energy spectra and the harmonic ellipticity as a function of the ratio of the intensities of the OTC laser-field components and the relative phase. Some combinations of the values of these parameters lead to the high-energy electrons, while the harmonic ellipticity depends strongly on the ratio of the intensities of the laser-field components. It is possible to find the value of this ratio for which the ellipticity of the emitted harmonics is large. The signes of ellipticity are opposite for the molecular orientations which are connected through the reflection with respect to the axis along the first OTC field component. This symmetry is explained using the expression which relates the T-matrix element and the harmonic ellipticity.

High-harmonic generation by aligned diatomic molecules in orthogonally po-larized two-color laser fields is considered using the molecular strong-field approximation. Regions of the parameter space with large harmonic ellipticity are identified.

We investigate emission rate and ellipticity of high-order harmonics generated exposing a homonuclear diatomic molecule, aligned in the laser-field polarization plane, to a strong orthogonally polarized two-color (OTC) laser field. The linearly polarized OTC-field components have frequencies rω and sω, where r and s are integers. Using the molecular strong-field approximation with dressed initial state and undressed final state, we calculate the harmonic emission rate and harmonic ellipticity for frequency ratios 1:2 and 1:3. The obtained quantities depend strongly on the relative phase between the laser-field components. We show that with the OTC field it is possible to generate elliptically polarized high-energy harmonics with high emission rate. To estimate the relative phase for which the emission rate is maximal we use the simple man’s model. In the harmonic spectra as a function of the molecular orientation there are two types of minima, one connected with the symmetry of the molecular orbital and the other one due to destructive interference between different contributions to the recombination matrix element, where we take into account that the electron can be ionized and recombine at the same or different atomic centers. We derive a condition for the interference minima. These minima are blurred in the OTC field except in the cases where the highest occupied molecular orbital is modeled using only s or only p orbitals in the linear combination of the atomic orbitals. This allows us to use the interference minima to assess which atomic orbitals are dominant in a particular molecular orbital. Finally, we show that the harmonic ellipticity, presented in false colors in the molecular-orientation angle vs. harmonic-order plane, can be large in particular regions of this plane. These regions are bounded by the curves determined by the condition that the harmonic ellipticity is approximately zero, which is determined by the minima of the T-matrix contributions parallel and perpendicular to the fundamental component of the OTC field.

Molecular strong-field approximation is applied to above-threshold detachment of homonuclear diatomic molecular negative ions. Differences between the photodetachment amplitudes for neutral diatomic molecules and diatomic anions, for both direct and rescattered electrons, are examined. Numerical results for the photoelectron spectra of $ {\rm C}_2^ - $C2− molecular anions for different intensities and wavelengths of a linearly polarized laser field and different molecular anion orientations are shown and discussed. Two-center destructive interference minima (suppression regions) in the rescattering part of the photoelectron spectra are observed. For molecules with molecular orientation defined by the angle $ {\theta _L} $θL with respect to the laser-field polarization axis, these minima manifest as two parallel straight lines in the distribution of the photoelectron yield presented in the photoelectron momentum plane. These lines make the angle $ {90^ \circ } - {\theta _L} $90∘−θL, with the momentum component parallel to the laser-field polarization axis. Focal-averaged photoelectron spectra are also presented and analyzed.