S-matrix theory is used in order to analyze the energy spectra of electron-atom potential scattering assisted by a bicircular (two-component circularly polarized) laser field having corotating field components. The double scattering (rescattering) is also included in the analysis by applying the second Born approximation in the expansion of the S-matrix element. We have investigated how the energy spectrum of scattered electrons is affected by the scattering angle. We have also analyzed the sensitivity of the energy spectrum to the relative phase and intensity ratio of the laser-field components. The calculated energy spectra are characterized by the plateau-like oscillatory structures with abrupt cutoffs. Positions of these cutoffs in the energy spectra are confirmed by a classical analysis. Rescattering effects can be observed in the calculated energy spectra for certain values of the scattering angle. These effects are represented by the second plateau in the energy spectrum. This is different from the process of above-threshold ionization/detachment by a bicircular laser field, where the (re)scattering effects in the photoelectron energy spectra cannot be observed in the case of corotating laser-field components.

The quantum-mechanical transition amplitude of an ionization process induced by a strong laser field is typically expressed in the form of an integral over the ionization time of a highly oscillatory function. Within the saddle-point (SP) approximation this integral can be represented by a sum over the contributions of the solutions of the SP equation for complex ionization time. It is shown that, for the general case of an elliptically polarized polychromatic laser field, these solutions can be obtained as zeros of a trigonometric polynomial of the order n and that there are exactly n relevant solutions, which are to be included in the sum. The results obtained are illustrated by examples of various tailored laser fields that are presently used in strong-field physics and attoscience. For some critical values of the parameters two SP solutions can coalesce and the topology of the ‘steepest descent’ integration contour changes so that some SPs are bypassed. Around the critical parameters a uniform approximation should be used instead of the SP method.

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.

High-order harmonic generation by orthogonally polarized two-color (OTC) laser fields is analysed using strong-field approximation and quantum-orbit theory. Results for the field components frequency ratio of 2:1 and 3:1 are presented and compared. We have shown that, depending on the relative phase between the field components, the shape of the high-harmonic spectrum can be very different from that obtained by a monochromatic linearly polarized laser field. It is also shown that it is possible to generate elliptically polarized high-order harmonics with very high photon energies using OTC laser field with the frequency ratio of 3:1 and a long fundamental wavelength. An effective relative phase control of the harmonic emission is demonstrated. The obtained results are explained using the quantum-orbit theory.

Over the past three decades numerous numerical methods for solving the time-dependent Schr\"odinger equation within the single-active electron approximation have been developed for studying ionization of atomic targets exposed to an intense laser field. In addition, various numerical techniques for extracting the photoelectron spectra from the time-dependent wave function have emerged. In this paper we compare photoelectron spectra obtained by either projecting the time-dependent wave function at the end of the laser pulse onto the continuum state having the proper incoming boundary condition or by using the window-operator method. Our results for three different atomic targets show that the boundary condition imposed onto the continuum states plays a crucial role for obtaining correct spectra accurate enough to resolve fine details of the interference structures of the photoelectron angular distribution.

High-order harmonics generated by a linearly polarized laser field are also linearly polarized. Having in mind that for various application, such as the exploration of magnetic materials, chiral molecules etc., we need circularly polarized high harmonics which serve as coherent soft x-rays, we explore high-order harmonic generation by the so-called bicircular laser field. This field consists of two coplanar counter-rotating circularly polarized fields of different frequencies equal to integer multiples of a fundamental frequency ω. High harmonics generated by such field are circularly polarized with helicity alternating between +1 and −1. Combining a group of such harmonics, instead of obtaining a circularly polarized attosecond pulse train, one obtains a pulse with unusual polarization properties. But, if the harmonics of particular helicity are stronger, i.e., if we have helicity asymmetry in a high-harmonic energy interval, then it is possible to generate an elliptical or even circular pulse train. We theoretically investigated a wide range of bicircular field-component intensities (I1 and I2) and found regions where both the harmonic intensity is high and the helicity asymmetry is large. Particular attention is devoted to the ω−2ω and ω−3ω bicircular fields and atoms having the s and p ground states. In our calculations we use strong-field approximation and quantum-orbit theory. We show that, even in the extreme case of I2 = 8I1, for an ω−3ω bicircular field, high-order harmonic generation is more efficient than in the I2 = I1 case. The obtained results are explained analyzing the relevant electron trajectories and velocities, which follow from the quantum-orbit theory. For the atoms having p ground state the helicity asymmetry parameter is large for a wide range of high-harmonic photon energies, while for the atoms having s ground state the helicity asymmetry parameter can be large only for low harmonics. We confirm this by averaging the obtained results over the intensity distribution in the laser focus.

We investigate strong-field ionization of linear molecules by a two-color laser field of frequencies rω and sω having coplanar counterrotating or corotating elliptically polarized components (ω is the fundamental laser field frequency and r and s are integers). Using the improved molecular strong-field approximation we analyze direct above-threshold ionization (ATI) and high-order ATI (HATI) spectra. More precisely, reflection and rotational symmetries of these spectra for linear molecules aligned in the laser-field polarization plane are considered. The reflection symmetries for particular molecular orientations, known to be valid for a bicircular field (this is the field with circularly polarized counterrotating components), are valid also for arbitrary component ellipticities. However, specific rotational symmetries that are satisfied for HATI by a bicircular field, are violated for an arbitrary elliptically polarized field with counterrotating components. For the corotating case and the N2 molecule we analyze molecular-orientation-dependent interferences and plateau structures for various ellipticities.

With the development of intense femtosecond laser sources it has become possible to study atomic and molecular processes on their own subfemtosecond time scale. Table-top setups are available that generate intense coherent radiation in the extreme ultraviolet and soft-X-ray regime which have various applications in strong-field physics and attoscience. More recently, the emphasis is moving from the generation of linearly polarized pulses using a linearly polarized driving field to the generation of more complicated elliptically polarized polychromatic ultrashort pulses. The transverse electromagnetic field oscillates in a plane perpendicular to its propagation direction. Therefore, the two dimensions of field polarization plane are available for manipulation and tailoring of these ultrashort pulses. We present a field that allows such a tailoring, the so-called bicircular field. This field is the superposition of two circularly polarized fields with different frequencies that rotate in the same plane in opposite directions. We present results for two processes in a bicircular field: High-order harmonic generation and above-threshold ionization. For a wide range of laser field intensities, we compare high-order harmonic spectra generated by bicircular fields with the spectra generated by a linearly polarized laser field. We also investigate a possibility of introducing spin into attoscience with spin-polarized electrons produced in high-order above-threshold ionization by a bicircular field.

ABSTRACT Quantum-orbit theory of high-order harmonic generation (HHG) by bicircular laser field is presented. HHG is a strong laser-field-induced process in which the energy absorbed from the laser field is emitted in the form of a high-energy photon. This process can be described using the strong-field approximation and its approximation – the quantum-orbit theory. We develop a classification of quantum orbits for HHG by bicircular field which consists of two coplanar counter-rotating circularly polarized field of frequencies and , where r and s are integers and ω is a fundamental frequency. Analysis of the contributions of particular quantum orbits to high-harmonic intensity enables a better understanding of the HHG process. The cases of the ω– and ω– bicircular fields and of the atoms having the s and the p ground state are analysed in detail. Particular attention is devoted to the influence of the ratio of the intensities and of the bicircular field components. For inert gases having the p ground state the asymmetry in the emission of the left- and right-circularly polarized harmonics can be large. This is explained comparing the partial harmonic intensities for HHG from the ground state having the magnetic quantum number m=+1 and m=−1 and analysing the contributions of particular quantum orbits and the corresponding electron trajectories and velocities. The contribution of the shortest quantum orbit is dominant. It was found that the electron velocity at the ionization time, which still allows the return of the electron to the parent ion, determines the height of the high-energy HHG plateau. For this velocity is large which, in the case of the p ground state, leads to a large helicity asymmetry parameter. On the other hand, for this velocity is small and the intensity of the high-energy plateau harmonics is high.