Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

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.

International Physics Conference in Bosnia and Herzegovina (PHYCONBA 2020) Organizer: Physical Society in Federation of Bosnia and Herzegovina with support of the Academy of Sciences and Arts of Bosnia and Herzegovina Date: October 19, 2020 Venue: Premises of The Academy of Sciences and Arts of Bosnia and Herzegovina, 7 Bistrik street, Sarajevo, Bosnia and Herzegovina. Memebers of Organizing committee: 1. Maja Đekić (Faculty of Science, University of Sarajevo), chairwoman, 2. Mirza Hadžimehmedović (Faculty of Science, University of Tuzla), member, 3. Rifat Omerović (Faculty of Science, University of Tuzla), member, 4. Ena Žunić-Ćejvanović, member, 5. Amra Salčinović Fetić, (Faculty of Science, University of Sarajevo), Technical secretary, 6. Benjamin Fetić (Faculty of Science, University of Sarajevo), member Members of Scientific committee: 1. Dejan Milošević (Faculty of Science, University of Sarajevo, Academy of Sciences and Arts of BiH), chairman, 2. Dijana Dujak (Faculty of Electrical Engineering, University of Sarajevo), member, 3. Hedim Osmanović (Faculty of Science, University of Tuzla), member, 4. Siniša Ignjatović (Faculty of Natural Sciences and Mathematics, University of Banja Luka), member.

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.

We consider the problem of the choice of gauge in nonrelativistic strong-laser-field physics. For this purpose, we use the phase-space path-integral formalism to obtain the momentum-space matrix element of the exact time-evolution operator. With the assumption that the physical transition amplitude corresponds to transitions between eigenstates of the physical energy operator rather than the unperturbed Hamiltonian H0=(−i∂/∂r)2/2+V(r), we prove that the aforementioned momentum-space matrix elements obtained in velocity gauge and length gauge are equal. These results are applied to laser-assisted electron-ion radiative recombination (LAR). The transition amplitude comes out identical in length gauge and velocity gauge, and the expression agrees with the one conventionally obtained in length gauge. In addition to the strong-field approximation (SFA), which is the zeroth-order term of our expansion, we present explicit results for the first-order and the second-order terms, which correspond to LAR preceded by single and double scattering, respectively. Our general conclusion is that in applications to atomic processes in strong-field physics the length-gauge version of the SFA (and its higher-order corrections) should be used. Using the energy operator as the basis-defining Hamiltonian, we have shown that the resulting transition amplitude is gauge invariant and agrees with the form commonly derived in length gauge.

Based on the strong-field approximation, we report results for high-order harmonic generation by bi-elliptical orthogonally polarized two-color (BEOTC) fields with frequency ratios of 2:1 and 3:1 and fundamental wavelengths of 800 and 1800 nm. A BEOTC field denotes the superposition of two copropagating counter-rotating elliptically polarized fields with different wavelengths and orthogonal semimajor axes. Its two limiting cases are the bicircular field and the linearly polarized orthogonal two-color field [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{} and W. Becker, Phys. Rev. A 100, 031401(R) (2019)]. A detailed analysis of the high-order harmonic intensities and ellipticities as functions of the harmonic order, the ellipticity, and the relative phase between the two driving-field components is presented. Regions of the parameter space are identified where the harmonic ellipticities are very high. Surprisingly, this can be the case already for very small ellipticity (as small as $\ensuremath{\varepsilon}=0.01$) of the driving field. This can be important for practical applications. In the opposite limit where the BEOTC field is close to bicircular, the selection rules that govern the latter case can also be very quickly invalidated. For the 2:1 case, this can result in an apparent shift of the selection rules by one harmonic order.

By analyzing angular and energy distributions of the photoelectrons emitted in strong-laser-field-induced ionization of molecules, one can obtain information about the molecular structure and the ground-state symmetry. High-energy part of the photoelectron spectra in the above-threshold ionization (ATI) is characterized by a plateau region in which the ionization probability is practically energy independent. The photoelectron yield drops off exponentially for electron energies higher than some critical energy, i.e. the mentioned plateau is followed by an abrupt cutoff. We investigate the influence of the molecular ground state symmetry on this plateau region and show that, analyzing the corresponding high-order ATI spectra, one can obtain information about the highest occupied molecular orbitals (HOMOs) of the considered molecules. We present results for different homonuclear diatomic molecules: N2, O2, Ar2 and C2 having, respectively, the σ g , π g , σ u and π u symmetries of the HOMO. Particular attention is devoted to the C2 molecule since high-order ATI spectra for this molecule have not been analyzed yet. We consider ATI by a linearly polarized laser field for which the mentioned plateau can be well-developed, depending on the orientation of the molecular axis with respect to the laser-field polarization axis. The HOMO-symmetry-dependent (dis)appearance of the plateau is particularly pronounced for the parallel and perpendicular orientations. Our findings are valid for a wide range of the laser-field intensities and wavelengths, which is important for realization of the suggested experiments. Using the improved molecular strong-field approximation, the theory which is particularly suitable for the analysis of high-energy ATI spectra, for the case of the C2 molecule and different molecular and laser parameters, we investigate various features of the plateau, such as its length and the interference minima and their positions.

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.