# Publications by

Birger Böning

## 2022

**Lorentz-force shifts in strong-field ionization with mid-infrared laser fields**

**4**, 033031 (2022)

**Abstract:** In the past, the ionization of atoms and molecules by strong, mid-infrared (IR) laser fields has attracted recurrent interest. Measurements with different IR pulses have demonstrated the crucial role of the magnetic field on the electron dynamics, classically known as the Lorentz force F-L = q (epsilon + v x B), that acts upon all particles with charge q in motion. These measurements also require the advancement of theory beyond the presently applied methods. In particular, the strong-field approximation (SFA) is typically based on the dipole approximation alone and neglects both the magnetic field and the spatial dependence of the driving electric field. Here we show and discuss that several, if not most, observations from strong-field ionization experiments with mid-IR fields can be quantitatively explained within the framework of SFA, if the Lorentz force is taken into account by nondipole Volkov states in the formalism. The details of such a treatment are analyzed for the (peak) shifts of the polar-angle distribution of above-threshold ionization photoelectrons along the laser propagation, the steering of electron momenta by two not quite collinear laser beams, or the enhanced momentum transfer to photoelectrons in standing-light fields. Moreover, the same formalism promises to explain the generation of high harmonics and other strong-field rescattering phenomena when driven by mid-IR laser fields. All these results show how strong-field processes can be understood on equal footings within the SFA, if one goes beyond the commonly applied dipole approximation.

## 2021

**Generation of elliptically polarized high-order harmonic radiation with bi-elliptical two-color laser beams**

**104**, 063118 (2021)

**Torus-knot angular momentum in twisted attosecond pulses from high-order harmonic generation**

**104**, 053116 (2021)

**Above-threshold ionization driven by Gaussian laser beams: beyond the electric dipole approximation**

**54**, 144002 (2021)

**Abstract:** Strong-field atomic experiments have recently become sensitive to nondipole (magnetic) interactions. In particular, photoelectrons emitted in above-threshold ionization possess a nonzero momentum along the beam axis as a result of the Lorentz force. Here, we show how this longitudinal momentum can be theoretically calculated based on a nondipole strong-field approximation that accounts not only for the temporal but also the spatial dependence of the laser field in the photoelectron continuum. If the driving laser beam is approximated as a plane wave, the theoretical values differ from known experimental results by a constant offset. We demonstrate that this offset can successfully be removed if a realistic Gaussian beam profile is accounted for in the quantum description of ATI. We also discuss the influence of the size of the beam waist in the focus.

**Elliptical dichroism in biharmonic ionization of atoms**

**104**, 013102 (2021)

**Abstract:** In multiphoton ionization of atoms, elliptical dichroism may arise in the photoelectron angular distributions due to the interference of the possible ionization pathways. We here consider the interaction of atoms with an elliptically polarized biharmonic $(\omega + 2\omega)$ field which simultaneously allows one- and two-photon ionization of the atoms. The interference between these two ionization pathways introduces contributions to the elliptical dichroism in addition to the dichroism that arises from the two-photon ionization alone. We show that these additional dichroism contributions can lead to a stronger dichroism in comparison to the one arising from two-photon ionization only. We present a relativistic analysis of the corresponding photoelectron angular distributions and discuss individual contributions to the dichroic phenomena. Detailed computations have been performed for biharmonic ionization of neutral helium atoms.

**Single-cycle versus multicycle nonsequential double ionization of argon**

**104**, 013105 (2021)

**Abstract:** Using an improved quantitative rescattering model, we calculate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization of Ar exposed to intense laser pulses with a wavelength of 790 nm at a peak intensity of 1.0×10¹⁴ W/cm². We analyze the drastic variations in the CMDs that were observed by Kübel et al. [New J. Phys. 16, 033008 (2014)] in the transition from near-single-cycle to multicycle driving laser pulses. Our model reproduces their experimental data well. We also find that the transition from near-single-cycle to multicycle driving laser pulses depends strongly on the details of the pulse envelope. Special attention is paid to the mechanisms responsible for the cross-shaped structure observed experimentally with 4 fs pulses. Our analysis reveals that the cross-shaped structure in the carrier-envelope phase-averaged CMD for near-single-cycle pulses can be attributed to strong backward scattering of the recolliding electron as well as the narrow momentum distributions of the tunnel-ionized electrons compared to those for long pulses. This also explains why the cross-shaped distributions collapse to a rather structureless distribution when the pulse duration is increased to 8 fs.

**A strong-field approach with realistic wave functions to the above-threshold ionization of Ba+**

**54**, 025602 (2021)

**Abstract:** We study the above-threshold ionization of atoms in intense circularly polarized laser pulses. In order to compute photoelectron energy spectra, we apply the strong-field approximation with different models for the initial state wave function. Specifically, we compare the spectra for singly ionized Barium (Ba^+) using hydrogenic wave functions and realistic one-particle wave functions obtained by multiconfiguration Dirac–Hartree–Fock computations, respectively. As a particular example, we discuss the dependence of the photoelectron spectra on the magnetic quantum number m of the initial state and we reproduce the well known m-selectivity in strong-field ionization. Here, we show that the photoelectron spectra exhibit noticeable differences for the two models of the initial state and that the m-selectivity is enhanced when realistic wave functions are used. We conclude that the description of strong-field processes within the strong-field approximation will benefit from a realistic description of the initial atomic state.

## 2020

**Partial-wave representation of the strong-field approximation**

**102**, 053108 (2020)

**Abstract:** The strong-field approximation (SFA) has been widely applied to model ionization processes in short and intense laser pulses. Several approaches have been suggested in order to overcome certain limitations of the original SFA formulation with regard to the representation of the initial bound and final continuum states of the emitted electron as well as a suitable description of the driving laser pulse. We here present a reformulation of the SFA in terms of partial waves and spherical tensor operators that supports a quite simple implementation and the comparison of different treatments of the active (photo)electron and the laser pulses. In particular, this reformulation helps to adapt the SFA to experimental setups, and it paves the way to extend the strong-field theory toward the study of nondipole contributions in light-atom interactions as well as of many-particle correlations in strong-field ionization processes. A series of detailed computations have been carried out in order to confirm the validity of the reformulation and to show how the representation of the bound and continuum states affects the predicted above-threshold ionization spectra and related observables.

**Polarization-dependent high-intensity Kapitza-Dirac effect in strong laser fields**

**101**, 031401 (2020)

**Abstract:** We study the deflection of photoelectrons in intense elliptically polarized standing light waves, known as the high-intensity Kapitza-Dirac effect. In order to compute the longitudinal momentum transfer to the photoelectron in above-threshold ionization, we utilize a complete description of the quantum dynamics in the spatially dependent field of the standing light wave. We propose experimental conditions under which low-energy photoelectrons can be generated with remarkably high longitudinal momenta that can be controlled via the polarization of the standing wave. We expect that future experimental realizations will provide additional insights into the momentum transfer in intense laser-atom interactions.

**Above-threshold ionization driven by spatially structured laser fields**

Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät (2020)

**Abstract:** Strong laser fields are a valuable tool to study the electron dynamics in atoms and molecules. A prominent strong-field process is the above-threshold ionization (ATI), where the momentum distributions of emitted photoelectrons encode not only details about the laser-atom interaction, but also properties of the driving laser field. Recent advances in the generation of intense laser beams at mid-infrared wavelengths enable the investigation of ATI in a new parameter range. Moreover, laser beams with a sophisticated spatial structure as a result of an orbital angular momentum (twisted light) have found applications in the strong-field regime. In this dissertation, we theoretically investigate ATI driven by mid-infrared and twisted light beams. We show that not only the temporal but also the spatial dependence of such beams has a pronounced impact on the ionization dynamics due to nondipole interactions. Therefore, we develop a quite general theoretical approach to ATI that incorporates this spatial structure: in order to extend the widely used strong-field approximation (SFA), we construct nondipole Volkov states which describe the photoelectron continuum dressed by the laser field. The resulting nondipole SFA allows the treatment of ATI and other strong-field processes driven by spatially structured laser fields and is not restricted to plane-wave beams. We apply this nondipole SFA to the ATI driven by mid-infrared plane-wave laser beams and show that peak shifts in the photoelectron momentum distributions can be computed in good agreement with experiments. As a second application, we consider the ATI driven by standing light waves, known as high-intensity Kapitza-Dirac effect. Here, we calculate the momentum transfer to photoelectrons for elliptically polarized standing waves and demonstrate that low- and high-energy photoelectrons exhibit markedly different angular distributions, which were not observed previously. Finally, we investigate the ATI of localized atomic targets driven by intense few-cycle Bessel pulses. Based on a local dipole approximation, we demonstrate that the photoelectrons can also be emitted along the propagation direction of the pulse owing to longitudinal electric field components. Moreover, when measured in propagation direction, the ATI spectra depend on both the opening angle and the orbital angular momentum of the Bessel pulse. To conclude, we also discuss the extension of this work towards long pulses, which can be treated within the above nondipole SFA.

## 2019

**High harmonic generation with Laguerre-Gaussian beams**

**21**, 094001 (2019)

**Abstract:** We summarize the development of high harmonic generation (HHG) with linearly polarized Laguerre–Gaussian (LG) beams and their superpositions to explain the non-perturbative aspects of HHG. Furthermore, we show that circularly polarized extreme ultraviolet vortices with well-defined orbital angular momentum (OAM) can be generated by HHG with bicircular LG beams. We introduce photon diagrams in order to explain how to calculate the OAM and the polarization of the generated harmonics by means of simultaneous conservation of spin angular momentum and OAM. Moreover, we show how the intensity ratio of the driving fields in HHG with bicircular LG beams further enhances the generation of circularly polarized twisted attosecond pulse trains.

**Coherence control in high-order harmonic generation with Laguerre-Gaussian beams**

**100**, 013422 (2019)

**Abstract:** We investigate phase matching for high-order harmonic generation with linearly polarized Laguerre-Gaussian (LG) beams with nonzero orbital angular momentum (OAM). We compare the conditions for efficient phase matching for LG beams with those of Gaussian beams. In particular, we show how the OAM of the incident beams affects the phase-matching conditions for the short and long trajectories that arise from the saddle-point approximation of the dipole moment. Thereby we illustrate that the coherence length for the short trajectories decreases for LG beams near the focus compared to Gaussian beams, whereas efficient phase matching can be achieved before and behind the focus. Furthermore, we demonstrate that the coherence length for the long trajectory behind the focus plane can be controlled by the OAM. This paper provides a route for the experiment in order to have good coherence control to enhance the conversion efficiency for high-order harmonic generation with beams carrying OAM.

**Nondipole strong-field approximation for spatially structured laser fields**

**99**, 053404 (2019)

**Abstract:** The strong-field approximation (SFA) is widely used to theoretically describe the ionization of atoms and molecules in intense laser fields. We here propose an extension of the SFA to incorporate nondipole contributions in the interaction between the photoelectron and the driving laser field. To this end, we derive Volkov-type continuum wave functions of an electron propagating in a laser field of arbitrary spatial dependence. Based on previous work by L. Rosenberg and F. Zhou [Phys. Rev. A 47, 2146 (1993)], we show how to construct such Volkov-type solutions to the Schrödinger equation for an electron in a vector potential that can be written as an integral superposition of plane waves. These solutions are therefore not restricted to plane waves but are also appropriate to deal with more complex laser fields like twisted Bessel or Laguerre-Gaussian beams, where the magnetic field plays an important role. As an example, we compute photoelectron spectra in the above-threshold ionization of atoms with a single-mode plane-wave laser field of midinfrared wavelength. Especially, we demonstrate how peak offsets in the p_z direction can be extracted that result from the nondipole nature of the interaction. Here, we find good agreement with previous theoretical and experimental studies for circular polarization and discuss differences for linear polarization.

**Dichroism in two-color above-threshold ionization with twisted XUV beams and intense infrared laser fields**

**99**, 023403 (2019)

**Abstract:** We theoretically investigate the two-color above-threshold ionization of atoms and ions by twisted XUV Bessel and Laguerre-Gaussian (LG) beams in the presence of a strong circularly polarized near-infrared (NIR) laser field. The presence of the NIR field modifies the continuum states accessible to the photoelectron. Based on the strong-field approximation, we explore the resulting energy and angular distributions of photoelectron as a function of the beam parameters. In particular, we analyze dichroism signals that arise due to the twisted nature of the XUV beam and the helicity of the NIR field. We focus on the comparison between LG beams and Bessel beams in the paraxial approximation. Here, we find that both beams yield similar results when the paraxial regime is valid. For localized targets, the dichroism signals strongly depend on the size and position of the atoms relative to the beam axis. Moreover, the dichroism signal tends to zero when the XUV LG beam is linear polarized. Detailed computations of the dichroism are performed and discussed for the 4s valence-shell photoionization of Ca⁺ ions.

**Strong-Field Ionization with Few-Cycle Bessel Pulses: Interplay Between Orbital Angular Momentum and Carrier Envelope Phase**

**Abstract:** We study strong-field ionization of a hydrogenic target by few-cycle Bessel pulses. In order to investigate the interplay between the carrier envelope phase (CEP) and the orbital angular momentum of a few-cycle pulse (OAM), we apply a semiclassical two-step model. In particular, we here compute and discuss photoelectron momentum distributions (PEMD) for localized atomic targets. We show how these momentum distributions are affected by the CEP and TAM of the incident pulse. In particular, we find that the OAM affects the PEMD in a similar way as the CEP, depending on the initial position of our target.

## 2018

**Above-threshold ionization by few-cycle Bessel pulses carrying orbital angular momentum**

**98**, 023407 (2018)

**Abstract:** We investigate theoretically the above-threshold ionization (ATI) of localized atomic targets by intense few-cycle Bessel pulses that carry orbital angular momentum (OAM), known also as twisted light. More specifically, we use the strong-field approximation (SFA) to compute the photoelectron energy spectra. While for plane-wave laser pulses the outgoing photoelectron is typically described by Volkov states within the SFA, no equivalent is known for an electron in a twisted laser field. Here, we therefore introduce a local dipole approximation for the (continuum) state of the photoelectron that is justified for few-cycle pulses. Based on this approximation, we demonstrate that the photoelectrons can also be emitted into the propagation direction of the pulse. When measured in propagation direction, moreover, we show that the magnitude of the ATI peaks depend on the opening angle and the (projection of) total angular momentum of the Bessel pulse.