Above-threshold Ionization Spectra Research Articles

Polarization control of above-threshold ionization spectrum in elliptically polarized two-color laser fields

We study the above-threshold ionization (ATI) process of atoms exposed to fundamental and high-frequency lasers with arbitrary ellipticity by applying the frequency-domain theory. It is found that the angular-resolved ATI spectrum is sensitive to ellipticities of two lasers and emitted angles of the photoelectron. Particularly for the photon energy of the high-frequency laser more than atomic ionization potential, the width of plateau tends to a constant with increasing ellipticity of fundamental field, the dip structure disappears with increasing ellipticity of the high-frequency field. With the help of the quantum channel analysis, it is shown that the angular distribution depends mainly on the ellipticity of high-frequency field in the case that its frequency is high. Moreover, one can see that the maximal and minimal energies in quantum numerical results are in good agreement with the classical prediction. Our investigation may provide theoretical support for experimental research on polarization control of ionization in elliptically polarized two-color laser fields.

Strong-field ionization and AC-Stark shifted Rydberg states in OCS

We present theoretical results for intensity-dependent above-threshold ionization (ATI) spectra from oriented OCS molecules probed by intense femtosecond laser pulses with wavelengths of 800 and 400 nm. The calculations were performed using the time-dependent Schrödinger equation within the single-active-electron approximation and including multielectron polarization effects. The results capture some of the experimental findings (Yu et al 2017 J. Phys. B: At. Mol. Opt. Phys. 50 235602), in particular when considering the sensitivity of the ATI spectra on the molecular orientation. We identify characteristic features in the ATI spectra which correspond to resonant multiphoton ionization via highly-excited Rydberg states are captured by the theory.

Investigation of the middle-energy region of the above-threshold ionization spectrum in a few-cycle laser field

We use the improved strong-field approximation (ISFA) theory to investigate the evolution of the energy spectra with the carrier-envelope phase (CEP) of a few-cycle laser pulse. The theoretical calculations are consistent with the experimental measurements performed by Lindner et al (2005 Phys. Rev. Lett. 95 040401) which can be attributed to the scattering electrons whose ionization rates are modulated by the CEP of the laser pulse. We further investigate the dynamic behavior of the relevant scattering electrons by a Wigner distribution-like function based on the ISFA. Our analysis indicates that the zeroth-return forward-scattering electrons that move directly to the parent ion after tunneling and scatter forward with the parent core play a key role in the energy range of 2U p ∼ 4U p and the backward-scattering electrons are responsible for the high-energy region. Meanwhile, it is found that the contribution of the second-return backward-scattering electron to the middle energy spectrum is also important in the few-cycle laser field case.

Multielectron effect in the strong-field ionization of aligned nonpolar molecules

We revisit strong-field ionization of aligned ${\mathrm{O}}_{2}, {\mathrm{CO}}_{2}$, and ${\mathrm{CS}}_{2}$ molecules in light of recent advances in the field of strong-field physics, in particular the inclusion of multielectron polarization in the numerical solution of the time-dependent Schr\"odinger equation (TDSE) within the singe-active-electron approximation. Multielectron polarization is modeled by the introduction of a long-range induced dipole term based on the polarizability of the cation, and a field at short distances that counteracts the applied external field and leads to a vanishing time-dependent interaction within a certain cutoff radius. For the probed molecules, the main effect of including multielectron polarization is the reduction of the total ionization yields (TIYs), and for molecules with large polarizability of their cation (${\mathrm{CO}}_{2}$ and ${\mathrm{CS}}_{2}$), the alignment angle of maximum TIY will shift. The photoelectron momentum distributions and above-threshold ionization spectra show little imprint of the multielectron polarization associated with the long-range part of the laser-induced dipole potential. For ${\mathrm{CO}}_{2}$ and ${\mathrm{CS}}_{2}$, the inclusion of multielectron polarization and the associated induced dipole potential in the TDSE model gives alignment-resolved distributions of total ionization yields which are in better agreement with the available experimental results.

Photoelectron spectra of argon in circularly polarized pulses studied by atom-Volkov strong-field approximation

We studied the above-threshold ionization (ATI) spectra of argon in circularly polarized pulse by the atom-Volkov strong-field approximation (SFA). A dip appears in the spectra due to the presence of a zero in the dipole matrix element, corresponding to a transition from the ground state to the L = 2 continuum at electron kinetic energy ∼30.6 eV. No such dip appears when the time-dependent Schrödinger equation (TDSE) is used instead, because the transition amplitude in SFA is the first-order term in the S-matrix series while TDSE contains all orders. In contrast, the effect of Cooper minimum shows up in high-order harmonic generations, which is an inverse process of photoionization where the recombination transition is first-order. We examine several sets of pulse parameters and found that when the SFA validity conditions are satisfied, the atom-Volkov SFA generates better ATI spectra than the simple SFA.

Effect of two-cutoff structure in laser-induced recollision dynamics

We theoretically identify a two-cutoff structure in the recollision energy distribution of the third-return recollision trajectories whose contribution is dominant in the high-energy part of the above-threshold ionization (ATI) spectrum. The additional second cutoff in the recollision energy distribution, resulted from the acceleration of Coulomb field to specific recollision trajectories, induces an extension of the Two-dimensional (2D) photoelectron momentum spectrum and will affect the differential cross-sections (DCS) extracted in laser-induced electron diffraction (LIED) scheme. Both the position and relative yield of the second cutoff decrease with increasing laser intensity. Therefore, the effect of the second cutoff should be taken into account when the laser intensity is not so high.

Low energy structure of above-threshold ionization spectra produced by mid-infrared laser pulses

The low-energy structure (LES) of above-threshold ionization (ATI) of atoms subjected to an intense laser field is a hot topic in the strong-field atomic physics. The rich physical insights behind LES attract a lot of attention. Based on a semi-classical model, a semi-classical two-step (SCTS) quantum trajectory model and numerical solution of the time-dependent Schrödinger equation (TDSE), we study the pulse-duration dependence of LES for Xe atom subjected to a mid-infrared laser field. It is found that the energy of LES becomes lower for shorter pulse duration. Further analysis shows that in the case of multi-cycle laser field, the LESn structure is closely related to the number of times of forward scattering and the initial transverse momentum. In the case of few-cycle laser pulse, the carrier-envelope phase (CEP) dependence of the peak position of LES is mainly due to the CEP dependence of the influence of both vector-potential of the laser field and the Coulomb potential. In addition, the bunching effect of electrons, caused by Coulomb potential, is the main reason for the formation of LES.

Polarization in strong-field ionization of excited helium

We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in helium prepared in an excited p state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using the ab initio B-spline algebraic diagrammatic construction, and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the strong-field approximation (SFA) and the Coulomb quantum-orbit strong-field approximation, we find that these specific physical mechanisms leave significant imprints in ATI spectra and photoelectron momentum distributions. Examples are changes of up to two orders of magnitude in the high-energy photoelectron region, and ramp-like structures that can be traced back to Coulomb-distorted trajectories. The present work also shows that electron exchange renders rescattering less effective, causing suppressions in the ATI plateau. Due to the long-range potential, the electron continuum dynamics are no longer confined to the polarization axis, in contrast to the predictions of traditional approaches. Thus, one may in principle probe excited-state configurations perpendicular to the driving-field polarization without the need for orthogonally polarized fields.

Modeling photoelectron spin polarization of xenon atoms in intense circularly polarized pulses

We propose a model for studying the ionization, photoelectron spectra, and spin polarization of xenon atoms under intense circularly polarized (CP) pulses by solving the time-dependent Schrödinger equation (TDSE) with an effective potential for Xe. The ionization mechanism is mainly due to multiphoton absorption in these strong CP fields. The effective potential of a single active electron for Xe consists of asymptotic Coulomb and parametric screening parts and yields low-lying levels that are comparable to those by other models for the total angular momentum J = 3 / 2 of X e + and new for J = 1 / 2 . We show in detail the absorption pathways, above-threshold ionization (ATI) spectra, and spin polarization mechanisms of photoelectrons originated from the initial state 5 p m l of Xe with the magnetic quantum number m l being − 1 , 0, or 1. There exists a substructure with sub-peaks in each of multiple ATI peaks from 5 p − 1 due to pulse effects on the valence electron passing through the absorption pathways. ATI and spin polarization results agree qualitatively with experimental data at the focal volume average to include the spatial effect of CP pulses. We also present the spin polarization results of the widely used strong-field approximation model (SFA), which are inconsistent with those of TDSE and experiments. This shows that TDSE is more accurate with more details than SFA for studying spin polarization in strong CP fields.

Strong chiral dichroism and enantiopurification in above-threshold ionization with locally chiral light

We derive here a new highly selective photoelectron-based chirality-sensing technique that utilizes 'locally-chiral' laser pulses. We show that this approach results in strong chiral discrimination, where the standard forwards/backwards asymmetry of photoelectron circular dichroism (PECD) is lifted. The resulting dichroism is much larger and more robust than conventional PECD, is found in all hemispheres, and is not symmetric or antisymmetric with respect to any symmetry operator. Remarkably, a CD of up to 10% survives in the angularly-integrated above-threshold ionization (ATI) spectra, and of up to 5% in the total ionization rates. We demonstrate these results through ab-initio calculations in the chiral molecules Bromochlorofluoromethane, Limonene, Fenchone, and Camphor. We also explore the parameter-space of the locally-chiral field and show that the observed CD is strongly correlated to the degree of chirality of the light, validating it as a measure for chiral-interaction strengths. Our results pave the way for highly selective probing of ultrafast chirality in ATI, can potentially lead to all-optical enantio-separation, and motivate the use of locally-chiral light for enhancing ultrafast spectroscopies.

Influence of polarization directions of the IR+XUV two-color laser fields on angle-resolved photoelectron energy spectrum.

By employing the frequency-domain theory, we investigate the influence of polarization directions on angle-resolved photoelectron energy spectrum in the above-threshold ionization (ATI) process of atoms exposed to the IR+XUV two-color laser fields, which shows the multiplateau structures. When the ionized electron is emitted along the IR laser's polarization direction, the width of each plateau keeps a certain energy range, and the jet structures and main lobes are determined by both the emission angle relative to the polarization direction of the XUV laser field and the number of the XUV photons absorbed by the electron. While when the ionized electron is emitted along the XUV laser's polarization direction, the width of each plateau depends on the polarization direction of the IR laser field, and the angular distribution of the ionized electron exhibits the isotropic characteristics. These results show that the ATI spectrum may be effectively controlled by changing the angle between the two laser fields' polarization directions.

High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau.

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.

Partial-wave representation of the strong-field approximation

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.

The interference fringes of above-threshold ionization spectrum of SF6 molecules in an IR + XUV laser field

The interference fringes of above-threshold ionization (ATI) spectrum from atoms or molecules have been extensively studied. In this paper, we investigate the ATI of the polyatomic molecule SF6 in IR + XUV two-color laser fields, and find that some interference fringes on the spectrum are from the molecular structure, which is independent of the parameters of the laser field. Based on the frequency-domain theory, we analyze the interference fringes for different orbitals of SF6 molecules in detail. It is found that the orbital of SF6 can be simplified by several terms in the region of high value of momentum, where the destructive interference fringes from these terms may carry the information of the molecular structure. Furthermore, we obtain destructive interference formulas from these simplified orbitals, which may predict the interference fringes on the ATI spectrum. Additionally, we may obtain the information about the bond length of molecules. It will be useful for the study of the ionization spectrum of polyatomic molecules.

Species-dependent tunneling ionization of weakly bound atoms in the short-wave infrared regime

We investigate the intensity- and species-dependent strong-field ionization of alkali metal atoms; sodium, potassium, rubidium and caesium; by intense, few-cycle laser pulses in the short-wave infrared (sw-IR) regime at 1800 nm. The low ionization potential, Ip, of these atoms allows us to scale the interaction and study the tunneling regime at sw-IR wavelengths using low intensities and pulse energies. Measurements of above-threshold ionization spectra in the alkali species exhibit distinct differences to rare gas spectra at 800 and 1800 nm. However, pairing the low ionization potential of these atoms with longer wavelengths results in the reemergence of some well-know features of nobel gas spectra in the visible, e.g., the plateau. Our focus lies on the comparison of high-energy rescattered electron yield among the different alkali species. The highly unfavorable plateau scaling known from rare gases at longer wavelengths is successfully circumvented by switching to low-Ip targets. In the investigated parameter range, we identify potassium as the most efficient rescatterer. In addition, this paves the way to a carrier-envelope phasemeter operating in the sw-IR/mid-wave IR regime, employing alkali metal atoms as a target.

Signature of molecular symmetry in the plateau region of the photoelectron spectra: Above-threshold ionization of the C2 molecule

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 , , and 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.

Observation of attosecond electron dynamics in the photoelectron momentum distribution of atoms using few-cycle laser pulses

The method of time-resolved measurement with ultrashort laser pulses is vital to the development of attosecond science. Pump-probe measurements using a train of attosecond pulses in combination with a near-infrared (NIR) multicycle driving laser have been successful in capturing the intercycle electron dynamics which repeats every optical cycle and leads to above-threshold ionization (ATI) spectra in the frequency domain. In this work, we study the effect of a carrier-envelope phase (CEP) in a few-cycle ($l6$ fs) NIR laser pulse on the photoelectron momentum distribution (PMD) of a hydrogen atom and show that interference patterns in a PMD change dramatically with CEPs in the few-cycle regime. When the few-cycle driving laser pulse has a sine shape, the double-slit interference with characteristic modulation of ATI peaks dominates the PMD. On the other hand, when the driving pulse has a cosine shape, the holographical interference featured by a spider-like pattern is isolated. Our results suggest that the CEP-stable few-cycle laser pulses can be used to identify different types of intracycle interference structures in a PMD which reveal the underlying subcycle electron dynamics on an attosecond timescale.

Effect of Coulomb field on laser-induced ultrafast imaging methods

By performing a joint theoretical and experimental investigation on the high-order above-threshold ionization (HATI) spectrum, the dominant role of the 3rd-return-recollision trajectories in the region near the cutoff due to the ionic Coulomb field is identified. This invalidates the key assumption adopted in the conventional laser-induced electron diffraction (LIED) approach that the 1st-returnrecollision trajectories dominate the spectrum according to strong field approximation (SFA). Our results show that the incident (return) electron beams produced by the 1st and 3rd returns possess distinct characteristics of beam energy, beam diameter and temporal evolution law due to the influence of Coulomb field, and therefore the extracted results in the LIED will be altered if the significance of the 3rd-return-recollision trajectories is properly considered in the analysis. Such Coulomb field effect should be taken into account in all kinds of laser-induced imaging schemes based on recollision.

Angular distribution of photoelectron momentum in above-threshold ionization by circularly polarized laser pulses

The above-threshold ionization (ATI) of argon atoms in intense circularly polarized laser fields has been investigated by numerically solving the three-dimensional time-dependent Schr\odinger equation and the classical Newton-Lorentz equation. There are obvious angular shifts of the photoelectron momentum distribution corresponding to the peaks in the ATI spectrum. They have little dependence on the external field and are mainly determined by the final kinetic energy. It is found that the angular shift is monotonically increasing as a function of the photoelectron final kinetic energy. Based on the classical simulations, the initial kinetic energy of electrons can be obtained by separating the contribution of the external field and Coulomb potential from the final kinetic energy. We conclude that the stronger the laser field, the bigger the initial velocity of electrons for a definite final kinetic energy. Then, based on the final kinetic energy and the laser parameters, the initial velocity can be evaluated.

Identifying two different configurations of the <inline-formula><tex-math id="Z-20200330064922-1">\begin{document}$ \rm H_3^{2+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330064922-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330064922-1.png"/></alternatives></inline-formula> by the direct above-threshold ionization spectrum in two-color laser field

Since imaging the geometrical structure of molecules can help to understand the microscopic world intuitively, and thereby to promote the development of physics, chemistry, material science and biological science, it has long been an important subject for scientists to probe the molecular internal structure. Generally, however, because of the relative complexity of the molecular internal structure, it is difficult to obtain the relevant information by ordinary experimental means. With the development of laser technology, especially the advent of intense ultrafast laser field, ultrafast laser pulse provides an unprecedented detection tool to investigate the related ultrafast dynamics. In recent years, strong field high-order nonlinear ultrafast processes, such as above-threshold ionization(ATI), high-order above-threshold ionization(HATI), high harmonic generation(HHG), and non-sequential double ionization (NSDI), were produced by using femtosecond ultrafast laser to excite molecules. Since the molecules excited in these processes emit the photon and electron signals pertinent to their internal structures, it is natural that one can obtain the imaging of molecular structure by extracting the signals. Recently, we have demonstrated that the structural information of SF<sub>6</sub> molecules can be obtained by the interference fringes on the ATI spectrum using the infrared and ultraviolet bichromatic laser fields[<i>arXiv</i>, 1912.08499 (2019)]. In this paper, we use frequency-domian method, which is based on non-perturbed quantum electrodynamics, to investigate the direct above-threshold ionization (ATI) process of triatomic molecular ion <inline-formula><tex-math id="Z-20200330065026-1">\begin{document}$ \rm H_3^{2+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330065026-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330065026-1.png"/></alternatives></inline-formula> with two different geometrical structures by monochromatic and bichromatic laser fields, and given the detailed analysis of the spectra for each case. Compared with the monochromatic laser field, it is found that the ATI spectrum by the bichromatic laser field is more sensitive to the geometrical configuration of molecular ion, thereby it can be applied to identify the different geometrical structure of molecules. In the case of bichromatic laser fields, the direct ATI spectrum show different interference fringes with different molecular configurations. We give the beginning and cutoff curves of each platform by employing the saddle-point approximation. Furthermore, we derive the destructive curves formulas for different molecular configurations in angle-resolved direct ATI energy spectra and momentum spectra, respectively, which carries the information about themolecular structure. In addition, it is found that the shape of the spectra can be modified by changing the molecular internuclear distance or varying the laser intensity. Thereby, it can be inferred that the ATI spectrum induced by bichromatic laser field has the ability to identify different configurations of the same molecules, which is instructive to image geometrical structure of complex molecules.