High-order Above-threshold Ionization Research Articles

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

Modified saddle-point method applied to high-order above-threshold ionization and high-order harmonic generation: Slater-type versus asymptotic ground-state wave function

Impact of the continuum Coulomb interaction in quantum-orbit-based treatments of high-order above-threshold ionization

Impact of the continuum Coulomb interaction in quantum-orbit-based treatments of high-order above-threshold ionization

Elliptic Dichroism in the Above-Threshold Ionization of Molecules Induced by a Strong Laser Field.

Using a strong-field-approximation theory, we investigate the high-order above-threshold ionization of diatomic molecules exposed to the monochromatic and bichromatic elliptically polarized fields. We devote particular attention to the difference between the photoelectron momentum distributions obtained with fields with opposite helicity. This difference is quantified using the elliptic-dichroism parameter, which represents the normalized difference between the differential ionization rates calculated with driving fields with opposite helicity. We find that this parameter strongly depends on the molecular orientation with respect to the laser field. In addition, this dependence is different for molecules with different types of highest-occupied molecular orbital. In other words, we show that the molecular structure is imprinted onto the elliptic-dichroism parameter for both monochromatic and bichromatic driving fields. This is explained by analyzing the interferences between various partial contributions to the differential ionization rate. In this way, elliptic dichroism also serves as a tool to analyze the electron dynamics. Finally, for heteronuclear diatomic molecules, we show that the elliptic dichroism is different from zero even for the direct electrons, i.e., the electrons that after liberation go directly to the detector. In this case, the dependence on the molecular orientation is far more pronounced for a bichromatic driving field.

High-Order Above-Threshold Ionization Using a Bi-Elliptic Orthogonal Two-Color Laser Field with Optimal Field Parameters

In the present paper, we study the high-order above-threshold ionization of noble-gas atoms using a bi-elliptic orthogonal two-color (BEOTC) field. We give an overview of the SFA theory and calculate the differential ionization rate for various values of the laser field parameters. We show that the ionization rate strongly depends on the ellipticity and the relative phase between two field components. Using numerical optimization, we find the values of ellipticity and relative phase that maximize the ionization rate at energies close to the cutoff energy. To explain the obtained results, we present, to the best of our knowledge, for the first time the quantum-orbit analysis in the BEOTC field. We find and classify the saddle-point (SP) solutions and study their contributions to the total ionization rate. We analyze quantum orbits and corresponding velocities to explain the contribution of relevant SP solutions.

High-order above-threshold ionization in elliptically polarized laser fields: Identifying the recollision time

We simulate the two-dimensional high-energy photoelectron momentum distributions (PMDs) for high-order above threshold ionization (HATI) of hydrogen atoms in intense elliptically polarized laser fields by using the strong-field approximation and solving the time-dependent Schr\"odinger equation. It is found that the centers of the left- and right-side circular rescattered ridges in the PMDs due to elastic collision of the returning electron with the parent ion, that locate on the polarization axis for linearly polarized laser field, move slightly below and above the major polarization axis, respectively, for elliptically polarized laser fields. We suggest that, by analyzing the center shift of the measured PMDs for HATI in elliptically polarized fields, one can identify the recollision time.

Spectral phase effects in above threshold ionization

We present theoretical studies of above threshold ionization (ATI) using sculpted laser pulses. The time-dependent Schrödinger equation is solved to calculate the ATI energy and momentum spectra, and a qualitative understanding of the electron motion after ionization is explored using the simple man’s model and a classical model that solves Newton’s equation of motion. Results are presented for Gaussian and Airy laser pulses with identical power spectra, but differing spectral phases. The simulations show that the third order spectral phase of the Airy pulse, which can alter the temporal envelope of the electric field, causes changes to the timing of ionization and the dynamics of the rescattering process. Specifically, the use of Airy pulses in the ATI process results in a shift of the Keldysh plateau cutoff to lower energy due to a decreased pondermotive energy of the electron in the laser field, and the side lobes of the Airy laser pulse change the number and timing of rescattering events. This translates into changes to the high-order ATI plateau and intra- and intercycle interference features. Our results also show that laser pulses with identical carrier envelope phases and nearly identical envelopes yield different photoelectron momentum distributions, which are a direct result of the pulse’s spectral phase.

Control of Electron Wave Packets Close to the Continuum Threshold Using Near-Single-Cycle THz Waveforms.

The control of low-energy electrons by carrier-envelope-phase-stable near-single-cycle THz pulses is demonstrated. A femtosecond laser pulse is used to create a temporally localized wave packet through multiphoton absorption at a well defined phase of a synchronized THz field. By recording the photoelectron momentum distributions as a function of the time delay, we observe signatures of various regimes of dynamics, ranging from recollision-free acceleration to coherent electron-ion scattering induced by the THz field. The measurements are confirmed by three-dimensional time-dependent Schrödinger equation simulations. A classical trajectory model allows us to identify scattering phenomena analogous to strong-field photoelectron holography and high-order above-threshold ionization.

High-order above-threshold ionization from a coherent superposition of states

Quantum theory of high-order above-threshold ionization (HATI) of atoms, prepared in a coherent superposition of bound states, by a strong laser field is formulated. Numerical results are obtained using the solutions of the time-dependent Schr\"odinger equation and the improved strong-field approximation. As an example, coherent superposition of the excited $2s$ and $2p$ states of the He atom is used. Applying a two-level model, it is shown how the relative amplitude and phase of the states in this coherent superposition can be controlled with a weak resonant laser pulse. Numerical results presented for HATI by a strong nonresonant probe laser pulse confirm that the photoelectron spectra and the momentum distributions strongly depend on the relative phase of the states in the prepared coherent superposition. For the case of HATI by a strong resonant laser pulse, we modify our strong-field-approximation theory by applying the two-level model to describe the time evolution of the atomic bound state before the instant of ionization. Contrary to the HATI from a single state by a long laser pulse, the corresponding photoelectron spectra of HATI from the coherent superposition of states depend on the carrier-envelope phase of the resonant ionizing pulse. Therefore, the strong-field ionization from a coherent superposition of states by a resonant laser pulse can be used to determine the carrier-envelope phase for long pulses for which the standard methods such as stereo--above-threshold ionization technique fail. The results strongly depend on the relative amplitude and phase of states in the coherent superposition of states, which can be controlled with a weak resonant laser pulse.

Nondipole effects and photoelectron momentum shifts in strong-field ionization by infrared light

High-order above-threshold ionization is studied theoretically beyond the electric dipole approximation. A hydrogen atom is assumed exposed to an ultrashort linearly polarized laser pulse with a central wavelength of 800 nm. The photoelectron momentum distribution from the corresponding nondipole multiphoton ionization process is calculated by means of numerical simulations with the time-dependent Schr\"odinger equation. In agreement with recent experiments as well as previous theoretical predictions, a forward-backward asymmetry with respect to the light propagation direction is revealed in the resulting momentum spectrum. Investigating separately the role of the linear and quadratic laser-matter interaction terms, i.e., the terms in the system Hamiltonian that are linear and quadratic in the laser's vector potential $\mathbit{A}$, respectively, it is found that the linear term introduces a shift of the electron momentum distribution in the laser propagation (forward) direction whereas the quadratic term is responsible for a corresponding backward shift. Nevertheless, only their net effect is observed in the final spectrum, and the quadratic contribution is shown to be responsible for the experimentally observed backward shift of the distribution for small electron momenta. Furthermore, for higher electron momenta it is found that the linear term takes over as the leading source of beyond-dipole ionization, effectively shifting the distribution in the forward direction.

High-order above-threshold ionization by a few-cycle laser pulse in the presence of a terahertz pulse

In our recent letter [D. B. Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, Opt. Lett. 47, 1669 (2022)] we proposed to apply a terahertz pulse to modify the ionization process induced by a strong midinfrared laser pulse. If the vector potentials of the laser and THz fields are comparable, the yield and the maximum energy of the photoelectrons emitted in the strong-field ionization process can be significantly increased. The time delay $\mathrm{\ensuremath{\Delta}}t$ between the THz pulse and the laser pulse is used as a control parameter. In the present work we further analyze this process, with particular emphasis on high-order above-threshold ionization (HATI). Using our improved strong-field approximation we calculate the ionization amplitude by numerical integration over the electron's ionization and travel times. We apply the quantum-orbit theory and the modified saddle-point method to provide a physical explanation. In addition to the previously considered ionization of Cs atoms by a 3100-nm midinfrared laser, we now show that qualitatively similar results can be obtained for HATI of Ar atoms by a much stronger 800-nm laser pulse. Furthermore, for HATI of Ar by a 3100-nm laser, assisted by a THz pulse of a few-MV/cm strength, we show that the photoelectron energy can be in the keV region.

Negative-travel-time quantum orbits in strong-field ionization by an elliptically polarized laser field

A long-standing problem in quantum-orbit theory has been exactly which solutions of the saddle-point equations to include in the decomposition of the ionization or harmonic-generation amplitude. Up to now, solutions corresponding to a negative travel time have always been discarded. For the case of an elliptically polarized driving laser field, we show that certain solutions with a negative travel time are relevant and have to be included, in addition to the customary orbits with positive travel times, in order to achieve good agreement with the result of a numerical evaluation. In fact, these solutions are responsible for a pronounced qualitative effect in the high-order above-threshold ionization amplitude: a feature with the shape of a coffee bean split along the direction of the major polarization axis, which dominates the velocity map especially for long wavelength. We also discuss the electron trajectories in complex space and time that correspond to these orbits.

Wigner analysis of electron correlation in high-order above-threshold ionization

We theoretically investigate the electron correlation effect on high-order above-threshold ionization (HATI) of the helium atom, by numerically solving the time-dependent Schr\"odinger equation. Our simulations show that, due to the electron correlation effect, the HATI amplitude shows a significant enhancement, and moreover, such an enhancement becomes weak for the long laser wavelength or high laser intensity. In terms of a Wigner analysis, we reveal that the HATI enhancement is caused by the Coulomb exclusion between the two electrons during the rescattering. With the increase of laser wavelength or intensity, the return energy of the rescattered electron increases, and accordingly, the Coulomb exclusion effect decreases relatively, leading to that the HATI enhancement becomes weak. Our work provides a deep insight into the two-electron correlated dynamics during the strong-field ionization.

Magnetic-Field Effect in High-Order Above-Threshold Ionization.

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Rydberg state excitation of atoms and molecules in ultrafast intense laser field

When atoms or molecules are irradiated by a strong laser field with pulse duration of tens of femtoseconds and intensity larger than 10<sup>13</sup> W/cm<sup>2</sup>, they will generally undergo tunneling ionization, which will induce various non-perturbative and highly nonlinear phenomena. Investigations into the strong field physical processes is of significance in studying attosecond physics, molecular orbital imaging, ultrafast electron diffraction and advanced short ultraviolet light sources. While there is a relatively long history of the studies of tunneling ionization induced physics including high-order above threshold ionization (HATI), high-order harmonic generation (HHG) and non-sequential double ionization (NSDI), it is until recently to surprisedly find that in the tunneling ionization region, neutral atoms or molecules can survive in strong laser fields in highly excited Rydberg states. As a basic process of the interaction between ultrafast strong laser fields and atoms or molecules, such a Rydberg state excitation (RSE) has been viewed as an important supplement to the physical picture of the tunneling ionization. During the past several years, the extensive research attention has been paid to the RSE process in strong laser field. Various theoretical and experimental methods have been developed to investigate the strong field RSE of both atoms and molecules, to understand the underlying physical mechanism behind the recapture of the tunneling electrons and to reveal the quantum features and molecular structure effect in RSE. These advances have brought about an in-depth understanding and a systematic view of the atomic and molecular RSE in strong laser fields, as well as their relations to the other tunneling ionization induced physical processes such as ATI, HHG and NSDI. Here, we systematically review recent research progress of the atomic and molecular RSE in strong laser fields. We particularly focus on several aspects of this strong field process, i.e. the physical mechanism of the recapture, the quantum feature and the interference of different orbits, and the structure effect in molecular RSE. In addition, neutral particle acceleration and coherent radiation which can be induced by the strong field RSE, are also discussed. Finally, we provide a short summary and prospect of the future studies on the strong field RSE.

Enhancement of Above Threshold Ionization in Resonantly Excited Helium Nanodroplets.

Clusters and nanodroplets hold the promise of enhancing high-order nonlinear optical effects due to their high local density. However, only moderate enhancement has been demonstrated to date. Here, we report the observation of energetic electrons generated by above-threshold ionization (ATI) of helium (He) nanodroplets which are resonantly excited by ultrashort extreme ultraviolet (XUV) free-electron laser pulses and subsequently ionized by near-infrared (NIR) or near-ultraviolet (UV) pulses. The electron emission due to high-order ATI is enhanced by several orders of magnitude compared with He atoms. The crucial dependence of the ATI intensities with the number of excitations in the droplets suggests a local collective enhancement effect.

Classical backpropagation for probing the backward rescattering time of a tunnel-ionized electron in an intense laser field

We present a method to estimate the backward rescattering time of a tunnel-ionized electron in an intense laser pulse. The idea of the classical backpropagation method is applied to determine the backward rescattering time and its dependence on various parameters such as the ionization potential of the parent ion, its spatial profile and the peak intensity and wavelength of the driving laser field. The accurate estimation of the rescattering time would provide critical information in analyzing ultrafast rescattering dynamics in applications such as high-order harmonic generation, above-threshold ionization, and laser-induced electron diffraction experiments. We find that the backward rescattering time is significantly affected by the peak intensity of the laser pulse. The rescattering time changes by a few hundred attoseconds when the peak intensity varies from $1\ifmmode\times\else\texttimes\fi{}{10}^{14}$ to $5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$.

Carrier-envelope phase dependence of high-order above-threshold ionization by few-cycle laser pulses

With a stereo above-threshold ionization (ATI) apparatus, we systematically investigate the carrier-envelope phase (CEP) dependence of the photoelectron kinetic energy spectra from high-order ATI of Xe atom subject to a strong few-cycle laser field. Our measurements reveal a prominent step structure and a maximum in the photoelectron kinetic energy dependence of the yield asymmetry. The observed structures can be well reproduced by the numerical solution of time-dependent Schrödinger equation (TDSE) and the improved strong field approximation (ISFA) theory. According to our analysis, the step structure can be ascribed to the interference of long and short orbits, while the maximum is closely related to the distinct kinetic energy distributions of photoelectrons which elastically scatter on the core at odd and even returns. Our work provides a more comprehensive understanding of the CEP effects on high energy photoelectron emissions in a few-cycle laser field.

Strong-field ionization of heteronuclear diatomic molecules using an orthogonally polarized two-color laser field

We apply the improved molecular strong-field approximation to investigate high-order above-threshold ionization (HATI) of heteronuclear diatomic molecules by an orthogonally polarized two-color (OTC) laser field. The OTC field consists of two linearly polarized components with frequencies $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$, where $r$ and $s$ are integers, and $\ensuremath{\omega}$ is the fundamental frequency. The molecule is aligned in the OTC laser field polarization plane. We show that the photoelectron momentum distribution obeys one reflection symmetry which is valid for arbitrary values of the relative phase between the OTC field components in the case when $r+s$ is odd. For molecules oriented along the polarization axis ${z}_{L}$ of the $r\ensuremath{\omega}$ component (${\ensuremath{\theta}}_{L}={0}^{\ensuremath{\circ}}$) and $r$ even and $s$ odd, the HATI spectrum exhibits the reflection symmetry with respect to the ${z}_{L}$ axis. When the molecular orientation is along the ${x}_{L}$ axis, which is perpendicular to the polarization axis of the $r\ensuremath{\omega}$ component (${\ensuremath{\theta}}_{L}={90}^{\ensuremath{\circ}}$), the spectrum exhibits the reflection symmetry with respect to the ${x}_{L}$ axis for $r$ odd and $s$ even. In addition, we analyze the asymmetry in the photoelectron spectra of heteronuclear molecules by comparing them with the photoelectron spectra obtained ionizing a homonuclear diatomic molecule. We also explore the influence of the shift of the relative phase by ${180}^{\ensuremath{\circ}}$ on the HATI spectra. We explain some characteristics of the obtained HATI spectra using a generalization of the classical two-dimensional simple man's model which includes ionization probabilities calculated using the imaginary-time method. Finally, we analyze the interference minima for different heteronuclear diatomic molecules and for particular values of the emission angle, laser-field parameters, and internuclear distance. These minima are well fitted with the curve obtained using the derived condition for the two-center destructive interference minima.

Laser-induced processes with homonuclear diatomic molecules in orthogonally polarized two-color laser field

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.

Strong-field ionization of homonuclear diatomic molecules using orthogonally polarized two-color laser fields

Using the improved molecular strong-field approximation we investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by an orthogonally polarized two-color (OTC) laser field. The OTC field components are linearly polarized, having the relative phase $\ensuremath{\varphi}$ and frequencies $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$ ($r$ and $s$ are integers and $\ensuremath{\omega}$ is the fundamental frequency). The molecule is aligned in the laser-field polarization plane. We have found that for even values of $r+s$ the HATI spectra obey the ${C}_{2}$ rotational symmetry regardless of the relative phase, component intensities, and molecular orientation, while the spectra calculated for odd values of $r+s$ and for certain molecular orientations exhibit the reflection symmetry. We have also explored the symmetry transformations of the HATI spectra for a shift of the relative phase by ${180}^{\ensuremath{\circ}}$ and for various values of $r$ and $s$. These symmetries are illustrated by numerical examples of the HATI spectra of the ${\mathrm{N}}_{2}$ molecule. For particular values of the laser-field parameters, internuclear distance, and the electron emission angle we observed minima in the ionization yield as a function of the molecular orientation angle and the photoelectron energy. These minima are well fitted with the curve obtained using a condition for the destructive interference minima which we derived for an arbitrary laser field and applied to the OTC field. The relative phase between the OTC field components can be used to control the length and shape of the HATI plateau, as well as the appearance of these destructive interference minima.