Above-threshold Ionization Spectra Research Articles

The Coulomb effect on a low-energy structure in above-threshold ionization spectra induced by mid-infrared laser pulses

We investigate the low-energy structure (LES) in the above-threshold ionization spectrum at a mid-infrared laser wavelength with a semiclassical model. Using a softened Coulomb potential (CP) and changing the softening parameter, we show that though the very low-energy structure (VLES) and high low-energy structure (HLES) are both due to the interaction between the ionic CP and the electron, the two structures have different physical mechanisms: the VLES can be attributed to the electron—ion Coulomb interaction at a rather small distance and the HLES is more likely to be ascribed to the electron—ion Coulomb interaction at a large distance.

Terracelike structure in the above-threshold-ionization spectrum of an atom in an IR+XUV two-color laser field

Based on the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in a two-color laser field with infrared (IR) and extreme ultraviolet (XUV) frequencies, where the photon energy of the XUV laser is close to or larger than the atomic ionization threshold. By using the channel analysis, we find that the two laser fields play different roles in an ionization process, where the XUV laser determines the ionization probability by the photon number that the atom absorbs from it, while the IR laser accelerates the ionized electron and hence widens the electron kinetic energy spectrum. As a result, the ATI spectrum presents a terrace-like structure. By using the saddle-point approximation, we obtain a classical formula which can predict the cutoff of each plateau in the terrace-like ATI spectrum. Furthermore, we find that the difference of the heights between two neighboring plateaus in the terrace-like structure of the ATI spectrum increases as the frequency of the XUV laser increases.

ClassSTRONG: Classical simulations of strong field processes

A set of Mathematica functions is presented to model classically two of the most important processes in strong field physics, namely high-order harmonic generation (HHG) and above-threshold ionization (ATI). Our approach is based on the numerical solution of the Newton-Lorentz equation of an electron moving on an electric field and takes advantage of the symbolic languages features and graphical power of Mathematica. Similarly as in the Strong Field Approximation (SFA), the effects of atomic potential on the motion of electron in the laser field are neglected. The SFA has proven to be an essential tool in strong field physics in the sense that it is able to predict with great precision the harmonic (in the HHG) and energy (in the ATI) limits. We have extended substantially the conventional classical simulations, where the electric field is only dependent on time, including spatial nonhomogeneous fields and spatial and temporal synthesized fields. Spatial nonhomogeneous fields appear when metal nanosystems interact with strong and short laser pulses and temporal synthesized fields are routinely generated in attosecond laboratories around the world. Temporal and spatial synthesized fields have received special attention nowadays because they would allow to exceed considerably the conventional harmonic and electron energy frontiers. Classical simulations are an invaluable tool to explore exhaustively the parameters domain at a cheap computational cost, before massive quantum mechanical calculations, absolutely indispensable for detailed analysis, are performed.

Photoionization of hydrogen atoms by coherent intense high-frequency short laser pulses: Direct propagation of electron wave packets on large spatial grids

The time-dependent Schr\"{o}dinger equation for the hydrogen atom and its interaction with coherent intense high-frequency short laser pulses is solved numerically exactly by propagating the single-electron wave packets. Thereby, the wavefunction is followed in space and time for times longer than the pulse duration. Results are explicitly shown for 3 and 10 fs pulses. Particular attention is paid to identifying the effect of dynamic interference of photoelectrons emitted with the same kinetic energy at different times during the rising and falling sides of the pulse predicted in [\emph{Ph.V. Demekhin and L.S. Cederbaum}, Phys. Rev. Lett. \textbf{108}, 253001 (2012)]. In order to be able to see the dynamic interference pattern in the computed electron spectra, the photoelectron wave packet has to be propagated over long distances. Clearly, complex absorption potentials often employed to compute spectra of emitted particles cannot be used to detect dynamic interference. For the considered high-frequency pulses of 3 and 10 fs durations, this requires enormously large spatial grids. The presently computed photoionization and above-threshold ionization spectra are found to exhibit pronounced dynamic interference patterns. Where available, the patterns are in very good agreement with previously published results on the photoionization spectra which have been computed using a completely different method, thus supporting the previously made assumption that the above-threshold ionization processes are very weak for the considered pulse intensities and high carrier frequency. The quiver motion in space and time of a free electron in strong laser pulses is also investigated numerically. Finally, a discussion is presented of how fast the atom is ionized by an intense pulse.

Effect of Electron Initial Longitudinal Velocity on Low-Energy Structure in Above-Threshold Ionization Spectra

Using a semiclassical model, we investigate the effect of the initial longitudinal velocity of the tunnel-ionized electron on low-energy structure (LES) in above-threshold ionization (ATI) spectra. Our analysis shows that the effect (reduction or enhancement) of the initial longitudinal velocity pz0 on the LES is dependent on the direction of the initial longitudinal velocity. For the initial longitudinal velocity along the direction of the laser electric field at the moment of tunneling (i.e., pz0 > 0), the Coulomb interaction between the photoelectron and ion core is enhanced, while for the initial longitudinal velocity in the opposite direction (i.e., pz0 < 0), the Coulomb effect is reduced. Our work provides solid evidence that the initial electron longitudinal velocity has considerable effect on the photoelectron dynamics in the ATI process.

Molecular above-threshold ionization with a circularly polarized laser field

Molecular above-threshold ionization by a circularly polarized laser field is investigated. Our theoretical approach is based on the modified molecular strong-field approximation. Various gauge-dependent versions of this approximation are considered and homonuclear and heteronuclear molecular species characterized by different symmetries are used as targets. As in the case of a linearly polarized field, the imprint of the molecular multicenter structure can be observed in the above-threshold ionization spectra. It manifests itself as minima in the rate of the ionized electrons as a function of their energy. The locations of these minima are strongly influenced by the symmetry of the corresponding highest occupied molecular orbital as well as the internuclear separation. Analyzing the interference structures of the electron spectra one can obtain information about the molecular symmetry.

Carrier-envelope phase effects in above-threshold ionization of atomic hydrogen

Recent experiments in ultrafast physics have established the importance of above-threshold ionization (ATI) experiments in measuring and controlling the carrier-envelope phase (CEP) of few-cycle laser pulses. We have performed an investigation of atomic hydrogen subjected to intense CEP-stable few-cycle laser pulses. The experimental ATI spectra have been compared to predictions from an ab initio numerical solution of the time-dependent Schrödinger equation in three dimensions. Good agreement between experiment and theory has been achieved without using any free fit parameters. Our results provide an important step towards obtaining calibrated reference data for a direct comparison of ATI electron yields for a range of gas species and experimental conditions.

Multiphoton above-threshold ionization in superintense free-electron x-ray laser fields: Beyond the dipole approximation

We present an accurate and efficient nondipole computational approach in momentum space for the nonperturbative study of multiphoton above-threshold ionization (ATI) of atoms in superintense and ultrashort-wavelength laser fields. This approach has been successfully used to investigate the multiphoton processes of a hydrogen atom exposed to superintense free-electron x-ray laser fields. We find that, compared to results of the dipole approximation, the nondipole ATI spectra are enhanced substantially in the high-energy regime, and the photoelectron angular distributions are distorted significantly in higher-intensity and/or longer-pulse laser fields; in particular two lobes are induced, one along and one against the laser propagation direction. The origin of these phenomena has been explored in detail.

Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases.

We demonstrate the significant role of long quantum orbits in strong-field atomic processes by investigating experimentally and theoretically the above-threshold ionization spectra of noble gases in intense elliptically polarized laser pulses. With increasing laser ellipticity, the yields of different energy regions of the measured electron spectrum in high-order above-threshold ionization drop at different rates. The experimental features can be reproduced by a theoretical simulation based on quantum-orbit theory, revealing that increasing ellipticity favors the contributions of the long quantum orbits in the high-order above-threshold ionization process.

Interaction of a model atom exposed to strong laser pulses: Role of the Coulomb potential

With the help of the solution of the time-dependent Schr\"odinger equation in momentum space, we study the above-threshold ionization spectrum resulting from the interaction of atomic hydrogen with an infrared and XUV short laser pulses. Our calculations are based on a model where the kernel of the nonlocal Coulomb potential is replaced by a finite sum of $N$ symmetric separable potentials, each of them supporting one bound state of atomic hydrogen. Here, we consider only the case of $1s$, $2s$, and $2p$ states. Thus, the theory fully accounting for the important $1s--2p$ transition, explains the photoelectron spectrum as well as the total ionization probability for the resonant case. We compared the results given by our theory with the numerical solutions of the time-dependent Schr\"odinger equation.

Low-Energy Peak Structure in Strong-Field Ionization by Mid-Infrared Laser Pulses

Using a quasiclassical approach, we demonstrate that the formation of the low-energy structure in above-threshold ionization spectra by intense, midinfrared laser pulses originates from a two-dimensional focusing of the strong-field dynamics in the energy-angular-momentum plane. We show that the low-energy structure is very sensitive to the carrier-envelope phase of the laser field.

Interaction of atomic hydrogen with a UV pulse: model based calculations of the energy transfers from the laser field into both the electron kinetic energy and the harmonics

We study both the above-threshold ionization spectrum and harmonics generation resulting from the interaction of atomic hydrogen with a UV pulse. Our calculations are based on the solution of the time-dependent Schrödinger equation in momentum space where the kernel of the non-local Coulomb potential is replaced by a sum of separable potentials, each of them supporting one bound state of atomic hydrogen. It is shown that the interaction of hydrogen with a field, the frequency of which corresponds to the 1s-2p transition, leads, quite unexpectedly, to the emission of very energetic electrons.

Exploring above-threshold ionization of hydrogen in an intense x-ray laser field through nonperturbative calculations

This paper addresses the problem of above-threshold ionization (ATI) of hydrogen interacting with a short and intense x-ray electromagnetic field. We consider the weakly relativistic regime where the speed of the photoelectron stays well below the velocity of the light $c$. We solve the time-dependent Schr\"odinger equation (TDSE) using a spectral approach with a basis of one-electron orbitals, calculated with ${L}^{2}$-integrable $B$-spline functions for the radial coordinate and bipolar spherical harmonics ${Y}_{lm}$ for the angular part. Retardation effects are included up to $O(1/c)$; they induce two extra terms leading to electric quadrupole and magnetic dipole transitions. These latter terms depend on the polarization and photon momentum directions, forcing the resolution of the TDSE in a three-dimensional space. Relativistic effects [of $O(1/{c}^{2})$] are fully neglected. Photoelectron energy and angular distributions are obtained for photon energies ranging from 200 eV to 3 keV. We study the lower energy region of the ATI spectrum and we analyze nondipole effects, through their $(l,m)$ components, in particular, for the lower two peaks. Although these effects are small, we show that, increasing the photon energy, the photoelectron angular distributions begin to differ significantly from the ones obtained in dipole approximation.

Low-energy peak structure in strong-field ionization by midinfrared laser pulses: Two-dimensional focusing by the atomic potential

We analyze the formation of the low-energy structure (LES) in above-threshold ionization spectra in strong-field ionization by midinfrared laser pulses by using both quasiclassical and quantum approaches. We show this structure to be largely classical in origin, resulting from a two-dimensional focusing in the energy--angular-momentum plane of the strong-field dynamics in the presence of the atomic potential. The latter is shown to cause the LES even in the absence of a long-range Coulomb tail. The peak at low energy is strongly correlated with high angular momenta of the photoelectrons. Quantum simulations confirm this scenario. We find the LES to be remarkably sensitive to the carrier-envelope phase of the laser field.

Dressed-bound-state molecular strong-field approximation: Application to above-threshold ionization of heteronuclear diatomic molecules

The molecular strong-field approximation (MSFA), which includes dressing of the molecular bound state, is introduced and applied to above-threshold ionization of heteronuclear diatomic molecules. Expressions for the laser-induced molecular dipole and polarizability as functions of the laser parameters (intensity and frequency) and molecular parameters [molecular orientation, dipole, and parallel and perpendicular polarizabilities of the highest occupied molecular orbital (HOMO)] are presented. Our previous MSFA theory, which incorporates the rescattering effects, is generalized from homonuclear to heteronuclear diatomic molecules. Angle- and energy-resolved high-order above-threshold ionization spectra of oriented heteronuclear diatomic molecules, exemplified by the carbon monoxide (CO) molecule, exhibit pronounced minima, which can be related to the shape of their HOMO-electron-density distribution. For the CO molecule we have found an analytical condition for the positions of these minima. We have also shown that the effect of the dressing of the HOMO is twofold: (i) the laser-induced Stark shift decreases the ionization yield and (ii) the laser-induced time-dependent dipole and polarizability change the oscillatory structure of the spectra.

Multielectron effects and nonadiabatic electronic dynamics in above threshold ionization and high-harmonic generation

We explore the effects of multiple participating final ion states during strong field ionization (SFI) and high-harmonic generation (HHG) using a two-electron two-center reduced-dimensionality model. In particular, we propose to use above threshold ionization (ATI) photoelectron spectra to identify ionic states that are active in SFI, and demonstrate the feasibility of our proposal to track multiple ionic states in a dissociation scenario. In addition to offering clear signatures of multiple participating ionic states, our method is shown to be sensitive to sub-cycle nonadiabatic laser-driven couplings between the ionic states. Finally, we calculate the high-harmonic emission and show how the multiple ionic states identified in the ATI spectra can manifest themselves in the high-harmonic spectra.

Angle-dependent molecular above-threshold ionization with ultrashort intense linearly and circularly polarized laser pulses

We present molecular above-threshold ionization (MATI) spectra generated by ultrashort intense linearly and circularly polarized laser pulses from nonperturbative numerical solutions of the corresponding time-dependent Schr\"odinger equation in the molecular-ion ${{\mathrm{H}}_{2}}^{+}$. It is found that high-order MATI spectra with maximum kinetic energy $32{U}_{p}$, where ${U}_{p}={I}_{0}/4{m}_{e}{\ensuremath{\omega}}_{0}^{2}$ is the ponderomotive energy at intensity ${I}_{0}$ and frequency ${\ensuremath{\omega}}_{0}$, can be obtained in ${{\mathrm{H}}_{2}}^{+}$ at great internuclear distances $R$ for both linear and circular polarizations. Quasiclassical laser-induced collision models confirm that such high-order MATIs mainly result from a collision with neighboring ions of the ionized electron. Interference patterns in the high-order MATI spectra are critically sensitive to both the internuclear distance $R$ of the molecules and the polarizations of the driving laser pulses. Moreover, with few-cycle laser pulses, the carrier-envelope phase sensitivity of MATI angular distributions is also investigated for varying internuclear distances $R$. At critical internuclear distances for charge-resonance-enhanced ionization, we also find that enhanced interference patterns occur.

Time analysis of above-threshold ionization in extreme-ultraviolet laser pulses

The strong field ionization dynamics of an atom in a strong extreme-ultraviolet radiation field is investigated using numerical solutions of the time-dependent Schr\odinger equation. The analysis of the electron quantum distribution in phase space after the interaction provides detailed information on the ionization time evolution. It evidences the interrelation among the periodic slow drift of the bound electron wave packet in the highly oscillating field, the modulation of the ionization wave packet, and the previously unknown fine structure of above-threshold ionization spectra in the stabilization regime.

Precision calculation of above-threshold multiphoton ionization in intense short-wavelength laser fields: The momentum-space approach and time-dependent generalized pseudospectral method

We present an approach in momentum ($\mathcal{P}$) space for the accurate study of multiphoton and above-threshold ionization (ATI) dynamics of atomic systems driven by intense laser fields. In this approach, the electron wave function is calculated by solving the $\mathcal{P}$-space time-dependent Schr\odinger equation (TDSE) in a finite $\mathcal{P}$-space volume under a simple zero asymptotic boundary condition. The $\mathcal{P}$-space TDSE is propagated accurately and efficiently by means of the time-dependent generalized pseudospectral method with optimal momentum grid discretization and a split-operator time propagator in the energy representation. The differential ionization probabilities are calculated directly from the continuum-state wave function obtained by projecting the total electron wave function onto the continuum-state subspace using the projection operator constructed by the continuum eigenfunctions of the unperturbed Hamiltonian. As a case study, we apply this approach to the nonperturbative study of the multiphoton and ATI dynamics of a hydrogen atom exposed to intense short-wavelength laser fields. High-resolution photoelectron energy-angular distribution and ATI spectra have been obtained. We find that with the increase of the laser intensity, the photoelectron energy-angular distribution changes from circular to dumbbell shaped and is squeezed along the laser field direction. We also explore the change of the maximum photoelectron energy with laser intensity and strong-field atomic stabilization phenomenon in detail.

Charge-distribution effect of imaging molecular structure by high-order above-threshold ionization

Using a triatomic molecular model, we show that the interference pattern in the high-order above-threshold ionization (HATI) spectrum depends dramatically on the charge distribution of the molecular ion. Therefore the charge distribution can be considered a crucial factor for imaging a molecular geometric structure. Based on this study, a general destructive interference formula for each above-threshold ionization channel is obtained for a polyatomic molecule concerning the positions and charge values of each nuclei. Comparisons are made for the HATI spectra of ${\mathrm{CO}}_{2}$, ${\mathrm{O}}_{2}$, ${\mathrm{NO}}_{2}$, and ${\mathrm{N}}_{2}$. These results may shed light on imaging complex molecular structure by the HATI spectrum.