Above-threshold Ionization Spectra Research Articles

Laser intensity determination using nonadiabatic tunneling ionization of atoms in close-to-circularly polarized laser fields.

We conceive an improved procedure to determine the laser intensity with the momentum distributions from nonadiabatic tunneling ionization of atoms in the close-to-circularly polarized laser fields. The measurements for several noble gas atoms are in accordance with the semiclassical calculations, where the nonadiabatic effect and the influence of Coulomb potential are included. Furthermore, the high-order above-threshold ionization spectrum in linearly polarized laser fields for Ar is measured and compared with the numerical calculation of the time-dependent Schrödinger equation in the single-active-electron approximation to test the accuracy of the calibrated laser intensity.

Low-energy backscattering quantum orbits in above-threshold ionization

Using the quantum–orbit formalism we consider the influence of the backward-scattering quantum orbits on the low-energy above-threshold ionization spectra. It is shown that the corresponding ionization rate exhibits sharp peaks for electron energies ( is the electron ponderomotive energy) at the same places where the forward-scattering-induced low-energy structures appear. The corresponding incident rescattering electron velocities are very small. Semiclassical expressions for the positions of these peaks as functions of and the ionization potential are derived.

Exploration of the electron multiple recollision dynamics in intense laser fields with Bohmian trajectories

Electron multiple recollision dynamics under intense midinfrared laser fields is studied by means of the de Broglie--Bohm framework of Bohmian mechanics. Bohmian trajectories contain all the information embedded in the time-dependent wave function. This makes the method suitable to investigate the coherent dynamic processes for which the phase information is crucial. In this study, the appearance of the subpeaks in the high-harmonic-generation time-frequency profiles and the asymmetric fine structures in the above-threshold ionization spectrum are analyzed by the comprehensive and intuitive picture provided by Bohmian mechanics. The time evolution of the individual electron trajectories is closely studied to address some of the major structural features of the photoelectron angular distributions.

Resonancelike enhancement in high-order above-threshold ionization of polyatomic molecules

We investigate the resonance-like enhancement (RLE) in high-order above-threshold ionization (ATI) spectra of the polyatomic molecules ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$. In the spectrum-intensity maps, strong and weak RLE areas emerge alternatively for both ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$ but in different sequences. Theoretical calculations using the strong-field approximation reproduce the experimental observation and analysis shows that the different characteristics of the two molecules can be attributed to interference effects of molecular orbitals with different symmetries. For ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$, the RLE structures are attributed to C--C centers of the highest occupied molecular orbital (HOMO) orbital. For ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$, in contrast, the C--C centers of the HOMO and HOMO-1 orbitals do not contribute to the RLE due to destructive interference but the hydrogen centers of the bonding HOMO-1 orbital give rise to the multiple RLE regions. In addition, clear experimental evidence of the existence of two types of the RLE and their dependence on the parity of ground state is shown. Our result, which strongly supports the channel-closing mechanism of the RLE, for the first time reveals the important role of low-lying orbitals and the differing roles of different atomic centers in the high-order ATI spectrum of molecules.

Photoelectron momentum distributions of the hydrogen atom driven by multicycle elliptically polarized laser pulses

Photoelectron momentum distributions (PMDs) of the hydrogen atom driven by multicycle elliptically polarized strong laser fields are studied in detail, based on the numerical solution of the time-dependent Schr\odinger equation and the Volkov wave propagation. Both short and long driving pulses of the 800-nm field are considered, as well as the ellipticity dependence, to describe the mechanism of symmetry breaking in the hydrogen-atom PMD. Moreover, we demonstrate that the value of a retardation angle in the longitudinal PMD can depend on the order of above-threshold ionization spectra.

Interference structures in nonlinear processes in strong infrared laser fields

Molecular strong-field approximation in the frame of the S-matrix theory is applied in order to investigate above-threshold ionization (ATI) and high-order harmonic generation (HHG) for diatomic molecules. By analyzing the HHG and ATI spectra for different orientations of molecular axis with respect to the direction of the laser polarization vector we have observed interference structures. The positions of the interference minima depend on the internuclear distance and on the relative contributions of the atomic orbitals in the linear combination of the atomic orbitals of the highest occupied molecular orbitals. The HHG and ATI spectra have been obtained for infrared laser wavelengths and linearly polarized laser field. The calculated results may also provide additional information about the molecular structure .

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

Above-threshold ionization (ATI) results from strong field laser-matter interaction and it is one of the fundamental processes that may be used to extract electron structural and dynamical information about the atomic or molecular target. Moreover, it can also be used to characterize the laser field itself. Here, we develop an analytical description of ATI, which extends the theoretical Strong Field Approximation (SFA), for both the direct and re-scattering transition amplitudes in atoms. From a non-local, but separable potential, the bound-free dipole and the re-scattering transition matrix elements are analytically computed. In comparison with the standard approaches to the ATI process, our analytical derivation of the re-scattering matrix elements allows us to study directly how the re-scattering process depends on the atomic target and laser pulse features -we can turn on and off contributions having different physical origins or corresponding to different physical mechanisms. We compare SFA results with the full numerical solutions of the time-dependent Schroedinger equation (TDSE) within the few-cycle pulse regime. Good agreement between our SFA and TDSE model is found for the ATI spectrum. Our model captures also the strong dependence of the photoelectron spectra on the carrier envelope phase of the laser field.

Influence of the Coulomb potential on above-threshold ionization: A quantum-orbit analysis beyond the strong-field approximation

We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semi-analytical, Coulomb-corrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories, and we identify a set of orbits which, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard SFA, we show that several features in the ATI spectra can be traced back to the influence of the Coulomb potential on different electron trajectories. These features include a decrease in the contrast, a shift towards lower energies in the interference substructure, and an overall increase in the photoelectron yield. All features encountered exhibit a very good agreement with the \emph{ab initio} solution of the time-dependent Schr\"odinger equation.

Dependence of above-threshold ionization spectrum on polarization directions of two-color laser fields**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474348 and 61275128).

Using the frequency-domain theory, we investigate the above-threshold ionization (ATI) process of an atom in two-color laser fields. When both photon energies of the two-color laser fields are much smaller than the atomic ionization threshold, the ATI spectrum depends on the angle between the two lasers’ polarization directions. While when the photon energy of one laser is comparable with or larger than the atomic ionization threshold, the ATI spectrum is independent of the angle, and only several dips appear at certain angles. By analyzing the contributions of different quantum channels, we find that, for the case that both frequencies of the two color lasers are low, the quantum interferences between the channels are strong, and hence the spectrum changes with the angle between the two lasers’ polarization directions. While for the case that the frequency of one of the two color lasers is high, the contributions of the channels to the ATI spectrum decrease dramatically with increasing channel order, hence the interferences between the channels disappear, and the ATI spectrum has a step-like structure, which is independent of the angle between the two lasers’ polarizations. These results can shed light on the study of the corresponding relation between classical and quantum mechanisms of the matter–laser interaction in high-frequency laser fields.

Molecular above-threshold ionization spectra as an evidence of the three-point interference of electron wave packets

We consider high-order above-threshold ionization (HATI) of polyatomic molecules ionized by a strong linearly polarized laser field. Improved molecular strong-field approximation by which the HATI process on polyatomic molecular species can be described is developed. Using this theory we calculate photoelectron angular-energy spectra for different triatomic molecules. Special attention is devoted to the minima that are observed in the calculated high-energy electron spectra of the ozone and carbon dioxide molecules. A key difference between these minima and minima that are observed in the corresponding spectra of diatomic molecules are presented.

Above-threshold ionization spectra asymmetrically broadened in the extreme-ultraviolet pulse train and infrared laser fields

We experimentally investigate the atomic ionization process in an extreme-ultraviolet (XUV) pulse train generated by the high-order harmonic generation process and an IR laser field. Compared with the electron spectrum ionized only by the XUV pulse train, the electron energy spectra generated in the two-color field exhibit two characterizations: (1) the spectrum is smoothed in the presence of a weak IR field, and (2) the spectrum is asymmetrically broadened when using an intense IR field. Simulation results based on the frequency-domain theory qualitatively agree with the experimental spectra. We demonstrate that the asymmetrically broadened spectrum could be interpreted by a clear two-step ionization picture: an electron wavepacket is ionized from the atomic ground state by the XUV pulse train, and then the energy of it is asymmetrically changed by absorbing or emitting specific IR photons.

Low-frequency approximation for above-threshold ionization by a laser pulse: Low-energy forward rescattering

In the context of the development of new sources of strong laser pulses in the mid-infrared region new nonperturbative methods for analysis of strong-laser-field induced or assisted atomic and molecular processes are welcome. We formulate such a theory of above-threshold ionization by a strong low-frequency laser pulse. We call this theory the low-frequency approximation (LFA). A detailed derivation of the LFA, both for short and long laser pulses, is given. As an example the LFA is applied to the analysis of recently discovered low-energy structures in the above-threshold ionization spectra of atoms ionized by long-wavelength laser pulses. It was found that these low-energy structures are caused by the forward soft recollision of the ionized electrons with the parent ion which is enhanced by the Coulomb effect.

Quantum control of electron-proton symmetry breaking in dissociative ionization of H2by intense laser pulses

Forward and backward electron/proton ionization/dissociation spectra from one-dimensional non-Born-Oppenheimer H2 molecule exposed to ultrashort intense laser pulses ( W/cm2, λ = 800 nm) have been computed by numerically solving the time-dependent Schrodinger equation. The resulting above-threshold ionization and above-threshold dissociation spectra exhibit the characteristic forward-backward asymmetry and sensitivity to the carrier-envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H2 has been established. It is found that the symmetry breaking of electron-proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.

Forward- and backward-scattering quantum orbits in above-threshold ionization

High-order above-threshold ionization (ATI) is characterized by the rescattering of the ionized electron off the parent ion. The ATI amplitude can be calculated applying the saddle-point (SP) method and the uniform approximation to a five-dimensional integral over the ionization time, intermediate electron momentum, and rescattering time. The so-obtained amplitude is a coherent sum of amplitudes associated to the two classes of the SP solutions. The low-energy structures in the ATI spectra are determined by the forward-scattering SP solutions, while the high-energy spectra (plateau and cutoff) are determined by the backward-scattering SP solutions. In order to properly describe the intermediate-electron-energy spectra, additional SP solutions should be taken into account. For these solutions, the imaginary part of the rescattering time can be large and, for their explanation, we introduce complex-time quantum orbits.

Heteronuclear diatomic molecules in a strong laser field with an arbitrary polarization

Processes of above-threshold ionization (ATI) and high-order harmonic generation (HHG) for heteronuclear diatomic molecules are investigated. By analyzing the HHG and ATI spectra for different molecular orientation with respect to the main laser polarization axis and for different values of the photon energies and electron energies and emission angle, we are able to draw some conclusions about the molecular structure. The partial elliptic dichroism effect in HHG spectra is also analyzed. Regarding the ATI spectra, two-center interference minima are visible, even for a circularly polarized laser field. The positions of the minima depend on the internuclear distance, on the relative contributions of the atomic orbitals to the highest occupied molecular orbital and on the laser field parameters.

Resonance-like enhancement in high-order above-threshold ionization of formic acid

We have investigated the high-order above-threshold ionization (HATI) spectrum of formic acid by means of high-resolution electron spectroscopy using 800-nm femtosecond laser light. The resonance-like enhancement structures in the HATI spectrum are shown to be experimentally reproducible and three enhancement-suppression patterns are observed in different energy regimes with increasing laser intensity. We simulated these patterns successfully by computing the exact solution of time-dependent Schr\"odinger equation based on the simple hydrogen-like atom, subject to a time-dependent high-intensity laser pulse. The agreement between experiment and theory shows that ``channel closing'' effects play an important role in the observed resonance-like enhancements (RLEs). The existence of the RLEs for formic acid, which lacks any symmetry, shows that molecular symmetry does not affect the RLEs.

Hybrid Gaussian–B-spline basis for the electronic continuum: Photoionization of atomic hydrogen

As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian--$B$-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with $B$ splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schr\odinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely $B$-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengths.

Analytic model for the description of above-threshold ionization by an intense short laser pulse

We present an analytic model for the description of above-threshold ionization (ATI) of an atom by an intense, linearly polarized short laser pulse. Our treatment is based upon a description of ATI by an infinitely long train of short laser pulses whereupon we take the limit that the time interval between pulses becomes infinite. In the quasiclassical approximation, we provide detailed quantum-mechanical derivations, within the time-dependent effective range (TDER) model, of the closed-form formulas for the differential probability $\mathcal{P}(\mathbf{p})$ of ATI by an intense, short laser pulse that were presented briefly by Frolov et al. [Phys. Rev. Lett. 108, 213002 (2012)] and that were used to describe key features of the high-energy part of ATI spectra for H and He atoms in an intense, few-cycle laser pulse, using a phenomenological generalization of the physically transparent TDER results to the case of real atoms. Moreover, we extend these results here to the case of an electron bound initially in a $p$ state; we also take into account multiple-return electron trajectories. The ATI amplitude in our approach is given by a coherent sum of partial amplitudes describing ionization by neighboring optical cycles near the peak of the intensity envelope of a short laser pulse. These results provide an analytical explanation of key features in short-pulse ATI spectra, such as the left-right asymmetry in the ionized electron angular distribution, the multiplateau structures, and both large-scale and fine-scale oscillation patterns resulting from quantum interferences of electron trajectories. Our results show that the shape of the ATI spectrum in the middle part of the ATI plateau is sensitive to the spatial symmetry of the initial bound state of the active electron. This sensitivity originates from the contributions of multiple-return electron trajectories. Our analytic results are shown to be in good agreement with results of numerical solutions of the time-dependent Schr\odinger equation for He and Ar atoms. Comparison of our results with those of quantitative rescattering theory is also discussed.

Intensity-resolved above-threshold ionization of xenon with short laser pulses

We present intensity-resolved above threshold ionization (ATI) spectra of xenon using an intensity scanning and deconvolution technique. Experimental data were obtained with laser pulses of 58 fs and central wavelength of 800 nm from a chirped-pulse amplifier. Applying a deconvolution algorithm, we obtained spectra that have higher contrast and are in excellent agreement with characteristic 2 $U_p$ and 10 $U_p$ cutoff energies contrary to that found for raw data. The retrieved electron ionization probability is consistent with the presence of a second electron from double ionization. This recovered ionization probability is confirmed with a calculation based on the PPT tunneling ionization model [Perelomov, Popov, and Terent'ev, Sov. Phys. JETP 23, 924 (1966)]. Thus, the measurements of photoelectron yields and the proposed deconvolution technique allowed retrieval of more accurate spectroscopic information from the ATI spectra and ionization probability features that are usually concealed by volume averaging.

Investigation on the influence of atomic potentials on the above threshold ionization

We systematically investigate the influence of atomic potentials on the above-threshold ionization (ATI) spectra in one-dimensional (1D) cases and compare them with the three-dimensional (3D) case by numerically solving the time-dependent Schrödinger equation. It is found that the direct ionization plateau and the rescattering plateau of the ATI spectrum in the 3D case can be well reproduced by the 1D ATI spectra calculated from the supersolid-core potential and the soft-core potential, respectively. By analyzing the factors that affect the yield of the ATI spectrum, we propose a modified-potential with which we can reproduce the overall 3D ATI spectrum. In addition, the influence of the incident laser intensities and frequencies on the ATI spectra calculated from the proposed modified potential is studied.