Two-photon Above-threshold Ionization Research Articles

Relativistic Two-Photon Matrix Elements for Attosecond Delays

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science by using Dirac–Fock formalism. A direct comparison of Wigner–Smith–Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the relativistic random phase approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated by using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as argon, show negligible relativistic effects, whereas heavier elements, such a krypton and xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notably close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner–Smith–Eisenbud delay and a universal continuum–continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

Fano’s propensity rule in angle-resolved attosecond interferometry

SynopsisAbove-threshold ionization is a corner stone of attsecond science. In this work we extend Fano’s propensity rule to two-photon above-threshold ionization and show that the asymmetry between absorption and emission of the second photon predicted by this propensity rule has strong implications for angle-resolved pump-probe experiments and in particular for attosecond photoelectron interferometry.

Angularly resolved two-photon above-threshold ionization of helium

Two-photon single ionization of helium is studied for photon energies from the two-photon ionization threshold up to 70 eV by numerically solving the full-dimensional time-dependent Schr\odinger equation. Analysis of the photoelectron angular distributions reveals the dominant two-photon mechanisms and the relevance of radial and electron correlation terms as a function of energy and pulse parameters, as well as the breakdown of a single-active-electron picture, qualitatively valid at low photon energies, at energies above ca. 50 eV.

Many-electron character of two-photon above-threshold ionization of Ar

The absolute generalized cross sections and angular distribution parameters of photoelectrons for the two-photon above threshold $3p$-ionization of Ar were calculated in the exciting photon energy range from 15.76 to 36 eV. The correlation function technique developed earlier was extended for the case when an intermediate-state function is of a continuum-type. We show that two-photon ionization of Ar near the $3p^{4}$ threshold to a large extent is determined by the $(3p\dashrightarrow\varepsilon d)^{2}$ two-photon absorption via the giant resonance. This many-electron correlation causes (i) an increase of the photoionization cross sections by more than a factor of 3; (ii) the appearance of resonances in the exciting-photon energy range of the doubly-excited states. The predictions are supported by a good agreement between length and velocity results obtained after taking into account of the higher-order perturbation theory corrections.

Wave-packet propagation based calculation of above-threshold ionization in the x-ray regime

We investigate the multi-photon process of above-threshold ionization for the light elements hydrogen, carbon, nitrogen, and oxygen in the hard x-ray regime. Numerical challenges are discussed and by comparing Hartree–Fock–Slater calculations with configuration–interaction–singles results we justify the mean-field potential approach in this regime. We present a theoretical prediction of two-photon above-threshold-ionization cross sections for the mentioned elements. Moreover, we study how the importance of above-threshold ionization varies with intensity. We find that for carbon, at x-ray intensities around , two-photon above-threshold ionization of the K-shell electrons is as probable as one-photon ionization of the L-shell electrons.

Photoelectron angular distributions in infrared one-photon and two-photon ionization of FEL-pumped Rydberg states of helium

The photoelectron angular distributions (PADs) have been investigated for infrared (IR) ionization of He atoms excited to Rydberg states by extreme ultraviolet free-electron laser pulses. The experiment was carried out with two pulses which do not overlap in time. Depending on the intensity of the IR pulses, one IR photon ionization or additionally two-photon above-threshold ionization is observed. For low IR intensity, the PAD is well described by a contribution of s and d partial waves in accordance with early experiments. At high IR intensity, the PAD for two IR photon ionization clearly shows the contribution of higher partial waves. The experimental data are compared with the results of theoretical calculations based on solving the time-dependent Schrödinger equation.

Anisotropy parameters in two-color two-photon above-threshold ionization

We employ the time-dependent $R$-matrix (TDRM) method to calculate anisotropy parameters for positive and negative sidebands of selected harmonics generated by two-color two-photon above-threshold ionization of argon. We consider odd harmonics of an 800-nm field ranging from the 13$\text{th}$ to 19$\text{th}$ harmonic, overlapped by a fundamental 800-nm IR field. The anisotropy parameters obtained using the TDRM method are compared with those obtained using a second-order perturbation theory with a model potential approach and a soft photon approximation approach. Where available, a comparison is also made to published experimental results. All three theoretical approaches provide similar values for anisotropy parameters. The TDRM approach obtains values that are closest to published experimental values. At high photon energies, the differences between each of the theoretical methods become less significant.

Two-photon above-threshold ionization using extreme-ultraviolet harmonic emission from relativistic laser–plasma interaction

We report on the observation of energy-resolved photoelectron (PE) spectra produced via two-extreme-ultraviolet-(XUV)-photon above-threshold ionization (ATI) of argon atoms. The XUV radiation consists of higher-order harmonics generated by the process of the relativistic oscillating mirror (ROM) in high-peak-power laser–pulse interaction with solid targets. The energetic XUV radiation is focused into an argon gas target at intensities high enough to induce two-photon ionization at yields that allow the recording of energy-resolved PE spectra. A clear two-XUV-photon ATI PE peak structure is observed in shot-to-shot measurements. This work is a first step towards a frequency-resolved optical gating-type characterization of attosecond pulse trains emanating from relativistic laser–plasma interactions and thus is important for XUV-pump–XUV-probe applications of these harmonics.

Two-photon above-threshold ionization of hydrogen over the photon energy range from 15 eV to 50 keV

We investigate the absorption of two identical photons from the ground state of hydrogen-like atoms over an energy range that extends beyond that explored up to now. Our approach is based on a hybrid formula, valid in second-order perturbation theory, in which the ${\mathbf{A}}^{2}$ contribution from the nonrelativistic Hamiltonian is treated exactly, while the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution is calculated in dipole approximation. We find that, at least up to 50 keV, the nonrelativistic dipole approximation, based only on the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution, determines the values of the total cross section. Our numerical results, covering photon energies from 90 nm (13.7 eV) to 0.0248 nm (50 keV) are in very good agreement with most previous theoretical works. Differences with recent results are discussed.

Above-threshold ionization in the x-ray regime

Two-photon above-threshold ionization processes in the x-ray regime are studied using atomic hydrogen as a model system. Within the minimal-coupling formalism of nonrelativistic quantum electrodynamics, two distinct interactions---$\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}\ensuremath{\cdot}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$ in second order and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ in first order---contribute to the two-photon absorption amplitude. The relative importance of these two interactions is assessed. It is found that above a photon energy of 6.8 keV, the contribution from ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ to the total two-photon absorption cross section dominates. In this high-energy regime, above-threshold ionization is a nonsequential purely nondipole process. Rate equations are employed to calculate the probabilities of ionization by Compton scattering, one-photon absorption, and two-photon absorption.

Method for calculating multiphoton above-threshold processes in atoms: Two-photon above-threshold ionization

The two-photon above-threshold ionization of atoms is calculated using numerical algorithms of the Pade approximation in the model-potential method with the Coulomb asymptotics. The total and differential cross sections of the above-threshold ionization of helium and alkali metal atoms by elliptically polarized radiation are presented. The dependence of the angular distribution of photoelectrons on the sign of the ellipticity of radiation (the elliptic dichroism phenomenon) is analyzed in the above-threshold frequency range.

Frequency-Resolved Optical Gating of Isolated Attosecond Pulses in the Extreme Ultraviolet

The pulse shape and phase of isolated attosecond extreme ultraviolet (XUV) pulses with a duration of 860 asec have been determined simultaneously by using frequency-resolved optical gating based on two-photon above-threshold ionization with 28-eV photons in He. From the detailed characterization, we succeeded in shaping isolated XUV pulses on an attosecond time scale by precise dispersion control with Ar gas density or by changing the driving pulse width. These results offer a novel way to excite and observe an electron motion in atoms and molecules.

Conclusive Evidence of an Attosecond Pulse Train Observed with the Mode-Resolved Autocorrelation Technique

We report on the direct observation of an attosecond pulse train with a mode-resolved autocorrelation technique. The chirp among the three harmonic fields is specified by analyzing two-photon above-threshold ionization spectra of electrons, resulting in a pulse duration that should be shorter than 450 as, which is, to our knowledge, the first determination of the chirp in the attosecond pulse train with an autocorrelation technique. These results will open the way to full characterization of an attosecond pulse train with its envelope.

Above-threshold ionization near the3p4dFo1autoionizing state in magnesium

Two-photon above-threshold ionization (ATI) relative cross sections from the $3\phantom{\rule{0.2em}{0ex}}^{1}P$ state of Mg have been measured using two-color ionization in the focus of a magnetic bottle spectrometer and have been calculated using the Green's-function method in the Feshbach formalism and an ${L}^{2}$-integrable close-coupling approach, with a basis of ${L}^{2}$-integrable $B$-spline functions. We report these cross sections in the region of $3d4p$ $^{1}F^{o}$ autoionizing state, with photon energies of $3.3--3.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. This is one of the few direct comparisons between ab initio theory and experiments in ATI in the vicinity of a Feshbach resonance. A good agreement between theory and experiment is found in the relative total cross sections.

Nonlinear optics in the extreme ultraviolet

Nonlinear responses to an optical field are universal in nature but have been difficult to observe in the extreme ultraviolet (XUV) and soft X-ray regions owing to a lack of coherent intense light sources. High harmonic generation is a well-known nonlinear optical phenomenon and is now drawing much attention in attosecond pulse generation. For the application of high harmonics to nonlinear optics in the XUV and soft X-ray regime, optical pulses should have both large pulse energy and short pulse duration to achieve a high optical electric field. Here we show the generation of intense isolated pulses from a single harmonic (photon energy 27.9 eV) by using a sub-10-femtosecond blue laser pulse, producing a large dipole moment at the relatively low (ninth) harmonic order nonadiabatically. The XUV pulses with pulse durations of 950 attoseconds and 1.3 femtoseconds were characterized by an autocorrelation technique, based on two-photon above-threshold ionization of helium atoms. Because of the small cross-section for above-threshold ionization, such an autocorrelation measurement of XUV pulses with photon energy larger than the ionization energy of helium has not hitherto been demonstrated. The technique can be extended to the characterization of higher harmonics at shorter wavelengths.

Observation of two-photon above-threshold ionization of rare gases by xuv harmonic photons.

We have successfully observed two-photon above-threshold ionization in rare gas atoms (Ar, Xe, and He) by the fifth harmonic (25 eV photon energy) of a KrF laser. Use of the energy-resolved photoelectron counting system together with our laser, providing strong 25 eV radiation at 40-100 Hz, enabled us to detect the very weak single-color two-photon above-threshold ionization signals. Experimental data are in good agreement with our theoretical calculations newly developed along the line of multichannel quantum defect theory.

Two-photon above-threshold ionization of magnesium

Two-photon above-threshold ionization cross sections and angular distributions have been calculated for Mg in the region between the $3p$ and $4s$ ionization thresholds. We have used the Green's function method in the Feshbach formalism and an ${L}^{2}$ close coupling method, with a basis of ${L}^{2}$ integrable B-spline functions. We report the positions, widths, and assignments of a number of ${}^{1}{S}^{e}$ and ${}^{1}{D}^{e}$ doubly excited Feshbach states. We have found that correlation is important in the Feshbach states, indicated by significant mixing among configurations, and identified a previously unnoticed $``3d5g''$ Feshbach state.

Interference effects in two-photon above-threshold ionization by multiple orders of high-order harmonics with random or locked phases

We numerically study 2-photon processes using a set of harmonics from a Ti:Sapphire laser and in particular interference effects in the Above Threshold Ionization spectra. We compare the situation where the harmonic phases are assumed locked to the case where they have a random distribution. Suggestions for possible experiments, using realistic parameters are discussed.

Transformed Coulomb Green function Sturmian expansion

Two Coulomb Green function Sturmian expansions are presented. Both of them are used to derive the transformed Coulomb Green function Sturmian expansion. The new Coulomb Green function representation is tested for calculating two-photon above-threshold ionization cross sections for atomic hydrogen. The new representation may be useful also in the case of more excess photons as well as for calculating free-free transitions.

Use of Coulomb Green function for the calculation of above-threshold multiphoton transitions

A new Coulomb Green function expansion in Laguere polynomials applicable for the positive-energy case is obtained and the cross section of two-photon above-threshold ionization from highly excited hydrogen states is calculated.