High-order Above-threshold Ionization Research Articles

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.

High-order above-threshold ionization with few-cycle laser pulses: Molecular improved strong-field approximation vs. molecular low-frequency approximation

We investigate high-order above-threshold ionization (HATI) of homonuclear diatomic molecules by a few-cycle laser pulse. In order to describe molecular HATI in ultrashort laser pulses we have modified our molecular improved strong-field approximation (MISFA), which was developed for long laser pulses and in which the rescattering of the ionized electron off the parent ion was described using the first-order Born approximation (1BA). Now, we introduce the so-called molecular low-frequency approximation (MLFA) in which the elastic rescattering amplitude is calculated exactly. The angle-resolved electron energy spectra for HATI of N2 and O2 obtained using the MLFA are compared with those obtained within the MISFA. The difference between these spectra becomes significant for larger (re)scattering angles. This is due to the fact that the exact scattering amplitude, used in the MLFA, has minima for some values of the rescattering angles that are absent in the 1BA. Also, the rescattering plateau is lower for the MLFA spectra. We investigate the influence of the carrier-envelope phase on the high-energy part of the molecular HATI spectra. As in the atomic case, the left-right (backward-forward) asymmetry is also observed in the molecular case.

High-order above-threshold ionization of heteronuclear diatomic molecules by a strong laser field with arbitrary polarization

The molecular strong-field approximation is applied to calculate angle-resolved photoelectron spectra in the process of high-order above-threshold ionization of carbon-monoxide molecules by an elliptically polarized laser field. The theory is formulated to include the Stark shift of the initial bound state of the valence electron. It is shown that the angle-resolved photoelectron spectra of aligned CO molecules exhibit pronounced minima which can be explained by destructive interference of two partial T-matrix contributions. The dependence of contributing partial amplitudes on the laser field ellipticity is analyzed in detail.

Application of the dressed-bound-state molecular strong-field approximation to above-threshold ionization of heteronuclear molecules: NO vs. CO

We theoretically investigate high-order above-threshold ionization (HATI) of heteronuclear diatomic molecules applying the molecular strong-field approximation which includes dressing of the molecular bound state. We consider HATI of nitrogen monoxide molecules, which are characterized by the π symmetry of their highest occupied molecular orbital. We show that the HATI spectra of NO exhibit characteristic interference structures. We analyze the differences and similarities of the HATI spectra of NO molecules and the spectra of CO (σ symmetry) and O(2) (π(g) symmetry) molecules. The symmetry properties of the molecular HATI spectra governed by linearly and elliptically polarized fields are considered in detail. The yields of high-energy electrons, contributing to the plateau region of the photoelectron spectra, strongly depend on the employed ellipticity.

Multiple-plateau structure and scaling relation in photoelectron spectra of high-order above-threshold ionization

By developing a full quantum scattering theory of high-order above-threshold ionization, we study the energy spectra and the angular distributions of photoelectrons from atoms with intense laser fields shining on them. We find that real rescattering can occur many times, and even infinite times. The photoelectrons from the rescattering process form a broad plateau in the kinetic-energy spectrum. We further disclose a multiple-plateau structure formed by the high-energy photoelectrons, which absorb many photons during the rescattering process. Moreover, we find that both the angular distributions and the kinetic-energy spectra of photoelectrons obey the same scaling law as that for directly emitted photoelectrons.

Plateau structures in laser-assisted and laser-induced processes

We present a quantum-mechanical laser-assisted scattering theory and show how the rescattering effects can be described within the second Born approximation. Also, we use two versions of the atomic (molecular) strong-field approximation in order to describe high-order above-threshold ionization. In the improved strong-field approximation, the rescattering of the ionized electron off the parent ion is described within the first-order Born approximation. A better approximation is the so-called low-frequency approximation in which the elastic rescattering amplitude is calculated exactly.

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.

Tunneling-induced shift of the cutoff law for high-order above-threshold ionization

We investigate the cutoff law for high-order above-threshold ionization (HATI) within a semiclassical framework. By explicitly adopting the tunneling effect and considering the initial position shift of the tunneled electron from the origin in the model, the cutoff energy position in HATI spectrum exhibits a well-defined upshift from the simple-man model prediction. The comparison between numerical results from our improved semiclassical model and the quantum-orbit theory shows a good agreement for small values of the Keldysh parameter gamma, implying the important role of the inherent quantum tunneling effect in HATI dynamics.

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.

Ellipticity dependence of high-order above-threshold ionization from aligned diatomic molecules

We investigate high-order above-threshold ionization of the Ar2 molecule by an elliptically polarized laser field. In order to describe this process we use the modified molecular strong-field approximation. We have found that the differential ionization rate is a very sensitive function of the ellipticity of the laser field and of the molecular orientation. For parallel orientation the rate has the maximum value for linear polarization, independently of the laser intensity. On the other hand, for perpendicular orientation the rate is maximal for a particular value of the ellipticity which is different from zero. Such a behavior can be related to the molecular symmetry. We consider the differential ionization rate of high-energy electrons as a function of the ellipticity for different internuclear distances. We also present, in the electron energy-emission angle plane, our new results for the focal-averaged spectra of electrons ionized by an elliptically polarized laser field. We have found that, in this case, the two-source two-rescattering-centers interference minima are blurred.

Low-frequency approximation for high-order above-threshold ionization

The low-frequency approximation (LFA) for high-order above-threshold ionization is presented. A factorization formula for the differential ionization rate is derived and its range of validity is analyzed. The theory developed is illustrated using the example of Ar atoms. Details of the modeling of the ground state and the rescattering potential for Ar are given. In particular, it is shown, by solving the stationary Schrödinger equation, that our rescattering potential reproduces the Hartree—Fock-type ground-state wave function that we used for the LFA. Electron momentum distributions for ionization of the Ar atom by a linearly polarized laser field having intensity 2.3 × 1014 W/cm2 and wavelength 800 nm are shown. The results obtained using the improved strong-field approximation on the one hand and the LFA on the other are compared.

Imaging the geometrical structure of theH2+molecular ion by high-order above-threshold ionization in an intense laser field

Using a frequency-domain theory, we demonstrate that an angle-resolved high-order above-threshold ionization (HATI) spectrum carries three pieces of important information: the fingerprint of the molecular wave function in the direct above-threshold-ionization amplitude, the geometrical structure of the molecule in the potential scattering between two plane waves, and the interaction between the ionized electron and the laser field, manifested in a phase factor associated with laser-assisted collisions. As a result all main interference features in the HATI spectrum can be physically explained. As an application it is pointed out that the skeleton structure of a molecule can be better imaged using lasers of higher frequencies.

Two-source double-slit interference in angle-resolved high-energy above-threshold ionization spectra of diatoms

When an electron from a diatomic molecule undergoes rescattering-tunneling ionization, a novel form of destructive interference can take place that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for O2, but not for N2.

Atoms and Molecules in a Strong Laser Field

We investigate high-order above-threshold ionization of diatomic molecules and their companion atoms by linearly polarized strong laser field using improved molecular (atomic) strong-field approximation. The most noticeable feature of the molecular spectra is the existence of minima that are absent in atomic case. We have derived an analytical formula for their position which is independent of the molecular symmetry.

Strong-field approximation for high-order above-threshold ionization of randomly oriented diatomic molecules

High-order above-threshold ionization of diatomic molecules by a strong linearly polarized field is considered using the molecular strong-field approximation. Tunneling–rescattering as the mechanism of this ionization gives rise to a novel two-source double-slit interference, which involves the four geometrical paths that are available to an electron, which can be ionized from and rescattered off either of the two centers of the diatomic molecule. For a comparison of this theory with experiments in the absence of molecular alignment, it is necessary to average the theoretical results over the molecular orientation. This paper presents technical details of this averaging procedure. It is shown that, depending on the molecular symmetry, the destructive two-source double-slit interference minima can survive the orientation averaging and can be observed in the angle-resolved electron spectra. This is illustrated on the examples of N 2 and O 2 molecules. It is also shown that two- and three-dimensional versions of orientation averaging lead to qualitatively similar results.

Strong-field approximation for ionization of a diatomic molecule by a strong laser field. III. High-order above-threshold ionization by an elliptically polarized field

We investigate high-order above-threshold ionization (HATI) of diatomic molecules having different symmetries by an elliptically polarized laser field using the modified molecular strong-field approximation. The yields of high-energy electrons contributing to the plateau region of the photoelectron spectra strongly depend on the employed ellipticity. This is more pronounced if the major axis of the polarization ellipse is parallel or perpendicular to the molecular axis and at the end of the high-energy plateau. For the ${\text{O}}_{2}$ molecule (characterized by ${\ensuremath{\pi}}_{\text{g}}$ symmetry) the maximum yield is observed for some value of the ellipticity $\ensuremath{\epsilon}$ different from zero. On the other hand, in the same circumstances, the ${\text{N}}_{2}$ molecule $({\ensuremath{\sigma}}_{\text{g}})$ behaves as an atom, i.e., the yield is maximum for $\ensuremath{\epsilon}=0$. These characteristics of the photoelectron spectra remain valid in a wide region of the molecular orientations and laser peak intensities. The symmetry properties of the molecular HATI spectra are considered in detail: by changing the molecular orientation one or other type of the symmetry emerges or disappears. Presenting differential ionization spectra in the ionized electron energy-emission angle plane we have observed similar interference effects as in the HATI spectra governed by a linearly polarized field.

Two-Source Double-Slit Interference in Angle-Resolved High-Energy Above-Threshold Ionization Spectra of Diatoms

When an electron from a diatomic molecule undergoes tunneling-rescattering ionization, a novel form of destructive interference can be realized that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for O_{2} but not for N_{2}. This effect is different from the suppression of ionization that is well known to occur for O_{2}.

The role of incoherent scattering in laser-induced and laser-assisted processes

We use the S-matrix formalism in order to investigate the possible role of incoherent scattering in different processes in a strong laser field. In the cases of above-threshold ionization (ATI) of atoms and above-threshold detachment (ATD) of negative ions, we assume that the ionized (detached) electron may scatter off a target other than its parent ion (atom). We call such a process incoherent in order to distinguish it from the coherent rescattering of an ionized (detached) electron off its parent ion (atom) which occurs in high-order above-threshold ionization (HATI) and high-order above-threshold detachment (HATD) processes. The same line of reasoning can be applied to the laser-assisted processes, such as the laser-assisted electron-ion radiative recombination (LAR) and the laser-assisted electron-atom scattering (LAS). If the density of the ionic beam used in a LAR experiment is high, it is possible that the electron scatters off an ionic target and subsequently recombines with another ion. Analogously, the electron that scatters on an atom in the LAS process may scatter once more off another atom. We show that the contribution of these incoherent processes to the energy spectra can be higher than that of the corresponding coherent processes if the density of atomic (ionic) targets is high enough. The spectra of the incoherent processes have a cutoff-like behavior and the cutoff energies are higher than those of the corresponding coherent processes. These results are explained by semiclassical analysis.

High-order above-threshold ionization beyond the first-order Born approximation

In the improved strong-field approximation, which describes high-order above-threshold ionization (HATI), the rescattering of the ionized electron on the parent ion is described within the first-order Born approximation. The low-frequency approximation for laser-assisted scattering goes beyond the first Born approximation. In the present paper, we derive the low-frequency approximation for HATI. The rescattering amplitude in the first Born approximation is replaced by the exact scattering amplitude calculated on the energy shell. Our numerical results for the angle-resolved HATI energy spectra show that the difference between the improved strong-field approximation and the low-frequency approximation is significant for scattering away from the laser polarization axis. In the context of quantum-orbit theory and the uniform approximation, we also show that on the back-rescattering ridge, the rescattering $T$-matrix element can be factorized into the product of the incoming flux and the elastic-scattering cross section so that the latter can be extracted from the angle- and energy-resolved HATI spectra.

High-Order Above-Threshold Ionization of H2+ in Intense Laser Field

The nonperturbative quantum electrodynamics method proposed by Fu et al. [Phys. Rev. A 75 (2007) 063419] is employed to study the high-order above-threshold ionization (ATI) of a diatomic molecule. Based on this frequency-domain theory, the high-order ATI process can be regarded as ATI followed by laser-assisted collision, where the total transition amplitude is the coherent summation of the contributions from each ATI channel. The angular-resolved ATI spectrum, which agrees with the results by Becker et al. based on the time-domain method, is obtained by this frequency domain theory. Furthermore, it is demonstrated that the interference characteristics representing the molecular structure in the ATI spectrum originates from the recollision of the electron with two-centre ion in each ATI channel.