Accurate prediction of interference minima in linear molecular harmonic spectra by a modified two-center model

We demonstrate that the interference minima in the linear molecular harmonic spectra can be accurately predicted by a modified two-center model. Based on systematically investigating the interference minima in the linear molecular harmonic spectra by the strong-field approximation(SFA), it is found that the locations of the harmonic minima are related not only to the nuclear distance between the two main atoms contributing to the harmonic generation, but also to the symmetry of the molecular orbital. Therefore, we modify the initial phase difference between the double wave sources in the two-center model, and predict the harmonic minimum positions consistent with those simulated by SFA.     

Valence orbital method of calculating harmonic emission from diatomic molecule

We present a valence orbital method of calculating high-order harmonic generation from a diatomic molecule with arbitrary orientation by using a space rotation operator. We evaluate the effects of each valence orbital on harmonic emissions from N₂ and O₂ molecules in detail separately. The calculation results confirm the different properties of harmonic yields from N₂ and O₂ molecules which are well consistent with available experimental data. We observe that due to the orientation dependence of \sigma and \pi orbitals, the bonding orbital (\sigma _{2pz} )^2 of N₂ determines the maximum of harmonic emission when the molecular axis of N₂ is aligned parallel to the laser vector, and the magnitude of the high harmonic signal gradually weakens with the orientation angle of molecular axis increasing. But for O₂ molecule the antibonding orbitals (\pi _{2py}^\ast )^1 and (\pi _{2pz}^\ast )^1 contribute to the maximum of harmonic yield when O₂ is aligned at 45^{\circ} and bonding orbitals (\pi _{2py} )^2 and (\pi _{2pz} )^2 slightly influence the orientation angle of maximum of harmonic radiation not exactly at 45^{\circ}.     

Effects of multi orbital contributions in the angular-dependent ionization of molecules in intense few-cycle laser pulses

We outline the details of our new method to calculate angular-dependent ionization probabilities based on electronic structure theory for diatomic and larger systems. To demonstrate its abilities, we compare our calculations to measured ionization probabilities of the four molecules D₂, N₂, O₂ and CO in the strong-field regime. The calculated angular distributions yield better agreement with the experimental data than those obtained from the widely used MO-ADK theory. For CO the measured angular distributions of ionic fragments indicate contributions to the ionization from both the HOMO and the HOMO-1 orbital, an effect that is addressed by the theory.     

异核双原子和三原子分子在红外强激光场中的电离抑制

Ionization is the fundamental process in interaction of atoms/molecules with femtosecond strong laser fields. Comparing to atoms, molecules exhibit peculiar behaviors in strong-field ionization because of their diverse geometric structures, molecular electronic orbitals as well as extra nuclear degrees of freedom. In this study, we investigate strong field single and double ionization of carbon monoxide (CO) and carbon dioxide (CO₂) in linearly polarized 50-fs, 800-nm laser fields with peak intensity in the range of 2×10¹³ W/cm² to 2×10¹⁴ W/cm² using time-of-flight mass spectrometer. By comparing the ionization yields with that of the companion atom krypton (Kr), which has similar ionization potential to the molecules, we investigate the effect of molecular electronic orbitals on the strong-field ionization. The results show that comparing to Kr, no significant suppression is observed in single ionization of both molecules and in non-sequential double ionization (NSDI) of CO, while the NSDI probability of CO₂ is strongly suppressed. Based on our results and previous studies on homonuclear diatomic molecules (N₂ and O₂), the mechanism of different suppression effect is discussed. It is indicated that the different structure of the highest occupied molecular orbitals of CO and CO₂ leads to distinct behaviors in two-center interference by the electronic wave-packet and angular distributions of the ionized electrons, resulting in different suppression effect in strong-field ionization.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.     

Angle-resolved high-order above-threshold ionization of a molecule: sensitive tool for molecular characterization

The strong-field approximation for ionization of diatomic molecules by an intense laser field is generalized to include rescattering of the ionized electron off the various centers of its molecular parent ion. The resulting spectrum and its interference structure strongly depend on the symmetry of the ground state molecular orbital. For N2, if the laser polarization is perpendicular to the molecular axis, we observe a distinct minimum in the emission spectrum, which survives focal averaging and allows determination of, e.g., the internuclear separation. In contrast, for O2, rescattering is absent in the same situation.     

New results in above-threshold ionization and high-order harmonic generation of atomic and molecular systems

Numerical results obtained applying the strong-field approximation to atomic and molecular processes in intense laser fields are presented. In particular, the forward-backward asymmetry in high-order above-threshold ionization (HATI) of Ar atoms by a few-cycle laser pulse is considered. It is shown that the resonantlike enhancements observed in the focal-averaged spectra disappear with the decreasing laser pulse duration. For HATI and high-order harmonic generation (HHG) by molecular systems, we present new results for diatomic molecules. The choice of gauge and the problem of dressing of the initial bound state are discussed. The appearance of the interference minima in molecular HATI and HHG spectra and their role in the characterization of the molecular structure are considered using the example of the Ar₂ molecule.     

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.     

Quantum state-resolved probing of strong-field-ionized xenon atoms using femtosecond high-order harmonic transient absorption spectroscopy

Femtosecond high-order harmonic transient absorption spectroscopy is used to resolve the complete |j,m quantum state distribution of Xe+ produced by optical strong-field ionization of Xe atoms at 800 nm. Probing at the Xe N4/5 edge yields a population distribution rhoj,|m| of rho3/2,1/2ratiorho1/2,1/2ratiorho3/2,3/2=75+/-6 :12+/-3 :13+/-6%. The result is compared to a tunnel ionization calculation with the inclusion of spin-orbit coupling, revealing nonadiabatic ionization behavior. The sub-50-fs time resolution paves the way for tabletop extreme ultraviolet absorption probing of ultrafast dynamics.     

An atomic diffraction theory of molecular photoionization cross sections

A theory of molecular photoionization cross sections is developed on the basis of locally atomic character of the one-electron final state in the Golden Rule expression for the molecular orbital cross section. Ionization amplitudes from several atomic centres are added and rotationally averaged to produce molecular orbital cross sections displaying a sum of pseudo-atomic cross sections weighted according to the LCAO composition of the orbital and also two-centre products reflecting interference effects. The atomic ionization amplitudes are obtained by use of an atomic central potential constructed by an inversion procedure from the form of the ground state orbital. The theory is of a simple chemical nature but usually of at least semi-quantitative accuracy. In this work we illustrate the nature of the two-centre interference effects in small diatomic molecules (H₂, HF, N₂).     

Bohmian trajectory perspective on strong field atomic processes

The interaction of an atom with an intense laser field provides an important approach to explore the ultrafast electron dynamics and extract the information of the atomic and molecular structures with unprecedented attosecond temporal and angstrom spatial resolution. To well understand the strong field atomic processes, numerous theoretical methods have been developed, including solving the time-dependent Schr ?dinger equation(TDSE), classical and semiclassical trajectory method, quantum S-matrix theory within the strong-field approximation, etc. Recently, an alternative and complementary quantum approach, called Bohmian trajectory theory, has been successfully used in the strong-field atomic physics and an exciting progress has been achieved in the study of strong-field phenomena. In this paper, we provide an overview of the Bohmian trajectory method and its perspective on two strong field atomic processes, i.e., atomic and molecular ionization and high-order harmonic generation, respectively.     

On the complex momentum spectra of photoelectrons formed from H<Subscript>2</Subscript> in a strong laser field

We have experimentally investigated the ionization of molecular hydrogen in a strong, linearly polarized laser field. The angularly-resolved photoelectron spectra of H₂ were determined as a function of laser intensity at 800 nm, using pulses of 100 fs duration. A substantial portion of the molecular photoelectron spectra mimics those of atomic hydrogen. We provide qualitative interpretations for this and other features in the spectra. The very high resolution of our data will pose a stringent test on the validity of strong-field theories.     

One and two-center processes in high-order harmonic generation in diatomic molecules: Influence of the internuclear separation

We analyze the influence of different recombination scenarios, involving one or two centers, on high-order harmonic generation (HHG) in diatomic molecules, for different values of the internuclear separation. We work within the strong-field approximation, and employ modified saddle-point equations, in which the structure of the molecule is incorporated. We find that the two-center interference patterns, attributed to high-order harmonic emission at spatially separated centers, are formed by the quantum interference of the orbits starting at a center C _j and finishing at a different center C _ν in the molecule with those starting and ending at a same center C _j . Within our framework, we also show that contributions starting at different centers exhibit different orders of magnitude, due to the influence of additional potential-energy shifts. This holds even for small internuclear distances. Similar results can also be obtained by considering single-atom saddle-point equations and an adequate choice of molecular prefactors.     

Influence of the internuclear vector on ionization of molecules in intense laser field

We theoretically study the influence of the internuclear vector on molecular ionization in linear polarization laser fields through taking O₂, CO₂ as model molecules. We find that the ionization rates of O₂ and CO₂ depend on the molecular orientations. For O₂, the molecular orientation corresponding to the maximum ionization rate is about φ_m = 45^°, which is independent of the laser intensity; while for CO₂, this kind of molecular orientation varies with laser intensity. We also find the ionization suppression of molecule depends on the molecular orientations and the internuclear distance. The ionization suppression easily disappears for molecules with larger internuclear distance.     

Atomic orbitals and photoelectron intensity angular distribution patterns of MoS2 valence band

The ratio of atomic orbitals contributing to the valence band can be determined from the photoelectron intensity angular distribution (PIAD) by using linearly polarized light and display-type spherical mirror analyzer. The experiment was done for MoS₂ using a linearly polarized light at the photon energy of 45 eV perpendicularly incident to the sample surface. Atomic orbitals contributing to the bands near the Fermi level were investigated. The PIAD patterns around the Γ point showed splitting of intensity. The intensity at the top and bottom K points was strong, while the intensity was weak at the left and right side K points. The PIAD patterns from various kinds of atomic orbitals were calculated. By comparing the experimental PIAD patterns to the simulated ones, we concluded that at the Γ point Mo 4d_z2 and S 3p_z atomic orbitals are the main components and at the K points the Mo 4d_xy atomic orbital is dominant. The atomic orbital Mo 4d_x2−y2 also gives contribution to the PIAD pattern. These results were in good agreement with the coefficients of the atomic orbitals derived using ab initio band calculation.     

Theory of the angular distribution of molecular orbitalK x rays seen in heavy-ion-atom collisions

Dynamical calculations of angular distributions and intensities of two-collision 1s σ molecular orbital x rays in 12–90-MeV Ni + Ni collisions are reported. The Coriolis and spin-orbit coupling between 2pσ and 2pπ and the 3pσ and 3pπ molecular orbitals is included. Due to Coriolis coupling, the molecular wavefunctions and therefore the transition dipoles do not follow the rotation of the internuclear axis in collisions with small impact parameters, but remain approximately fixed in direction. Consequently one can predict the symmetry relations between the laboratoryx, y, andz components of the molecular orbital intensity and therefore the anisotropy of the radiation seen at energies near the united atomK α x-ray line. These relations are used to predict anisotropies of molecular orbital radiation in encounters with large united atom atomic numbers,Z ₁ +Z ₂>137. For Ni + Ni encounters, a lower population of the 2pπ and 3pπ orbitals than the 2pσ and 3pσ orbitals is needed to reproduce the observed anisotropies.     

The microwave spectrum and structure of chloryl fluoride

The microwave spectra of three isotopic species of chloryl fluoride, FClO₂, in its ground vibrational state, have been measured in the frequency region 8–37 GHz. The spectra have yielded values for the rotational constants, centrifugal distortion constants, and chlorine nuclear quadrupole coupling constants, as well as the molecular dipole moment, 1.722 ± 0.03 D. The molecule has been shown to have C_s symmetry, and a pyramidal configuration, with the chlorine atom at the apex of the pyramid. The following internuclear parameters were obtained:r(Cl?F)1.697±0.003 A r(Cl?F)=1.418±0.002AThe structural parameters, quadrupole coupling constants, dipole moment and force field are explained in terms of a bonding scheme in which a fluorine 2p atomic orbital overlaps with the highest occupied orbital of ClO₂; there is considerable evidence for withdrawal of electron density from this singly occupied antibonding orbital of ClO₂ toward the fluorine atom.     

Quasimolecular KX-ray excitation by bombarding La targets with La and Xe ions

The X-ray emission from 85 to 150 MeV Xe and 115 MeV La bombardments of thick natural La targets has been measured. The spectra and yields of X-ray emission are obtained. Continuous X-ray distributions have been found to lie beyond the target and projectile characteristic X-ray energies. The high-energy parts of these continua are interpreted as K-radiation of quasi-molecules with effective atomic numbers Z = 111 and Z = 114, respectively.     

Interpretation of the photoelectron spectra of OF2 and SF2

The photoelectron spectra of OF₂ and SF₂ are assigned, based on ab initio many-body Green's function calculations. In the energy range beyond about 20 eV the molecular orbital picture of ionization breaks down.     

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.