Ellipticity dependence of high-order harmonic generation from aligned molecules

We report ellipticity dependence of high-order harmonic generation (HHG) from aligned N2, O2, and CO2 molecules. Experimentally, we find that the ellipticity dependence is sensitive to molecular alignment and to the shape and symmetry of the valence orbitals. It is also found that the destructive interference in the recombination process affects the ellipticity dependence. Theoretically, we extend the original Lewenstein model to a more generalized model, which can be applicable to HHG from molecules, by introducing an electron acceleration parameter xi(theta) and by combining the molecular orbital method. The present observations are successfully explained by our model.     

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.     

高阶阈值上电离的量子电动力学理论

用非微扰量子电动力学理论研究一个由再散射产生的高阶阈值上电离（ATI）.利用形式散射理论给出了高阶ATI谱的解析形式，并且讨论了在高阶ATI中不同ATI通道的干涉效应和光电子以不同角度入射时的高阶ATI谱. 关键词： 阈值上电离 再散射 跃迁概率     

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.     

Molecular imaging using high-order harmonic generation and above-threshold ionization

Accurate molecular imaging via high-order harmonic generation relies on comparing harmonic emission from a laser-irradiated molecule and an adequate reference system. However, an ideal reference atom with the same ionization properties as the molecule is not always available. We show that for suitably designed, very short laser pulses, a one-to-one mapping from high-order harmonic frequencies to electron momenta in above-threshold ionization exists. Comparing molecular and atomic momentum distributions then provides the electron recollision amplitude in the molecule for enhanced molecular imaging. The method retrieves the molecular recombination transition moments highly accurately, even with suboptimal reference atoms.     

Polarization state of high-order harmonic emission from aligned molecules

High harmonic emission in isotropic gases is polarized in the same direction as the incident laser polarization. Laser-induced molecular alignment allows us to break the symmetry of the gas medium. By using aligned molecules in high harmonic generation experiments, we show that the polarization of the extreme ultraviolet emission depends strongly on the molecular alignment and the orbital structure. Polarization measurements give insight into the molecular orbital symmetry. Furthermore, molecular alignment will allow us to produce attosecond pulses with time-dependent polarization.     

Electron impact ionization of diatomic molecules

Cross sections for the ionization of N₂, CO and O₂ diatomic molecules by electron impact are calculated. The applied distorted wave model is based on our previous studies for positron impact, the molecular orbitals being described by Gaussian wavefunctions. Our study emphasizes the importance of electron exchange and of using correct distorted waves for the ejected electron.     

Near-threshold high-order harmonic spectroscopy with aligned molecules

We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization threshold. This Letter shows that high-harmonic spectroscopy can be extended to the near-threshold spectral range, which is in general spectroscopically rich.     

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.     

Even-odd harmonics generated from above-threshold ionization

We are reporting a theoretical prediction： The photoelectrons forming above-threshold-ionization （ATI） peaks emit both even and odd harmonics. These harmonics exhibit plateau and cut-off features similar to those odd-only harmonics observed in ATI experiments.     

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.     

Temperature dependence of polarizability of diatomic homonuclear molecules

The temperature dependence of the mean polarizability of the H₂, N₂, and O₂ molecules are calculated in the temperature range up to 2000 K. The values of polarizability derivatives of these molecules from the literature are used in the calculation. The temperature dependence of the mean polarizability of molecules is represented in the form of a second degree polynomial.     

Vibrational excitation of diatomic molecular ions in strong field ionization of diatomic molecules

A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.     

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.     

Role of resonances in the high-order harmonic enhancement in diatomic molecules

We present the study of high-order harmonic generation from the diatomic molecules produced during the laser plasma formation at the surfaces of semiconductors (InSb, InGaP, InP, GaAs). The discrepancy between the calculated molecular spectra and the observed resonance-enhanced harmonics in semiconductor molecules was attributed to the much greater influence of the strong electric field of laser radiation on the dynamical modification of the molecular spectra. The Stark shift of the energy levels of diatomic molecules was considered the main reason of the decrease of single harmonic efficiency compared to the monoatomic plasmas (In, As, Sb), where the enhancement of single harmonic was attributed to the closeness of the harmonic wavelength and the ionic transitions possessing strong oscillator strength.     

Angle-resolved spectra of the direct above-threshold ionization of diatomic molecule in IR + XUV laser fields

The direct above-threshold ionization(ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet(IR+XUV) laser fields is investigated by the frequency–domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ionization probability and the kinetic energy of the ionized electron, while the infrared(IR) laser field can broaden the energy distribution of the ionized electron. Our results demonstrate that, by using IR+XUV two-color laser fields, the angle-resolved spectra of the direct ATI can image the structural information of molecules without considering the recollision process of the ionized electron.     

Coulomb asymmetry in strong field multielectron ionization of diatomic molecules

We measure the angular distribution of an electron emitted by a strong elliptically polarized two-color laser field from exploding doubly charged molecular nitrogen. This angular distribution is vastly different for emission of the electron from the up-field core of the molecule as compared to that from the down-field core. The emission from the down-field core leads to a slight rotation with respect to the internuclear axis in the direction expected by the Coulomb effect of the remaining ion, while, for the emission from the up-field core, this direction is inversed. Our semiclassical simulations suggest that this unexpected angular distribution is caused by an initial longitudinal momentum of the electron freed by over-the-barrier ionization above the inner barrier in the molecule. The initial kinetic energy is in the range of the potential energy of the Stark-shifted orbital above the barrier.     

Ratiometric comparison of intense field ionization of atoms and diatomic molecules

Intense-laser ionization rates for rare gas atoms and diatomic molecules have been precisely compared by making simultaneous measurements of ionization yield vs laser intensity for mixed atomic and molecular targets. At a given laser intensity, the N (2) and F (2) ionization yields are slightly greater than that of Ar. Conversely, comparison of O (2) and S (2) with Xe indicates significant ionization suppression in these molecules. Recent molecular ionization models that successfully describe ionization suppression in O (2) and its absence in N (2) fail to explain our observations in F (2) and S (2).     

Iterative procedure for determining high-order corrections to the vibration-rotation spectra of diatomic molecules

The one-dimensional Schrödinger equation is reduced to a system of algebraic equations on the basis of the complex WKB method. As a result, recursion relations are obtained for the numerical calculation of high-order corrections to the vibration-rotation spectra of diatomic molecules. Various nonpolynomial representations of the potential are investigated.V. V. Kuibyshev State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 9–16, June, 1994.     

Nonsequential double ionization of diatomic molecules by elliptically polarized laser pulses

Using the classical ensemble method, we investigate nonsequential double ionization （NSDI） of diatomic molecules by elliptically polarized laser pulses. The results show that the ellipticity of the laser field has a strong suppression effect on NSDI probabilities both in parallel and perpendicular alignments. The double ionization （DI） channel is commonly dominated by NSDI, and the NSDI channel changes with ellipticity. As ellipticity increases, more and more NSDIs occur through recollision excitation with subsequent field ionization （RESI）. Moreover, like the case of linear polarization, the two electrons involved in NSDI for perpendicularly aligned molecules are more likely to emit into the opposite hemispheres as compared to the case of parallel alignment. Additionally, this alignment effect increases as ellipticity increases.