Molecular Strong-field Approximation Research Articles

Simulation of the above-threshold-ionization experiment using the molecular strong-field approximation: The choice of gauge

We investigate how various versions of the molecular strong-field approximation (MSFA) agree with the experiment by Grasbon et al. [Phys. Rev. A 63, 041402(R) (2001)], in which the suppression of the ionization yield in the low-energy spectrum of the ${\mathrm{O}}_{2}$ molecule, compared to the spectrum of its companion atom Xe, was observed. In this experiment, it was also found that the spectrum of the ${\mathrm{N}}_{2}$ molecule is comparable to the corresponding spectrum of its companion atom Ar. We show that the length-gauge version of the MSFA with the initial state dressed by the laser field gives the best agreement with the experimental data for both ${\mathrm{O}}_{2}$ and ${\mathrm{N}}_{2}$ molecules.

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.

Single-active-electron approximation for molecules in strong laser fields : Test application to H2

A new method for solving the electronic three-dimensional time-dependent Schrödinger equation (TDSE) for molecules in ultrashort intense laser fields was developed. In this method the molecules are described within the single-active-electron (SAE) approximation using density-functional theory (DFT). The method and its implementation is tested for H2 for which a full six-dimensional two-electron solution is obtained via a time-dependent configuration-interaction approach. For larger molecular systems (for which no full solution is possible) the novel SAE method can, e.g., be used to test the validity of simplified SAE-based models like the molecular strong-field approximation (MO-SFA) or the molecular-orbital Ammosov-Delone-Krainov (MO-ADK) model.

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.

Theory of strong-field ionization of alignedCO2

A theoretical framework for studying strong-field ionization of aligned molecules is presented, and alignment-dependent ionization yields are computed for ${\text{CO}}_{2}$. Our calculations are in unprecedented agreement with recent experiments. We find that the ionization process is affected by intermediate resonance states, and the alignment-dependent ionization yields do not follow the electron density of the initial states. The theory explains the breakdown of semianalytical theories, such as the molecular tunneling theory and strong-field approximation, where excited electronic structure is neglected.

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.

Comparative study of strong-field ionization in laser-irradiatedF2and other diatomic molecules: Density-functional-theory-based molecular strong-field approximation

The puzzling phenomenon of no suppression observed in experiments on strong-field ionization of laser-irradiated diatomic ${\mathrm{F}}_{2}$ molecules (as compared to its atomic counterpart Ar of nearly equal ionization potential) is addressed within the velocity-gauge formulation of molecular strong-field approximation (SFA). The approach essentially exploits the density-functional-theory (DFT) method applied for numerical composition of initial (laser-free) molecular states using the modified van Leuwen--Baerends (LB-$\ensuremath{\alpha}$) intramolecular binding potential, which incorporates both the exchange and correlation local-spin-density approximation (LSDA) potentials and also allows for construction of initial (laser-free) wave function correctly reproducing molecular and/or atomic valence shells and respective binding energies. Unlike the respective results of earlier alternative strong-field considerations (all predicting a high suppression in ${\mathrm{F}}_{2}$ ionization), our DFT SFA based calculation results unambiguously demonstrate no suppression in strong-field ionization of ${\mathrm{F}}_{2}$ versus its atomic (Ar) and molecular $({\mathrm{N}}_{2})$ counterparts. Our presented results also suggest that the predominant contribution to ${\mathrm{F}}_{2}$ ionization will always be from the $1{\ensuremath{\pi}}_{g}$ highest occupied molecular orbital (HOMO, corresponding to the outermost valence shell) and allow for quite a transparent physical interpretation. Namely, the phenomenon of no suppression in ${\mathrm{F}}_{2}$ ionization is just explained by the closed-shell nature of its $1{\ensuremath{\pi}}_{g}$ HOMO (and thus by its substantially more enhanced and pronounced electron-correlated response to an incident laser field). Quantitatively, the latter becomes manifest through equally large contributions from the correlation and exchange parts of the intramolecular LSDA potential to ${\mathrm{F}}_{2}$ and ${\mathrm{N}}_{2}$ valence shells, in contrast to ${\mathrm{O}}_{2}$ valence shells, to which the exchange part of the LSDA potential proved to contribute well, predominantly resulting in a high suppression of ionization relative to the atomic counterpart Xe.

Interference effects in high-order harmonic generation by homonuclear diatomic molecules

A theory of high-order harmonic generation by diatomic molecules is introduced. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are investigated. Using examples of homonuclear diatomic molecules such as ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$, it is shown that clear two-center interference minima in the harmonic spectra as a function of the molecular orientation appear only if the final molecular state is undressed. For ${\mathrm{H}}_{2}$ the positions of these minima are in agreement with the ab initio numerical results. Physically, the returned electron wave packet recombines into a molecular orbital, which is a linear combination of the atomic orbitals having different parities. The interference minima in the harmonic spectrum are caused by the destructive interference of the corresponding partial recombination amplitudes. In accordance with this, we have derived an interference minima condition which is valid for arbitrary homonuclear diatomic molecules.

Strong-field approximation for Coulomb explosion ofH2+andD2+by short intense laser pulses

We present a simple quantum mechanical model to describe Coulomb explosion of $\mathrm{H}_{2}{}^{+}$ and $\mathrm{D}_{2}{}^{+}$ by short, intense infrared laser pulses. The model is based on the length gauge version of the molecular strong-field approximation and is valid when the process of dissociation prior to ionization is negligible. The results are compared with recent experimental data for the proton kinetic energy spectrum [Th. Ergler et al., Phys. Rev. Lett. 95, 093001 (2005); D. S. Murphy et al., J. Phys. B 40, S359 (2007)]. Using a Franck-Condon distribution over initial vibrational states, the theory reproduces the overall shape of the spectrum with only a small overestimation of slow protons. The agreement between theory and experiment can be made perfect by using a non-Frank-Condon initial distribution characteristic for $\mathrm{H}_{2}{}^{+}\phantom{\rule{0.3em}{0ex}}(\mathrm{D}_{2}{}^{+})$ targets produced by strong-field ionization of ${\mathrm{H}}_{2}\phantom{\rule{0.3em}{0ex}}({\mathrm{D}}_{2})$. For comparison, we also present results obtained by two different tunneling models for this process.

Alignment-dependent above-threshold ionization of molecules

Within the molecular strong-field approximation, we study the effect of molecular alignment with respect to the linear polarization of an external electromagnetic field in above-threshold ionization rates for some diatomic and polyatomic molecules. We find that the shape of the above-threshold photoelectron ionization spectrum is largely independent of the orientation of the major molecular axis for N2, meaning that the spectra can be put on top of each other when appropriately scaled. This is also our general finding for electrons emitted along the polarization direction for other molecules, e.g., O2, C2H4 and C6H6, although at some special geometries ionization is suppressed by symmetry selection rules. For N2, our calculations support recent experimental findings in N2 by Zeidler et al (2006 J. Phys. B: At. Mol. Opt. Phys. 39 L159).

Strong-field approximation for ionization of a diatomic molecule by a strong laser field

We present a theory of ionization of diatomic molecules by a strong laser field. A diatomic molecule is considered as a three-particle system, which consists of two heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. The exact $S$-matrix element for ionization is presented in a form in which the laser-molecule interaction is emphasized. This form is useful for application of the molecular strong-field approximation (SFA). We introduced two forms of the molecular SFA, one with the field-free and the other with the field-dressed initial molecular bound state. We relate these two forms of our modified molecular SFA to the standard molecular SFAs, introduced previously using the length gauge and the velocity gauge. Numerical examples of the ionization rates of ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$ molecules are shown and compared for all four versions of the molecular SFA and we suggest that our modified molecular SFA should be used instead of the standard molecular SFA.

Comment on “Strong-field ionization of laser-irradiated light homonuclear diatomic molecules: A generalized strong-field approximation–combination of atomic orbitals model”

V. I. Usachenko and S.-I. Chu [Phys. Rev. A, 71, 063410 (2005)] discuss the molecular strong-field approximation in the velocity gauge formulation and indicate that some of our earlier velocity gauge calculations are inaccurate. Here we comment on the results of Usachenko and Chu. First, we show that the molecular orbitals used by Usachenko and Chu do not have the correct symmetry, and second, that it is an oversimplification to describe the molecular orbitals in terms of just a single linear combination of two atomic orbitals. Finally, some values for the generalized Bessel function are given for comparison.

High-order harmonic generation in laser-irradiated homonuclear diatomics: The velocity gauge version of the molecular strong-field approximation

The generation of high harmonics in laser-irradiated light homonuclear diatomics (H2+, N2 and O2) compared to that in atomic counterparts (of nearly identical binding energy) is studied within the velocity gauge version of conventional strong-field approximation. The applied strong-field approach (we alternatively developed earlier to incorporate rescattering effects beyond the conventional saddle-point approximation) is currently extended to molecular case by means of supplement the standard linear combination of atomic orbitals} and molecular orbitals method. The associated model proved to adequately reproduce a general shape and detailed structure of molecular harmonic spectra, which demonstrate a number of remarkable distinctive differences from respective atomic spectra calculated under the same laser pulses. The revealed differences are found to be strongly dependent on internuclear separation and also very sensitive to the orbital and bonding symmetry of contributing molecular valence shell. In particular, the model correctly predicts the behavior of high-frequency plateau (both for its extent and even details of structure) in molecular harmonic spectra at small (nearly equilibrium) and large internuclear separations. In addition, for some group of harmonics, the harmonic emission rates were ascertained to dominate by contribution from inner molecular shells of higher binding energy and different orbital symmetry compared to the outermost molecular orbital normally predominantly contributing.

Strong-field ionization of diatomic molecules and companion atoms: Strong-field approximation and tunneling theory including nuclear motion

We present a detailed comparison of strong-field ionization of diatomic molecules and their companion atoms with nearly equal ionization potentials. We perform calculations in the length and velocity gauge formulations of the molecular strong-field approximation and with the molecular tunneling theory, and in both cases we consider effects of nuclear motion. A comparison of our results with experimental data shows that the length gauge strong-field approximation gives the most reliable predictions.

Influence of molecular symmetry on strong-field ionization: Studies on ethylene, benzene, fluorobenzene, and chlorofluorobenzene

Using the molecular strong-field approximation we consider the effects of molecular symmetry on the ionization of molecules by a strong, linearly polarized laser pulse. Electron angular distributions and total ionization yields are calculated as a function of the relative orientation between the molecule and the laser polarization. Our studies focus on ethylene (C$_2$H$_4$), benzene (C$_6$H$_6$), fluorobenzene (C$_6$H$_5$F), and ortho chlorofluorobenzene (1,2 C$_6$H$_4$ClF), the molecules representing four different point groups. The results are compared with experiments, when available, and with the molecular tunneling theory appropriately extended to non-linear polyatomic molecules. Our investigations show that the orientational dependence of ionization yields is primarily determined by the nodal surface structure of the molecular orbitals.

Strong-field ionization of N2: length and velocity gauge strong-field approximation and tunnelling theory

Molecular strong-field approximation calculations in the length and velocity gauges are performed on N2 to produce photoelectron angular distributions, total ionization rates and ion signals as a function of the orientation between the laser field and the molecule. Our study is supplemented by molecular tunnelling calculations, the results of which are in qualitative agreement with the experimental findings and the length gauge molecular strong-field approximation results.