Harmonic Generation In Molecules Research Articles

Site-specific tunnel-ionization in high harmonic generation in molecules

We demonstrate that the standard picture of strong-field tunnel-ionization from molecules should be reformulated. The extended nature of the molecular potential implies the separation of some of the molecular sites from the edge of the ionization barrier. We show that the dependence of the tunnel probability with the distance to the barrier is translated into the ionized wavepacket, modifying substantially the high-order harmonic emission. The introduction of the dependence of tunnel ionization with the molecular site significantly improves the theoretical description of high-order harmonic generation in molecules, which is used as a cornerstone in high-harmonic spectroscopy and attosecond imaging.

Signatures of Coriolis effects in molecular bichromatic circularly polarized high-order harmonic generation

SynopsisCircularly polarized high-order harmonic generation in molecules by bicircular pulses has been studied. We describe the laser induced electron dynamics in a rotating frame. The Coriolis effects give rise to orthogonal polarization harmonics. It is found that harmonic property depends on pulse frequencies and helicities, molecular orbital symmetries, and electron localizations, illustrating the importance of the field-molecule symmetry. The feature is described by dynamical symmetry theory and time profile analysis of harmonics.

Controlling circularly polarized high-order harmonic generation in molecules by intense tricircular laser pulses

We present a scheme to control circularly polarized high-order harmonic generation (HHG) in molecules, the source of extreme ultraviolet and x-ray pulses, by multiple frequency co- and counter-rotating circularly polarized laser pulses. Simulations are performed on the oriented single electron molecular ions with cyclic equilateral geometry, ${\mathrm{H}}_{3}^{2+}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{\mathrm{H}}_{4}^{3+}$, as benchmark models, by numerically solving time-dependent Schr\"odinger equations. Results show that circularly polarized HHG can be produced with extended harmonic order cutoffs, which depend on the intensity ratio of fields and the field-molecule symmetry. We describe the laser induced electron dynamics in a rotating frame to examine recollision dynamics and Coriolis effects. The resulting modulation of HHG spectra arises from a combination of two bicircular fields with counter-rotating and co-rotating components. It is also found that harmonic polarization is a function of the pulse frequencies and helicities, illustrating the importance of matching the field-molecule symmetry. The results in principle illustrate a method for controlling circular polarization properties of harmonics in molecules.

Electron correlations and pre-collision in the re-collision picture of high harmonic generation

We discuss the seminal three-step model and the re-collision picture in the context of high harmonic generation in molecules. In particular, we stress the importance of multi-electron correlation during the first and the third of the three steps of the process: (1) the strong-field ionization and (3) the recombination. We point out how an accurate account of multi-electron correlations during the third recombination step allows one to gauge the importance of pre-collision: the term coined by Eberly ( private communication) to describe unusual pathways during the first, ionization, step.

Circularly polarized molecular high harmonic generation using a bicircular laser

We investigate the process of circularly polarized high harmonic generation in molecules using a bicircular laser field. In this context, we show that molecules offer a very robust framework for the production of circularly polarized harmonics, provided their symmetry is compatible with that of the laser field. Using a discrete time-dependent symmetry analysis, we show how all the features (harmonic order and polarization) of spectra can be explained and predicted. The symmetry analysis is generic and can easily be applied to other target and/or field configurations.

Exchange and polarization effect in high-order harmonic imaging of molecular structures

We analyze the importance of exchange, polarization, and electron-electron correlation in high-order harmonic generation in molecules interacting with intense laser fields. We find that electron exchange can become particularly important for harmonic emission associated with intermediate excitations in the molecular ion. In particular, for orbitals associated with two-hole one-particle excitations, exchange effects can eliminate structure-related minima and maxima in the harmonic spectra. Laser-induced polarization of the neutral molecule may also have major effects on orbital structure-related minima and maxima in the harmonic spectra. Finally, we show how exchange terms in recombination can be viewed as a shakedownlike process induced by sudden electronic excitation in the ion.

Single attosecond pulse generation from aligned molecules using two-color polarization gating

We theoretically investigate high-order harmonic generation from the diatomic molecules in an orthogonally polarized two-color few-cycle optical field by controlling the incident angle of the recolliding electron. We show that the combination of molecules and two-color polarization gating allows us to significantly suppress undesirable satellite pulses owing to the orientation dependence of high-order harmonic generation in molecules, giving rise to the generation of single attosecond pulses.

Assessing different forms of the strong-field approximation for harmonic generation in molecules

We analyse three different formulations of the strong-field approximation for high-harmonic generation in diatomic molecules, based on length, velocity and acceleration form for the recombination amplitude. We compare the predictions for the two-centre interference with those from the time-dependent Schrödinger equation. We find that the velocity form gives the closest agreement with the exact results while being the simplest from a computational point of view.

High-order harmonic generation in light molecules: moving-nuclei semiclassical simulations

A simple semiclassical approach has been proposed recently to describe the strong-field phenomena in molecules beyond the Born–Oppenheimer approximation. We use this approach to study high harmonic generation in molecules with moving nuclei. We study how the interplay between the vibrational and rotational excitations, as well as dissociation and ionization, influences the harmonic spectra from light molecules. Special attention is paid to the limitations imposed by the nuclear motion in light molecules on the observability of the two-centre recombination interference in molecular high harmonic generation. The possibilities of using the nuclear motion to control the temporal confinement of harmonic radiation are discussed.

Influence of nuclear vibration on harmonic generation in molecules

The effect of vibrational motion on harmonic generation in molecules is studied within the strong-field approximation. Simple expressions are given for the cut-off energy and for the ratio of spectral intensities from two isotopes. The latter is based on electronic trajectories from the simple-man's model. The influence of vibration is given by a correlation function that is sensitive to the overlap between the initial vibrational wave packet and the wave packet after the evolution in the Born–Oppenheimer potential of the ionized molecule.

Probing Proton Dynamics in Molecules on an Attosecond Time Scale

We demonstrate a technique that uses high-order harmonic generation in molecules to probe nuclear dynamics and structural rearrangement on a subfemtosecond time scale. The chirped nature of the electron wavepacket produced by laser ionization in a strong field gives rise to a similar chirp in the photons emitted upon electron-ion recombination. Use of this chirp in the emitted light allows information about nuclear dynamics to be gained with 100-attosecond temporal resolution, from excitation by an 8-femtosecond pulse, in a single laser shot. Measurements on molecular hydrogen and deuterium agreed well with calculations of ultrafast nuclear dynamics in the H2+ molecule, confirming the validity of the method. We then measured harmonic spectra from CH4 and CD4 to demonstrate a few-femtosecond time scale for the onset of proton rearrangement in methane upon ionization.

Molecular orbital dependence of high-order harmonic generation1

We examine the role of the electronic orbital of a molecule in the process of high-order harmonic generation. To do this, measurements of high-order harmonic generation in molecules (O2, N2, H2, CO2 and small alkanes) and atoms (Xe, Ar and Kr) have been carried out with intense few-optical-cycle pulses. Comparison between molecules and their ‘companion' atoms (i.e. those with nearly equal ionization potential) was made. The molecule response in the high-field regime is treated by adopting an ‘atom-like' model for the forms of the molecular orbitals employing the Lewenstein et al. model, properly modified in order to account for the nonlinear dipole moment of a randomly oriented molecule ensemble. The calculation procedure is described here in detail. There is good agreement between the spectra calculated using this model and the harmonic cut-off position and the shape of the measured spectra. The cut-offs of O2 and CO2 extend far beyond the cut-offs of Xe and Kr respectively, in contrast with N2 and H2 which exhibit cutoffs very close to that of Ar. This behaviour is well explained by adopting the atom-like approximation. A series of alkanes has also been investigated and again the spectra are well matched by this simple model.

Analysis of recombination in high-order harmonic generation in molecules

We show that the dependence of high-order harmonic generation (HHG) on the molecular orientation can be understood within a theoretical treatment that does not involve the strong field of the laser. The results for ${\mathrm{H}}_{2}$ show excellent agreement with time-dependent strong-field calculations for model molecules, and this motivates a prediction for the orientation dependence of HHG from the ${\mathrm{N}}_{2}$ $3{\ensuremath{\sigma}}_{g}$ valence orbital. For both molecules, we find that the polarization of recombination photons is influenced by the molecular orientation. The variations are particularly pronounced for the ${\mathrm{N}}_{2}$ valence orbital, which can be explained by the presence of atomic $p$ orbitals.

Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects

We solve exactly the three-dimensional time-dependent Schr\"odinger equation for the ${\mathrm{H}}_{2}^{+}$ molecular ion in a combination of intense short laser pulses and static magnetic fields using a newly developed adaptive grid method. This allows for a study of the control of high-order harmonic generation in molecules by various orientations of the magnetic and laser fields in order to control electron recollision with nuclei. In particular, we find regimes of pure even harmonic or even and odd harmonic generation for particular field and frequency configurations. Furthermore, magnetic fields are found to extend harmonic generation plateaus to higher order as a result of further nonlinear coupling between charges and fields.

Orientation dependence of high-order harmonic generation in molecules

We present two- and three-dimensional model calculations of high-order harmonic generation in ${\mathrm{H}}_{2}^{+}.$ The harmonic spectra exhibit clear signatures of intramolecular interference. An interference minimum appears at a harmonic order that depends on the molecular orientation. Harmonic generation in three-center molecules is studied on the basis of two-dimensional calculations for a ${\mathrm{H}}_{3}^{2+}$ model system. From analytical considerations, the orientation dependence of the harmonic intensities in three-center molecules exhibits a double minimum due to intramolecular interference. In the numerical results, the double minimum is broadened into a single wide minimum. The effect of nonzero laser ellipticity on harmonic generation is investigated by means of two-dimensional simulations for ${\mathrm{H}}_{2}^{+}.$ We find that harmonic generation with elliptical polarization is governed by interference effects similar to linear polarization.

Attosecond control of ionization and high-order harmonic generation in molecules

Attosecond control of ionization and high-order harmonic generation in molecules