Probing orbital structure of polyatomic molecules by high-order harmonic generation

Theoretical Simulation of the High–Order Harmonic Generated from Neon Atom Irradiated by the Intense Laser Pulse

Based on the strong field approximation theory and numerical solution of Maxwell’s propagation equations, the high–order harmonic is generated from a neon (Ne) atom irradiated by a high–intensity laser pulse whose central wavelength is 800 nm. In the harmonic spectrum, it is found that in addition to the odd harmonics of the driving laser, a new frequency peak appeared. By examining the time–dependent behavior of the driving laser, it is found that the symmetry of the laser field is broken. We demonstrated that these new spectrum peaks are caused by the intensity reduction and frequency blue shift of the high–intensity laser during propagation. Our results reveal that it is feasible to modulate the harmonics of the specific energy to produce high–intensity harmonic emission by changing the gas density and the position of the gas medium interacting with the laser pulse.

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H⁺ and C²⁺ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of [Formula: see text] demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

Orientation and Alignment dynamics of polar molecule driven by shaped laser pulses

We review the theoretical status of intense laser induced orientation and alignment-a field of study which lies at the interface of intense laser physics and chemical dynamics and having potential applications such as high harmonic generation, nano-scale processing and control of chemical reactions. The evolution of the rotational wave packet and its dynamics leading to orientation and alignment is the topic of the present discussion. The major part of this article primarily presents an overview of recent theoretical progress in controlling the orientation and alignment dynamics of a molecule by means of shaped laser pulses. The various theoretical approaches that lead to orientation and alignment such as static electrostatic field in combination with laser field(s), combination of orienting and aligning field, combination of aligning fields, combination of orienting fields, application of train of pulses etc. are discussed. It is observed that the train of pulses is quite an efficient tool for increasing the orientation or alignment of a molecule without causing the molecule to ionize. The orientation and alignment both can occur in adiabatic and non-adiabatic conditions with the rotational period of the molecule taken under consideration. The discussion is mostly limited to non-adiabatic rotational excitation (NAREX) i.e. cases in which the pulse duration is shorter than the rotational period of the molecule. We have emphasised on the so called half-cycle pulse (HCP) and square pulse (SQP). The effect of ramped pulses and of collision on the various laser parameters is also studied. We summarize the current discussion by presenting a consistent theoretical approach for describing the action of such pulses on movement of molecules. The impact of a particular pulse shape on the post-pulse dynamics is also calculated and analysed. In addition to this, the roles played by various laser parameters including the laser frequency, the pulse duration and the system temperature etc. are illustrated and discussed. The concept of alignment is extended from one-dimensional alignment to three-dimensional alignment with the proper choice of molecule and the polarised light. We conclude the article by discussing the potential applications of intense laser orientation and alignment.

Dissociative Ionization of Argon Dimer by Intense Femtosecond Laser Pulses

We experimentally and theoretically studied dissociative ionization of argon dimer driven by intense femtosecond laser pulses. In the experiment, we measured the ion yield and the angular distribution of fragmental ions generated from the dissociative ionization channels of (1,1) (Ar₂²⁺ → Ar⁺ + Ar⁺) and (2,1) (Ar₂³⁺ → Ar²⁺ + Ar⁺) using a cold target recoil ion momentum spectroscopy. The channel ratio of (2,1)/(1,1) is 4.5-7.5 times of the yield ratio of double ionization to single ionization of argon monomer depending on the laser intensity. The measurement verified that the ionization of Ar⁺ is greatly enhanced if there exists a neighboring Ar⁺ separated by a critical distance. In addition, the fragmental ions exhibit an anisotropic angular distribution with the peak along the laser polarization direction and the full width at half maximum becomes broader with increasing laser intensity. Using a full three-dimensional classical ensemble model, we calculated the angle-dependent multiple ionization probability of argon dimer in intense laser fields. The results show that the experimentally observed anisotropic angular distribution of fragmental ions can be attributed to the angle-dependent enhanced ionization of the argon dimer in intense laser fields.

Molecular frame photoemission by a comb of elliptical high-order harmonics: a sensitive probe of both photodynamics and harmonic complete polarization state

Due to the intimate anisotropic interaction between an XUV light field and a molecule resulting in photoionization (PI), molecular frame photoelectron angular distributions (MFPADs) are most sensitive probes of both electronic/nuclear dynamics and the polarization state of the ionizing light field. Consequently, they encode the complex dipole matrix elements describing the dynamics of the PI transition, as well as the three normalized Stokes parameters s₁, s₂, s₃ characterizing the complete polarization state of the light, operating as molecular polarimetry. The remarkable development of advanced light sources delivering attosecond XUV pulses opens the perspective to visualize the primary steps of photochemical dynamics in time-resolved studies, at the natural attosecond to few femtosecond time-scales of electron dynamics and fast nuclear motion. It is thus timely to investigate the feasibility of measurement of MFPADs when PI is induced e.g., by an attosecond pulse train (APT) corresponding to a comb of discrete high-order harmonics. In the work presented here, we report MFPAD studies based on coincident electron-ion 3D momentum imaging in the context of ultrafast molecular dynamics investigated at the PLFA facility (CEA-SLIC), with two perspectives: (i) using APTs generated in atoms/molecules as a source for MFPAD-resolved PI studies, and (ii) taking advantage of molecular polarimetry to perform a complete polarization analysis of the harmonic emission of molecules, a major challenge of high harmonic spectroscopy. Recent results illustrating both aspects are reported for APTs generated in unaligned SF₆ molecules by an elliptically polarized infrared driving field. The observed fingerprints of the elliptically polarized harmonics include the first direct determination of the complete s₁, s₂, s₃ Stokes vector, equivalent to (ψ, ε, P), the orientation and the signed ellipticity of the polarization ellipse, and the degree of polarization P. They are compared to so far incomplete results of XUV optical polarimetry. We finally discuss the comparison between the outcomes of photoionization and high harmonic spectroscopy for the description of molecular photodynamics.

Velocity map imaging with non-uniform detection: Quantitative molecular axis alignment measurements via Coulomb explosion imaging

We present a method for inverting charged particle velocity map images which incorporates a non-uniform detection function. This method is applied to the specific case of extracting molecular axis alignment from Coulomb explosion imaging probes in which the probe itself has a dependence on molecular orientation which often removes cylindrical symmetry from the experiment and prevents the use of standard inversion techniques for the recovery of the molecular axis distribution. By incorporating the known detection function, it is possible to remove the angular bias of the Coulomb explosion probe process and invert the image to allow quantitative measurement of the degree of molecular axis alignment.

Quantum unidirectional rotation directly imaged with molecules

A gas-phase molecular ensemble coherently excited to have an oriented rotational angular momentum has recently emerged as an appropriate microscopic system to illustrate quantum mechanical behavior directly linked to classical rotational motion, which has a definite direction. To realize an intuitive visualization of such a unidirectional molecular rotation, we report high-resolution direct imaging of direction-controlled rotational wave packets in nitrogen molecules. The rotational direction was regulated by a pair of time-delayed, polarization-skewed laser pulses, introducing the dynamic chirality to the system. The subsequent spatiotemporal propagation was tracked by a newly developed Coulomb explosion imaging setup. From the observed molecular movie, time-dependent detailed nodal structures, instantaneous alignment, angular dispersion, and fractional revivals of the wave packet are fully characterized while the ensemble keeps rotating in one direction. The present approach, providing an accurate view on unidirectional rotation in quantum regime, will guide more sophisticated molecular manipulations by utilizing its capability in capturing highly structured spatiotemporal evolution of molecular wave packets.

Probing rotational wave-packet dynamics with the structural minimum in high-order harmonic spectra

We investigate the alignment-dependent high-order harmonic spectrum generated from nonadiabatically aligned molecules around the first half rotational revival. It is found that the evolution of the molecular alignment is encoded in the structural minima. To reveal the relation between the molecular alignment and the structural minimum in the high-order harmonic spectrum, we perform an analysis based on the two-center interference model. Our analysis shows that the structural minimum position depends linearly on the inverse of the alignment parameter <cos²θ>. This linear relation indicates the possibility of probing the rotational wave-packet dynamics by measuring the spectral minima.

Quantum mechanical properties of graphene nano-flakes and quantum dots

In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference.

Extracting continuum electron dynamics from high harmonic emission from molecules

We show that high harmonic generation is the most sensitive probe of rotational wave packet revivals, revealing very high-order rotational revivals for the first time using any probe. By fitting high-quality experimental data to an exact theory of high harmonic generation from aligned molecules, we can extract the underlying electronic dipole elements for high harmonic emission and uncover that the electron gains angular momentum from the photon field.

Ripple induced changes in the wavefunction of graphene: an example of a fundamental symmetry breaking

Ideally, graphene may be regarded as a strictly 2-D structure. However, as it exists in a 3-D world, perturbations often distort this ideal 2-D structure. Under a variety of conditions graphene has been shown to develop ripples, which may have undesirable consequences for a variety of properties of graphene, such as electron transport. In addition to this, it has been speculated that ripples may be an intrinsic property of graphene, and it has also been suggested that unlocking the secrets of these ripples could be useful in the search for (an understanding of) the elusive Higgs boson. However, ripples in graphene can only be avoided, or utilized, if they can be reproducibly detected. Here we explore the most fundamental aspect of these ripples, that is, the effect of a static ripple structure on various properties of large graphene nanoflakes. We find that the mechanical, thermodynamic and electronic properties are unaltered by this fundamental rippling, but this spontaneous symmetry breaking induces a significant change in the structure of the wavefunction. This profound effect occurs only at the most basic level, but it should be, in principle, experimentally observable.

Scaling law for energy-momentum spectra of atomic photoelectrons

A scaling law which was used to classify photoelectron angular distributions (PADs) is now extended to photoelectron kinetic energy spectra. Both a theoretical proof and an independent verification are presented. Considering PADs are of photoelectron momentum spectra, this extension really extends the scaling law to the entire energy-momentum spectra. The scaling law for photoelectron energy-momentum spectra applies to both directly ionized and rescattered photoelectrons. Re-scaling experimental input parameters without loosing the physical essence with this scaling law may ease the experimental conditions and reduce the material and the energy consumptions in the experiments.

Laser-induced alignment and anti-alignment of rotationally excited molecules

We numerically investigate the post-pulse alignment of rotationally excited diatomic molecules upon nonresonant interaction with a linearly polarized laser pulse. In addition to the simulations, we develop a simple model which qualitatively describes the shape and amplitude of post-pulse alignment induced by a laser pulse of moderate power density. In our treatment we take into account that molecules in rotationally excited states can interact with a laser pulse not only by absorbing energy but also by stimulated emission. The extent to which these processes are present in the interaction depends, on the one hand, on the directionality of the molecular angular momentum (given by the M quantum number), and on the other hand on the ratio of transition frequencies and pulse duration (determined by the J number). A rotational wave packet created by a strong pulse from an initially pure state contains a broad range of rotational levels, over which the character of the interaction can change from non-adiabatic to adiabatic. Depending on the laser pulse duration and amplitude, the transition from the non-adiabatic to the adiabatic limit proceeds through a region with dominant rotational heating, or alignment, for short pulses and a large region with rotational cooling, and correspondingly preferred anti-alignment, for longer pulses.

High energy proton ejection from hydrocarbon molecules driven by highly efficient field ionization

We investigated the ejection of energetic protons from a series of polyatomic hydrocarbon molecules exposed to 790 nm 27 fs laser pulses. Using multiparticle coincidence imaging we were able to decompose the observed proton energy spectra into the contributions of individual fragmentation channels. It is shown that the molecules can completely fragment already at relatively low peak intensities of a few 10(14)  W/cm(2), and that the protons are ejected in a concerted Coulomb explosion from unexpectedly high charge states. The observations are in agreement with enhanced ionization taking place at many C-H bonds in parallel.

Retrieving angular distributions of high-order harmonic generation from a single molecule

We present a novel method to retrieve angular distributions of high-order harmonic generation from a single molecule. This technique uses an iterative procedure based only on experimental results of time and angle-dependent harmonic signals, and no actual shape of molecular orbital is assumed. The molecular axis distribution in a target gas can simultaneously be deduced in this procedure. The angle-dependent signal retrieved for a single N2 and O2 molecule is demonstrated to reflect the highest occupied molecular orbital, excluding the ambiguity due to the imperfect alignment.

Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells

Detailed electronic many-body configurations are extracted from quantitatively measured time-resolved nonlinear absorption spectra of resonantly excited GaAs quantum wells. The microscopic theory assigns the observed spectral changes to a unique mixture of electron-hole plasma, exciton, and polarization effects. Strong transient gain is observed only under cocircular pump-probe conditions and is attributed to the transfer of pump-induced coherences to the probe.

Extension of high harmonic spectroscopy in molecules by a 1300 nm laser field

The emerging techniques of molecular spectroscopy by high order harmonic generation have hitherto been conducted only with Ti:Sapphire lasers which are restricted to molecules with high ionization potentials. In order to gain information on the molecular structure, a broad enough range of harmonics is required. This implies using high laser intensities which would saturate the ionization of most molecular systems of interest, e.g. organic molecules. Using a laser at 1300 nm, we are able to extend the technique to molecules with relatively low ionization potentials (approximately 11 eV), observing wide harmonic spectra reaching up to 60 eV. This energy range improves spatial resolution of the high harmonic spectroscopy to the point where interference minima in harmonic spectra of N(2)O and C(2)H(2) can be observed.

Ideal waveform to generate the maximum possible electron recollision energy for any given oscillation period

We present the perfect waveform which, during a strong field interaction, generates the maximum possible electron recollision energy for any given oscillation period, over 3 times as high as that for a pure sinusoidal wave. This ideal waveform has the form of a linear ramp with a dc offset. A genetic algorithm was employed to find an optimized practically achievable waveform composed of a longer wavelength field, to provide the offset, in addition to higher frequency components. This second waveform is found to be capable of generating electron recollision energies as high as those for the perfect waveform while retaining the high recollision amplitudes of a pure sinusoidal wave. Calculations of high harmonic generation demonstrate this enhancement, by increasing the cutoff energy by a factor of 2.5 while maintaining the harmonic yield, providing an enhanced tool for attosecond science.

Dynamic properties of angle-dependent high-order harmonic generation from coherently rotating molecules

High-order harmonic generation from coherently rotating N2 and O2 molecules has been observed for different alignment angles in a pump and probe experiment using femtosecond laser pulses. The results obtained are in excellent agreement with those calculated using a recently developed theory, which represent the characteristic properties predicted for angle-dependent harmonic generation. It is shown that polarization geometry and alignment distribution play essential roles in potential applications to probe electronic structure and dynamics of molecular systems.

Dynamic two-center interference in high-order harmonic generation from molecules with attosecond nuclear motion

We report a new dynamic two-center interference effect in high-harmonic generation from H2, in which the attosecond nuclear motion of H2+ initiated at ionization causes interference to be observed at lower harmonic orders than would be the case for static nuclei. To enable this measurement we utilize a recently developed technique for probing the attosecond nuclear dynamics of small molecules. The experimental results are reproduced by a theoretical analysis based upon the strong-field approximation which incorporates the temporally dependent two-center interference term.

Internal momentum state mapping using high harmonic radiation

We numerically demonstrate so-far undescribed features in ionization and high harmonic generation from bound states with nonvanishing electronic angular momentum. The states' modified response to a strong laser pulse can be exploited for novel measurement and pulse production schemes. It is shown that angularly asymmetric tunneling from the states can be mapped onto variations of high harmonic intensities and that near-circularly polarized isolated attosecond extreme ultraviolet or x-ray pulses can be produced.

Interplay of polarization geometry and rotational dynamics in high-order harmonic generation from coherently rotating linear molecules

Recent reports on intense-field pump-probe experiments for high-order harmonic generation (HHG) from coherently rotating linear molecules have revealed remarkable characteristic effects of the simultaneous variation of the polarization geometry and the time delay on the high-order harmonic signals. We analyze the effects and give a unified theoretical account of the experimental observations. Furthermore, characteristic behavior at critical polarization angles are found that can help to identify the molecular orbital symmetry in connection with the problem of molecular imaging from the HHG data.

Molecular recollision interferometry in high harmonic generation

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned CO(2) molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.