Laser Polarization Axis Research Articles

Molecular orbital tomography of HOMO and HOMO-1 of the nonlinear molecule H2O: The study on multi-orbital effects

Molecular orbital tomography (MOT) through high-order harmonic generation (HHG) is a crucial method for probing individual molecular orbitals. Previous studies mainly focused on linear molecules such as N2, and CO, where valence orbitals were imaged by detecting harmonic emission at various alignments. In this study, we investigate the HHG from the water molecules, with the aim of exploring MOT for nonlinear molecules. By employing the time-dependent density functional theory, we obtain HHG spectra for different angles between the laser polarization and molecular symmetry axis. By manipulating the scanning planes (planes perpendicular to the laser propagation direction and contain the field polarization direction), specific orbitals can be selectively imaged. Particularly, a well-reconstructed highest occupied molecular orbital (HOMO) is obtained when the laser scanning plane approximately aligns with the nodal plane of HOMO-1. However, when the laser polarization deviates from the nodal plane, multiple orbitals contribute to the HHG process, and we visualize the orbital distortions resulting from such effects. Furthermore, HOMO-1, can be reconstructed when the laser scanning plane aligns with the nodal plane of HOMO. This research significantly advances the development of MOT and opens up intriguing possibilities for reconstructing orbitals of more complex molecules.

Elliptical high-order harmonic generation from current-carrying orbitals of prealigned molecules

The polarization of high harmonics generated from current-carrying state of nitric oxide molecules irradiated by linear laser fields is investigated by numerically solving the three-dimensional time-dependent Schrödinger equation. It is found that the ellipticity of high harmonics is obviously dependent on the polar angle between the driving laser polarization and molecular axis which is interpreted by the strong field approximation model. Moreover, our results also show that the helicity of near-threshold harmonics is opposite to that of plateau harmonics when the molecule is at any polar angle. To analyze this phenomenon, we simulate the dipole matrix element numerically. Finally, the attosecond pulses with opposite helicities can be obtained by synthesizing near-threshold and plateau harmonics. The ellipticity can be tuned by the alignment angle of molecules. Our work may provide a theoretical guiding and detection tool for the electron dynamics of molecular current-carrying states.

Non-adiabatic dissociation dynamics of Ar⋯I2 (E, v) intermolecular vibrational levels probed using velocity-map imaging.

Ion time-of-flight velocity-map imaging was used to measure the kinetic-energy distributions of the I2 ion-pair fragments formed after photoexcitation of Ar⋯I2 complexes to intermolecular vibrational levels bound within the Ar + I2 (E, vE = 0-2) potential energy surfaces. The kinetic-energy distributions of the I2 products indicate that complexes in the Ar⋯I2 (E, vE) levels preferentially dissociate into I2 in the D and β ion-pair states with no change in I2 vibrational excitation. The energetics of the levels prepared suggest that there is a non-adiabatic coupling of the initially prepared levels with the continuum of states lying above the Ar + I2 (D, vD = vE) and Ar + I2 (β, vβ = vE) dissociation limits. The angular anisotropies of the I2 product signals collected for many of the Ar⋯I2 (E, vE) levels have maxima parallel to the laser polarization axis. This contradicts expectations for the prompt dissociation of complexes with T-shaped geometries, which would result in images with maxima perpendicular to the polarization axis. These anisotropies suggest that there is a perturbation of the transition moment in these clusters or there are additional intermolecular interactions, likely those sampled while traversing above the attractive wells of the lower-energy potentials during dissociation. I2 (D', vD') products are also identified when preparing several of the low-lying levels localized in the T-shaped well of the Ar + I2 (E, vE = 0-2) potentials, and they are formed in multiple νD' vibrational levels spanning energy ranges up to 500cm-1.

Relativistic Two-Photon Matrix Elements for Attosecond Delays

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science by using Dirac–Fock formalism. A direct comparison of Wigner–Smith–Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the relativistic random phase approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated by using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as argon, show negligible relativistic effects, whereas heavier elements, such a krypton and xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notably close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner–Smith–Eisenbud delay and a universal continuum–continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

Anisotropy Measurements from the Near-Threshold Photodissociation of the N2-NO Complex.

We have used velocity map ion imaging to measure the angular anisotropy of the NO (A) products from the photodissociation of the N2-NO complex. Our experiment ranged from 108 to 758 cm-1 above the threshold energy to form NO (A) + N2 (X) products, and these measurements reveal, for the first time, a strong angular anisotropy from photodissociation. At 108 cm-1 above the photodissociation threshold, we observed NO (A) photoproducts recoil preferentially perpendicular to the laser polarization axis with an average anisotropy parameter, β = -0.25; however, as the available energy was increased, the anisotropy increased, and at 758 cm-1 above the threshold energy, we found an average β = +0.28. The observed changes in the angular anisotropy of the NO (A) photoproduct are qualitatively similar to those observed for the photodissociation of the Ar-NO complex and likely result from changes in the region of the excited state potential energy surface accessed during the electronic excitation. At the lowest available energy, we also noted a large contribution from hotband excitation; however, this contribution decreased as the available energy increased. The outsized contribution at the lowest available energy may result from hotbands having better Franck-Condon overlap with the excited electronic state near threshold. Finally, we contrast the experimental center of mass translational energy distribution with a statistical energy distribution determined from phase space theory. The experimental and statistical distributions show pronounced disagreement, particularly at low kinetic energies, with the experimental one showing less dissociation resulting in high rotational levels of the fragments.

A vector correlation study using a hexapole-oriented molecular beam: photodissociation dynamics of oriented isohaloethane.

The photodissociation dynamics of isohaloethane (1-bromo-2-chloro-1,1,2-trifluoroethane) at 234 nm was studied by a sliced imaging technique combined with an oriented molecular beam. The speed and angular distributions of the competitive products of spin-orbit selected Br and Cl atoms were determined by analysis of the obtained images. The anisotropic parameter, β, was found to be 2.0 ± 0.2 for the excited state of Br(2P1/2) (Br*) and 1.2 ± 0.3 for the ground state of Br(2P3/2) (Br). The speed distributions for both Br and Br* exhibited Gaussian-like characteristics. These results indicate that Br atoms were generated by direct formation after excitation through the nσ*(C-Br) potential energy surfaces. In contrast, the angular distributions for the Cl fragments were almost isotropic, while the speed distributions displayed Boltzmann-like characteristics. This suggests that the Cl atoms may form through long-lived parent molecules after photoexcitation. The branching ratio for Br and Cl atom formation was found to be approximately 1.2, that is, Br atom formation occurred preferentially, in contrast to the case of halothane photodissociation reported in our previous work [Che et al., J. Phys. Chem. A, 2020, 124, 5288]. A vector correlation study between the laser polarization axis and the direction of the dipole moment revealed a similar tendency for all photofragments, suggesting that the fragments were formed through a common excited state of isohaloethane. The vector correlation was also studied theoretically for comparison with the experimental results. The angle between the transition dipole moment in photodissociation and the permanent dipole moment was found to be 42 ± 15°. The obtained results indicate that this vector correlation approach combined with an oriented molecular beam is a powerful tool for determining the transition dipole moments in photodissociation.

Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics.

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles.

Tomography of photoelectron distributions produced through strong-field photodetachment of Ag−

We have applied a tomographic imaging method to recreate the full three-dimensional distribution of photoelectrons produced in a strong-field photodetachment process. The method is general and can be applied to any laser polarization. This stands in contrast to traditional imaging inversion methods, such as Abel inversion, which require prior knowledge of the symmetries of the electron distribution and are therefore limited to experiments using linear or circular polarization. Our method is also useful in a situation where linear polarization is used, since it compensates for detector inhomogeneities by spreading the information on a larger detector surface. In addition, it facilitates a method to detect polarization defects. Measurements were made for photodetachment of ${\mathrm{Ag}}^{\ensuremath{-}}$ at laser wavelengths of 1310 and 2055 nm, and were found to agree well with simulations in the strong field approximation. The data in the 1310 nm case revealed an unexpected asymmetry in the plane in which the laser polarization axis is rotated. Using a quasistationary quasienergy state model, a residual elliptical polarization of $\ensuremath{\varepsilon}=0.21\ifmmode\pm\else\textpm\fi{}0.01$ consistently explains the observed asymmetry. We conclude that the method described in this paper has the potential to be applied in experiments where a more complete characterization of electron emission distributions is required.

Retrieval of full angular- and energy-dependent complex transition dipoles in the molecular frame from laser-induced high-order harmonic signals with aligned molecules

High-order harmonic signals generated in molecules are the consequence of coherent summation of complex laser-induced transition dipoles $d(\ensuremath{\theta},\ensuremath{\omega})$ with each fixed-in-space molecule; here $\ensuremath{\theta}$ is the angle of the molecular axis with respect to the laser polarization axis and $\ensuremath{\omega}$ is the harmonic energy. In the so-called rotational coherent spectroscopy, it is proposed to extract the fixed-in-space $d(\ensuremath{\theta},\ensuremath{\omega})$ in the molecular frame by measuring harmonics generated by a probing laser from the rotational molecular wave packets that have been prepared by a prior pump laser. By varying the time delay between the two lasers, methods have been utilized to extract the $\ensuremath{\theta}$ dependence of both the amplitude and phase of each individual harmonic, but the relative phase between harmonics cannot be retrieved. Here we report that this limitation can be removed. It requires the additional measurement of harmonic spectra versus the pump-probe angles at one fixed time delay. The two-dimensional input harmonic data (time-delay and pump-probe angle) are then used to retrieve the full complex transition dipole $d(\ensuremath{\theta},\ensuremath{\omega})$ using a retrieval method based on machine learning algorithms. We demonstrate this method on ${\mathrm{N}}_{2}$ and ${\mathrm{CO}}_{2}$ molecules.

Ultrarelativistic polarized positron jets via collision of electron and ultraintense laser beams

Relativistic spin-polarized positron beams are indispensable for future electron-positron colliders to test modern high-energy physics theory with high precision. However, present techniques require very large scale facilities for those experiments. We put forward a novel efficient method for generating ultrarelativistic polarized positron beams employing currently available laser fields. For this purpose, the generation of polarized positrons via multiphoton Breit-Wheeler pair production and the associated spin dynamics in single-shot interaction of an ultraintense laser pulse with an ultrarelativistic electron beam is investigated in the quantum radiation-dominated regime. The pair production spin asymmetry in strong fields, significantly exceeding the asymmetry of the radiative polarization, produces locally highly polarized particles, which are split by a specifically tailored small ellipticity of the laser field into two oppositely polarized beams along the minor axis of laser polarization. In spite of radiative de-polarization, a dense positron beam with up to about 90% polarization can be generated in tens of femtoseconds. The method may eventually usher high-energy physics studies into smaller-scale laser laboratories.

Characterization of laser-driven proton acceleration from water microdroplets

We report on a proton acceleration experiment in which high-intensity laser pulses with a wavelength of 0.4 μm and with varying temporal intensity contrast have been used to irradiate water droplets of 20 μm diameter. Such droplets are a reliable and easy-to-implement type of target for proton acceleration experiments with the potential to be used at very high repetition rates. We have investigated the influence of the laser’s angle of incidence by moving the droplet along the laser polarization axis. This position, which is coupled with the angle of incidence, has a crucial impact on the maximum proton energy. Central irradiation leads to an inefficient coupling of the laser energy into hot electrons, resulting in a low maximum proton energy. The introduction of a controlled pre-pulse produces an enhancement of hot electron generation in this geometry and therefore higher proton energies. However, two-dimensional particle-in-cell simulations support our experimental results confirming, that even slightly higher proton energies are achieved under grazing laser incidence when no additional pre-plasma is present. Illuminating a droplet under grazing incidence generates a stream of hot electrons that flows along the droplet’s surface due to self-generated electric and magnetic fields and ultimately generates a strong electric field responsible for proton acceleration. The interaction conditions were monitored with the help of an ultra-short optical probe laser, with which the plasma expansion could be observed.

Ultrafast isomerization-induced cooperative motions to higher molecular orientation in smectic liquid-crystalline azobenzene molecules

The photoisomerization of molecules is widely used to control the structure of soft matter in both natural and synthetic systems. However, the structural dynamics of the molecules during isomerization and their subsequent response are difficult to elucidate due to their complex and ultrafast nature. Herein, we describe the ultrafast formation of higher-orientation of liquid-crystalline (LC) azobenzene molecules via linearly polarized ultraviolet light (UV) using ultrafast time-resolved electron diffraction. The ultrafast orientation is caused by the trans-to-cis isomerization of the azobenzene molecules. Our observations are consistent with simplified molecular dynamics calculations that revealed that the molecules are aligned with the laser polarization axis by their cooperative motion after photoisomerization. This insight advances the fundamental chemistry of photoresponsive molecules in soft matter as well as their ultrafast photomechanical applications.

Diffractive Imaging of C60 Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100fs (1 fs=10^{-15} s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6 μm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

Parametric feedback cooling of rigid body nanodumbbells in levitated optomechanics

We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered non-negligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession about the laser polarization axis together with spin about the nanoparticle's symmetry axis. Cooling the remaining mode requires an asymmetry in the two librational frequencies associated with motion about the polarization axis as well as information about the two frequencies of rotation about the polarization axis. Introducing an asymmetric potential allows full cooling of the librational coordinates if the frequencies of both are used in the feedback modulation and is an avenue for entering the librational quantum regime. The asymmetry in the potential needs to be large enough for practical cooling times as the cooling rate of the system depends non-linearly on the degree of asymmetry, a condition that is easily achieved experimentally.

Strong-field polarizability-enhanced dissociative ionization

We investigate dissociative single and double ionization of HeH+ induced by intense femtosecond laser pulses. By employing a semi-classical model with nuclear trajectories moving on field-dressed surfaces and ionization events treated as stochastical jumps, we identify a strong-field mechanism wherein the molecules dynamically align along the laser polarization axis and stretch towards a critical internuclear distance before getting dissociative ionized. As the tunnel-ionization rate is greater for larger internuclear distance and for aligned samples, ionization is enhanced. The strong dynamical rotation is traced back to a maximum in the parallel component of the internuclear-distance-dependent polarizability tensor. Qualitative agreement with our experimental observations is found. Finally the criteria for observing the isotope effect for the ion angular distribution is discussed.

High-order harmonic generation from highly excited states in acetylene

High-order harmonic generation (HHG) from aligned acetylene molecules interacting with mid infra-red (IR), linearly polarized laser pulses is studied theoretically using a mixed quantum-classical approach in which the electrons are described using time-dependent density-functional theory while the ions are treated classically. We find that for molecules aligned perpendicular to the laser polarization axis, HHG arises from the highest-occupied molecular orbital (HOMO), while for molecules aligned along the laser polarization axis, HHG is dominated by the HOMO-1. In the parallel orientation we observe a double plateau with an inner plateau that is produced by ionization from and recombination back to an autoionizing state. Two pieces of evidence support this idea. First, by choosing a suitably tuned vacuum ultraviolet pump pulse that directly excites the autoionizing state we observe a dramatic enhancement of all harmonics in the inner plateau. Second, in certain circumstances, the position of the inner plateau cutoff does not agree with the classical three-step model. We show that this discrepancy can be understood in terms of a minimum in the dipole recombination matrix element from the continuum to the autoionizing state.

Unambiguous Signature of the Berry Phase in Intense Laser Dissociation of Diatomic Molecules.

We report strong evidence of Berry phase effects in intense laser dissociation of D2+ molecules, manifested as Aharonov-Bohm-like oscillations in the photofragment angular distribution (PAD). Our calculations show that this interference pattern strongly depends on the parity of the diatom initial rotational state, (-1) j. Indeed, the PAD local maxima (minima) observed in one case ( j odd) correspond to local minima (maxima) in the other case ( j even). Using simple topological arguments, we clearly show that such interference conversion is a direct signature of the Berry phase. The sole effect of the latter on the rovibrational wave function is a sign change of the relative phase between two interfering components, which wind in opposite senses around a light-induced conical intersection (LICI). Therefore, encirclement of the LICI leads to constructive ( j odd) or destructive ( j even) self-interference of the initial nuclear wavepacket in the dissociative limit. To corroborate our theoretical findings, we suggest an experiment of strong-field indirect dissociation of D2+ molecules, comparing the PAD of the ortho and para molecular species in directions nearly perpendicular to the laser polarization axis.

Effect of magnetic field on isotope-selective photoionization of atomic samarium using polarized lasers

The effect of an external magnetic field on the isotopic selectivity in a two-color three-step polarization-based isotope-selective photoionization of atomic samarium has been studied. Isotope-selective photoionization of samarium is realized through a level scheme having total angular momentum (J) sequence 0-1-1-continuum by using two lasers linearly polarized in the same direction and the isotopic selectivity is measured by varying the magnetic field strength perpendicular to the laser polarization axis while keeping the delay between the laser pulses fixed and vice versa. The experimental data have been analyzed and compared with the results of the numerical calculations. The magnetic field perpendicular to the laser polarization axis present in the laser-atom interaction region has been found to degrade the isotopic selectivity. Further, the Lande factor () of the excited energy level 16 690.76 cm−1 (J = 1) of samarium has been determined from the observed oscillation in the isotopic selectivity. The value of thus obtained, is in good agreement with that reported in the literature.

Directional quantum-controlled chemistry: Generating aligned ultracold molecules via photoassociation

Photoassociation of ultracold atoms is shown to lead to alignment of the product molecules along the excitation laser polarization axis. We theoretically investigate pulsed photoassociation of $^{87}Rb$ atoms into a specific weakly-bound level of the a $^3\Sigma_u^+$ metastable electronic state and find both stationary and time-dependent field-free alignment. Although a transform-limited pulse yields significant alignment, a frequency-chirped pulse dramatically enhances the molecular formation rate at the cost of a slight decrease in the alignment. Employing multiple pulses synchronized with the vibrational and rotational periods leads to coherent enhancement of both population and alignment of the target state.

Order of Magnitude Dissociative Ionization Enhancement Observed for Pulses with High Order Dispersion.

While the interaction of atoms in strong fields is well understood, the same cannot be said about molecules. We consider how dissociative ionization of molecules depends on the quality of the femtosecond laser pulses, in particular, the presence of third- and fourth-order dispersion. We find that high-order dispersion (HOD) unexpectedly results in order-of-magnitude enhanced ion yields, along with the factor of 3 greater kinetic energy release compared to transform-limited pulses with equal peak intensities. The magnitude of these effects is not caused by increased pulse duration. We evaluate the role of pulse pedestals produced by HOD and other pulse shaping approaches, for a number of molecules including acetylene, methanol, methylene chloride, acetonitrile, toluene, and o-nitrotoluene, and discuss our findings in terms of processes such as prealignment, preionization, and bond softening. We conclude, based on the quasi-symmetric temporal dependence of the observed enhancements that cascade ionization is likely responsible for the large accumulation of charge prior to the ejection of energetic fragments along the laser polarization axis.