Helicity-Selective Enhancement and Polarization Control of Attosecond High Harmonic Waveforms Driven by Bichromatic Circularly Polarized Laser Fields

Two-color high-harmonic generation from relativistic plasma mirrors

High-intensity laser solid interactions are capable of generating attosecond light bursts via high-harmonic generation-most work focuses on single beam interactions. In this paper, we perform a numerical investigation on the role of wavelength and polarization in relativistic, high-harmonic generation from normal-incidence, two-beam interactions off plasma mirrors. We find that the two-beam harmonic-generation mechanism is a robust process described by a set of well-defined selection rules. We demonstrate that the emitted harmonics from normal-incidence interactions exhibit an intensity optimization when the incident fields are of equal intensity for two-color circularly polarized fields.

Generation of the isolated highly elliptically polarized attosecond pulse using the polarization gating technique: TDDFT approach

This paper theoretically investigates the generation of isolated elliptically polarized attosecond pulses with a tunable ellipticity from the interaction of Cl₂ molecule and a polarization-gating laser pulse. A three-dimensional calculation based on the time-dependent density functional theory is done. Two different methods are proposed for generating elliptically polarized single attosecond pulses. The first method is based on applying a single-color polarization gating laser and controlling the orientation angle of the Cl₂ molecule with respect to the polarization direction of the laser at the gate window. An attosecond pulse with an ellipticity of 0.66 and a pulse duration of 275 as is achieved by tuning the molecule orientation angle to 40° in this method and superposing harmonics around the harmonic cutoff. The second method is based on irradiating an aligned Cl₂ molecule with a two-color polarization gating laser. The ellipticity of the attosecond pulses obtained by this method can be controlled by adjusting the intensity ratio of the two colors. Employing an optimized intensity ratio and superposing harmonics around the harmonic cutoff would lead to the generation of an isolated, highly elliptically polarized attosecond pulse with an ellipticity of 0.92 and a pulse duration of 648 as.

Controlling Photon Transverse Orbital Angular Momentum in High Harmonic Generation

High harmonic generation (HHG) with longitudinal optical orbital angular momentum has attracted much attention over the past decade. Here, we present the first study on the HHG with transverse orbital angular momentum driven by the spatiotemporal optical vortex (STOV) pulses. We show that the produced spatial-resolved harmonic spectra reveal unique structures, such as the spatially spectral tilt and the fine interference patterns. We show these spatiospectral structures originate from both the macroscopic and microscopic effect of spatiotemporal optical singularity in HHG. Employing two-color counterspin and countervorticity STOV pulses, we further discuss a robust method to control the spatiotemporal topological charge and spectral structure of high-order harmonics. The conservation rule of photon transverse orbital angular momentum in HHG process is also discussed when mixing with photon spin angular momenta.

Bright, single helicity, high harmonics driven by mid-infrared bicircular laser fields

High-harmonic generation (HHG) is a unique tabletop light source with femtosecond-to-attosecond pulse duration and tailorable polarization and beam shape. Here, we use counter-rotating femtosecond laser pulses of 0.8 µm and 2.0 μm to extend the photon energy range of circularly polarized high-harmonics and also generate single-helicity HHG spectra. By driving HHG in helium, we produce circularly polarized soft x-ray harmonics beyond 170 eV-the highest photon energy of circularly polarized HHG achieved to date. In an Ar medium, dense spectra at photon energies well beyond the Cooper minimum are generated, with regions composed of a single helicity-consistent with the generation of a train of circularly polarized attosecond pulses. Finally, we show theoretically that circularly polarized HHG photon energies can extend beyond the carbon K edge, extending the range of molecular and materials systems that can be accessed using dynamic HHG chiral spectro-microscopies.

Study on spin angular momentum balance in harmonics generated from counter-rotating two-color laser fields

High-order harmonics generated from Xe driven by counter-rotating two-color driving fields are studied in the frame of a quantum-field scattering theory, and the spin angular momentum transfer is discussed. The driving field is composed by a circularly polarized (CP) mode and an elliptically polarized (EP) mode. We treat the EP mode as a compostition of counter-rotating CP fields of unequal intensity. We use a pair of phased generalized Bessel functions to describe the harmonic generation amplitude, and the conservation of the spin angular momentum during harmonic generation in the two-color field is derived in a solid base and in a straightforward way. The experimentally observed V-type and Λ-type distributions of the harmonic spectra with ellipticity are recovered theoretically. Balance pattern of the spin angular momentum is disclosed substantially.

Bayesian optimal control of the ultrashort circularly polarized attosecond pulse generation by two-color polarization gating

We present ab initio simulations of optimal control of high-order-harmonic generation spectra that enable the synthesis of a circularly polarized 53-attosecond pulse in a single Helium atom response. The Bayesian optimization is used to achieve control of a two-color polarization gating laser waveform such that a series of harmonics in the plateau region are phase-matched, which can be used for attosecond pulse synthesis. To find the underlying mechanisms for generating these harmonics, we perform a wavelet analysis for the induced dipole moment in acceleration form, and compare the time-energy representation with the quantum paths extracted from the semiclassical calculation. We found that these coherent harmonics are excited along the short trajectories. The proposed method has the potential to migrate to laboratories for generation of isolated circularly polarized ultrashort attosecond pulses.

Signature of Molecular Orbital Symmetry in High-Order Harmonic Generation by Bichromatic Circularly Polarized Laser Pulses

Molecular orbital symmetry is shown to be an important factor in determining orders and helicities (polarizations) of high-order harmonic generation (HHG) by intense femtosecond counter-rotating bichromatic circularly polarized laser pulses. Numerical solutions of time-dependent Schrödinger equations (TDSE) for the one-electron molecular ions H₂⁺ and H₃²⁺ for different initial electronic states show that harmonic orders and helicities are dependent on orbital symmetries and of the net incident pulse electric field. The numerical results and properties of the harmonics are described by dynamical symmetry theory and time profile analysis of the high-order harmonics, thus confirming that orbital and laser pulse symmetry dependence are generic in HHG of molecules.

Shortcut to study angular momentum transfer of harmonic generation in intense laser fields

High-order harmonics generated from atoms driven by counter-rotating two-color circularly (CRTC) polarized laser fields are studied in the frame of a quantum-field scattering theory. We use a pair of generalized phased Bessel (GPB) functions to describe the harmonic generation amplitude. The use of GPB functions allows us to define the phase of a harmonic channel accurately, by which we obtain the spin angular momentum conservation relation in a straightforward way. The known selection rule of harmonic order in the CRTC field is obtained concisely. Main features of the harmonic spectra are recovered. Our treatment provides a shortcut to study the angular momentum transfer in intense laser fields.

Elliptically polarized high-harmonic radiation for production of isolated attosecond pulses

Circularly polarized attosecond pulses are powerful tool to study chiral light-matter interaction via chiral electron dynamics. However, access to isolated circularly polarized attosecond pulses enabling straightforward interpretation of measurements, still remains a challenge. In this work, we experimentally demonstrate the generation of highly elliptically polarized high-harmonics in a two-color, bi-circular, collinear laser field. The intensity and shape of the combined few-cycle driving radiation is optimized to produce a broadband continuum with enhanced spectral chirality in the range of 15-55 eV supporting the generation of isolated attosecond pulses with duration down to 150 as. We apply spectrally resolved polarimetry to determine the full Stokes vector of different spectral components of the continuum, yielding a homogenous helicity distribution with ellipticity in the range of 0.8-0.95 and a negligible unpolarized content.

Investigation of electron vortices in time-delayed circularly polarized laser pulses with a semiclassical perspective

We theoretically investigate strong-filed electron vortices in time-delayed circularly polarized laser pulses by a generalized quantum-trajectory Monte Carlo (GQTMC) model. Vortex interference patterns in photoelectron momentum distributions (PMDs) with various laser parameters can be well reproduced by the semiclassical simulation. The phase difference responsible for the interference structures is analytically identified through trajectory-based analysis and simple-man theory, which reveal the underlying mechanism of electron vortex phenomena for both co-rotating and counter-rotating component. This semiclassical analysis can also demonstrate the influences of laser intensity and wavelength on the number of arms of vortices. Furthermore, we show the influence of the Coulomb effect on the PMDs. Finally, the controlling of the ionization time intervals in the tens to hundreds of attosecond magnitude is qualitatively discussed.

Generation of isolated circularly polarized attosecond pulses by three-color laser field mixing

We propose and theoretically demonstrate a method to generate the circularly polarized supercontinuum with three-color electric fields. The three-color field is synthesized from an orthogonally polarized two-color (OTC) laser field and an infrared gating field. All driving pulse durations are extended to 40 fs. We demonstrate that the three-color field imposes curved trajectories for ionized electrons and extends the time interval between each harmonic emitting. Through adjusting intensity ratios among three components of the driving field, a nearly circular isolated attosecond pulse can be generated.

Two-dimensional photoelectron holography in strong-field tunneling ionization by counter rotating two-color circularly polarized laser pulses

Strong-field photoelectron holography (SFPH), originating from the interference of the direct electron and the rescattering electron in tunneling ionization, is a significant tool for probing structure and electronic dynamics in molecules. We theoretically study SFPH by counter rotating two-color circularly (CRTC) polarized laser pulses. Different from the case of the linearly polarized laser field, where the holographic structure in the photoelectron momentum distribution (PEMD) is clustered around the laser polarization direction, in the CRTC laser fields, the tunneling ionized electrons could recollide with the parent ion from different angles and thus the photoelectron hologram appears in the whole plane of laser polarization. This property enables structural information delivered by the electrons scattering the molecule from different angles to be recorded in the two-dimensional photoelectron hologram. Moreover, the electrons tunneling at different laser cycles are streaked to different angles in the two-dimensional polarization plane. This property enables us to probe the sub-cycle electronic dynamics in molecules over a long time window with the multiple-cycle CRTC laser pulses.

Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy

We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and molecules, based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-symmetric laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented atomic or molecular media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible physical mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calculations.

Perspective: Towards single shot time-resolved microscopy using short wavelength table-top light sources

Time-resolved imaging allows revealing the interaction mechanisms in the microcosm of both inorganic and biological objects. While X-ray microscopy has proven its advantages for resolving objects beyond what can be achieved using optical microscopes, dynamic studies using full-field imaging at the nanometer scale are still in their infancy. In this perspective, we present the current state of the art techniques for full-field imaging in the extreme-ultraviolet- and soft X-ray-regime which are suitable for single exposure applications as they are paramount for studying dynamics in nanoscale systems. We evaluate the performance of currently available table-top sources, with special emphasis on applications, photon flux, and coherence. Examples for applications of single shot imaging in physics, biology, and industrial applications are discussed.

Polarization-based tachometer for measuring spinning rotors

We report on the polarization analysis of shortpulse ultraviolet radiation produced by third-harmonic generation in a gas of coherently spinning molecules. A pulse of twisted linear polarization imprints a unidirectional rotational motion to the molecules leading to an orientation of their rotational angular momenta. A second pulse, time-delayed with respect to the first one, circularly polarized in the plane of rotation of the molecules, acts as a driving field for third-harmonic generation. The angular momentum and energy conservation applied to this process foresees the generation of two Doppler-shifted circularly-polarized harmonics of opposite handedness. Our analysis reveals that spinning molecules enable the generation of a well polarized third-harmonic radiation exhibiting a high degree of ellipticity. Tracking the orientation of the latter allows a time-capture of the molecular axis direction from which the average angular velocity of the rotating molecules is inferred. This method provides a user-friendly polarization-based tachometer for measurement of the rotational speed of spinning nonlinear rotors.

Evidence of depolarization and ellipticity of high harmonics driven by ultrashort bichromatic circularly polarized fields

High harmonics generated by counter-rotating laser fields at the fundamental and second harmonic frequencies have raised important interest as a table-top source of circularly polarized ultrashort extreme-ultraviolet light. However, this emission has not yet been fully characterized: in particular it was assumed to be fully polarized, leading to an uncertainty on the effective harmonic ellipticity. Here we show, through simulations, that ultrashort driving fields and ultrafast medium ionization lead to a breaking of the dynamical symmetry of the interaction, and consequently to deviations from perfectly circular and fully polarized harmonics, already at the single-atom level. We perform the complete experimental characterization of the polarization state of high harmonics generated along that scheme, giving direct access to the ellipticity absolute value and sign, as well as the degree of polarization of individual harmonic orders. This study allows defining optimal generation conditions of fully circularly polarized harmonics for advanced studies of ultrafast dichroisms.

Scaling Law of High Harmonic Generation in the Framework of Photon Channels

A photon channel perspective on high harmonic generation (HHG) is proposed by quantizing both the driving laser and high harmonics. It is shown that the HHG yield can be expressed as a sum of the contribution of all the photon channels. From this perspective, the contribution of a specific photon channel follows a simple scaling law and the competition between the channels is well interpreted. Our prediction is shown to be in good agreement with the simulations by solving the time-dependent Schrödinger equation. It also can explain well the experimental results of the HHG in the noncollinear two-color field and bicicular laser field.

Spectral control of high harmonics from relativistic plasmas using bicircular fields

We introduce two-color counterrotating circularly polarized laser fields as a way to spectrally control high harmonic generation (HHG) from relativistic plasma mirrors. Through particle-in-cell simulations, we show that only a selected group of harmonic orders can appear owing to the symmetry of the laser fields and the related conservation laws. By adjusting the intensity ratio of the two driving field components, we demonstrate the overall HHG efficiency, the relative intensity of allowed neighboring harmonic orders, and that the polarization state of the harmonic source can be tuned. The HHG efficiency of this scheme can be as high as that driven by a linearly polarized laser field.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation

Optical chirality (OC)-one of the fundamental quantities of electromagnetic fields-corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin-orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Signatures of Electronic Structure in Bicircular High-Harmonic Spectroscopy

High-harmonic spectroscopy driven by circularly polarized laser pulses and their counterrotating second harmonic is a new branch of attosecond science which currently lacks quantitative interpretations. We extend this technique to the midinfrared regime and record detailed high-harmonic spectra of several rare-gas atoms. These results are compared with the solution of the Schrödinger equation in three dimensions and calculations based on the strong-field approximation that incorporate accurate scattering-wave recombination matrix elements. A quantum-orbit analysis of these results provides a transparent interpretation of the measured intensity ratios of symmetry-allowed neighboring harmonics in terms of (i) a set of propensity rules related to the angular momentum of the atomic orbitals, (ii) atom-specific matrix elements related to their electronic structure, and (iii) the interference of the emissions associated with electrons in orbitals corotating or counterrotating with the laser fields. These results provide the foundation for a quantitative understanding of bicircular high-harmonic spectroscopy.

Extended ellipticity control for attosecond pulses by high harmonic generation

Attosecond (1  as=10^-18  s) pulses produced through high harmonic generation (HHG) are a basis for studies of electron dynamics during light-matter interaction on an electron's natural time scale. Extensively exploited HHG technology has, however, a few unsolved problems, where producing of circularly polarized or chiral attosecond pulses belongs to them. We have demonstrated experimentally a way to control the ellipticity of attosecond pulse trains produced via HHG in two-color, bi-circular laser fields. We show that the combination of a nonlinear medium position and the intensities of the two-color driving laser fields create an effective helicity-dependent filter. Based on this approach, we report generation of chiral spectra providing potential to produce attosecond pulses with polarization tuned from the rotating, but linear to highly elliptic, with ellipticity as much as ϵ=0.75. This new way to create a chiral-sensitive element offers a simple and practical knob to control polarization for a combined harmonics field in a smooth and predictable manner.