High Harmonic Radiation Research Articles

Focal cone high harmonic generation driven by a 400 TW laser

The generation of self-focusing beams of extreme ultraviolet (XUV) radiation using the focal cone high harmonic generation (FCHHG) technique is examined for high energy lasers. The FCHHG geometry is created by passing a focusing laser beam through a gas sheet prior to reaching focus and thus creating a converging beam of high harmonic radiation. This leads to a larger interaction area that increases the total area of XUV emission while not exceeding the saturation intensity of the target atoms or increasing the density of the atoms. Such a method allows for scaling of HHG to any incident laser power. An experiment was conducted demonstrating such scaling to incident 400 TW pulses, showing both the expected spectral signature of HHG and the converging cone of XUV radiation. It was found that this technique is very sensitive to spatial non-uniformity in the driving laser, which has become more prevalent in high energy laser systems.

XUV Absorption Spectroscopy and Photoconversion of a Tin-Oxo Cage Photoresist.

Extreme ultraviolet lithography has recently been introduced in high-volume production of integrated circuits for manufacturing the smallest features in high-end computer chips. Hybrid organic/inorganic materials are considered as the next generation of photoresists for this technology, but detailed knowledge about the response of such materials to the ionizing radiation used (13.5 nm, 92 eV) is still scarce. In the present work, we use broadband high-harmonic radiation in the energy range 22-70 eV for absorption spectroscopy and photobleaching (that is, the decrease of absorbance) of thin films of an n-butyltin oxo-cage, a representative of the class of metal-based EUV photoresist. The shape of the absorption spectrum in the range 22-92 eV matches well with the spectrum predicted using tabulated atomic cross sections. The photobleaching results are consistent with loss of the butyl side groups due to the breaking of Sn-C bonds following photoionization. Bleaching is strongest in the low-energy range (<40 eV), where the absorption is largely due to the carbon atoms in the organic groups. At higher energies (42-70 eV), absorption is dominated by the tin atoms, and since these remain in the film after photoconversion, the absorption change in this region is smaller. It is estimated that after prolonged irradiation (up to ∼3 J cm-2 in the range 22-40 eV) about 70% of the hydrocarbon groups are removed from the film. The rate of bleaching is high at the beginning of exposure, but it rapidly decreases with increasing conversion. We rationalize this using density functional theory calculations: the first Sn-C bonds are efficiently cleaved (quantum yield Φ ≈ 0.9), because the highest occupied molecular orbitals (HOMOs) (from which an electron is removed after photoionization) are located on Sn-C sigma bonds. In the photoproducts, the HOMO is localized on tin atoms that have lost their hydrocarbon group (formally reduced to the Sn(II) oxidation state), and holes formed on those tin atoms lead to less efficient cleavage reactions. Our results reveal the primary reaction steps following excitation with ionizing radiation of tin-oxo cages. Our methodology represents a systematic approach of studying and quantitatively assessing the performance of new photoresists and as such enables the development of future EUV photoresists.

Spectral splitting in phase mismatched harmonics.

Spectral splitting of high harmonic radiation is observed when a gas target is irradiated with a high-energy laser pulse, having an extreme amount of frequency chirp. The phenomenon, which may be observed only by using a multi-TW laser system, originates from the temporal evolution of the phase-matching conditions. We illustrate how these conditions are mapped to the spectral domain, and present experimental evidence which is validated by our model.

A novel scheme based on angular dispersion-induced microbunching mechanism for harmonic generation in storage ring

Angular dispersion-induced microbunching (ADM) scheme was proposed to generate high harmonic coherent radiation in the storage ring with weak energy modulation amplitude. However, it is still difficult to convert the external UV seed laser into the sub-nanometer wavelength. In this paper, we proposed a novel scheme based on ADM mechanism. By properly choosing the parameters, theory and one order simulation demonstrate that it is possible to produce ultrahigh harmonic coherent radiation in the storage ring. The high harmonic conversion efficiency of the proposed scheme may open up a new opportunity to produce sub-nanometer X-ray coherent radiation in the storage ring.

Ionization Dynamics for Atomic and Molecular Ions in Relativistic, Ultrastrong Laser Fields

The discovery of laser-driven rescattering and high harmonic radiation out to a maximum photon energy of 3.17 times the ponderomotive energy (Up ) laid the groundwork for attosecond pulse generation and coherent X-rays. As the laser field drives the interaction to higher energies, relativity and the Lorentz force from the laser magnetic field enter into the dynamics. We present the results of recent studies of laser rescattering, including these effects, to give a quantitative description of rescattering dynamics in the high-energy limit, ie, recollision energies of order 1,000 hartree (27 keV). The processes investigated include inner K- and L-shell excitation and the ultimate limit of high harmonic generation via rescattering bremsstrahlung. The results indicate the path to the frontier area of x-ray strong field processes.

High-harmonic generation from a flat liquid-sheet plasma mirror

High-harmonic radiation can be generated when an ultra-intense laser beam is reflected from an over-dense plasma, known as a plasma mirror. It is considered a promising technique for generating intense attosecond pulses in the extreme ultraviolet and X-ray wavelength ranges. However, a solid target used for the formation of the over-dense plasma is completely damaged by the interaction. Thus, it is challenging to use a solid target for applications such as time-resolved studies and attosecond streaking experiments that require a large amount of data. Here we demonstrate that high-harmonic radiation can be continuously generated from a liquid plasma mirror in both the coherent wake emission and relativistic oscillating mirror regimes. These results will pave the way for the development of bright, stable, and high-repetition-rate attosecond light sources, which can greatly benefit the study of ultrafast laser-matter interactions.

Ultrafast behavior of induced and intrinsic magnetic moments in CoFeB/Pt bilayers probed by element-specific measurements in the extreme ultraviolet spectral range

The ultrafast and element-specific response of magnetic systems containing ferromagnetic $3d$ transition metals and $4d/5d$ heavy metals is of interest both from a fundamental as well as an applied research perspective. However, to date no consensus about the main microscopic processes describing the interplay between intrinsic $3d$ and induced $4d/5d$ magnetic moments upon femtosecond laser excitation exist. In this work we study the ultrafast response of CoFeB/Pt bilayers by probing element-specific, core-to-valence-band transitions in the extreme ultraviolet spectral range using high harmonic radiation. We show that the combination of magnetic scattering simulations and analysis of the energy- and time-dependent magnetic asymmetries allows us to accurately disentangle the element-specific response in spite of overlapping Co and Fe ${\mathit{M}}_{2,3}$ as well as Pt ${\mathit{O}}_{2,3}$ and ${\mathit{N}}_{7}$ resonances. We find a considerably smaller demagnetization time constant as well as much larger demagnetization amplitudes of the induced moment of Pt compared to the intrinsic moment of CoFeB. Our results are in agreement with enhanced spin-flip probabilities due to the high spin-orbit coupling localized at the heavy metal Pt, as well as with the recently formulated hypothesis that a laser-generated, incoherent magnon population within the ferromagnetic film leads to an overproportional reduction of the induced magnetic moment of Pt.

Enhancement and redshift of vortex harmonic radiation in epsilon-near-zero materials.

The harmonic radiation from a vortex laser field interacting with an epsilon-near-zero (ENZ) material is numerically investigated via solving the Maxwell-paradigmatic-Kerr equations. For a laser field of long duration, the harmonics up to the seventh-order can be generated with a low laser intensity (∼109 W/cm2). Moreover, the intensities of high order vortex harmonics at the ENZ frequency are higher than at other frequency points due to the ENZ field enhancement effects. Interestingly, for a laser field of short duration, the obvious frequency redshift occurs beyond enhancement in high order vortex harmonic radiation. The reason is that the strong change of the laser waveform propagating in the ENZ material and the non-constant field enhancement factor around the ENZ frequency. Because the topological number of harmonic radiation is linearly proportional to its harmonic order, the high order vortex harmonics with redshift still possess the exact harmonic orders indicated by the transverse electric field distribution of each harmonic.

Gate-tunable quantum pathways of high harmonic generation in graphene

Under strong laser fields, electrons in solids radiate high-harmonic fields by travelling through quantum pathways in Bloch bands in the sub-laser-cycle timescales. Understanding these pathways in the momentum space through the high-harmonic radiation can enable an all-optical ultrafast probe to observe coherent lightwave-driven processes and measure electronic structures as recently demonstrated for semiconductors. However, such demonstration has been largely limited for semimetals because the absence of the bandgap hinders an experimental characterization of the exact pathways. In this study, by combining electrostatic control of chemical potentials with HHG measurement, we resolve quantum pathways of massless Dirac fermions in graphene under strong laser fields. Electrical modulation of HHG reveals quantum interference between the multi-photon interband excitation channels. As the light-matter interaction deviates beyond the perturbative regime, elliptically polarized laser fields efficiently drive massless Dirac fermions via an intricate coupling between the interband and intraband transitions, which is corroborated by our theoretical calculations. Our findings pave the way for strong-laser-field tomography of Dirac electrons in various quantum semimetals and their ultrafast electronics with a gate control.

Lattice design for an improved angular dispersion-induced microbunching scheme

In this paper, an improved angular dispersion-induced microbunching (ADM) scheme [1] is studied to generate fully coherent soft x-ray radiation pulses in an electron storage ring light source with a limited energy modulation amplitude. This scheme releases the coupling between the dispersion function and the momentum compaction in the original ADM scheme. The lattice structure of the improved ADM is simple, which only adds a chicane following the dogleg compared to the original one. With the chicane, even higher harmonic radiation can be generated. Numerical simulation results show that soft x-ray radiation with photon energy covering the water window range can be produced.

Absolute EUV reflectivity measurements using a broadband high-harmonic source and an in situ single exposure reference scheme.

We present a tabletop setup for extreme ultraviolet (EUV) reflection spectroscopy in the spectral range from 40 to 100 eV by using high-harmonic radiation. The simultaneous measurements of reference and sample spectra with high energy resolution provide precise and robust absolute reflectivity measurements, even when operating with spectrally fluctuating EUV sources. The stability and sensitivity of EUV reflectivity measurements are crucial factors for many applications in attosecond science, EUV spectroscopy, and nano-scale tomography. We show that the accuracy and stability of our in situ referencing scheme are almost one order of magnitude better in comparison to subsequent reference measurements. We demonstrate the performance of the setup by reflective near-edge x-ray absorption fine structure measurements of the aluminum L2/3 absorption edge in α-Al2O3 and compare the results to synchrotron measurements.

Multispectral time-resolved energy-momentum microscopy using high-harmonic extreme ultraviolet radiation.

A 790-nm-driven high-harmonic generation source with a repetition rate of 6kHz is combined with a toroidal-grating monochromator and a high-detection-efficiency photoelectron time-of-flight momentum microscope to enable time- and momentum-resolved photoemission spectroscopy over a spectral range of 23.6-45.5eV with sub-100fs time resolution. Three-dimensional (3D) Fermi surface mapping is demonstrated on graphene-covered Ir(111) with energy and momentum resolutions of ≲100 meV and ≲0.1 Å-1, respectively. The tabletop experiment sets the stage for measuring the kz-dependent ultrafast dynamics of 3D electronic structure, including band structure, Fermi surface, and carrier dynamics in 3D materials as well as 3D orbital dynamics in molecular layers.

Coherent control of extreme ultraviolet emission generated through frustrated tunneling ionization

Coherent extreme ultraviolet (EUV) line emissions can be generated from an atom excited through frustrated tunneling ionization (FTI). The phase variation of the EUV emission in a generation medium along the propagation direction is a critical parameter that determines the phase-matching condition of this new light source. Here we show that the EUV emission sensitively depends on the intensity and phase of a driving laser pulse and the target position. Angle-resolved EUV spectra measured at different target positions and the carrier-envelope phases of the laser pulse exhibit an intensity modulation, showing similar behavior to that of a long-trajectory high harmonic radiation. The four-step model developed for the FTI emission accurately describes the coherent control of the EUV emission. These findings are essential ingredients for developing coherent extreme ultraviolet sources with high photon flux and for utilizing the FTI emission in time-resolved spectroscopy.

Separating Non-linear Optical Signals of a Sample from High Harmonic Radiation in a Soft X-ray Free Electron Laser

Second harmonic generation (SHG) is a unique non-linear optical effect that can be used to investigate chemical states of molecules at surfaces/interfaces. By the use of soft X-rays, SHG gains element selectivity through the inner-core excitation resonance. However, it is challenging to observe SHG signals separately from the second-order light generated from the undulator. Here, we report a new ellipsometry method for soft X-ray SHG to suppress the contribution of second-harmonic radiation from the light source. Through measurements of a GaAs(100) crystal, we demonstrate that pure SHG signals can be obtained for the horizontally polarized component. The present method is generally applicable regardless of the incident photon energy and hence the absorption edge of the targeted materials. If combined with optical filters blocking the second-harmonic radiation and equipped with soft X-ray phase shifters, the method allows one to obtain further information from SHG signals such as tensor components of second-order non-linear susceptibility.

Enhanced Amplification of Attosecond Pulses in a Hydrogen-like Plasma-Based X-ray Laser Modulated by an Infrared Field at the Second Harmonic of Fundamental Frequency

In a recent work (Antonov et al., Physical Review Letters 123, 243903 (2019)), it was shown that it is possible to amplify a train of attosecond pulses, which are produced from the radiation of high harmonics of the infrared field of the fundamental frequency, in the active medium of a plasma-based X-ray laser modulated by a replica of the infrared field of the same frequency. In this paper, we show that much higher amplification can be achieved using the second harmonic of the fundamental frequency for modulating of a hydrogen-like active medium. The physical reason for such enhanced amplification is the possibility to use all (even and odd) sidebands induced in the gain spectrum in the case of the modulating field of the doubled fundamental frequency, while only one set of sidebands (either even or odd) could participate in amplification in the case of the modulating field of the fundamental frequency due to the fact that the spectral components of the high-harmonic field are separated by twice the fundamental frequency. Using the plasma of hydrogen-like C5+ ions with an inverted transition wavelength of 3.38 nm in the water window as an example, it is shown that the use of a modulating field at a doubled fundamental frequency makes it possible to increase the intensity of amplified attosecond pulses by an order of magnitude in comparison with the previously studied case of a fundamental frequency modulating field.

The effect of initial phase on the emission characteristics of forward electron colliding with a tightly focused linearly polarized few-cycle laser pulse

We have studied the high harmonic radiation property from the scattering of an electron with a focused few-cycle laser pulse by analyzing the distribution of the radiation field and the motion state of the electron. In the time domain, temporal width of the compressed radiation can reach 33 zs (zeptosecond), thus an ultrashort x-ray pulse was generated in the interaction process. The radiation in this process is vastly similar to high harmonic generation in the process of atomic strong-field. The latter depends to a large extent on the phase of carrier-envelope (CE) driving laser pulse. The cutoff of radiation spectrum can reach , and whether the high-order harmonic spectrum in the cut-off region can be well resolved depends on the CE phase. We have investigated the relationship between the maximum radiation intensity and the CE phase, and discussed a potential method to characterize the CE phase of an intense few-cycle laser pulse for broader application prospects.

Torus-knot angular momentum in twisted attosecond pulses from high-order harmonic generation

Bicircular twisted Laguerre-Gaussian beams possess a definite torus knot angular momentum (TKAM) $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{{J}_{\ensuremath{\gamma}}}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}+\ensuremath{\gamma}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}$ as an alternative a form of angular momentum. TKAM is conserved in nonlinear atomic processes such as high harmonic generation and can be classified by a time delay parameter $\ensuremath{\tau}$ and a coordination parameter $\ensuremath{\gamma}$. These parameters are defined by the respective projected orbital angular momentum ${\ensuremath{\ell}}_{i}$ and the energy $\ensuremath{\hbar}{p}_{i}{\ensuremath{\omega}}_{0}$ of the two superimposed Laguerre-Gaussian beams. We derive a consistent geometric method to determine $\ensuremath{\tau}$ and $\ensuremath{\gamma}$ from the driving beam as well as from the high harmonic radiation. The method relates both invariance parameters ($\ensuremath{\tau}$ and $\ensuremath{\gamma}$) to a torus knot which can be constructed from the emitted high harmonic radiation. These knots are constructed from the spatiotemporal evolution of the electric field of the respective high harmonic radiation or the driving beam. We demonstrate the classification of the invariance parameters for a planar atomic gas target irradiated by bicircular Laguerre-Gaussian beams explicitly. In addition, we demonstrate that the respective torus knots determined by $\ensuremath{\tau}$ and $\ensuremath{\gamma}$ can be mapped onto each other within minor modifications. The numerical calculations are done within the strong-field approximation and the associated quantum orbit approach. Therefore, we also briefly review high harmonic generation by bicircular twisted light beams. This introduced geometric method is a different approach to interpret the invariance parameters $\ensuremath{\tau}$ and $\ensuremath{\gamma}$, as well as their underlying relations, compared to a purely formal derivation. The investigations presented in this work are in good agreement with previous findings and provide insight into the dynamical symmetry of TKAM in the context of high harmonic generation induced by bicircular twisted Laguerre-Gaussian beams.

Ultrafast high-harmonic nanoscopy of magnetization dynamics

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescales has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our compact experimental setup demonstrates the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with high sensitivity to chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics.

Analysis of the spectral properties of free electron lasers in X-RAY and other bands

Analytical formalism for the description of free electron laser (FEL) spectrum is proposed with account for the electron beam size, divergences, beam energy spread, the off-axis deflection and the periodic harmonic and non-periodic constant magnetic field components in undulators. The exact analytical expressions for the spontaneous undulator radiation (UR) are obtained in terms of generalized Bessel and Airy functions, which describe the spectrum line shape and intensities. The obtained analytical formulae distinguish the effects of each installation and beam parameter on the FEL harmonic radiation. The enhanced phenomenological model is employed for the FEL modeling; it describes the harmonic powers evolution along the undulators and gradual saturation around the saturation length with account for the saturated powers oscillations. With this model, we study the generation of FEL harmonics, including even, in several instances of FEL experiments at LCLS, LEUTL and PAL-XFEL. We analytically demonstrate the even harmonics reasons in the LCLS and LEUTL FEL experiments. The spectrum line split due to the beam size is demonstrated analytically and compared with experimentally measured spectral characteristics. The PAL-XFEL experiment is analyzed and compared with the LCLS experiment; the possibility of high harmonic radiation in it is explored. The modeling results fully agree with the measured values in the studied FELs. The analytical formalism shows physical background for each harmonic in every FEL. It allows the analysis of the radiation and beam alignment in projected, built and working FELs and it can help minimizing losses and correcting magnetic fields as well as projecting experiments with FELs.

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.