We demonstrate analytically and numerically that focusing of high harmonics produced by the reflection of a few femtosecond laser pulse from a concave plasma surface opens a new way towards unprecedentally high intensities. The key features allowing for boosting of the focal intensity is the harmonic coherency and the small exponent of the power-law decay of the harmonic spectrum. Using the similarity theory and direct particle-in-cell simulations we find that the intensity at the Coherent Harmonic Focus (CHF) scales as $I_{\tiny CHF} \propto a_0^3 I_0$, where $a_0$ and $I_0\propto a_0^2$ are the dimensionless relativistic amplitude and the intensity of the incident laser pulse. The scaling suggests that due to the CHF, the Schwinger intensity limit can be achieved using lasers with $I_0 \approx 10^{22}$ W/cm$^2$. The pulse duration at the focus scales as $τ_{\tiny CHF} \propto 1/a_0^2$ and reaches the subattosecond range.
A technique using vector Slepian harmonics and multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or electric field distribution in the focal volume is approximated using numerical optimization and the corresponding illuminating field at the entrance pupil is constructed. Three examples from the recent literature have been chosen to illustrate the method.
Controlling the wavefront of an extreme ultraviolet (XUV) high-order harmonic beam during the generation process offers to focus the beam without resorting to any XUV optics. By characterizing the XUV intensity profile and wavefront, we quantitatively retrieve both the size and the position of the waist of each generated harmonics and show that optics-free focusing leads to focused XUV spot with micrometer size. We use this remarkable coherent effect to demonstrate efficient and adjustable spectral filtering of the XUV light, along with a strong rejection of the fundamental beam, without using…
By experimentally studying high-order harmonic beams generated in gases, we show how the spatial characteristics of these ultrashort XUV beams can be finely controlled under standard generation conditions. For the first time, we demonstrate that these XUV beams can be emitted as converging beams and get thereby focused after generation. We study this mirrorless focusing using a spatially chirped beam that acts as a spatially localized probe located inside the harmonic generation medium. We analyze the XUV beam evolution with an analytical model providing the beam characteristics and obtain ver…
Scattering has usually be considered as detrimental for optical focusing or imaging. Recently, more and more research has shown that strongly scattering materials can be utilized to focus coherent light by controlling or shaping the incident light. Here, purposeful focusing of second-harmonic waves, which are generated and scattered from nonlinear turbid media via feedback-based wavefront shaping is presented. This work shows a flexible manipulation of both disordered linear and nonlinear scattering signals, indicating more controllable degrees of freedom for the description of turbid media. T…
In this work we study the impact of chromatic focusing of few-cycle laser pulses on high-order harmonic generation (HHG) through analysis of the emitted extreme ultraviolet (XUV) radiation. Chromatic focusing is usually avoided in the few-cycle regime, as the pulse spatio-temporal structure may be highly distorted by the spatiotemporal aberrations. Here, however, we demonstrate it as an additional control parameter to modify the generated XUV radiation. We present experiments where few-cycle pulses are focused by a singlet lens in a Kr gas jet. The chromatic distribution of focal lengths allow…
We present an optical system based on two toroidal mirrors in a Wolter configuration to focus broadband XUV radiation. Optimization of the focusing optics alignment is carried out with the aid of an XUV wavefront sensor. Back-propagation of the optimized wavefront to the focus yields a focal spot of 3.6$\times$4.0 $μ$m$^2$ full width at half maximum, which is consistent with ray-tracing simulations that predict a minimum size of 3.0$\times$3.2 $μ$m$^2$. This work is important for optimizing the intensity of focused high-order harmonics in order to reach the nonlinear interaction regime.
Novel table-top sources of extreme-ultraviolet light based on high-harmonic generation yield unique insight into the fundamental properties of molecules, nanomaterials, or correlated solids, and enable advanced applications in imaging or metrology. Extending high-harmonic generation to high repetition rates portends great experimental benefits, yet efficient extreme-ultraviolet conversion of correspondingly weak driving pulses is challenging. Here, we demonstrate a highly efficient source of femtosecond extreme-ultraviolet pulses at 50-kHz repetition rate, utilizing the ultraviolet second-harm…
The interaction of strong near-infrared (NIR) laser pulses with wide-bandgap dielectrics produces high harmonics in the extreme ultraviolet (XUV) wavelength range. These observations have opened up the possibility of attosecond metrology in solids, which would benefit from a precise measurement of the emission times of individual harmonics with respect to the NIR laser field. Here we show that, when high-harmonics are detected from the input surface of a magnesium oxide crystal, a bichromatic probing of the XUV emission shows a clear synchronization largely consistent with a semiclassical mode…
Circularly-polarized extreme UV and X-ray radiation provides valuable access to the structural, electronic and magnetic properties of materials. To date, this capability was available only at large-scale X-ray facilities such as synchrotrons. Here we demonstrate the first bright, phase-matched, extreme UV circularly-polarized high harmonics and use this new light source for magnetic circular dichroism measurements at the M-shell absorption edges of Co. We show that phase matching of circularly-polarized harmonics is unique and robust, producing a photon flux comparable to the linearly polarize…
We theoretically study the scaling with the driving wavelength of the high-order harmonic generation (HHG) under the simultaneous irradiation of an extreme ultraviolet (XUV) pulse. Surprisingly, when the cutoff energy and ionization yield are fixed, the harmonic yield is nearly independent of the driving wavelength. We identify its origin as the combination of the initial spatial width of the states excited by the XUV pulse, making the wavepacket spreading less prominent, and the shallowing of the ionization potential, which suggests complex nature of the wavelength dependence of HHG.
Experiments on the excitation of propagating surface plasmons (SPs) by ultrashort, high intensity laser interaction with "grating" targets are reviewed. At intensities exceeding $10^{19}~\mbox{W cm}^{-2}$ on target, i.e. in the strongly relativistic regime of electron dynamics, multi-MeV electrons are accelerated by the SP field as dense bunches collimated in a near-tangent direction. By the use of a suitable blazed grating, the bunch charge can be increased up to $\simeq $660 picoCoulomb. Intense XUV high harmonics (HH) diffracted by the grating are observed when a plasma with sub-micrometer …
Vector beam, with a spatial nonuniform polarization distribution, is important for many applications due to its unique field characteristics and novel effects when interacting with matter. Here through three-dimensional particle-in-cell simulations, we demonstrate that intense vector beams in the extreme-ultraviolet to x-ray spectral region can be generated by means of high harmonic generation (HHG) in the relativistic regime. The vector features of the fundamental laser beam can be transferred to the higher frequency emission coherently during the extreme nonlinear HHG dynamics from relativis…
We demonstrate a new scheme of spectromicroscopy in the extreme ultraviolet (EUV) spectral range, where the spectral response of the sample at different wavelengths is imaged simultaneously. It is enabled by applying ptychographical information multiplexing (PIM) to a tabletop EUV source based on high harmonic generation, where four spectrally narrow harmonics near 30 nm form a spectral comb structure. Extending PIM from previously demonstrated visible wavelengths to the EUV/X-ray wavelengths promises much higher spatial resolution and more powerful spectral contrast mechanism, making PIM an a…
We performed extreme ultraviolet spectroscopy using an 80 lines/mm TEM mesh as dispersive element. We present the usefulness of this instrument for dispersing a high harmonic spectrum from the 13th to the 29th harmonic of a Ti:Sapph laser, corresponding to a wavelength range from 60 to 27 nm. The resolution of the instrument is limited by the image size of the high harmonic generation region on the detector. The best resolution in first order diffraction is under 2 nm over the entire spectral range.
Frequency multiplication of terahertz signals on a solid state platform is highly sought-after for the next generation of high-speed electronics and the creation of frequency combs. Solutions to efficiently generate extreme harmonics (up to the $31^{\rm{st}}$ harmonic and beyond) of a terahertz signal with modest input intensities, however, remain elusive. Using fully nonperturbative simulations and complementary analytical theory, we show that 3D Dirac semimetals (DSMs) have enormous potential as compact sources of extreme terahertz harmonics, achieving energy conversion efficiencies beyond $…
Extreme ultraviolet (XUV) lasers are essential for the investigation of fundamental physics. Especially high repetition rate, high photon flux sources are of major interest for reducing acquisition times and improving signal to noise ratios in a plethora of applications. Here, an XUV source based on cascaded frequency conversion is presented, which delivers due to the drastic better single atom response for short wavelength drivers, an average output power of (832 +- 204) μW at 21.7 eV. This is the highest average power produced by any HHG source in this spectral range surpassing precious demo…
The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wavefunction, and in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme-ultraviolet and soft X-ray high harmonic combs. The on-axis HHG emission has extremely low d…
Vigorous efforts to harness the topological properties of light have enabled a multitude of novel applications. Translating the applications of structured light to higher spatial and temporal resolutions mandates their controlled generation, manipulation, and thorough characterization in the short-wavelength regime. Here, we resort to high-order harmonic generation (HHG) in a noble gas to upconvert near-infrared (IR) vector, vortex, and vector-vortex driving beams that are tailored respectively in their Spin Angular Momentum (SAM), Orbital Angular Momentum (OAM), and simultaneously in their SA…
Circularly polarized extreme ultraviolet (XUV) radiation is highly interesting for investigation of chirality-sensitive light-matter interactions. Recent breakthroughs have enabled generation of such light sources via high harmonic generation (HHG) from rare gases. There is a growing interest in extending HHG medium from gases to solids, especially to 2D materials, as they hold great promise to develop ultra-compact solid-state photonic devices and provide insights into electronic properties of the materials themselves. However, HHG in graphene driven by terahertz to mid-infrared fields report…
In this work, the polar tetrahedron [PN$_2$O$_2$] was revealed as a new deep-ultraviolet (deep-UV) nonlinear optically active unit. Accordingly, a thermodynamically stable compound (PNO) consisting of the polar [PN$_2$O$_2$] units was predicted and suggested as a promising candidate of deep-UV nonlinear optical (NLO) material. Compared with other deep-UV materials known to date, PNO possesses the strongest second harmonic generation (SHG) coefficient (about 6 times that of KH$_2$PO$_4$ (KDP)). Moreover, its three-dimensional connectivity endows it with good mechanical and thermal properties. T…
The majority of sources of coherent optical radiation rely on laser oscillators driven by population inversion. Despite their technological importance in communications, medicine, industry, and other fields, it remains a challenge to access the spectral range of 0.1-10 THz (the "terahertz gap"), a frequency band for applications ranging from spectroscopy to security and high-speed wireless communications. Here, we propose a way to produce coherent radiation spanning the THz gap by efficient second-harmonic generation (SHG) in low-loss dielectric structures, starting from technologically mature…
We show that the divergence of extreme ultraviolet pulses from high harmonic generation, which is directly linked to the shape and size of the refocused beam, can be controlled by the relative delay between the fundamental and its intense orthogonally polarized second harmonic in two-color high-harmonic generation. We find that the divergence is minimized close to the delays were the number of emitted photons is maximized. These findings are rationalized as suppression and enhancement of long and short electron trajectories as function of the phase of the two-color laser field, respectively. T…
After decades of supremacy of the Titanium:Sapphire technology, Ytterbium-based high-order harmonic sources are emerging as an interesting alternative for experiments requiring high flux of ultrashort extreme ultraviolet (XUV) radiation. In this article we describe a versatile experimental setup delivering XUV photons in the 10-50 eV range. The use of cascaded high-harmonic generation enables us to reach 1.8 mW of average power at 18 eV. Several spectral focusing schemes are presented, to select either a single harmonic or group of high-harmonics and thus an attosecond pulse train. In the pers…
Recent progress in laser-based high-repetition rate extreme ultraviolet (EUV) lightsources and multidimensional photoelectron spectroscopy enable the build-up of a new generation of time-resolved photoemission experiments. Here, we present a setup for time-resolved momentum microscopy driven by a 1 MHz femtosecond EUV table-top light source optimized for the generation of 26.5 eV photons. The setup provides simultaneous access to the temporal evolution of the photoelectron's kinetic energy and in-plane momentum. We discuss opportunities and limitations of our new experiment based on a series o…
The interplay between spin and orbital angular momentum in the up-conversion process allows us to control the macroscopic wave front of high harmonics by manipulating the microscopic polarizations of the driving field. We demonstrate control of orbital angular momentum in high harmonic generation from both solid and gas phase targets using the selection rules of spin angular momentum. The gas phase harmonics extend the control of angular momentum to extreme-ultraviolet wavelength. We also propose a bi-color scheme to produce spectrally separated extreme-ultraviolet radiation carrying orbital a…
Laser pulses with a duration of one femtosecond or shorter can be generated both in the IR-VIS and in the extreme UV, but the deep UV is a spectral region where such extremely short pulses have not yet been demonstrated. Here, a method for the synthesis of ultrashort pulses in the deep UV is demonstrated, which utilizes the temporal and spatial harmonics that are generated by two noncollinear IR-VIS pulses in a thin MgF2 plate. By controlling the groove-envelope phase of the IR-VIS pulses, spatial harmonics are concatenated to form deep UV waveforms with a duration of 1.5 fs.
We demonstrate a new high-order harmonic generation mechanism reaching the `water window' spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/sr pulses. Harmonics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.
Attosecond metrology sensitive to sub-optical-cycle electronic and structural dynamics is opening up new avenues for ultrafast spectroscopy of condensed matter. Using intense lightwaves to precisely control the extremely fast carrier dynamics in crystals holds great promise for next-generation electronics and devices operating at petahertz bandwidth. The carrier dynamics can produce high-order harmonics of the driving light field extending up into the extreme-ultraviolet region. Here, we introduce polarization-state-resolved high-harmonic spectroscopy of solids, which provides deeper insights …
High harmonic generation is a convenient way to obtain extreme ultraviolet light from table-top laser systems and the experimental tools to exploit this simple and powerful light source for time-resolved spectroscopy are being developed by several groups. For these applications, brightness and stability of the high harmonic generation is a key feature. This article focuses on practical aspects in the generation of extreme ultraviolet pulses with ultrafast commercial lasers, namely generation parameters and online monitoring as well as analysis of generation yield and stability.
We present a table-top extreme ultraviolet (XUV) beamline for measuring time- and frequency-resolved XUV excited optical luminescence (XEOL) with additional femtosecond-resolution XUV transient absorption spectroscopy functionality. XUV pulses are generated via high-harmonic generation using a near-infrared pulse in a noble gas medium, and focused to excite luminescence from a solid sample. The luminescence is collimated and guided into a streak camera, where its spectral components are temporally resolved with picosecond temporal resolution. We time-resolve XUV excited luminescence and compar…
Time-domain analysis of harmonic fields with sub-cycle resolution is now experimentally viable due to the emergence of sensitive, on-chip techniques for petahertz-scale optical-field sampling. We demonstrate how such a time-domain, field-resolved analysis uncovers the extreme nonlinear electron dynamics responsible for high-harmonic generation within solids. Time-dependent density functional theory was used to simulate harmonic generation from a solid-state band-gap system driven by near- to mid-infrared waveforms. Particular attention was paid to regimes where both intraband and interband emi…
The advent of Petawatt-class laser systems allows generating electro-magnetic fields of unprecedented strength in a controlled environment, driving increasingly more efforts to probe yet unobserved processes through their interaction with the quantum vacuum. Still, the lowest intensity scale governing these effects lies orders of magnitude beyond foreseen capabilities, so that such endeavor is expected to remain extremely challenging. In recent years, however, plasma mirrors have emerged as a promising bridge across this gap, by enabling the conversion of intense infrared laser pulses into coh…
High harmonic generation (HHG) enables extreme ultraviolet radiation with table-top setups. Its exceptional properties, such as coherence and (sub)-femtosecond pulse durations, have led to a diversity of applications. Some of these require a high photon flux and megahertz repetition rates, e.g. to avoid space charge effects in photoelectron spectroscopy. To date this has only been achieved with enhancement cavities. Here, we establish a novel route towards powerful HHG sources. By achieving phase-matched HHG of a megahertz fibre laser we generate a broad plateau (25 eV - 40 eV) of strong harmo…
We review the main research directions ongoing in the development of high-harmonic generation-based extreme ultraviolet sources for the synthesization and application of trains and isolated attosecond pulses to time-resolved spectroscopy. A few experimental and theoretical works will be discussed in connection to well-established attosecond techniques. In this context, we present the unique possibilities offered for time-resolved investigations on the attosecond timescale by the new Extreme Light Infrastructure Attosecond Light Pulse Source, which is currently under construction.
We theoretically investigate the piezo-optic effect of high-harmonic generation (HHG) in shear-strained semiconductors. By focusing on a typical semiconductor, GaAs, we show that there is optical activity, meaning different responses to right-handed and left-handed elliptically polarized electric fields. We also show that this optical activity is more pronounced for higher harmonics whose perturbative order exceeds the band-gap energy. These findings point to a useful pathway for strain engineering of nonlinear optics to control the reciprocity of HHG.
3D Dirac semimetals (DSMs) are promising materials for terahertz high harmonic generation (HHG). We show that 3D DSMs' high nonlinearity opens up a regime of nonlinear optics where extreme subwavelength current density features develop within nanoscale propagation distances of the driving field. Our results reveal orders-of-magnitude enhancement in HHG intensity with thicker 3D DSM films, and show that these subwavelength features fundamentally limit HHG enhancement beyond an optimal film thickness. This decrease in HHG intensity beyond the optimal thickness constitutes an effective propagatio…
Intrinsic to the process of high-order harmonic generation is the creation of plasma and the resulting spatiotemporal distortions of the driving laser pulse. Inside a high finesse cavity where the driver pulse and gas medium are reused, this can lead to optical bistability of the cavity-plasma system, accumulated self-phase modulation of the intracavity pulse, and coupling to higher order cavity modes. We present an experimental and theoretical study of these effects and discuss their implications for power scaling of intracavity high-order harmonic generation and extreme ultraviolet frequency…
Characterizing and controlling electronic properties of quantum materials require direct measurements of non-equilibrium electronic band structures over large regions of momentum space. Here, we demonstrate an experimental apparatus for time- and angle-resolved photoemission spectroscopy using high-order harmonic probe pulses generated by a robust, moderately high power (20 W) Yb:KGW amplifier with tunable repetition rate between 50 and 150 kHz. By driving high-order harmonic generation (HHG) with the second harmonic of the fundamental 1025 nm laser pulses, we show that single-harmonic probe p…
Full coherent soft X-ray attosecond pulses are now available through high-order harmonic generation (HHG); however, its insufficient output energy hinders various applications, such as attosecond-scale soft X-ray nonlinear experiments, the seeding of soft X-ray free-electron lasers, attosecond-pump-attosecond-probe spectroscopies, and single-shot imaging. In this paper, towards the implementation of these exciting studies, we demonstrate a soft X-ray harmonic beam that is more than two orders of magnitudes stronger up to the water window region compared to previous works. This was achieved by …
In our recent study [Commun. Phys. 3, 92 (2020)], we have developed an approach for energy-scaling of high-order harmonic generation in water-window region under neutral-medium condition. More specifically, we obtained nanojoule-class water-window soft x-ray harmonic beam under phase match condition. It has been achieved by combining a newly developed terawatt-class mid-infrared femtosecond laser and a loose focusing geometry for high-order harmonic generation. The generated beam is more than 100 times intense compared to previously reported results. The experimental setup included two key par…
In this study the generation of energetic coherent extreme ultraviolet (XUV) radiation with controlled polarization, is reported. The XUV radiation results from the process of high harmonic generation (HHG), in a gas phase atomic medium, driven by an intense two-color circularly polarized counter-rotating laser field, under loose focusing geometry conditions. The energy of the XUV radiation emitted per laser pulse is found to be of the order of ~100 nJ with the spectrum spanning from 17 to 26 eV. The demonstrated energy values along with tight focusing geometries is sufficient to induce nonlin…
Active Control of Extreme Ultraviolet Photon Flux and Resolution with a Plane Ruled Reflection Grating Spectrometer that Measures Diverging High-Harmonics
High harmonic generation (HHG) is an extreme nonlinear frequency up-conversion process during which extremely short duration optical pulses at very short wavelengths are emitted. A major concern of HHG is the small conversion efficiency at the single emitter level. Thus ensuring that the emission at different locations are emitted in phase is crucial. At high pump intensities it is impossible to phase match the radiation without reverting to ordered modulations of either the medium or the pump field itself, a technique known as Quasi-Phase-Matching (QPM). To date, demonstrated QPM techniques o…
In this work the experimental realization of a tunable high photon flux extreme ultraviolet light source is presented. This is enabled by high harmonic generation of two temporally delayed driving pulses, resulting in a tuning range of 0.8 eV at the 19th harmonic at 22.8 eV. The implemented approach allows for fast tuning of the spectrum, is highly flexible and is scalable towards full spectral coverage at higher photon energies.
Significant enhancement of evanescent spatial harmonics inside the slabs of media with extreme optical anisotropy is revealed. This phenomenon results from the pumping of standing waves and has the feature of being weakly sensitive to the material losses. Such characteristics may enable subwavelength imaging at considerable distances away from the objects.
We present a theoretical study of high-order harmonic generation (HHG) and propagation driven by an infrared field carrying orbital angular momentum (OAM). Our calculations unveil the following relevant phenomena: extreme-ultraviolet harmonic vortices are generated and survive to the propagation effects, vortices transport high-OAM multiple of the corresponding OAM of the driving field and, finally, the different harmonic vortices are emitted with similar divergence. We also show the possibility of combining OAM and HHG phase-locking to produce attosecond pulses with helical pulse structure.
Ultrafast light sources have become an indispensable tool to access and understand transient phenomenon in material science. However, a simple and easy-to-implement method for harmonic selection, with high transmission efficiency and pulse duration conservation, is still a challenge. Here we showcase and compare two approaches for selecting the desired harmonic from a high harmonic generation source while achieving the above goals. The first approach is the combination of extreme ultraviolet spherical mirrors with transmission filters and the second approach uses a normal-incidence spherical g…
Recent progresses in femtosecond ytterbium-doped fiber laser technology areopening new perspectives in strong field physics and attosecond science. Highorder harmonic generation from these systems is particularly interesting because it provides high flux beams of ultrashort extreme ultraviolet radiation. A lot of efforts have been devoted to optimize the macroscopic generation parameters. Here we investigate the possibility of enhancing the single-atom response by producing high-harmonics from the second, third and fourth harmonics of a turnkey Yb-fiber laser at 1030 nm. We show that the harmo…
