Ultrafast electron localization and screening in a transition metal dichalcogenide.

The coupling of light to electrical charge carriers in semiconductors is the foundation of many technological applications. Attosecond transient absorption spectroscopy measures simultaneously how excited electrons and the vacancies they leave behind dynamically react to the applied optical fields. In compound semiconductors, these dynamics can be probed via any of their atomic constituents with core-level transitions into valence and conduction band. Typically, the atomic species forming the compound contribute comparably to the relevant electronic properties of the material. One therefore expects to observe similar dynamics, irrespective of the choice of atomic species via which it is probed. Here, we show in the two-dimensional transition metal dichalcogenide semiconductor MoSe2, that through a selenium-based core-level transition we observe charge carriers acting independently from each other, while when probed through molybdenum, the collective, many-body motion of the carriers dominates. Such unexpectedly contrasting behavior can be explained by a strong localization of electrons around molybdenum atoms following absorption of light, which modifies the local fields acting on the carriers. We show that similar behavior in elemental titanium metal [M. Volkov et al., Nat. Phys. 15, 1145-1149 (2019)] carries over to transition metal-containing compounds and is expected to play an essential role for a wide range of such materials. Knowledge of independent particle and collective response is essential for fully understanding these materials.

Ultrafast Transition from State-Blocking Dynamics to Electron Localization in Transition Metal ß-Tungsten.

We describe an ultrafast transition of the electronic response of optically excited transition metal ß-tungsten with few-femtosecond time resolution. The response moves from a regime where state filling of the excited carrier population around the Fermi level dominates towards localization of carriers onto the outer d orbitals. This is in contrast to previous measurements using ultrafast element-specific core-level spectroscopy enabled by attosecond transient absorption spectroscopy on transition metals such as titanium and around the transition metal atom in transition metal dichalchogenides MoTe_{2} and MoSe_{2}. This surprisingly different dynamical response for ß-tungsten can be explained by considering the electron-electron dynamics on a few-femtosecond timescale and the slower electron-phonon thermalization dynamics.

Water-window high harmonic generation with 0.8-µm and 2.2-µm OPCPAs at 100 kHz.

We compare the generation of high-order harmonics in the water window (283-543 eV) with 0.8-µm and 2.2-µm few-cycle lasers at a pulse repetition rate of 100 kHz. Using conventional phase matching with the 2.2-µm driver and what we attribute to nonadiabatic self-phase-matching with the 0.8-µm driver, photons up to 0.6 keV (2 nm) are generated in both cases. Special attention is paid to the understanding of the generation mechanism with the 0.8-µm laser amplifier system. We use the same beamline and pump laser for both drivers, which allows for a direct flux comparison at the two driving wavelengths. For photon energies around 280 eV, a 10-100 times higher flux is obtained from the 2.2-µm versus the 0.8-µm laser system in helium and neon. The crossover at which the 2.2-µm yields a higher flux compared to the 0.8-µm driver is found to be as high as 0.2 keV. Our study supports the common approach of using long-wavelength lasers in a phase-matched regime for efficient generation of water-window harmonics, but also shows that the more widespread 0.8-µm wavelength can be used to generate water-window harmonics with an efficiency close to the one of a less common 2.2-µm source.

High-power few-cycle near-infrared OPCPA for soft X-ray generation at 100 kHz.

We present a near-infrared optical parametric chirped-pulse amplifier (OPCPA) and soft X-ray (SXR) high-harmonic generation system. The OPCPA produces few-cycle pulses at a center wavelength of 800 nm and operates at a high repetition rate of 100 kHz. It is seeded by fully programmable amplitude and phase controlled ultra-broadband pulses from a Ti:sapphire oscillator. The output from the OPCPA system was compressed to near-transform-limited 9.3-fs pulses. Fully characterized pulse compression was recorded for an average power of 22.5 W, demonstrating pulses with a peak power greater than 21 GW. Without full temporal characterization, high-power operation was achieved up to 35 W. We demonstrate that at such high repetition rates, spatiotemporally flattened pump pulses can be achieved through a cascaded second-harmonic generation approach with an efficiency of more than 70%. This combination provides a compelling OPCPA architecture for scaling the peak power of high-repetition-rate ultra-broadband systems in the near-infrared. The output of this 800-nm OPCPA system was used to generate SXR radiation reaching 190 eV photon energy through high-harmonic generation in helium.

Phase stabilization of an attosecond beamline combining two IR colors.

We present a phase-stabilized attosecond pump-probe beamline involving two separate infrared wavelengths for high-harmonic generation (HHG) and pump or probe. The output of a Ti:sapphire laser is partly used to generate attosecond pulses via HHG and partly to pump an optical parametric amplifier (OPA) that converts the primary Ti:sapphire radiation to a longer wavelength. The attosecond pulse and down-converted infrared are recombined after a more than 20-m-long Mach-Zehnder interferometer that spans across two laboratories and separate optical tables. We demonstrate a technique for active stabilization of the relative phase of the pump and probe to within 450 as rms, without the need for an auxiliary continuous wave (cw) laser. The long-term stability of our system is demonstrated with an attosecond photoelectron streaking experiment. While the technique has been shown for one specific OPA output wavelength (1560 nm), it should also be applicable to other OPA output wavelengths. Our setup design permits tuning of the OPA wavelength independently from the attosecond pulse generation. This approach yields new possibilities for studying the wavelength-dependence of field-driven attosecond electron dynamics in various systems.

High-power OPCPA generating 1.7 cycle pulses at 2.5 µm.

We present a high-power mid-infrared (mid-IR) optical parametric chirped-pulse amplifier (OPCPA) generating 14.4 fs pulses centered at 2.5 µm with an average power of 12.6 W and a repetition rate of 100 kHz. The short pulses are obtained without nonlinear pulse compression. This is in contrast to most few-cycle systems operating in the mid-IR. In our case, the ultrashort pulse duration is enabled by a careful design of the gain profile of each amplification stage as well as a precise control of the signal dispersion throughout the system. A pulse shaper is used in the seed beam to adjust the spectral phase at the output of the OPCPA system. This approach allows for a clean temporal profile leading to a high peak power of 6.3 GW.

Decoupling phase-matching bandwidth and interaction geometry using non-collinear quasi-phase-matching gratings.

In optical parametric amplification (OPA) of broadband pulses, a non-collinear angle between the interacting waves is typically introduced in order to achieve broadband phase-matching. Consequently, bandwidth and beam geometry are closely linked. This coupling restricts the geometrical layout of an OPA system. Here, we demonstrate a quasi-phase-matching (QPM) geometry for broadband OPA in which a transverse component is introduced to the QPM grating to impose an additional momentum on the generated wave. This momentum shift detunes the wavelength where the signal and the idler are group-velocity matched, thereby allowing for broadband phase-matching without having to add a non-collinear angle between the interacting waves. We present two experimental configurations making use of this principle, and propose a third configuration with the potential to further simplify ultra-broadband OPA system architectures.

Gouy phase shift for annular beam profiles in attosecond experiments.

Attosecond pump-probe measurements are typically performed by combining attosecond pulses with more intense femtosecond, phase-locked infrared (IR) pulses because of the low average photon flux of attosecond light sources based on high-harmonic generation (HHG). Furthermore, the strong absorption of materials at the extreme ultraviolet (XUV) wavelengths of the attosecond pulses typically prevents the use of transmissive optics. As a result, pump and probe beams are typically recombined geometrically with a center-hole mirror that reflects the larger IR beam and transmits the smaller XUV, which leads to an annular beam profile of the IR. This modification of the IR beam can affect the pump-probe measurements because the propagation that follows the reflection on the center-hole mirror can strongly deviate from that of an ideal Gaussian beam. Here we present a detailed experimental study of the Gouy phase of an annular IR beam across the focus using a two-foci attosecond beamline and the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) technique. Our measurements show a Gouy phase shift of the truncated beam as large as 2π and a corresponding rate of 50 as/mm time delay change across the focus in a RABBITT measurement. These results are essential for attosecond pump-probe experiments that compare measurements of spatially separated targets.

Erratum: Resonance Effects in Photoemission Time Delays [Phys. Rev. Lett. 115, 133001 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.133001.

Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media.

Advances in the amplification and manipulation of ultrashort laser pulses have led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device that is bandwidth- and power-scalable. The approach is based on two-dimensional (2D) patterning of quasi-phase-matching (QPM) gratings combined with optical parametric interactions involving spatially dispersed laser pulses. Our proof of principle experiment demonstrates this technique via mid-infrared optical parametric chirped pulse amplification of few-cycle pulses. Additionally, we present a detailed theoretical and numerical analysis of such 2D-QPM devices and how they can be designed.

Comparison of attosecond streaking and RABBITT.

Recent progress in the generation of ultra-short laser pulses has enabled the measurement of photoionization time delays with attosecond precision. For single photoemission time delays the most common techniques are based on attosecond streaking and the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT). These are pump-probe techniques employing an extreme-ultraviolet (XUV) single attosecond pump pulse for streaking or an attosecond pump pulse train for RABBITT, and a phase-locked infrared (IR) probe pulse. These techniques can only extract relative timing information between electrons originating from different initial states within the same atom or different atoms. Here we address the question whether the two techniques give identical timing information. We present a complete study, supported by both experiments and simulations, comparing these two techniques for the measurement of the photoemission time delay difference between valence electrons emitted from the Ne 2p and Ar 3p ground states. We highlight not only the differences and similarities between the two techniques, but also critically investigate the reliability of the methods used to extract the timing information.

Semi-classical approach to compute RABBITT traces in multi-dimensional complex field distributions.

We present a semi-classical model to calculate RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) traces in the presence of a reference infrared field with a complex two-dimensional (2D) spatial distribution. The evolution of the electron spectra as a function of the pump-probe delay is evaluated starting from the solution of the classical equation of motion and incorporating the quantum phase acquired by the electron during the interaction with the infrared field. The total response to an attosecond pulse train is then evaluated by a coherent sum of the contributions generated by each individual attosecond pulse in the train. The flexibility of this model makes it possible to calculate spectrograms from non-trivial 2D field distributions. After confirming the validity of the model in a simple 1D case, we extend the discussion to describe the probe-induced phase in photo-emission experiments on an ideal metallic surface.

Ptychographic reconstruction of attosecond pulses.

We demonstrate a new attosecond pulse reconstruction modality which uses an algorithm that is derived from ptychography. In contrast to other methods, energy and delay sampling are not correlated, and as a result, the number of electron spectra to record is considerably smaller. Together with the robust algorithm, this leads to a more precise and fast convergence of the reconstruction.

Resonance Effects in Photoemission Time Delays.

We present measurements of single-photon ionization time delays between the outermost valence electrons of argon and neon using a coincidence detection technique that allows for the simultaneous measurement of both species under identical conditions. The analysis of the measured traces reveals energy-dependent time delays of a few tens of attoseconds with high energy resolution. In contrast to photoelectrons ejected through tunneling, single-photon ionization can be well described in the framework of Wigner time delays. Accordingly, the overall trend of our data is reproduced by recent Wigner time delay calculations. However, besides the general trend we observe resonance features occurring at specific photon energies. These features have been qualitatively reproduced and identified by a calculation using the multiconfigurational Hartree-Fock method, including the influence of doubly excited states and ionization thresholds.

Light-Matter Interaction at Surfaces in the Spatiotemporal Limit of Macroscopic Models.

What is the spatiotemporal limit of a macroscopic model that describes the optoelectronic interaction at the interface between different media? This fundamental question has become relevant for time-dependent photoemission from solid surfaces using probes that resolve attosecond electron dynamics on an atomic length scale. We address this fundamental question by investigating how ultrafast electron screening affects the infrared field distribution for a noble metal such as Cu(111) at the solid-vacuum interface. Attosecond photoemission delay measurements performed at different angles of incidence of the light allow us to study the detailed spatiotemporal dependence of the electromagnetic field distribution. Surprisingly, comparison with Monte Carlo semiclassical calculations reveals that the macroscopic Fresnel equations still properly describe the observed phase of the IR field on the Cu(111) surface on an atomic length and an attosecond time scale.

Mid-infrared pulse generation via achromatic quasi-phase-matched OPCPA.

We demonstrate a new regime for mid-infrared optical parametric chirped- pulse amplification (OPCPA) based on achromatic quasi-phase-matching. Our mid-infrared OPCPA system is based on collinear aperiodically poled lithium niobate (APPLN) pre-amplifiers and a non-collinear PPLN power amplifier which is operated in an achromatic phase-matching configuration. The idler output has a bandwidth of 800 nm centered at 3.4 µm. After compression, we obtain a pulse duration of 44.2 fs and a pulse energy of 21.8 µJ at a repetition rate of 50 kHz. We explain the wide applicability of the non-collinear QPM amplification scheme we used, including how it could enable octave-spanning OPCPA in a single device when combined with an aperiodic QPM grating.

Revealing the time-dependent polarization of ultrashort pulses with sub-cycle resolution.

We report on the first experiments characterizing the complete time-dependent 2D vector potential of a few-cycle laser pulse. The instantaneous amplitude and orientation of the electric field is determined with sub-cycle resolution, directly giving access to the polarization state of the pulse at any instant in time. This is achieved by performing an attosecond streaking experiment using a reaction microscope, where the full pulse characterization is performed directly in the target region.

Design constraints of optical parametric chirped pulse amplification based on chirped quasi-phase-matching gratings.

Chirped quasi-phase-matching (QPM) gratings offer efficient, ultra-broadband optical parametric chirped pulse amplification (OPCPA) in the mid-infrared as well as other spectral regions. Only recently, however, has this potential begun to be realized [1]. In this paper, we study the design of chirped QPM-based OPCPA in detail, revealing several important constraints which must be accounted for in order to obtain broad-band, high-quality amplification. We determine these constraints in terms of the underlying saturated nonlinear processes, and explain how they were met when designing our mid-IR OPCPA system. The issues considered include gain and saturation based on the basic three-wave mixing equations; suppression of unwanted non-collinear gain-guided modes; minimizing and characterizing nonlinear losses associated with random duty cycle errors in the QPM grating; avoiding coincidentally-phase-matched nonlinear processes; and controlling the temporal/spectral characteristics of the saturated nonlinear interaction in order to maintain the chirped-pulse structure required for OPCPA. The issues considered place constraints both on the QPM devices as well as the OPCPA system. The resulting experimental guidelines are detailed. Our results represent the first comprehensive discussion of chirped QPM devices operated in strongly nonlinear regimes, and provide a roadmap for advancing and experimentally implementing OPCPA systems based on these devices.

Breakdown of the dipole approximation in strong-field ionization.

We report the breakdown of the electric dipole approximation in the long-wavelength limit in strong-field ionization with linearly polarized few-cycle mid-infrared laser pulses at intensities on the order of 10¹³ W/cm². Photoelectron momentum distributions were recorded by velocity map imaging and projected onto the beam propagation axis. We observe an increasing shift of the peak of this projection opposite to the beam propagation direction with increasing laser intensities. From a comparison with semiclassical simulations, we identify the combined action of the magnetic field of the laser pulse and the Coulomb potential as the origin of our observations.

Design of quasi-phasematching gratings via convex optimization.

We propose a new approach to quasi-phasematching (QPM) design based on convex optimization. We show that with this approach, globally optimum solutions to several important QPM design problems can be determined. The optimization framework is highly versatile, enabling the user to trade-off different objectives and constraints according to the particular application. The convex problems presented consist of simple objective and constraint functions involving a few thousand variables, and can therefore be solved quite straightforwardly. We consider three examples: (1) synthesis of a target pulse profile via difference frequency generation (DFG) from two ultrashort input pulses, (2) the design of a custom DFG transfer function, and (3) a new approach enabling the suppression of spectral gain narrowing in chirped-QPM-based optical parametric chirped pulse amplification (OPCPA). These examples illustrate the power and versatility of convex optimization in the context of QPM devices.