The robustness of attosecond streaking measurements

Understanding attosecond streaking

This tutorial provides an overview on the theory of attosecond streaking, a pump-probe scheme to extract timing information of ionization processes that has been widely used in the past decade. Emphasis is put on the origin of the Coulomb-laser-coupling (CLC) term, which is crucial in the interpretation of streaking delays. Having gained a proper understanding of how the CLC terms in various publications relate to each other, we will be able to analyze in which regime the streaking delay can be split into a measurement-induced CLC term and a 'pure' ionization delay and under which conditions this splitting may break down. Thus we address the long-standing question of the validity of the widely applied interpretation of the streaking delay as a sum of the CLC term and a 'pure' ionization delay.

Noise effects and the impact of detector responses on the characterization of extreme ultraviolet attosecond pulses

We employ numerical simulations to study the effects of noise on the reconstruction of the duration and satellite intensity ratio for transform-limited single and double pulses of 200 as duration. The forms of noise we implement are delay jitters between the attosecond pulse and the near-IR laser field, energy resolution of the photoelectron detector, and Poisson noise in streaking spectrograms with different count levels. We use the streaking method to characterize the pulse and the extended ptychographic iterative engine retrieval algorithm to reconstruct the pulse from the simulated streaking spectrogram. We found that, for practical purposes, when implementing a combination of all three mentioned noise contributions, the attosecond pulse duration will be overestimated when the photoelectron count level is low. Furthermore, the satellite pulse amplitude of the attosecond double pulse can be retrieved within 10% accuracy.

Accuracy and precision of the RABBIT technique

One of the most ubiquitous techniques within attosecond science is the so-called reconstruction of attosecond beating by interference of two-photon transitions (RABBIT). Originally proposed for the characterization of attosecond pulses, it has been successfully applied to the accurate determination of time delays in photoemission. Here, we examine in detail, using numerical simulations, the effect of the spatial and temporal properties of the light fields and of the experimental procedure on the accuracy of the method. This allows us to identify the necessary conditions to achieve the best temporal precision in RABBIT measurements. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Investigation of valence band reconstruction methods for attosecond streaking data from surfaces

We analyze simulated streaked valence band photoemission with atomic streaking theory-based reconstruction methods to investigate the differences between atomic gas-phase streaking and valence band surface streaking. The careful distinction between atomic and surface streaking is a prerequisite to justify the application of atomic streaking theory-based reconstruction methods to surface streaking measurements. We show that neglecting the band structure underestimates the width of reconstructed photoelectron wavepackets, consistent with the Fourier transform limit of the band spectrum. We find that a fit of Gaussian wavepackets within the description of atomic streaking is adequate to a limited extent. Systematic errors that depend on the near-infrared skin depth, an inherently surface-specific property, are present in temporal widths of wavepackets reconstructed with atomic streaking theory-based methods.

Attosecond Pulse Shaping by Multilayer Mirrors

The emerging research field of attosecond science allows for the temporal investigation of one of the fastest dynamics in nature: electron dynamics in matter. These dynamics are responsible for chemical and biological processes, and the ability to understand and control them opens a new door of fundamental science, with the possibility to influence all lives if medical issues can thereby be addressed. Multilayer optics are key elements in attosecond experiments; they are used to tailor attosecond pulses with well-defined characteristics to facilitate detailed and accurate insight into processes, e.g., photoemission, Auger decay, or (core-) excitons. Based on the investigations and research efforts from the past several years, multilayer mirrors today are routinely used optical elements in attosecond beamlines. As a consequence, the generation of ultrashort pulses, combined with their dispersion control, has proceeded from the femtosecond range in the visible/infrared spectra to the attosecond range, covering the extreme ultraviolet and soft X-ray photon range up to the water window. This article reviews our work on multilayer optics over the past several years, as well as the impact from other research groups, to reflect on the scientific background of their nowadays routine use in attosecond physics.

Photoemission and photoionization time delays and rates

Ionization and, in particular, ionization through the interaction with light play an important role in fundamental processes in physics, chemistry, and biology. In recent years, we have seen tremendous advances in our ability to measure the dynamics of photo-induced ionization in various systems in the gas, liquid, or solid phase. In this review, we will define the parameters used for quantifying these dynamics. We give a brief overview of some of the most important ionization processes and how to resolve the associated time delays and rates. With regard to time delays, we ask the question: how long does it take to remove an electron from an atom, molecule, or solid? With regard to rates, we ask the question: how many electrons are emitted in a given unit of time? We present state-of-the-art results on ionization and photoemission time delays and rates. Our review starts with the simplest physical systems: the attosecond dynamics of single-photon and tunnel ionization of atoms in the gas phase. We then extend the discussion to molecular gases and ionization of liquid targets. Finally, we present the measurements of ionization delays in femto- and attosecond photoemission from the solid-vacuum interface.

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.

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.

Chromium/scandium multilayer mirrors for isolated attosecond pulses at 145 eV

Recent advances in the development of attosecond soft x-ray sources toward photon wavelengths below 10 nm are also driving the development of suited broadband multilayer optics for steering and shaping attosecond pulses. We demonstrate that current attosecond experiments in the sub-200-eV range benefit from these improved optics. We present our achievements in utilizing ion-beam-deposited chromium/scandium (Cr/Sc) multilayer mirrors, optimized by tailored material dependent deposition and interface polishing, for the generation of single attosecond pulses from a high-harmonic cut-off spectrum at a central energy of 145 eV. Isolated attosecond pulses have been measured by soft x-ray-pump/NIR-probe electron streaking experiments and characterized using frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG/CRAB). The results demonstrate that Cr/Sc multilayer mirrors can be used as efficient attosecond optics for reflecting 600-attosecond pulses at a photon energy of 145 eV, which is a prerequisite for present and future attosecond experiments in this energy range.

Partially coherent ultrafast spectrography

Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter.

Effects of driving laser jitter on the attosecond streaking measurement

Driving laser jitter is one of the main factors affecting the attosecond streaking measurement. The effect of carrier-envelope phase (CEP) jitter and the pulse energy jitter on the attosecond pulse characterization is studied in this paper. We have theoretically calculated and experimentally confirmed that CEP jitter could result in a symmetry trace in the streaking spectrogram, while the intensity jitter could result in a slight shift and broadening of the trace. Both of them can lead to an underestimate of the retrieved attosecond pulse duration.

Waveform-controlled near-single-cycle milli-joule laser pulses generate sub-10 nm extreme ultraviolet continua

We demonstrate the generation of waveform-controlled laser pulses with 1 mJ pulse energy and a full-width-half-maximum duration of ∼4  fs, therefore lasting less than two cycles of the electric field oscillating at their carrier frequency. The laser source is carrier-envelope-phase stabilized and used as the backbone of a kHz repetition rate source of high-harmonic continua with unprecedented flux at photon energies between 100 and 200 eV (corresponding to a wavelength range between 12-6 nm respectively). In combination we use these tools for the complete temporal characterization of the laser pulses via attosecond streaking spectroscopy.

Attosecond dispersion control by extreme ultraviolet multilayer mirrors

We report the first experimental demonstration of a-periodic multilayer mirrors controlling the frequency sweep (chirp) of isolated attosecond XUV pulses. The concept was proven with about 200-attosecond pulses in the photon energy range of 100-130 eV measured via photoelectron streaking in neon. The demonstrated attosecond dispersion control is engineerable in a wide range of XUV photon energies and bandwidths. The resultant tailor-made attosecond pulses with highly enhanced photon flux are expected to significantly advance attosecond metrology and spectroscopy and broaden their range of applications.

Attosecond streaking enables the measurement of quantum phase

Attosecond streaking, as a measurement technique, was originally conceived as a means to characterize attosecond light pulses, which is a good approximation if the relevant transition matrix elements are approximately constant within the bandwidth of the light pulse. Our analysis of attosecond streaking measurements on systems with a complex response to the photoionizing pulse reveals the relation between the momentum-space wave function of the outgoing electron and the result of conventional retrieval algorithms. This finding enables the measurement of the quantum phase associated with bound-continuum transitions.