# Publications by

Daniel Würzler

## 2021

**High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau**

**126**, 113201 (2021)

**Abstract:** Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1 μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

## 2020

**Carrier-envelope-phase measurement of few-cycle mid-infrared laser pulses using high harmonic generation in ZnO**

**28**, 7314 (2020)

**Abstract:** High-harmonic generation (HHG) in crystals offers a simple, affordable and easily accessible route to carrier-envelope phase (CEP) measurements, which scales favorably towards longer wavelengths. We present measurements of HHG in ZnO using few-cycle pulses at 3.1 µm. Thanks to the broad bandwidth of the driving laser pulses, spectral overlap between adjacent harmonic orders is achieved. The resulting spectral interference pattern provides access to the relative harmonic phase, and hence, the CEP.

**Accurate retrieval of ionization times by means of the phase-of-the-phase spectroscopy, and its limits**

**101**, 033416 (2020)

**Abstract:** By applying recently introduced, phase-of-the-phase spectroscopy [S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015)], we analyze the phase-dependent photoelectron signal from Xe ionized in intense, parallel, two-color (1800 nm and 900 nm) laser fields. With such a field configuration, tuning of the relative phase between the ionizing, ω , and the perturbative, 2ω, field results in a modulation of the ionization rate, as well as modifications of the trajectories of electrons propagating in the laser-dressed continuum. Based on a semiclassical model, we confirm that phase dependencies, due to the perturbation of the ionization rate, encode the ionization times of the electrons. Here, using the fork structure, a well-known feature originating from well-defined dynamics allows us to distinguish between electrons ionized within distinct time windows. However, due to the simultaneous perturbation of the electron trajectories, the assignment of the ionization times can be distorted by up to 80 as, i.e., a 10° phase shift, which is independent of the degree of the perturbation.

**Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions**

**124**, 133202 (2020)

**Abstract:** The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?

## 2019

**Untersuchung und Simulation der Ionisations- und Streudynamik von Photoelektronen mithilfe von Zwei-Farben-Feldern**

Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät (2019)

**Abstract:** If atoms or molecules are exposed to strong laser ﬁelds, various processes can occur after ionization, and the dynamics of these processes depend on the trajectory of the emitted electrons. Both the ionization rates and the electrons trajectory depend strongly on the shape of the laser ﬁeld. Thus, tailoring strong laser ﬁelds on the sub-cycle and sub-femtosecond time scale, the insight and control of the underlying dynamics of these processes has been signiﬁcantly increased in the last two decades. Here, orthogonal and parallel two-color laser ﬁelds represent an eﬀective approach to manipulate the ionization rates and the subsequent electron movement in the laser-dressed continuum. This is achieved by varying the relative phase, ϕrel , between both ﬁeld components ( ω and 2 ω ). In this thesis orthogonal and parallel two-color laser ﬁelds are used to study the ionization and scattering dynamics of noble gases. Further, phases-dependent photoelectron spectra- captured by a velocity map imaging spectrometer, are studied by applying the recently introduced phase-of-the-phase analysis [1].

The measured results are compared with three dimensional semi-classical calculations, which can be performed for arbitrarily polarized laser ﬁelds, while taking higher order scattering events into account. These simulation also allows for the separation and investigation of diﬀerent classes of photoelectrons (e.q. direct and scattered electrons), which alows for analysis of the underlying dynamics.

In one vmi measurement in this thesis, an orthogonal two-color laser ﬁeld ( λω = 800 nm, λ2ω = 400 nm)with an unconventional orientation, i.e. with the polarization of the ionizing laser ﬁeld perpendicular to the detector surface and the steering ﬁeld parallel to it, is used. This allows for the investigation of the phase-dependent photoelectron spectra, as the deﬂections of photoelectrons due to the 2 ω -ﬁeld are directly mapped onto the detector. The phase dependence of the photoelectron spectra of neon and xenon shows clear phase shifts between scattered and direct electrons. When comparing the phase dependency of neon and xenon, a strong target dependency is observed. Namely xenon show vastly more complex phase dependence then neon. Further investigations of xenon where perfomed using parallel two-color ﬁeld within the short-wave infrared range ( λω = 1800 nm, λ2ω = 900 nm). To measure electrons with high energy, which are created during ionization with these long wavelengths, a high-energy VMI spectrometer was developed based on the design presented in [2]. Using this device, electron energies up to 320 eV can be detected. The intention of this measurement is to retrieve the ionization time of the photoelectrons contributing to the characteristic fork structure [3] based on the phase dependencies of the contributing photoelectrons. Using these wavelengths, the fork structure can be easily detected and provides a well-suited benchmark for this study. Based on the semi-classical model it is shown that phase-dependent photoelectron signal, which encodes information about the contributing ionization times, is convoluted with the phase dependencies resulting from perturbation of the electron trajectories propagating in the laser-dressed continuum. Independent on the degree of the perturbation this can mislead assignment of the ionization time by up to 80 as.

## 2017

**Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths**

**42**, 5150 (2017)

**Abstract:** A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

**Velocity map imaging of scattering dynamics in orthogonal two-color fields**

**51**, 015001 (2017)

**Abstract:** In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.