Supplement 1: Probing electron delays in above-threshold ionization

Originally published in Optica on 20 December 2014 (optica-1-6-361

Electron Correlation Effects in Attosecond Photoionization of CO2_{2}

A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multi-electron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance

phil-trans-data from On the limits of observing motion in time-resolved X-ray scattering

raw data for the processed Legendre decomposition of the x-ray scattering image

Multi-Particle Three-Dimensional Covariance Imaging: “Coincidence” Insights into the Many-Body Fragmentation of Strong-Field Ionized D₂O

We demonstrate the applicability of covariance analysis to three-dimensional velocity-map imaging experiments using a fast time stamping detector. Studying the photofragmentation of strong-field doubly ionized D2O molecules, we show that combining high count rate measurements with covariance analysis yields the same level of information typically limited to the “gold standard” of true, low count rate coincidence experiments, when averaging over a large ensemble of photofragmentation events. This increases the effective data acquisition rate by approximately 2 orders of magnitude, enabling a new class of experimental studies. This is illustrated through an investigation into the dependence of three-body D2O2+ dissociation on the intensity of the ionizing laser, revealing mechanistic insights into the nuclear dynamics driven during the laser pulse. The experimental methodology laid out, with its drastic reduction in acquisition time, is expected to be of great benefit to future photofragment imaging studies

Femtosecond pulse parameter estimation from photoelectron momenta using machine learning

Deep learning models have provided huge interpretation power for image-like data. Specifically, convolutional neural networks (CNNs) have demonstrated incredible acuity for tasks such as feature extraction or parameter estimation. Here we test CNNs on strong-field ionization photoelectron spectra, training on theoretical data sets to `invert' experimental data. Pulse characterization is used as a `testing ground', specifically we retrieve the laser intensity, where `traditional' measurements typically leads to 20\% uncertainty. We report on crucial data augmentation techniques required to successfully train on theoretical data and return consistent results from experiments, including accounting for detector saturation. The same procedure can be repeated to apply CNNs in a range of scenarios for strong-field ionization. Using a predictive uncertainty estimation, reliable laser intensity uncertainties of a few percent can be extracted, which are consistently lower than those given by traditional techniques. Using interpretability methods can reveal parts of the distribution that are most sensitive to laser intensity, which can be directly associated to holographic interferences. The CNNs employed provide an accurate and convenient ways to extract parameters, and represent a novel interpretational tool for strong-field ionization spectra

Overcoming the absorption limit in high-harmonic generation from crystals

Since the new millennium coherent extreme ultra-violet and soft x-ray radiation has revolutionized the understanding of dynamical physical, chemical and biological systems at the electron's natural timescale. Unfortunately, coherent laser-based upconversion of infrared photons to vacuum-ultraviolet and soft x-ray high-order harmonics in gaseous, liquid and solid targets is notoriously inefficient. In dense nonlinear media, the limiting factor is strong re-absorption of the generated high-energy photons. Here we overcome this limitation by allowing high-order harmonics generated from a periodic array of thin one-dimensional crystalline silicon ridge waveguides to propagate in the vacuum gaps between the ridges, thereby avoiding the high absorption loss of the bulk nonlinear material and resulting in a ~ 100-fold increase in propagation length. As the grating period is varied, each high-harmonic shows a different and marked modulation, indicating the onset of coherent addition which is otherwise suppressed in absorption-limited emission. By beating the absorption limit, our results pave the way for bright coherent short-wavelength sources and their implementation in nano-photonic devices

Strong Field Ionization of Water II: Electronic and Nuclear Dynamics En Route to Double Ionization

We investigate the role of nuclear motion and strong-field-induced electronic couplings during the double ionization of deuterated water using momentum-resolved coincidence spectroscopy. By examining the three-body dicationic dissociation channel, D$^{+}$/D$^{+}$/O, for both few- and multi-cycle laser pulses, strong evidence for intra-pulse dynamics is observed. The extracted angle- and energy-resolved double ionization yields are compared to classical trajectory simulations of the dissociation dynamics occurring from different electronic states of the dication. In contrast with measurements of single photon double ionization, pronounced departure from the expectations for vertical ionization is observed, even for pulses as short as 10~fs in duration. We outline numerous mechanisms by which the strong laser field can modify the nuclear wavefunction en-route to final states of the dication where molecular fragmentation occurs. Specifically, we consider the possibility of a coordinate-dependence to the strong-field ionization rate, intermediate nuclear motion in monocation states prior to double ionization, and near-resonant laser-induced dipole couplings in the ion. These results highlight the fact that, for small and light molecules such as D$_2$O, a vertical-transition treatment of the ionization dynamics is not sufficient to reproduce the features seen experimentally in the strong field coincidence double-ionization data

Enhanced High-Harmonic Generation from an All-Dielectric Metasurface

The recent observation of high-harmonic generation from solids creates a new possibility for engineering fundamental strong-field processes by patterning the solid target with subwavelength nanostructures. All-dielectric metasurfaces exhibit high damage thresholds and strong enhancement of the driving field, making them attractive platforms to control high-harmonics and other high-field processes at nanoscales. Here we report enhanced non-perturbative high-harmonic emission from a Si metasurface that possesses a sharp Fano resonance resulting from a classical analogue of electromagnetically induced transparency. Harmonic emission is enhanced by more than two orders of magnitude compared to unpatterned samples. The enhanced high harmonics are highly anisotropic with excitation polarization and are selective to excitation wavelength due to its resonant feature. By combining nanofabrication technology and ultrafast strong-field physics, our work paves the way for designing new compact ultrafast photonic devices that operate under high intensities and short wavelengths

Time-Resolved X‑ray Photoelectron Spectroscopy: Ultrafast Dynamics in CS₂ Probed at the S 2p Edge

Recent developments in X-ray free-electron lasers have enabled a novel site-selective probe of coupled nuclear and electronic dynamics in photoexcited molecules, time-resolved X-ray photoelectron spectroscopy (TRXPS). We present results from a joint experimental and theoretical TRXPS study of the well-characterized ultraviolet photodissociation of CS2, a prototypical system for understanding non-adiabatic dynamics. These results demonstrate that the sulfur 2p binding energy is sensitive to changes in the nuclear structure following photoexcitation, which ultimately leads to dissociation into CS and S photoproducts. We are able to assign the main X-ray spectroscopic features to the CS and S products via comparison to a first-principles determination of the TRXPS based on ab initio multiple-spawning simulations. Our results demonstrate the use of TRXPS as a local probe of complex ultrafast photodissociation dynamics involving multimodal vibrational coupling, nonradiative transitions between electronic states, and multiple final product channels

Time-Resolved X‑ray Photoelectron Spectroscopy: Ultrafast Dynamics in CS₂ Probed at the S 2p Edge

Recent developments in X-ray free-electron lasers have enabled a novel site-selective probe of coupled nuclear and electronic dynamics in photoexcited molecules, time-resolved X-ray photoelectron spectroscopy (TRXPS). We present results from a joint experimental and theoretical TRXPS study of the well-characterized ultraviolet photodissociation of CS2, a prototypical system for understanding non-adiabatic dynamics. These results demonstrate that the sulfur 2p binding energy is sensitive to changes in the nuclear structure following photoexcitation, which ultimately leads to dissociation into CS and S photoproducts. We are able to assign the main X-ray spectroscopic features to the CS and S products via comparison to a first-principles determination of the TRXPS based on ab initio multiple-spawning simulations. Our results demonstrate the use of TRXPS as a local probe of complex ultrafast photodissociation dynamics involving multimodal vibrational coupling, nonradiative transitions between electronic states, and multiple final product channels