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We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse’s induced refractive index profile in the form of a phase-shift “streak,” in which frequency–domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles. 

Abstract Plasma wakefield accelerators use tabletop equipment to produce relativistic femtosecond electron bunches. Optical and X-ray diagnostics have established that their charge concentrates within a micrometre-sized volume, but its sub-micrometre internal distribution, which critically influences gain in free-electron lasers or particle yield in colliders, has proven elusive to characterize. Here, by simultaneously imaging different wavelengths of coherent optical transition radiation that a laser-wakefield-accelerated electron bunch generates when exiting a metal foil, we reveal the structure of the coherently radiating component of bunch charge. The key features of the images are shown to uniquely correlate with how plasma electrons injected into the wake: by a plasma-density discontinuity, by ionizing high-Zgas-target dopants or by uncontrolled laser–plasma dynamics. With additional input from the electron spectra, spatially averaged coherent optical transition radiation spectra and particle-in-cell simulations, we reconstruct coherent three-dimensional charge structures. The results demonstrate an essential metrology for next-generation compact X-ray free-electron lasers driven by plasma-based accelerators. 

Temporal networks serve as abstractions of many real-world dynamic systems. These networks typically evolve according to certain laws, such as the law of triadic closure, which is universal in social networks. Inductive representation learning of temporal networks should be able to capture such laws and further be applied to systems that follow the same laws but have not been unseen during the training stage. Previous works in this area depend on either network node identities or rich edge attributes and typically fail to extract these laws. Here, we propose Causal Anonymous Walks (CAWs) to inductively represent a temporal network. CAWs are extracted by temporal random walks and work as automatic retrieval of temporal network motifs to represent network dynamics while avoiding the time-consuming selection and counting of those motifs. CAWs adopt a novel anonymization strategy that replaces node identities with the hitting counts of the nodes based on a set of sampled walks to keep the method inductive, and simultaneously establish the correlation between motifs. We further propose a neural-network model CAW-N to encode CAWs, and pair it with a CAW sampling strategy with constant memory and time cost to support online training and inference. CAW-N is evaluated to predict links over 6 real temporal networks and uniformly outperforms previous SOTA methods by averaged 15% AUC gain in the inductive setting. CAW-N also outperforms previous methods in 5 out of the 6 networks in the transductive setting. 

Edge streams are commonly used to capture interactions in dynamic networks, such as email, social, or computer networks. The problem of detecting anomalies or rare events in edge streams has a wide range of applications. However, it presents many challenges due to lack of labels, a highly dynamic nature of interactions, and the entanglement of temporal and structural changes in the network. Current methods are limited in their ability to address the above challenges and to efficiently process a large number of interactions. Here, we propose F-FADE, a new approach for detection of anomalies in edge streams, which uses a novel frequency-factorization technique to efficiently model the time-evolving distributions of frequencies of interactions between node-pairs. The anomalies are then determined based on the likelihood of the observed frequency of each incoming interaction. F-FADE is able to handle in an online streaming setting a broad variety of anomalies with temporal and structural changes, while requiring only constant memory. Our experiments on one synthetic and six real-world dynamic networks show that F-FADE achieves state of the art performance and may detect anomalies that previous methods are unable to find. 

We visualize plasma bubbles driven by 0.67 PW laser pulses in a plasma of density ne≈5×1017cm−3 by imaging Faraday rotation patterns imprinted on linearly polarized probe pulses of wavelength λpr=1.05  μm and duration τpr=2 or 1 ps that cross the bubble's path at right angles. When the bubble captures and accelerates tens to hundreds of pC of electron charges, we observe two parallel streaks of length cτpr straddling the drive pulse propagation axis, separated by ∼45 μm, in which probe polarization rotates by 0.3° to more than 5° in opposite directions. Accompanying simulations show that they result from Faraday rotation within portions of dense bubble side walls that are pervaded by the azimuthal magnetic field of accelerating electrons during the probe transit across the bubble. Analysis of the width of the streaks shows that quasi-monoenergetic high-energy electrons and trailing lower energy electrons inside the bubble contribute distinguishable portions of the observed signals, and relativistic flow of sheath electrons suppresses Faraday rotation from the rear of the bubble. The results demonstrate favorable scaling of Faraday rotation diagnostics to 40× lower plasma density than previously demonstrated.