Attosecond pulse retrieval from noisy streaking traces with conditional variational generative network

Abstract

Accurate characterization of an attosecond pulse from streaking trace is an indispensable step in studying the ultrafast electron dynamics on the attosecond scale. conventional attosecond pulse retrieval methods face two major challenges: the ability to incorporate a complete physics model of the streaking process, and the ability to model the uncertainty of pulse reconstruction in the presence of noise. Here we propose a pulse retrieval method based on conditional variational generative network (cVGn) that can address both demands. instead of learning the inverse mapping from a streaking trace to a pulse profile, the CVGN models the distribution of the pulse profile conditioned on a given streaking trace measurement, and is thus capable of assessing the uncertainty of the retrieved pulses. this capability is highly desirable for low-photon level measurement, which is typical in attosecond streaking experiments in the water window X-ray range. in addition, the proposed scheme incorporates a refined physics model that considers the Coulomb-laser coupling and photoelectron angular distribution in streaking trace generation. cVGn pulse retrievals under various simulated noise levels and experimental measurement have been demonstrated. the results showed high pulse reconstruction consistency for streaking traces when peak signal-to-noise ratio (SNR) exceeds 6, which could serve as a reference for future learning-based attosecond pulse retrieval. The generation of isolated attosecond extreme ultraviolet (XUV)/soft X-ray pulses is a milestone toward investigating the ultrafast electron dynamics on its natural time scale. Accurate temporal and spectral characterization of these XUV pulses is a crucial step in attosecond pump-probe experiments 1. Because the spectrum of the XUV pulses can be measured relatively easily with a spectrometer, knowing its spectral phase will enable a complete reconstruction of the XUV pulse in both time-and frequency-domain. Adapted from an iterative femtosecond pulse retrieval method FROG (Frequency Resolved Optical Gating), Frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG-CRAB) has been widely used for phase retrieval from attosecond streaking traces 2. Compared to its femtosecond counterpart FROG, attosecond phase retrieval suffers from both experimental and theoretical challenges. The photon flux of attosecond soft X-ray is much lower than that in a typical FROG experiment, giving rise to higher statistic noise in the streaking trace. Currently the effect of noise on the error and uncertainty of retrieved pulse is yet to be understood, and there lacks a guideline on the signal-to-noise ratio (SNR) requirement for accurate pulse retrieval. In addition, phase retrieval of ultra-broadband XUV/X-ray pulses requires a more thorough theoretic description of the photoelectron wave packet during the streaking process, including its energy and angular distribution, as well as its interaction with the laser field, which are either simplified or omitted in exi...

Principle and technology of attosecond pulse characterization

“…[53] Figure 8 Retrieval of 2 experimental streaking traces with conditional variational generative network [53] . (a1), (a2) Measured streaking trace; (b1), (b2) average of reconstructed streaking trace from 10 retrieved pulses.…”

Real-time phase-retrieval and wavefront sensing enabled by an artificial neural network

“…face identification) or medical diagnosis [2,3]. Furtheremore, artificial neural networks have become an effective solution for solving many problems in optics, particularly phase retrieval [4][5][6][7]. This is mainly due to increasingly affordable graphics cards computational power required to train neural networks, and the recent advancements in neural network architecture design and training.…”

Perspectives for analyzing non-linear photo-ionization spectra with deep neural networks trained with synthetic Hamilton matrices

“…Machine learning (ML) has recently been applied not only in physics 1,2,3 , but more specifically also in strong-field physics 4,5,6 . One of the most abundant topic has been the reconstruction of the temporal shape of an ultrashort laser pulse, aided by ML techniques 7,8,9 . The most popular technique for this reconstruction have been different variants of streaking techniques which require normally considerable additional experimental effort, namely a Terahertz laser light source.…”

“…The most popular technique for this reconstruction have been different variants of streaking techniques which require normally considerable additional experimental effort, namely a Terahertz laser light source. With its help one can generate a large amount of data -the streaking traces -which can be processed with ML to extract the attosecond pulse shape 7,8 . However, also a Max Planck Institute for the Physics of Complex Systems Nöthnitzer Str.…”