Universal in-line waveform characterization using arbitrary non-linear responses

TL;DR

The paper addresses the challenge of setup-specific waveform-resolved characterization by introducing a universal, in-line framework based on TIPTOE: perturbing a strong field with a weaker one and extracting relative yields to recover the waveform $E(t)$. It leverages CRIME and the newly proposed lazyCRIME to reconstruct waveforms from relative measurements across arbitrary observables and media, achieving attosecond accuracy on a standard workstation within minutes. Across ambient-air and in-situ vacuum ATAS configurations, the method demonstrates medium- and observable-independence, with consistent reconstructions from ion yields, high-harmonic yields, fluorescence, and even acoustic signals. The approach enables non-invasive, routine waveform diagnostics integrated into standard ultrafast workflows, and the authors provide open-source codes to encourage broad adoption and reproducibility, significantly lowering barriers to in-line pulse characterization.

Abstract

Contemporary schemes for waveform-resolved characterization are constrained by setup-specific requirements, which severely limits their adaptability and fails to establish standard procedures for routine in-line diagnostic. This work reports a comprehensive experimental demonstration that relative yield measurements from a broad variety of media and nonlinear observables, combined with our family of open-source reconstruction algorithms (CRIME and lazyCRIME), allow for robust waveform retrieval with attosecond accuracy on a standard workstation in just minutes. We have further adapted this framework to multiple configurations -- including non-invasive, simultaneous waveform characterization during an attosecond transient absorption spectroscopy (ATAS) experiment -- showcasing the low-cost and non-intrusive nature of the new pulse characterization approach. Together, this work establishes an easy-to-implement universal characterization scheme for in-line diagnostic of ultrashort pulses that is readily accessible to the broader ultrafast science community.

Figures (8)

• Figure 1: Schematic representation of the TIPTOE measurement scheme (adapted from Wiese:24). At three different delays $\tau_1$, $\tau_2$ and $\tau_3$ between $\epsilon_{\text{hi}}$ (red) and $\epsilon_{\text{lo}}$ (blue), the strong field drives a general nonlinear response that is modulated by the weak field. The combined field (purple) produces a delay-dependent response (orange area).
• Figure 2: (a) Sketch of the setup for measurements in ambient air, using fluorescence and acoustic signals. (b) Sketch of the setup for in-situ measurements in the vacuum compartments of the beamline, using TOF spectrometry, high-harmonic and fluorescence spectroscopy.
• Figure 3: (a) Measured (black dots) and simulated relative yield of $\mathrm{N}_2^+$ ion using CRIME (red) and lazyCRIME (blue) reconstructed waveform. (b) Reconstructed field $\epsilon_\text{lo}$ using CRIME and $\epsilon_\text{lo}$ from lazyCRIME, respectively, including their envelopes (dashed lines). The time axis is inverted to illustrate similarity between $\epsilon_\text{lo}$ and $Q_\text{ion}$.
• Figure 4: (a) Measured (dot) and simulated (solid line) relative yields $Q$ of Ar+ ions (blue) and total high harmonics from Ar (brown). Shaded areas: one standard deviation. (b), (c) Reconstructed electric fields with envelopes (dashed).
• Figure 5: (a),(b) Measured $H_\mathrm{e,\lambda}$ (green) of $\epsilon_{\text{hi}}$ and $\epsilon_{\text{lo}}$ with $N_{\text{hi}} = N_{\text{lo}} = 40$ frequency bands (green bars) for CRIME reconstruction. (c) Measured (dot) and simulated (solid line) relative signal yield from integrated plasma fluorescence $Q_\mathrm{Flu}$ (red) and $\mathrm{N}_2^+$ ion yield $Q_\mathrm{ion}$ (blue). Shaded areas: one standard deviation. (d),(e) Reconstructed $\epsilon_{\text{hi}}$ and $\epsilon_{\text{lo}}$ with envelopes (dashed).