Background-free Tracking of Ultrafast Hole and Electron Dynamics with XUV Transient Grating Spectroscopy

Extreme ultraviolet (XUV) transient absorption (TA) and transient reflectivity (TR) spectroscopies enable element-specific insights into attosecond-timescale processes in solids. XUV transient grating spectroscopy (TGS) is an emerging tool that combines the advantages of both absorption and reflectivity while offering intrinsically background-free detection. Here, we implement XUV-TGS by generating a transient grating in germanium solid using two few-cycle near-infrared pulses and probing it with an attosecond XUV pulse, produced via tabletop high-harmonic generation. The spectrally resolved, diffracted XUV pulses directly visualize the separate ultrashort decay times of both photoexcited electrons and holes, without the need for iterative deconvolution. By combining XUV-TA and -TG spectroscopy, we extract the evolution of the complex refractive index, ñ, without the need for Kramers-Kronig reconstruction, as required in XUV-TR, allowing us to extract the roots of the induced optical response. We find reflectivity changes of up to 34% via the real part of ñ, whereas changes in the imaginary part only result in a variation in reflectivity of around 0.5%.

💡 Research Summary

This paper presents a tabletop implementation of extreme‑ultraviolet transient grating spectroscopy (XUV‑TGS) to monitor ultrafast electron and hole dynamics in germanium without any background signal. By intersecting two few‑cycle near‑infrared (NIR) pump pulses at a controlled angle, a spatially periodic carrier density grating with an 11 µm period is written into a 50 nm Ge film. An attosecond XUV probe (25–45 eV) generated by high‑harmonic generation interrogates the grating after a variable delay. The diffracted XUV orders (±1) are recorded simultaneously with the transmitted and reflected XUV spectra, providing both transient grating (TG) and conventional transient absorption (TA) data from the same sample geometry.

The TG signal is intrinsically background‑free because only light that satisfies the phase‑matching condition of the grating is diffracted; consequently the measured signal is purely positive and free of the overlapping positive/negative features that plague TA. This simplicity enables a direct visualisation of two distinct spectral regions: around 29 eV (holes in the valence band) and around 30 eV (electrons in the conduction band). After removing spin‑orbit contributions with a Fourier filter, the TG map is partitioned into “hot” (non‑thermal) and thermalised carrier regions. Exponential fits to the integrated TG intensity yield recombination times of 659 ± 12 fs for electrons and 1160 ± 23 fs for holes, while hot‑carrier cooling times are 351 ± 22 fs (electrons) and 352 ± 22 fs (holes). These values agree with earlier TA‑only studies but are obtained without iterative deconvolution.

By combining TG (which is mainly sensitive to changes in the real part of the refractive index, n) with TA (sensitive to the imaginary part, k), the authors reconstruct the full complex refractive index ñ = n + ik as a function of time, without invoking Kramers–Kronig transformations. The extracted Δn reaches values that, at an incidence angle of 66°, modify the reflectivity by up to 34 %, whereas the Δk‑induced reflectivity change is only ≈0.5 %. Calculations show that reflectivity is maximally sensitive to n near the critical angle for total external reflection, while its sensitivity to k vanishes there. This explains why conventional transient‑reflectivity measurements are dominated by n‑related effects and why extracting the full dielectric response from TR alone is fundamentally limited.

The study demonstrates that XUV‑TGS provides a clean, quantitative probe of carrier dynamics and dielectric‑function evolution in solids. It eliminates the need for background subtraction, iterative spectral decomposition, and Kramers–Kronig reconstruction, while delivering both amplitude and phase information (the latter accessible via heterodyne detection, suggested for future work). The authors anticipate extending the technique to more complex materials, such as low‑dimensional semiconductors and strongly correlated systems, where element‑specific, attosecond‑resolution measurements will be invaluable.