Unraveling coupled electronic and lattice dynamics in germanium via SVD-assisted ultrafast ellipsometry

Abstract

We demonstrate a Singular Value Decomposition (SVD)-based framework to disentangle overlapping electronic and lattice dynamics in germanium probed by femtosecond spectroscopic ellipsometry. The transient dielectric response is shown to possess a physically meaningful low-rank structure, allowing the spectro-temporal dataset to be represented by a small set of orthogonal spectral modes and their time-dependent amplitudes. Modes B2–B4 resolve the dominant transient response in the E1–E1+Δ1 region, separating nonequilibrium carrier redistribution and exciton-sensitive reshaping from delayed thermoelastic/strain modulation. By coupling SVD with targeted line shape modeling, we extract characteristic energies, broadenings, and timescales across the electronic and lattice-driven response. Crucially, the reduced-rank decomposition isolates an exciton-sensitive mode (B3), a chirped coherent acoustic phonon signature in C3(t), and a ∼50 ps lattice-driven decay in C4(t) that remain only partially separated in the direct dielectric-function representation of the original dataset. These results establish SVD as a compact framework for resolving weak, spectrally overlapped processes in time-resolved ellipsometry and related multidimensional spectroscopies.