As Terahertz Time Domain Spectroscopy (THz-TDS) increasingly permeates analytical domains, the need for robust and standardized data processing methods becomes indispensable to ensure reliable and reproducible results. We present our latest advancements in addressing this critical need, focusing on novel methodologies for quantifying and mitigating noise and uncertainties in THz-TDS data processing.

Data process in THz-TDS began with the thorough analysis of the source of uncertainties. We showed that in fibered systems the major part of it was linked to a small delay between consecutively recorded time traces (~10 fs) we attributed to a variation of temperature in the optical fibers. Our approach includes a thorough analysis of uncertainty sources, implemented in our open-source software Correct@TDS, which provides a reliable and less biased estimation of the signal by significantly reducing noise [1].

Once the time-traces are recorded and the best signal estimator derived, the extraction of the information follows either retrieving the refractive index of the sample or analysing the data by fitting in the time domain.

Building upon this, our software Fit@TDS [2] utilizes these quantified uncertainties within a Bayesian framework [3] to enable a quantitative comparison between different material models and extract more reliable parameters.

Finally, a critical requirement to spread THz-TDS in analytical applications is not only the estimation of a result but also the precision of that result (error bars). By combining the uncertainties estimation on the measurements, along with our fitting software, we aim to provide error bars for the extracted material parameters. This methodology showed good results as far as the main source of discrepancy from the model to the signal came from the signal variations. On the spectral region where the signal to noise ratio is very good, the discrepancy comes from other sources specifically the approximation withing the model.

To conclude, several efforts are underway to establish good practices, for example in recorded data format standardization [4], alongside improved analysis of system components [5]. These initiatives demonstrate the community's early recognition of these needs and ongoing efforts to achieve these standards. We hope that these combined efforts will soon enable THz-TDS to reach its full potential in various analytical and industrial applications by providing reliable measurements with quantified uncertainties. The development of tools like Correct@TDS and Fit@TDS, which address noise reduction, signal estimation, and uncertainty quantification, represents a step towards this goal. We envision future work involving even closer collaborations between the THz and signal processing communities to develop more sophisticated data processing methods tailored for the evolving landscape of THz-TDS technologies, including novel setups based on optoelectronic devices and dual-comb spectroscopy

We present an ultrafast frequency-domain THz sensing technique optimized for high measurement rates, targeting industrial inline measurements and imaging. Conventional THz spectrometers perform well in laboratory environments but often struggle in industrial process monitoring due to their measurement rates, typically under 1 kHz [1]. While time-domain spectroscopy has achieved kHz-rates, it introduces considerable system complexity [2]. Our measurement scheme determines both amplitude and phase for a single THz frequency at 10 kHz. This approach employs direct frequency modulation of a distributed feedback laser (DFB) with a pathlength difference, enabling precise phase measurements without moving parts or intricate phase shifters. Our optoelectronic system integrates this modulated DFB laser with a tunable static laser source, allowing flexible selection of THz frequencies ranging from 100 GHz to 5.5 THz. We validate our THz spectrometer through rapid thickness measurements of Fused Deposition Modeling (FDM) printed polylactide (PLA) samples (Figure 1a) and demonstrate its spectroscopic accuracy with stepped frequency scans across multiple water vapor absorption lines (Figure 1b).

[1] L. Liebermeister et al., ‘Optoelectronic frequency-modulated continuous-wave terahertz spectroscopy with 4 THz bandwidth’, Nat. Commun., vol. 12, no. 2021, pp. 1–10, 2021.

[2] R. J. B. Dietz et al., ‘All fiber-coupled THz-TDS system with kHz measurement rate based on electronically controlled optical sampling’, Opt. Lett., vol. 39, no. 22, pp. 6482–6485, Nov. 2014.

Solvated electrons represent one of the most important reductive species in aqueous solution. The spectroscopic evidence of the solvated electrons in iodide aqueous solution upon excitation with visible light (400 nm) using ultrafast THz transient absorption has been comprehensively discussed in the literature [1, 2]. We investigated the temperature dependence ultrafast dynamics of solvated electrons in aqueous iodide solution using optical pump and THz probe spectroscopy. The THz probe reveals distinct shifts in the delocalization of electrons, solvation shell reorganization, and relaxation kinetics. The localization process is slower at lower temperatures due to hindered solvent reorganization. Once it is localized, the electron will remain more stable and in a tightly bound state, resulting in an extended lifetime. In contrast, due to the thermal fluctuation at higher temperatures, the solvation structure is more disordered, which leads to reduced localization and significantly shorter lifetimes. These findings highlight the potent role of thermal energy in modulating electron solvation and provide new insights into the coupling between delocalized electron and their aqueous environment on ultrafast timescales.

Reference:

[1] F. Novelli, K. Chen, A. Buchmann, T. Ockelmann, C. Hoberg, T. Head-Gordon, & M. Havenith, Proc. Natl. Acad. Sci. U.S.A. 120, 8 (2023).

[2] J. Savolainen, F. Uhlig, S. Ahmed, P. Hamm, P. Jungwirth, Nat. Chem. 6, 697–701 (2014).

[3] F. Novelli, A. Buchmann, I. Yousaf, L. Stiewe, W. Bronsch, F. Cilento, C. Hoberg, and M. Havenith

ACS Omega 10 (5), (2025).

With the increasing insights into quantum material coexisting phases and intertwined degrees of freedom, the idea of light control of material properties has gained attention, leading to dedicated researches on out-of-equilibrium photo-induced condensed matter phases. The physical phenomena consecutive to photo-excitation are hence key elements to understand to envision controlling materials with light. In particular, the carrier dynamics following an optical pump pulse is an essential point to apprehend, to further interpret the couplings and intertwinements with the structure, leading to potential phase transitions, as in topological semimetals.

In this work we present a case study of photo-induced carrier dynamics in a low bandgap semiconductor InSb, using THz time domain spectroscopy (THz-TDS) as a sensitive probe for carriers. With the same method, we provide insights on carrier dynamics in the topological semimetal ZrTe₅, where photo-induced topological phase transition has been recently under investigation ^1–3. We extract the carrier dynamics from the relatively broadband reflectivity at different pump-probe delays, a spectral approach⁴ that prevents distortions due to pump-induced shifts of the THz temporal trace, and provides more complete picture on the carrier dynamics at play. Here the rather borad spectrum is obtained from optical rectification in an organic BNA crystal, first demonstration of its use for THz spectroscopy to our knowledge.

Figure 1 shows the THz reflectivity from bulk InSb at different pump-probe delays, following an optical pump at 1030 nm. The photo-induced highly reflective state relaxes progressively towards equilibrium, and the reflectivity can be fitted using the Drude-Lorentz model, accounting for the penetration depths.

The Reststrahlen band in dielectrics represents the high-reflectivity region between the frequencies of longitudinal- (LO) and transverse-optical (TO) phonons. In highly polar materials, it is characterized by strong phonon–photon coupling. While such coupling also exists outside this band, the distinct dielectric response in this region can enhance nonlinear optical effects including optical rectification (OR), as demonstrated in LiNbO₃ waveguides [1].
We investigate OR and terahertz (THz) emission in wurtzite GaN and ZnO single crystals, specifically in the m-plane orientation. These materials are of particular interest due to their high LO and TO phonon frequencies and the large splitting between them. Reducing our wide-gap samples to thin layers with a thickness below 1 µm with a focused ion beam, we reach optically thin conditions over large parts of this region.
Our experiments reveal a pronounced enhancement of the THz emission spectrum at the LO phonon frequency. This feature is also reproduced in self-developed numerical simulations assuming a frequency-dependent nonlinearity d. This nonlinearity is calculated using the Faust-Henry model with experimentally determined coefficients [2]. The feature vanishes when a constant nonlinearity is assumed. Further reducing the film thickness to around 100 nm, we expect similar amplification of TO phonons in THz emission.

Reference:

[1] B.N. Carnio et al. Opt. Lett. 43, 1694-1697 (2018)

[2] W. L. Faust et al. Phys. Rev. 173, 781 (1968)