10-fold SNR Improvement Thanks to Boxcar Averaging in THz Spectroscopy

Time-resolved terahertz (THz) spectroscopy is a powerful tool for probing carrier dynamics in novel materials, ranging from two-dimensional perovskites for photovoltaics to transition metal dichalcogenides (TMDs) for cutting-edge electronic devices. By exciting a sample with infrared femtosecond lasers and probing it with THz pulses, researchers gain direct insight into carrier motion and scattering processes.

However, these advantages come with a major experimental challenge: often, the measurements’ signal-noise-ratio (SNR) ends up being extremely poor as the interactions are inherently transient and extremely weak, usually < 0.1% of the THz pulses amplitude. This is particularly the case in low-dimensional materials with reduced thickness, which interact only briefly and weakly with the THz pulses.

At Politecnico di Milano and CNR‑IFN (Istituto di Fotonica e Nanotecnologie), in the lab of Federico Grandi and Dr. Eugenio Cinquanta, they employ an ultrafast time-resolved THz spectroscopy setup to study the transient carrier dynamics of these low-dimensional materials. In their experiment, the observable is the change in the THz electric‑field amplitude at the pulse peak, −ΔE/E. 

Their setup consists of an 800 nm, 50 fs, 1 kHz laser beam whose output is split into three branches: an optical pump excites the sample, and subsequently, a time-delayed THz probe interrogates the sample again. The resulting THz waveform after the interaction is detected by a third copy of the main laser beam, using a technique known as “electro-optic sampling”, where balanced detection, in combination with lock-in amplification with an MFLI Lock-in Amplifier, allows full reconstruction of the instantaneous THz electric field (Fig. 1).
By scanning the delay between the optical pump and THz probe, the information on the sample carrier dynamics is retrieved. 

The challenge

Due to the low repetition rate and short pulse duration, the signal has an ultra-low duty cycle, meaning that the signal of interest exists only in a very narrow time slice around the THz pulse. At 1 kHz repetition rate, almost all the millisecond period contains no information -- just noise. A lock‑in amplifier averages over the entire period and is exceptionally effective when the signal has a high duty cycle. Here, however, in the case of a low-duty-cycle signal, most of the averaging time is spent integrating “off” time. Even with careful choice of time constants, the lock‑in under‑utilizes the available measurement time, so very weak transients require heavy averaging to stand out. In practice, only signals down to 1% of the peak THz electric field could reliably be resolved in a reasonable time, while ~0.1% remained at the edge of detectability.

The solution

Adding the MF‑BOX Boxcar Averager to the MFLI Lock‑in Amplifier changes the game for low‑duty‑cycle measurements. The MF‑BOX opens the measurement window only when the THz information is present – exactly at the chosen instant of the electro‑optic sampled waveform -- and ignores everything else inside the period (for more details, please refer to our Principle of Boxcar Averaging white paper). Gate width and delay are tuned to the sample’s response so that integration happens only where the signal lives. 
In the measurements shown here, the MF‑BOX is inserted in series ahead of the lock-in demodulation – performed as well with the MFLI -- so that the detection chain is hybrid (boxcar + lock‑in). Practically, the photodiode signal is first time‑gated by the MF‑BOX Boxcar Averager at the 1 kHz laser repetition rate and, subsequently, the boxcar output is demodulated at both the pump and the THz generation modulation frequencies to extract the amplitude variation of the electric field measured at the peak of the THz pulse, i.e, −ΔE/E (more details on the implementation of the double modulation scheme can be found in Ref [1]).

Crucially, both approaches -- lock‑in only and boxcar + lock-in -- run on the same instrument, so we can display both results and SNRs simultaneously. 
 

Results

With identical measurement time per delay point, a single lock‑in trace -- i.e. without any preceding boxcar averaging -- is visibly noise‑dominated, and the transient is hard to follow, while a single hybrid trace – i.e. boxcar + lock-in -- taken at the same time already reveals a sharp drop at time zero and a noisy but visible picosecond‑scale relaxation (Fig. 2, left vs right). 

Further averaging helps both methods, but the gap widens: ten averaged lock‑in traces still show substantial noise, whereas ten averaged hybrid traces resolve the dynamics with a much higher SNR, enabling robust fits to carrier‑recombination dynamics (Fig. 3, left vs right). This improvement is not cosmetic; it moved the customer from “about 1% in reasonable time” to routinely resolving 0.1–0.2% changes in −ΔE/E, allowing measurements on thinner and more weakly interacting samples.

Try both on one hardware platform

Not every experiment is duty‑cycle limited, and that is exactly why the MFLI + MF‑BOX combination is so practical. The same instrument lets you compare simultaneously and consistently the SNR of lock‑in and boxcar measurements side by side, with identical detection chains. 
In fact, in many situations, there is no a priori clear-cut solution to which measurement approach leads to the best SNR. That’s because the duty cycle, per se, despite being an important parameter, is not the only factor to consider: the actual frequency of the signal, some specific noise sources and other factors; additionally, the interplay among all these factors might not be trivial. Therefore, often the best approach is to explore both options and then evaluate which one leads to the best SNR.

Conclusion

Short‑lived, low‑duty‑cycle signals are where boxcar averaging excels. By adding the MF‑BOX to an MFLI Lock-in Amplifier in their THz spectroscopy setup, the researchers at Politecnico achieved a clear, repeatable ten-fold SNR improvement of the THz transients from low-dimensional materials. Something that previously required long averaging or remained out of reach. The ability to switch seamlessly between lock‑in and boxcar detection on the same platform ensures you always use the right measurement tool according to the characteristics of your signal.

Acknowledgments

We thank Federico Grandi and Dr. Eugenio Cinquanta for sharing their data and the details of their experimental setup. We also acknowledge the joint Politecnico di Milano/CNR‑IFN laboratory; the MF‑BOX module used in this work was funded by CNR‑IFN.

References

[1] Krzysztof Iwaszczuk, David G. Cooke, Masazumi Fujiwara, Hideki Hashimoto, and Peter Uhd Jepsen, "Simultaneous reference and differential waveform acquisition in time-resolved terahertz spectroscopy," Opt. Express 17, 21969-21976 (2009) DOI: https://doi.org/10.1364/OE.17.02196