Multidimensional spectroscopy, first developed for nuclear magnetic resonance and then adapted for the infrared, visible, and UV regions of the spectrum, is a powerful tool to dissect inherent couplings between different degrees of freedom [1]. Light–matter interactions in the terahertz (THz) region lay the foundation for studying low-energy excitations [2] such as molecular rotations in gases [3,4], molecular dynamics in liquids [5,6], lattice vibrations and electronic transitions in solids [7–12], and spin dynamics in magnetic materials [13,14]. Extending multidimensional spectroscopy to this frequency range could provide unambiguous evidence for the nonlinear couplings between such excitations. However, unlike its counterpart in other frequency ranges, two-dimensional THz spectroscopy is still in its nascent stage and has been progressing slowly. One major issue that impedes the widespread adoption of this technique is the long data acquisition time [3]. In 2D THz spectroscopy, a sequence of strong-field THz pulses is used to successively interact with the system and the resulting nonlinear time-dependent THz signal is measured. Therefore, to construct a 2D THz spectrum, two delay times—the temporal separation between THz pulses and the signal measurement time—must be scanned over the desired range. This often necessitates very long data acquisition times, typically days, to reach sufficient signal-to-noise ratios to resolve weak nonlinear spectral features. One potential solution is to read out the THz waveform on a single-shot basis [15], eliminating or reducing the need to scan a second time delay. However, previous implementations of single-shot THz measurements could not ensure shot-to-shot balanced detection with a high repetition rate readout [16–18], which is critical to ensure high sensitivity. Here, we overcome this limitation and demonstrate an echelon-based single-shot 2D THz spectroscopy setup operating at a kHz repetition rate. The multiplexing advantage leveraged by this technique permits acquisition of full 2D THz spectra two orders of magnitude faster than with dual delay scans, reducing data acquisition times from days to hours or minutes.

Figure 1(a) illustrates our experimental setup. A Ti:Sapphire amplifier system (Coherent Legend Elite Duo HE+) seeded by a Ti:Sapphire oscillator (Coherent Vitara T) delivers 12-mJ, 35-fs laser pulses at 800 nm at a 1-kHz repetition rate. This near-infrared (NIR) laser beam is split into two portions by a 95% reflector. The reflected beam is used for THz generation, while the transmitted beam is used to measure the time-dependent THz signal field through electro-optic (EO) sampling [19]. For generating two time-delayed THz pulses, the reflected NIR beam is divided equally into two beams with a variable time delay between the pulses. The two NIR pulses are recombined with a tilted-pulse-front geometry [20] in a 0.6% MgO-doped stoichiometric LiNbO₃ (LN) crystal to generate two time-delayed intense THz pulses (separated by >3 ps to avoid nonlinearities in the LN crystal), which are collimated and focused at the sample position by a 4f imaging system consisting of two off-axis parabolic mirrors. The transmitted THz field and the copropagating THz signal field are collimated and focused in an EO crystal (1-mm GaP for measuring THz waveforms and 2-mm ZnTe for 2D THz measurements) by another 4f imaging system.

 

Fig. 1. 2D THz spectroscopy setup with single-shot detection. (a) Schematic drawing of the experimental setup. BS, beam splitter; HWP, half-wave plate; L0 (f = 8 cm), lens for imaging the tilted pulse front onto the LiNbO₃ (LN) crystal; L1–4, two 1:3 telescopes for expanding the probe beam; L5–8 (f = 15, 5, 30, 15 cm) two pairs of 4f imaging systems to relay the probe beam array onto the CMOS camera (Zyla 5.5 sCMOS); PBS, pellicle beam splitter; QWP, quarter-wave plate; BD, beam displacer (Thorlabs BD40); CL (f = 5 cm), cylindrical lens; reflective echelon (Sodick, Inc., 30 × 30 mm, 500 steps, step height 7 µm, step width 60 µm). The imaging detection optics with BD, CL, and the CMOS camera are marked with a dashed box. (b) Side view of the imaging detection optics. (c) Camera image of the two orthogonally polarized beam arrays. (d) Data acquisition scheme. The laser repetition rate is 1 kHz. Two chopping frequencies are set to 500 Hz and 250 Hz for differential chopping detection. The TTL signals out of the timing controller for the laser and two choppers trigger the CMOS camera.

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In conventional EO sampling, the THz field is overlapped with a single NIR probe pulse in the EO crystal. The change in probe polarization is read out with a pair of balanced photodetectors. The measurement is repeated for signal averaging. Then the arrival time of the NIR pulse is varied with a delay stage, and at the new delay time, the measurement with appropriate signal averaging is carried out. This process is repeated with many different delay times to determine the time-dependent THz field profile. Here, we employ a reflective-echelon based single-shot technique for EO sampling. To accomplish this, we first expand the probe beam by a 1:3 telescope (L1 and L2) and use an iris to select a nearly uniform intensity profile around the center of the beam. The selected beam profile is further expanded by the second telescope (L3 and L4) to allow it to fully cover the front surface of the echelon. The stair-step echelon profile generates a one-dimensional array of 500 reflected pulses with successive time delays of ∼40 fs, covering a ∼20-ps time window. The probe beam array is focused by L5 and reflected by a pellicle beam splitter (PBS) whereupon it is overlapped with the focused THz beam in the EO crystal. After its interaction with the THz field, the probe beam array is passed through a pair of 4f imaging systems (L5–L6 and L7–L8) for relay imaging onto the CMOS camera. A quarter-wave plate (QWP) is inserted to balance the intensity of the two orthogonal probe polarizations absent in any THz field. Since 2D THz spectroscopy measurements detect weak nonlinear signals, it is crucial to ensure shot-to-shot, balanced detection at a high repetition rate. However, previous single-shot studies of measuring THz waveforms or THz-induced Kerr effects could not combine balanced detection with a kHz readout [18,21] because doing so requires squeezing two beam arrays onto a small area of a camera (h = 38 px or 247 µm) to allow for fast acquisitions. To overcome this problem, we introduce a simple optical design consisting of a beam displacer (BD) and a cylindrical lens (CL), as highlighted in the dashed box in Fig. 1(a). A side view of this design is illustrated in Fig. 1(b). The BD separates the probe beam after the QWP into two orthogonally polarized beams parallel to one other, and the CL focuses the beams into two closely separated lines on the camera, as shown in Fig. 1(c). The spacing between these lines and their thickness can be fine-tuned by adjusting the focal lengths and relative positions of L8 and CL. This gives us precise control of the region of interest on which the two sets of beams are detected and thereby enables readout at a 1-kHz repetition rate. Two one-dimensional detector arrays that can be read out at a kHz repetition rate could also be used.

The data acquisition scheme for 2D THz spectroscopy measurements is presented in Fig. 1(d). We insert two optical choppers that operate at subharmonics of the laser repetition rate in each THz generation path. Labelling the two THz pump pulses “A” and “B,” chopper 1 modulates pump A at 500 Hz and chopper 2 modulates pump B at 250 Hz. Both are synchronized to the 1-kHz output signal by the synchronization and delay generator of our laser amplifier. This differential chopping scheme leads to a sequence of images with four different pulse combinations (i.e., ${I_{{A_{on}}/{B_{on}}}}$, ${I_{{A_{on}}/{B_{off}}}}$, ${I_{{A_{off}}/{B_{on}}}}$, and ${I_{{A_{off}}/{B_{off}}}}$). All these individual images are captured by our camera, which is also synchronized to the kHz amplifier. The nonlinear signal is extracted by subtracting all unwanted signals,

To demonstrate the functionality of our single-shot detection method and to compare its performance relative to that of a conventional dual-stage scan, we first examine the readout of a single-cycle THz pulse. We obtain the THz waveform on a single-shot basis by first collecting a sequence of images with the THz field on and off. The THz signal is spatially encoded on the acquired echelon images as can be shown in the normalized differential of the THz-on and THz-off images, as shown in Fig. 2 (no sample). The two orthogonally polarized probe beam arrays yield inverse signals, labeled ${I^ + }$ and ${I^ - }$, which result from the field-dependent birefringence induced by the THz pulse. These mirrored images are subsequently partitioned vertically and then binned to obtain raw THz signals as a function of pixel position, ${I^{ +{/} - }}(x)$. To convert from the spatial axis of the image to a signal-field detection delay, a calibration is performed once per alignment. Subtracting the two traces yields an accurate retrieval of the THz waveform with only a single laser shot (see Supplementary material).

 

Fig. 2. THz waveforms extracted from camera images. The differential image shows the change of the intensity profile of the probe beams with the THz electric field, on which the EO sampling signals (1-mm GaP EO crystal, no sample) for each polarization are superposed. Two traces show almost identical signals but inversed signs.

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We now compare the signal-to-noise of the single-shot technique and the conventional delay line method. First, we highlight the importance of balanced detection in the single-shot scheme. Figure 3(a) compares the root mean square (RMS) deviation of the overall balanced signal versus that of each of the individual polarization components as a function of the number of laser shots, N. Balancing roughly halves the observed noise at low N by reducing the effect of laser power fluctuations. This effect continues for large N, as the RMS deviations of all signals decay with an approximately $1/\sqrt N $ scaling relation, which is typical for uncorrelated laser noise. Though the trend line is the same, we note that for intermediate N, the individual polarization components show significant excursions due to noise with short-time correlations. This noise, however, is well corrected for in the balanced signal and is thus greatly diminished. Overall, balanced detection improves the SNR of the single-shot detection scheme by up to a factor of four. Figure 3(b) compares the RMS deviation between echelon-based EO sampling and conventional stage-scan EO sampling as a function of laser shots under equivalent scan conditions (20-ps range, 500 steps) along with corresponding fits to a $1/\sqrt N $ scaling relation. Since one laser shot in the echelon-based technique corresponds to 500 laser shots in the conventional stage scan, the multiplexing advantage of the single-shot technique is clear. Comparing the two lines shows that the single-shot scan requires 220× fewer shots compared to the stage scan under noise-equivalent circumstances, which is less than the theoretical 500× given by the multiplexing factor alone but of the same order of magnitude. As such, by operating at the kilohertz repetition rate of the amplified laser system, our single-shot setup can achieve a roughly 200-fold speedup in the acquisitions of 1D and 2D THz spectra.

 

Fig. 3. Signal-to-noise performance of the single-shot detection method. (a) RMS noise performance of single-shot detection of the THz waveform (1-mm GaP EO crystal, no sample) as a function of laser shots with and without balanced detection. Balancing improves the SNR by reducing excursions due to noise with short-time correlations and by better correcting shot-to-shot noise. (b) Comparison of the RMS noise recorded using echelon-based single-shot detection and conventional delay-line scan method. The solid lines are fits to a $1/\sqrt N $ scaling relation.

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Now, we compare the acquisition time and data quality of our single-shot detection method with the conventional delay-line scanning detection method for 2D THz spectroscopy measurements. For a fair comparison, both detection schemes are performed with the same THz generation and EO sampling conditions with gas-phase acetonitrile as the sample [5]. The experimental 2D time-domain traces and the resulting 2D rotational spectra of acetonitrile acquired by both methods are displayed in Fig. 4. For the conventional method, acquiring such a 2D time-domain trace involves moving two delay lines and recording signals at each inter-pulse delay $\tau $ and signal field detection time t, which can be immensely time-consuming. With both delay times extending up to roughly 100 ps, and averaging over 100 shots at each (t,τ) time point, the acquisition time of our 2D time-domain trace, as shown in Fig. 4(a), is 2.5 days, and this is typical with the conventional method. However, with our single-shot technique, the acquisition time for taking the same 2D time-domain trace is reduced to roughly 4 hours, even though we average over 5000 shots for each inter-pulse delay τ. Because our single-shot technique can cover a time window of ∼20 ps, we only need to move the detection window a few times (six in the present case) to cover the entire range while still scanning the inter-pulse delay line to vary $\tau $. All these acquired data are smoothly connected by averaging the overlapped temporal region to form the 2D time-domain signal shown in Fig. 4(e). It is evident that our single-shot method significantly improves the data quality with far shorter acquisition times. More concretely, if we compare the noise floor of both 2D scans, we find that the RMS deviation of the single-shot scan is roughly 3.2× lower (see Supplementary material) than that of the conventional scan. This combined with the 16-fold decrease in acquisition time translates to a roughly 160-fold speedup when comparing on a noise-normalized basis—in line with the anticipated speedup from our previous analysis. Differences are also observed from the comparison of 2D THz spectra in Figs. 4(b)–4(d), where the conventional method is used, and in Figs. 4(f)–4(h), where the single-shot technique is used. Although all the main features, including the non-rephasing (NR) signals, rephasing (R) signals, and two-quantum (2Q) signals, are resolved in both spectra, the 2D spectrum acquired by the single-shot technique eliminates much of the background noise. This helps resolve the much weaker nonlinear signals in the 2D THz spectra, such as the 2Q signals, which is readily apparent if we directly compare the 2Q signals acquired by both methods as shown in Figs. 4(d) and 4(h). In the conventional method, the spectral features are obscured, and the 2Q signal is quite noisy. However, with our single-shot technique, this becomes less of an issue and some fine spectral features, like the far-off diagonal peaks, are more clearly resolved. For other systems of interest with shorter dephasing times, e.g., collective spin waves (magnons), the typical data collection time is less than one hour, compared to several days as reported earlier [3].

 

Fig. 4. Comparison of 2D THz spectra acquired by conventional detection and single-shot detection methods. (a) and (e) Normalized 2D time-domain signals acquired by both methods. (b) and (f) Corresponding 2D THz rotational spectra of acetonitrile using a 2-mm ZnTe EO crystal. Enlarged views of the NR signals within the purple dashed boxes are shown (c) for conventional and (g) for single-shot detection. Enlarged views of the 2Q signals within the blue dashed boxes are shown (d) for conventional and (h) for single-shot detection, with both spectral amplitudes magnified by 8×. In this case, the conventional EO sampling scan took 2.5 days while the single-shot detection scan took only 4 hours. An enlarged version of this figure can be found as Fig. S5 in the Supplemental Document.

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We have demonstrated a novel echelon-based 2D THz spectrometer that has the benefit of reduced acquisition time, high sensitivity, and easy integration into existing setups. The ability to perform experiments that once took days in a matter of hours not only makes these measurements more practical, but enables a wide swath of previously difficult experiments including three-dimensional THz spectroscopies. We believe that this design represents an important step forward in the maturing of the technique of 2D THz spectroscopy by extending the capabilities of the field and allowing for wider adoption within the broader scientific community.