Experimental configuration and THz pulse train generation
The lower part of Fig. 1(a) illustrates the process of generation of the train of optical pulses by the illumination of an echelon mirror measuring 20 × 10 mm2 in size and having 150 μm wide and 75 μm high pitches. To achieve an illumination with 0 degrees of incidence on the echelon mirror, an optical switch, composed of a polarizer beam splitter cube and a quarter-wave plate, is used (see Materials and Methods section). Before reaching the step mirror, a 2X to 8X variable beam expander (BE) (Edmund Optics model 87-570) is inserted into the pump beam path. This configuration has the double advantage of allowing an adjustment of the number of steps illuminated while maintaining constant the size of the pump beam at the exit of the polarizer cube. This beam is then imaged with a 2X apochromatic microscope objective on a CCD (Edmund Optics model 46-142) camera to validate the magnification and the position of the echelon image. The top part of figure (a) shows the image obtained from the echelon mirror. In the zoomed view, we can see that 3 steps correspond approximately to 230 µm on the CCD image, the equivalent of a magnification of 1 at the image plane.
In the bottom illustration of Fig. 1(b), the DMD is inserted at the image plane of the 2X lens. To ensure that the DMD is correctly positioned in the image plane, a second apochromatic 5X lens (Mitutoyo MY5X-822) is used to relay the image reflected from the DMD to the CCD camera. To validate the exact position of the DMD with respect to the image plane of the 2X lens, a horizontal pattern of lines and spaces is applied to the DMD (see the Supplementary information S1 for more details). As can be seen in the upper part of Fig. 1(b), the echelon image, together with the mask formation on the DMD, are well overlapped, i.e., the echelon image plane matches the DMD image position. In the zoomed-in view, we determined through measurement that the image of 3 steps from the echelon is projected onto an area corresponding to 21 active micromirrors.
To date, echelon mirrors have mainly been used for single-shot time-domain THz spectroscopy [39, 40] and for the development of intense THz sources using the tilted-pulse front-pumping (TPFP) scheme [8, 41]. The idea behind using an echelon mirror is to temporally shape the reflected optical pulse at different delay times without dispersion, i.e., while preserving the ultrashort property for each reflected optical beamlet. For single-shot THz spectroscopy, the idea is to instantaneously probe each part of a THz pulse with a segmented ultrashort probing beamlet [39, 40]. In the case of intense THz generation using the TPFP configuration, a tilted pulse must be generated at the image plane in order to meet the phase matching condition inside a lithium niobate crystal along the Cherenkov angle [8, 41]. Interestingly, the DMD can also act as an active echelon mirror for ultrafast pulse measurements  and the TPFP scheme . However, in contrast to previous works [8, 39–43], we are interested in converting each ultrafast optical beam into a single THz pulse train at a specific carrier frequency, thus generating a fixed frequency pulse train.
To perform the task of converting a two-dimensional spread beamlet to a consecutive series of optical pulses, a single optical lens is used. Temporally delayed by the height of each step of the echelon mirror, the beamlets, after passing through the lens, undergo a different temporal delay at the focal point. To validate this time combing assumption at the focal point, we performed finite difference time domain (FDTD) simulations using the Lumerical software. Figure 2(a) to (e) show time snapshots of a femtosecond laser beam after reflection from a stair-step metal surface. This reflected beam is transferred to a biconvex lens, and a monitor placed at the focus of this lens reveals the temporal passage of these beamlets (see the full-length simulation in the Supplementary video S2). In Fig. 2 (a) and Fig. 2 (b), we can see that pumping the step mirror on the 75 µm high side changes the initial 100 fs optical pump pulses to an optical wave packet with a temporal separation of 500 fs. Being non-dispersive, each wave packet, after reflection on the echelon mirror, preserves a duration of 100 fs for the entire simulation propagation. As can be seen in the last time map (e) of this figure, the short femtosecond laser pulses are separated in time and pass through the same location at the focus.
For THz wave generation via optical rectification in bulk nonlinear crystal, the phase matching condition between the pump light and the generated THz beam is essential to achieve good conversion efficiency [8,41]. With our method, the image aberration and the tilt of the step mirror projection may cause an additional problem in obtaining a good phase matching condition if a thick bulk nonlinear crystal emitter is used. In order to overcome this possible restrictive condition, here, we used the recently developed spintronic THz emitter (STE) . Because it is made of thin films, this device is practically insensitive to phase matching conditions and alignment. In addition, the generation of long pulse trains can also represent a significant problem when the generating mechanism produces an echo from its finite thickness. Again, the STE can be positioned such as to prevent the presence of this echo from being a nuisance, and is therefore a prime candidate for our application.
In Figs. 2(f) and (g), we show the results of generating two THz pulse trains obtained when the step mirror is illuminated on the facet with step heights of 150 µm and 75 µm, respectively. The respective insets to these figures represent a zoomed view of these pulse trains. In the inset, the time domain traces of the THz pulse train obtained with the 75 µm steps look like a quasi-perfect sine wave. However, looking at the whole set of time domain traces, we can clearly see an envelope with a Gaussian profile, which corresponds to the intensity profile of the pumping beam. Also in Fig. 2(f), approximatively 128 pulses were generated over a maximum of 133 pulses according to the size of our echelon mirror and its step size.
In Fig. 2(h), the frequency spectra of both pulse trains show a strong peak located at 1 THz (red) and 2 THz (blue), with a bandwidth at full width at half maximum (FWHM) of 13 GHz and 60 GHz, respectively. Since the STE produces broadband THz pulses, the Fourier transform of these pulse trains also produces the harmonics corresponding to the initial carrier frequency of the two pumping conditions, i.e., pumping on the facets with step heights of 150 µm and 75 µm, respectively. In both cases of excitation of the echelon mirror, we perceive a small replica of up to 4 THz, limited by the bandwidth of our THz detector (see Materials and Methods section). The inset in Fig. 2(h) shows the same frequency spectrum on a logarithmic scale. It is striking to note the very narrow bandwidth of our pulse train generation mechanism. Specifically, we estimate the Q-factor of these frequency combs to be 86 and 51 for pulse trains centered at 1 THz and 2 THz, respectively, which is about 10 times sharper than recently reported THz pulse trains [37, 42].
Parallel Modulation And Coding
As mentioned earlier, varying the diameter of the pump beam using the beam expander changes the number of steps illuminated on the echelon mirror, which results in changes of the number of THz cycles generated in the time domain, but with no changes of the carrier frequency of the emitted pulse train. Therefore, we can fine-tune the duration of the THz pulse train by simply changing the illumination size on the echelon. For the following experiments, we reduced the diameter of the pumped optical beam to 3.17 mm at FWHM and illuminated the 150 µm side, corresponding to a carrier frequency of 1 THz. In Fig. S3 (a), we show the intensity profile extract from Fig. S1 (a) of the step image and Fig. S3 (b) shows its corresponding generated THz pulse train. These results clearly show that each generated THz pulse corresponds to a step position of the echelon, which is in agreement with the simulations in Fig. 2. We noticed that due to the angle of incidence of the pump on the echelon mirror and the sharpness performance of the apochromatic lens, which had a depth of field of a few micrometers, the edges of the image appeared blurred while the center was perfectly imaged. As we will see in the next section, a blurred image on the DMD loses precision on the pulse modulation.
By using the DMD with vertical line patterns instead of the horizontal lines used in the alignment procedure in Fig. 1(b), each step of the echelon mirror can be imaged on the DMD and selected (or not selected) on demand by simply activating the micro-mirrors. In Fig. 3, we show an example of pulse separation using some vertical line and space patterns applied on the DMD. Fig. 3(a), (b) and (c) show the line and space patterns for a selected series of 13, 10 and 5 on and off pulses, respectively. The zoomed-in top view clearly shows the precision of the pulse selection as well as the high signal-to-noise ratio (SNR) of this demonstration in the central part of the pulse train. Indeed, the peripheral positions of the pulse train have a lower SNR than its central part, but this problem could be circumvented by using an appropriate shaping of the pump beam in square shape and top hat intensity .
To demonstrate the range of control of the THz pulse train, the DMD also allows each THz pulse to be individually coded via a 7 micro-mirror wide vertical line. For this demonstration, we used the ASCII binary protocol and on-off keying modulation. In the ASCII code, each character is produced from 8 bits. To simplify the understanding of our first test, we used 3 THz pulses per bit to generate the three letters forming the word "ETS". Figure 4(a) shows the result obtained for the 72 modulated pulses in an OOK 3 pulses per bit protocol. The corresponding binary pattern is: <0100 0101 0101 0100 0101 0011>. The signal is clearly observable and understandable from a binary point of view with a Gaussian-shaped amplitude versus time profile. In Fig. 4(b), we go to the limit of the OOK protocol by modulating each THz pulse for one bit. With 64 pulses for this demonstration, we encoded the eight letters: "ETS2021!", corresponding to the bit pattern: <0100 0101 0101 0100 0101 0011 0011 0010 0011 0000 0011 0010 0011 0001 0010 0001>. Indeed, this experiment was first done in 2021. For these two OOK modulation results, the carrier frequency remains stable at 1 THz.
As can be noted, the central part of Fig. 4(b) shows a clear contrast between the transported on and off information of the THz pulses, while the peripheral positions become more blurred and more difficult to discretize. As mentioned above, the reason why the information is less legible at the edges of the beam (or for the beginning and end of the pulse train) is directly related to the imaging conditions, and not to the speed of an electronic component (see the Supplementary information S3 for more details). This is important to note because this ultrafast modulation is not related to a fast electronic process, but rather, is only dictated by geometric optics. One way to circumvent this problem would be to use a suitable mask on the DMD. Since the edge of the step image on the DMD is blurred, a larger modulation area should be used, e.g., having lines and spaces matched according to the position on the DMD. Another approach would be to design an imaging solution capable of imaging an inclined plane with a larger working distance, especially for the imaged plane of the echelon.