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Abstract
Classical terahertz spectroscopy usually requires the use of Fourier transform or Time-Domain Spectrometers. However, these classical techniques become impractical when using recent high peak power terahertz sources – based on intense lasers or accelerators – which operate at low repetition rate. We present and test the design of a novel Time-Domain Spectrometer, that is capable of recording a whole terahertz spectrum at each shot of the source, and that uses a 1550 nm probe fiber laser. Single-shot operation is obtained using chirped-pulse electro-optic sampling in Gallium Arsenide, and high bandwidth is obtained by using the recently introduced Diversity Electro-Optic Sampling (DEOS) method. We present the first real-time measurements of THz spectra at the TeraFERMI Coherent Transition Radiation source. The system achieves 2.5 THz bandwidth with a maximum dynamic range reaching up to 25 dB. By reducing the required measurement time from minutes to a split-second, this strategy dramatically expands the application range of high power low-repetition rate THz sources.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High peak power terahertz sources, with nanojoule to millijoule pulse energy, have recently widespread, thanks to the development of specific terahertz beamlines on accelerator-based light sources [1–12], (see also Ref. [13] for a review) and to the discovery of extremely efficient terahertz sources based on high-power femtosecond lasers [14–21]. These new THz sources have open novel research directions. However a large part of those sources operate at low repetition rates, down to tens of hertz or below for the most intense ones. This low-repetition rate is a source of a major complication because in common spectroscopy systems, such as Fourier-transform spectroscopy [22] and Time-Domain Spectroscopy (TDS) [23,24], obtaining a spectrum requires – by design – to record data for a large number of THz shots. This is due to the fact that those methods necessitate to scan a delay between a probe laser and the THz light to be characterized (for TDS), or between the two arms of an interferometer (for Fourier transform spectroscopy).
For these reasons, these last two decades have seen an intense activity aiming at the development of methods that are capable of recording a whole terahertz spectrum (or equivalently a terahertz signal trace) in a single-shot. The strategies generally include two steps. The terahertz signal to be analyzed modulates a single laser pulse, by electro-optic interaction in a Pockels crystal. Then, the modulated laser pulse properties are analyzed, which allows the terahertz pulse shape (and its spectrum) to be retrieved. Various measurement strategies have naturally been explored, in particular using encoding in the longitudinal direction of a laser pulse [25–33], in the transverse profile of a laser (time-to-space conversion) [34–37], and in the angular distribution of laser beamlets (time-to-angle conversion) [37,38].
In addition to the detection scheme itself, the operating wavelength also plays a major role in the application range of single-shot TDS. After pioneer works at 800 nm, an important milestone concerned the demonstration of single-shot THz recorders and TDS systems at 1030 nm wavelength [39]. Using this "fiber-friendly" wavelength opened the way to fiber laser-based TDS [40], which flexibility enabled direct applications in accelerator operation and research [41–43], as well new ways to reach multi-megahertz repetition rate, using the so-called photonic time-stretch technique [32,40].
In this Article, we address a next step in fiber-laser-based single-shot TDS, which consists of using the 1550 nm telecommunication wavelength for the probe laser. As an important motivation, large facilities usually already include erbium fiber laser references for synchronizing various critical equipment [44]. Moreover, using the 1550 nm wavelength enables both the use of detection crystals the are phase-matched and with large bandwidth: Gallium Arsenide (GaAs) [45] or 4-N,N- dimethylamino-4’-N’-methyl-stilbazolium tosylate (DAST) [46,47]. In addition, using the 1550 nm wavelength enables to take advantage of the large choice of components available (often at moderate cost) in the telecommunication market. Pioneer electro-optic sampling demonstration, using a 1550 nm scanned probe can be found in Refs. [45,48].
We present here a single-shot time-domain spectrometer that is based on an erbium fiber laser at 1550 nm, and the corresponding tests at the TeraFERMI beamline of the Italian FERMI Free-Electron Laser. In addition, in order to reach the required bandwidth for TDS, we use the recently proposed Diversity Electro-Optic Sampling (DEOS) technique, which associates a special electro-optic detection system with a diversity-based [33] numerical reconstruction algorithm.
2. Experimental setup
The single-shot THz-TDS system (see Fig. 1(a)) is based on the the so-called diversity electro-optic sampling (DEOS) design [33]. The probe pulses are produced using an amplified erbium-doped fiber laser operating at 1550 nm (Menlo C-Fiber, with 78.895 MHz repetition rate). The laser delivers 1.5 nJ pulses to the TDS system, with 100 nm bandwidth, that are synchronized with the main Radio-Frequency (RF) reference of the FERMI facility (and thus to the THz source) and are stretched to $25$ ps using a transmission grating-based Treacy stretcher. The probe laser pulses are modulated – in single-shot – by the THz signal under interest, using the electro-optic effect in a 100 $\mu$m-thick GaAs crystal, a series of waveplates, and a polarizing beam-splitter. A home-made spectrometer, based on transmission gratings, records simultaneously the optical spectra at the two exits of the polarizer (polarizations 1 and 2 in Fig. 1(a)), and the spectrum of the unmodulated laser. Recording the optical spectra of polarizations 1 and 2 is the main point of the DEOS method [33]. The data analysis (i.e., the electric field retrieval from the two recorded optical spectra) is described in the next Section.
Fig. 1. (a) Experimental setup. Microjoule THz pulses are produced at the TeraFERMI beamline, at 50 Hz repetition rate. The field evolution of each THz pulse is probed in single-shot by a 1550 nm chirped laser pulse, using the Pockels effect in a GaAs crystal. The output spectrometer records simultaneously three optical spectra: the two outputs exiting the polarizing beam-splitter (which contains the main information for retrieving the THz signals), and an unmodulated laser spectrum reference (for taking into account the laser shot-to-shot fluctuations). (b) Typical raw data provided by the linear detector array. At each THz shot $n$, the linear camera successively records three lines. The first line contains the optical spectra of electro-optic signals (the two polarization outputs $S_{1,n}$ and $S_{2,n}$ and the reference unmodulated laser $S_{0,n}$ – see text). In addition, the line camera also records two background reference signals without THz: one line with laser, and one line without laser (dark line). GaAs: $100\,\mu$m-thick Gallium Arsenide 110-cut crystal. PBS: polarizing beam-splitter. QWP and HWP: achromatic quarter-wave and half-wave plates. OAP: Off-axis parabolic mirror with mm focal length. L$_1$ and L$_2$: lenses with $100$ mm focal length. L$_3$: camera objective lens (plano-convex, with 100 mm focal length). The crystal and waveplates orientations are summarized in Table 2.
The terahertz pulses sent to the THz-TDS system are delivered by the TeraFERMI beamline [2], at 50 Hz repetition rate. The terahertz emission is produced by using the Coherent Transition Radiation or CTR [49] effect. This consists in placing a thin metallic foil on the path of the relativistic electron beam. Typical electron beam parameters at the end of the FERMI accelerator are given in Table 1. Then, by crossing the vacuum-metal interface, the electrons produce a coherent and broadband THz pulses, with bandwidth up to $6$ THz here [2,50]. The THz pulses are transported, under vacuum, to the user area, and are linearly polarized, using a linear polarizer (Tydex HDPE polarizer). At the exit of the TeraFERMI beamline, the few tens of microjoule pulses, after focusing, have a peak electric field in the MV/cm range [50].
Table 1. Experimental electron beam parameters at the end of the FERMI LINAC.
The timing of the THz source, probe laser pulses and camera trigger are designed so that convenient references are provided for data analysis. At each THz pulse to be measured (i.e., every 20 ms), a pulse picker selects two successive probe laser pulses. One pulse is synchronous with the THz pulse to be analyzed and is used for the electro-optic sampling. The other laser pulse does not interact with the THz signal, and is used for calibration purposes, at the data analysis stage. At each THz shot, in addition to recording the two corresponding laser spectra (with and without THz), the camera also records a dark reference. The camera raw data hence consist of three lines at each THz shot, as displayed in Fig. 1(b).
The specificity of the DEOS strategy consists of retrieving numerically the THz signal under interest, from the information contained in the two optical spectra at the two outputs of the polarization beam-splitter. This requires using a special arrangement of the waveplates (see Table 2, and Ref. [33]). In this situation, it has been shown that the TDS pulse shape and spectrum can be retrieved with large bandwidth (limited in principle by the laser and crystal bandwidths) using a simple numerical algorithm, called maximum ratio combining. The retrieval algorithm is described in Ref. [33], and reminded below.
Table 2. Polarizations, crystal and waveplates orientations of the DEOS setup in Fig. 1. $^{(*)}$: The HWP$_1$ is set to have a laser polarization at 45 degrees with respect to the THz field at the input of the GaAs crystal.
3. Results – single-shot THz-TDS spectra
A typical THz TDS spectrum of the TeraFERMI source is displayed in Fig. 2(d), and the corresponding time-domain electric field trace is displayed in Fig. 2(c). These data are obtained at a rate of 50 TDS spectra per second, i.e., at the repetition rate of the source.
Fig. 2. Typical raw data and deduced terahertz TDS spectrum obtained in single-shot at the TeraFERMI coherent transition radiation source. (a): Electro-optic sampling traces extracted from the camera image. The blue and green curves are the data corresponding to the two polarizations channels, before applying the DEOS reconstruction algorithm (only basic background subtraction and normalization by the laser spectrum shape have been made – the laser spectral shape, $S_0^\text {ref}$, is indicated as a dash-dotted line). (b): Fourier spectra of the two electro-optic signals signals (blue and green lines). (c) and (d): actual shapes of the single-shot input THz signal and the corresponding terahertz optical spectrum, that have been obtained from the raw data (a) and (b), using the DEOS phase-diversity-based algorithm. The dash-dotted line in (c) represents the window function $w(t)$ that has been applied prior to the reconstruction. Note that the present TDS spectrometer provides 50 terahertz spectra per second, and are displayed in real-time during the experiment.
As mentioned above, key to these measurements is the numerical reconstruction of the TDS traces (Fig. 2(c),d) from the recording of the two polarizations exiting the setup (see Fig. 1(a) and (b)). In the following, we remind the main steps of the DEOS reconstruction algorithm [33] used, including the cancellation scheme for the laser shot-to-shot fluctuations.
In a first step, we extract, at each shot $n$ the three pixel arrays $S_{0,n}$, $S_{1,n}$, $S_{2,n}$ and their corresponding background references without THz and without laser (see Fig. 1). Then we compute the normalized TDS traces $Y_{1,n}$ and $Y_{2,n}$ on each polarization channel, at each shot $n$:
where $\beta _{i} = S_{i,n}^{\text {ref}} / S_{0, n}^{\text {ref}}$ corresponds to the channel "i" transmission of the setup that takes into account the optics transmission and "$\text {ref}$" refers to the signal in absence of THz electric field (see Fig. 1(b)). Note that, for clarity, we did not explicit the interpolation process that is needed to obtain consistent arrays as well as the camera background subtraction (reference without THz and laser) to $S_{i,n}$ and $S_{i,n}^{\text {ref}}$.For small THz-induced phase shift $\Delta \phi _{\text {THz},n}$ in the EO crystal, it has been shown that the EO signals $Y_{i, n}$ are related to $\Delta \phi _{\text {THz},n}$ by transfer functions. In Fourier space :
where the tilde stands for the Fourier transform, and $\Omega$ is the frequency in the THz domain. The phase-shift corresponds to the THz electric field-induced birefringence in the electro-optic crystal. For the orientation chosen here: where $n_{0}$ is the refractive index at the optical wavelength $\lambda$, $d$ is the crystal thickness and $r_{41}$ the electro-optic coefficient. $E_{\text {THz}}(t)$ is the THz electric field inside the crystal.The input can be then retrieved by using a simple algorithm, known as Maximal Ratio Combining (MRC):
For this method to work (i.e., being mathematically well-posed), special orientations of the waveplates and crystal have been used [33], so that the zeros of $\tilde H_1$ and $\tilde H_2$ do not occur at the same frequencies. We use here the orientations used in Ref. [33] and reminded in Table 2. This special layout leads to transfer functions of the form:
where the parameter $B$ is related to the chirp rate of the stretched probe laser. The parameter $B$ is easily determined from the data themselves using a simple fit (see Ref. [33] for details).The input phase-shift $\Delta \phi _{\text {THz}}^\text {MRC}(t)$ (or THz electric-field $E_{\text {THz}}^\text {MRC}(t)$) is obtained by performing an inverse Fourier transform.
Main intermediate steps of the reconstruction are displayed in Fig. 2. The raw TDS signals $Y_{1,n}$ and $Y_{2,n}$ on the two polarization channels (i.e., before application of the DEOS algorithm) are shown in Fig. 2(a). Note that these two raw signals correspond to the standard spectral-encoding technique, and are thus strongly distorted with respect to the real input signal. The retrieved signal (i.e., after applying the DEOS reconstruction algorithm) is displayed in Figs. 2(c),d.
4. Comparison between single-shot TDS signals with scanned electro-optic sampling
Obtaining the TDS traces and spectra in single-shot required to use the relatively novel DEOS reconstruction algorithm. Although the method has been already tested using 800 nm and 1030 nm laser-based measurement systems in [33], we also tested the quality of the reconstruction versus "classical" electro-optic sampling, i.e., by using a compressed laser pulse as the probe, and scanning the delay between the probe laser and the terahertz source arrival times. Technically, this experiment has been done by simply bypassing the grating stretcher. A comparison of the single-shot TDS traces (obtained using DEOS) and the scanned TDS data is presented Fig. 3. The traces are extremely similar, with only slight differences, that may be attributed to the slightly different paths (inside the electro-optic crystal) for the two setups.
Fig. 3. Comparison between single-shot THz TDS signals, and classic scanned electro-optic sampling. Shaded areas: superposition of 50 single-shot TDS traces (each being reconstructed using DEOS). Red curve: same data averaged over 50 successive shots (i.e., corresponding to 1 second of acquisition time). Black dashed line: classical (scanned) electro-optic sampling trace. Inset: corresponding Fourier spectra of the single-shot and scanned terahertz signals.
Advantages of the single-shot technique not-only concerns the possibility to obtain one TDS spectrum per shot of the terahertz source. It is also important to note that in such facilities, the probe laser and terahertz source present time jitter that – though relatively small – considerably degrades the performances of scanned TDS systems (see Ref. [51] for a deep study of this fundamental problem and recent solutions). In our case, the arrival time of the THz CTR is subject to a jitter directly related to the arrival time jitter of the electron bunches in the accelerators, which is of the order of $40$ fs at FERMI. Single-shot TDS thus also presents a considerable advantage, since the terahertz spectra are inherently insensitive to moderate jitter between the laser and the THz light to be analyzed. In our case, the overall time jitter is of the order of $66$ fs and is visible when examining the superposition of the single-shot traces in Fig. 3. This time jitter is the sum of two contributions: the first one comes from the inherent arrival time jitter of the electron bunches in the accelerator and the second one comes from the jitter of the optical pulses with respect to the master clock of the accelerator.
5. Sensitivity and dynamic range of the single-shot THz-TDS
In order to evaluate the sensitivity (i.e., the smallest detectable electric field) quantitatively, an efficient way consists of examining the noise in absence of THz signal (Fig. 4). The analysis process is exactly the same than for the previous TDS signals. A $5$ THz low-pass filtering (i.e., slighty exceeding the signal’s bandwidth) has been applied. It is worth mentioning that the noise level is not stationary, due to the variation of the laser power with time (see Fig. 2(a), dashed line). In this setup, the noise-equivalent phase-shift $\Delta \phi _\text {MRC}(t)$ is less than 4.5 mrad over a 15 ps window. Using Eq. (5), with $r_{41}=1.5$ pm/V and $n_0 = 3.38$ [45,52], this corresponds to a sensitivity below $0.4$ MV/m (inside the crystal) for the present 100 $\mu$m-thick Gallium Arsenide crystal (note that this estimation is made assuming $r_{41}$ is frequency-independent).
Fig. 4. Measured sensitivity and dynamic range. (a) Sensitivity, defined as the input noise (standard deviation) in the absence of THz signal. The left vertical axis represents the noise-equivalent phase shift in the electro-optic crystal. The right vertical axis is the noise-equivalent electric field inside the crystal. The noise is computed over a $5$ THz bandwidth. (b) Visualization of the dynamic range in spectral domain: normalized spectra with (red) and without (blue) terahertz.
An other figure of merit of the system is the dynamic range [53]. For that purpose, we compare the measured normalized spectra with and without THz (Fig. 4(b)). The dynamic range of our single-shot setup is of the order of $25$ dB.
6. Discussion: foreseen constraints on single-shot TDS designs at 1550 nm wavelength
It is important to note that several other options are possible for single-shot spectrometers in general, and are worth to be tested also at the 1550 nm wavelength. However, in contrast to other near-infrared wavelengths,) performing TDS at 1550 nm presents specific constraints, because of the much lower pixel number available in state-of-art mid-infrared cameras. This constraint motivated us to use the spectral encoding method, together with DEOS, precisely because it optimizes the number of pixels required per time data (three pixels per time sample), and also because it requires only a low-cost line photodetector array.
In contrast, the moderate resolution of state-of-art 1550 nm cameras may represents an additional challenge for other methods, that are based on transverse [34–37] or angular [37,38] encoding (which require more expensive two-dimensional cameras). This challenge may also affect spectral interferometry-based TDS [54] as these methods inherently requires to resolve fine fringes throughout the recorded optical spectrum. However dedicated tests will be necessary in order to obtain fair and precise conclusions on the pros and cons of the different variants.
Finally, another interesting option for the readout consists of using the so-called stretch technique [55]. This method basically uses a single photodetector (instead of a camera) for the readout, and is capable of TDS at high repetition rates (above the MHz range) [28,32,40]. We can foresee that this 1550 nm TDS option, optionally associated with the DEOS technique, will be a particularly viable strategy for single-shot TDS at high repetition rates.
7. Conclusion
We show that a single-shot Time-Domain Spectrometer can be efficiently operated using a chirped nanojoule 1550 nm probe, together with the recently-developed bandwidth-enhancement known as Diversity Electro-Optic Sampling (DEOS). Such single-shot measurements using the 1550 nm wavelength are expected to be important for the numerous light source facilities that naturally use networks of synchronization systems, that are based on a 1550 nm femtosecond lasers. The single-shot capability allows terahertz spectra to be recorded in situations for which classical methods (such as Fourier-transform spectroscopy or classical TDS) would require tens of minutes or hours of acquisition. Concerning the system’s performance, it is important to note that the dynamic range ($25$ dB) and sensitivity ($2.8$ mrad or $0.2$ MV/m) are given for a single-shot. In classical spectroscopy situations, where averaging can be made, the final values will be straightforwardly improved (by a factor $\sqrt {N}$ for $N$ shots). For instance, in the case of TeraFERMI, which operates at 50 Hz, an improvement by factor 10 in sensitivity is expected for 2 seconds of acquisition only.
Funding
CNRS Momentum 2018 (METEOR); LABEX CEMPI (ANR-11-LABX- 0007); Ministère de l'Enseignement supérieur, de la Recherche et de l'Innovation, Conseil Régional Hauts-de-France, European Regional Development Fund (CPER Photonics for Society P4S); Consiglio Nazionale delle Ricerche-Fondazione Istituto Oncologico del Mediterraneo.
Acknowledgments
This work was supported by the CNRS Momentum METEOR, the LABEX CEMPI (ANR-11-LABX-0007) and Ministry of Higher Education and Research, Hauts de France council and European Regional Development Fund (Contrat de Projets Etat-Region CPER Photonics for Society P4S). We thank CNR-IOM for the use of the MENLO C-Fiber780 laser.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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