1. Introduction

The use of terahertz (THz) radiation in scientific and industrial applications has been continuously growing over the last twenty years [1]. On the one hand, THz pulses shorter than 100 fs (i.e., pulses with a bandwidth wider than 10 THz) are desired to investigate optical properties and fingerprints of materials in a wide frequency range [2,3], as well as to monitor dynamics in condensed-matter systems via ultrafast 2D spectroscopy [4] with high temporal resolution. On the other hand, high THz electric fields (>100 kV/cm) are required to enable nonlinear investigations, including, e.g., the modulation of absorption in semiconductors [5] and the coherent control of molecular orientations, rotations, and spin waves [6]. Finally, the possibility of achieving high average powers, through high repetition rates, leads to an improved signal-to-noise ratio in THz measurements. Such broadband and intense THz pulses can be obtained via, e.g., optical rectification (OR) in organic crystals [7] and two-color plasma sources [8]. The advantage of using plasma for THz generation relies on the fact that, unlike bulk nonlinear crystals, gases do not suffer from damage thresholds and are continuously renewable, thus they can be pumped at extremely high intensities [9]. Peak electric fields higher than MV/cm can therefore be generated, proportionally to the available laser pulse intensity [10]. Detection of such extreme time transients can be performed via the so-called air-biased coherent detection (ABCD) technique [11]. Due to the very low dispersion of gases, their use as THz emitter and detector allows the generated THz bandwidth to be practically limited only by the laser pulse duration [11]. To effectively generate broadband THz radiation via two-color plasma, pulse energies greater than 100 µJ and durations shorter than 100 fs are required. In addition, laser wavelengths longer than 1 µm can strongly boost THz emission [8]. In recent years, Yb laser technology has been surpassing the well-established Ti:Sapphire technology in terms of efficiency and average output power. This is mainly due to (i) the availability of efficient high-power diodes to pump Yb transitions, (ii) the small quantum defect (<10%) of Yb-doped materials resulting in a lower heat deposition, and (iii) the possibility of engineering the surface-to-volume ratio in thin-disks-, fibers- or slab-based architectures, which significantly improves heat removal [12]. In particular, commercial amplified bulk laser systems can nowadays achieve mJ-level pulse energy at kHz repetition rate (W-level average power) while the emerging thin-disk and fiber technology can deliver mJ-level pulses at the MHz repetition rate (kW-level average power). Despite this impressive power upscaling, such systems are still limited to hundreds of fs (at best) pulse durations, due to the limited gain bandwidth and gain narrowing effects [13]. Post-pulse compression techniques can bring the merits of Yb lasers into the few-cycle regime, which is desirable in various ultrafast applications. In a pioneering paper [14], 4-fold compression via self-phase modulation (SPM)- induced broadening in an Ar-filled hollow-core fiber (HCF), followed by compression with a chirped mirror pair [15], was used to obtain ultra-wide THz bandwidth with Ti:Sapphire systems, yet starting from pulses that were already extremely short (few 10s of fs). On the other hand, sub-microjoule pulses from a Yb system coupled to an Ar-filled kagomé-type photonic crystal fiber allowed to achieve THz pulses extending up to 6 THz via OR [16]. We have recently shown that ultrashort pulses, potentially down to the single-cycle level, and compression factors greater than 30 can be easily achieved starting from energetic, hundreds of fs-long pulses emitted by commercially-available Yb amplified laser systems [17]. This was obtained by moderately driving SPM in HCFs over an extended propagation distance, to obtain extremely broadened and well-behaved spectra that can be straightforwardly compressed. In this way, high compression factors, high transmission, and high beam quality can be achieved. In addition, HCFs can withstand average powers higher than 100 W [18] and high pulse energies [19]. These advantages make HCFs, in combination with Yb lasers, an ideal tool for the generation of high-average-power, high-field and extremely broadband THz radiation via two-color-excited air plasma. In this work, as a proof-of-concept, we demonstrate extremely broadband THz generation (up to 60 THz), with peak electric fields higher than 50 kV/cm, starting from 170-fs-long Yb laser pulses (∼2.6 THz of bandwidth full-width at half maximum - FWHM). Our approach opens a path for the next generation of table-top THz time-domain setups combining high THz average powers (up to the W-level) and broadband operation, which can be a simpler alternative to THz sources relying on large facilities such as synchrotrons [20] or free-electron lasers [21].

2. Experimental results

In our investigation, we used 170-fs-long laser pulses centered at 1030 nm with energy of 0.94 mJ and repetition rate of 6 kHz (6 W of average power), emitted by a commercial Yb:KGW regenerative amplifier (Pharos, Light Conversion). We focused the pump pulses into a 1.6-m-long HCF (500 µm of inner diameter - few-cycle Inc.) through an input 1-mm-thick fused silica window, anti-reflection coated at 1030 nm, while the output window was left uncoated not to introduce an uncontrolled spectral phase (Fig. 1). Then, Ar gas at the static pressure of 2.8 bar was introduced into the HCF to provide the required third-order nonlinearity (Kerr) and broaden the pulse spectrum, mostly via SPM. The output beam was collimated with an Al-coated mirror (f = 1 m) and compressed by four bounces on broadband chirped mirrors (PC1611, UltraFast Innovations. High-reflectivity between 800 nm and 1200 nm, providing -150 fs² at each bounce, for a total group delay dispersion GDD of -600 fs²).

 

Fig. 1. Setup configuration. HCF – hollow-core fiber; BS – 90:10 beam splitter; OPM1 – off-axis parabolic mirror f = 4”; OPM2, OPM3, and OPM4 f = 3”; OPM5 f = 2”; F1 – long-pass filter; HV – high voltage electrodes; F2 – short-pass filter for 515 nm; PMT – photomultiplier tube.

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The spectrum of the compressed pulses was recorded (Fig. 2(a)) with two real-time spectrometers (Avantes UV-NIR Duo), while their temporal duration was retrieved via a second-harmonic autocorrelator employing a 50-µm-thick β-BaB₂O₄ (β-BBO) crystal (Fig. 2(b)). The spectrum was broadened along the propagation in the HCF by SPM between approximately 900 nm and 1100 nm, with an overall transmission efficiency exceeding 70%. After the chirped mirrors, the pump pulses were compressed down to ∼18 fs FWHM (compression factor of about 9) which is close to the Fourier limit of ∼15 fs calculated by taking the FFT of the output spectrum (orange line) illustrated in Fig. 2(a). Only a small pedestal remained after compression (Fig. 2(b)), as the compensation of higher-orders dispersion terms was not optimal. The output spectrum is in very good agreement with numerical simulations (Fig. 2(c)) based on the model reported in [17]. The compressed pulses were then sent into a THz time-domain setup, as shown in Fig. 1. The input beam (waist of 2.4 mm at 1/e² of the intensity) was separated by a 90:10 beam-splitter into a pump and a probe beam. The pump beam, which accounted for about 471 µJ of energy (≈ 26 GW of peak power), was focused through a 100-µm-thick β-BBO crystal by means of an off-axis parabolic mirror (OPM1) with a focal length of 4 inches. The thickness of the BBO crystal was chosen not to significantly alter the pump pulse duration (total crystal GDD of about 4.2 fs²). The fundamental and second harmonic waves were mixed together at the focal position in order to generate a two-color plasma filament (length of about 3 mm). A second mirror (OPM2) with both focal length and diameter of 2 inches collimated the emitted ultra-broadband THz radiation, while a 1-mm-thick filter (Edmund long-pass 1.65 µm, multilayer dielectric on silicon substrate) was used to reflect the residual pump and second harmonic light. An appropriate selection of this filter for Yb-based systems becomes particularly critical since silicon plates, typically employed in setups utilizing Ti:Sapphire lasers, are not suitable to properly block light at wavelengths longer than 1000 nm (silicon bandgap at 1.14 eV ≅ 1087 nm). Moreover, high-reflective coatings are a stringent requirement for high-power operation, due to the fact that even a small fraction of optical absorption can thermally fracture (or melt) the filter. A set of OPMs of focal lengths equal to 3, 3, and 2 inches, respectively, directed the radiation towards the detection stage (see Fig. 1). Coherent detection of the ultra-broadband THz pulses was obtained via the ABCD technique [11], by focusing together the THz and the probe pulses (73 µJ of energy) within a 1-mm-wide gap between two electrodes and applying a square bipolar voltage (up to 1.7 kV peak-to-peak) synchronized at half of the repetition rate of the laser.

 

Fig. 2. (a) Experimental input (blue) and output (orange) pulse spectra. (b) Autocorrelation trace corresponding to the compressed spectrum, showing the ∼18-fs-long pulse (assuming the deconvolution factor for a Gaussian pulse of 1.41). (c) Simulated spectrum (blue) and spectral phase (orange) at the output of the HCF.

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The THz waveform was acquired in a nitrogen-purged environment by recording the THz-field-induced second-harmonic light with a photomultiplier tube (PMM01, Thorlabs) as a function of the relative delay between the THz and probe pulses (with a step of 5 fs). As illustrated in Fig. 3(a), the THz waveform shows a nearly single-cycle behavior with sub-50 fs temporal features. A peak THz electric field of 55 kV/cm was estimated by using the method described in [22]. A maximum dynamic range, defined as in [23], of 200 was measured at the maximum bias voltage of 1.7 kV. The corresponding spectrum, numerically calculated via FFT, extends up to 60 THz (at the noise floor in logarithmic scale) (Fig. 3(b)), thus effectively exploiting the frequency content of the compressed pump pulses (∼1/18 fs = 55.6 THz). The oscillation in time on the trailing edge of the THz pulse, and the corresponding absorption dips in the spectrum, are due to the long-pass filter employed to block the residual pump/second-harmonic light.

 

Fig. 3. (a) E-field waveform of the THz pulses retrieved via ABCD method. Inset shows the intensity envelope featuring a main peak with time duration of 33 fs FWHM. (b) Corresponding E-field spectrum calculated via FFT.

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To verify this, we employed two different Fourier-transform spectrometers (FTSs), in order to cover the entire THz emission band: a custom-made THz-FTS for the 2–12 THz region (Blue Sky Spectroscopy) and an IR-FTS (Bruker) for the region above 12 THz. As it is possible to observe in Fig. 4, the filter transmission below 30 THz, where most of the THz pulse energy is located, is below 50%. Moreover, the two absorption dips appearing in the THz spectrum at around 18 and 30 THz (Fig. 3(b)) are also clearly visible in the FTS spectral transmission of the filter.

 

Fig. 4. Transmission of the filter employed in our investigation, as obtained by combining the measurements of the two FTSs.

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The first sharp feature (red shaded area in Fig. 3(b) and Fig. 4) is related to the two-phonon absorption of the silicon substrate [24], while the second one (green shaded area in Fig. 3(b) and Fig. 4) is likely due to the THz response of the (proprietary) dielectric coating of the filter. This clearly underlines the importance for this type of THz source (and especially for high power applications) of a properly designed filter. In particular, this component has to ideally feature high and flat transmission in the range 1–100 THz, as well as high reflectivity within the 800–1200 nm band. We also investigated the dependence of the THz emission on the input pump pulse energy. Figure 5(a) shows spectra (in log scale) recorded as the pump power was varied from 100 to 471 µJ, while Fig. 5(b) illustrates the peak electric field as a function of the input pulse energy. As it is possible to see from Fig. 5(b), the peak electric field shows a (quasi) quadratic dependence on the input pulse energy (${E_{THz}} \propto \; E_p^{2.15}$ through a least square fitting), which is consistent with the scaling reported in [25]. It is worth underlining that, for high pulse peak intensities (target of the proposed technique), this scaling is expected to be modified, as properly described by a well-established model considering as the THz source a plasma current generated by the asymmetric two-color field (see, for example, [26]). Finally, we measured the THz pulse energy by means of a pyroelectric detector (THZ-I-BNC, Gentec-EO). At the maximum incident pump energy of about 471 µJ, the generated THz pulses reached an energy value of about 35 nJ per pulse (average power of 210 µW at 6 kHz), corresponding to an energy conversion efficiency of 7.4 × 10⁻⁵.

 

Fig. 5. (a) Spectra and (b) peak electric fields recorded by varying the input pulse energy from 100 to 471 µJ.

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3. Conclusion

Table-top THz time-domain systems are evolving in the direction of broad bandwidths, intense field strengths, and stable performance, but it has been challenging to pursue all these requirements simultaneously. In this work we have introduced, as a proof-of-principle, a Yb laser-based THz-time-domain system providing an extremely broad bandwidth (up to 60 THz) with peak electric fields higher than 50 kV/cm, by employing an HCF pulse-compression stage and a two-color plasma generation scheme. Ultra-broadband generation is achieved thanks to the HCF-based pulse compression, which converts 170-fs-long pulses emitted from an Yb laser amplifier into 18-fs-long pulses (∼9-fold compression). Our method opens the route to the exploitation of the many advantages of Yb laser technology (including the availability of very high average powers) for ultra-broadband THz generation. For high-repetition-rate (MHz) Yb systems, high frequency switching voltages would be required to perform ABCD detection. In such cases, a promising alternative is represented by a recently developed THz detection technique, named solid-state-biased coherent detection (SSBCD) [27]. Indeed, SSBCD can be biased with only ∼10 V [22] and can thus easily operate at MHz switching frequencies, showing a great potential to be combined with the generation method proposed herein for the development of the next-generation of ultra-broadband, high-field, high-repetition-rate THz time-domain systems.