1. Introduction

Terahertz (THz, 1 THz $={10}^{12}$ Hz, corresponding to a wavelength of 300 μm in vacuum) technology has grown dramatically, especially thanks to the development of novel ultrafast THz sources [1]. The potential of such radiation for scientific research and industrial applications has been demonstrated through a plethora of studies regarding e.g., time-domain spectroscopy, molecular dynamics, imaging, telecommunications, chemical sensing, and quality monitoring in manufacturing [2–7]. In this context, intense THz sources can play a key role in providing sufficient signal-to-noise ratio for advanced 2D THz imaging [8,9] as well as real-time THz near-field microscopy [10], and have also been exploited for the recent implementation of ultrafast THz scanning tunnelling microscopy [11]. Furthermore, high THz electric fields of the order of hundreds of kV/cm are necessary to explore the nonlinear regime of THz radiation-matter interactions, as recently shown in several matter systems, including semiconductors [12], graphene [13], topological insulators [14], superconductors [15] and multiferroics [16].

One of the most commonly used mechanism to generate few-cycle THz pulses is optical rectification (OR) in nonlinear crystals [2]. The phase matching condition at 800 nm (the emission wavelength of Ti:Sapphire lasers, which are the most commonly used sources for THz pulse generation) can be satisfied in zinc telluride (ZnTe) [17]. However, the peak electric field of the THz pulses generated in such inorganic crystal reaches a maximum value of the order of ~10 kV/cm when standard amplified Ti:Sapphire lasers with energy per pulse of about 1 mJ are used, due to an intrinsically low conversion efficiency (reported as 3 × 10⁻⁵ in [18].). Although higher conversion efficiencies can be obtained exploiting difference frequency generation [19,20], this approach leads to a narrowband emission that is not appropriate for several of the applications listed above, which require few-cycle pulses. To achieve broadband emission and high peak electric fields, of the order of hundreds of kV/cm up to MV/cm, OR in lithium niobate (LiNbO₃) crystals can be employed [21]. However, such highly nonlinear crystal requires a complex non-collinear pumping scheme, which exploits the pump pulse front tilt to ensure phase matching [22]. Recently, high-energy THz pulses have also been obtained by pumping a ZnTe crystal at 1.7 µm, beyond the three-photon absorption edge. Yet, the phase matching condition was again satisfied through the tilt of the pump pulse front imposed by a grating structure directly fabricated on the crystal surface [23].

As a promising alternative for efficient intense THz generation, organic crystals have been proposed [24–27], since they feature a higher nonlinear response than inorganic crystals (e.g., in DAST the nonlinear optical coefficient is d₁₁ = 290 pm/V at 1.5 μm, while the electro-optic coefficient is r₁₁ = 77 pm/V at 0.8 µm and r₁₁ = 47 pm/V at 1.5 µm [24]). These organic emitters can be used to generate high THz peak electric fields (up to MV/cm [25]) via OR in a collinear geometry. Nevertheless, the optimal wavelength to fulfill the phase matching condition typically lies in the range 1.3-1.5 µm, usually requiring a further optical parametric amplifier to be coupled to the femtosecond laser system as a pumping source. Recently, the new organic crystal HMQ-TMS (2-(4-hydroxy-3-methoxystyryl)-1-methilquinolinium-2,4,6-trimethylbenzenesulfonate) has been introduced for THz applications [28–31]. Compared to other organic nonlinear optical crystals, HMQ-TMS shows better environmental stability and many advantageous crystal characteristics, providing the possibility of an easy control of the crystal thickness and aperture size [29]. Furthermore, the optimal molecular packing structure of this crystal maximizes its electro-optic response, resulting in a diagonal component of the effective hyperpolarizability tensor (${\beta }_{333}^{eff}$ = 185 × 10⁻³⁰ esu) that is comparable to the state-of-the-art organic crystals (such as OH1, DAST, and HMQ-T [29]). Finally, since HMQ-TMS possesses a large OR phase-matching band, it can also be pumped at wavelengths shorter than those required by, e.g., DAST and OH1 [28], yet keeping a high conversion efficiency.

In this work, we show how ultrafast ytterbium (Yb) laser technology can be effectively used to pump an HMQ-TMS organic crystal to generate few-cycle high-peak-electric-field THz pulses in a simple collinear scheme, an advantageous geometry for many practical implementations. Indeed, fully diode-pumped Yb-based laser systems, emitting at the central wavelength of 1030 nm, are becoming an increasingly important technology in a wide range of industrial and scientific applications, surpassing Ti:Sapphire systems in terms of compactness, lower cost, thermal stability, higher efficiency, and higher output powers [32]. To date, Yb-based lasers are commonly used in combination with GaP crystals for THz generation in a collinear geometry [33]. However, the maximum peak electric field is in this case limited to few kV/cm. While LiNbO₃ crystals are also available at 1030 nm for more intense THz generation, they still require a complex pulse front tilt pumping scheme [34–37]. Here, we demonstrate that an HMQ-TMS crystal pumped by an amplified solid-state Yb-doped potassium-gadolinium tungstate (Yb:KGW) laser offers a simple solution for the generation of few-cycle intense THz pulses with peak electric fields of hundreds of kV/cm. In addition, in a proof-of-principle experiment, we show that this source can be straightforwardly employed to investigate THz nonlinear phenomena in condensed matter.

2. Experimental results

In our study, an HMQ-TMS crystal with a thickness of 630 µm was used for the generation of THz pulses. For the THz electric field characterization, we exploited a standard time-domain spectroscopy setup in a nitrogen-purged environment, as shown in Fig. 1. We employed 170-fs-long pulses from an Yb:KGW amplified laser (Pharos PH1-SP-1mJ, Light Conversion), centered at λ₀ = 1030 nm, with a maximum pulse energy of 1 mJ and a repetition rate set at 500 Hz (controlled by the internal pulse picker, to reduce the average output power and the corresponding thermal load on the crystal). The residual pump radiation after the HMQ-TMS crystal was blocked by means of a 100-µm-thick black polyethylene sheet. The generated THz radiation was collected and finally focused onto a 300-µm-thick <110> GaP crystal by means of a set of gold off-axis parabolic mirrors (OPMs). We acquired the time trace of the THz electric field through the standard electro-optical sampling (EOS) technique [38], exploiting the GaP crystal as the detector, with a delay step of 15 fs. Since the laser output beam waist (4.5 mm in diameter at 1/e² of the intensity) is larger than the clear aperture of the HMQ-TMS crystal (diameter of 3 mm), a pinhole was used to limit the pump beam size to the crystal aperture. We found this configuration more effective than the use of an optical telescope to reduce the pump beam size, since long term exposure of the organic crystal to a pump beam with spot size < 3 mm eventually resulted in local damage and a subsequent reduction of the conversion efficiency.

 

Fig. 1 Schematic of the time-domain spectroscopy setup used for the characterization of the THz pulses emitted by the HMQ-TMS crystal. BS – beam splitter 80:20, OPM – 90-deg off-axis parabolic mirrors (focal length of OPM1: 0.5”, OPM2: 6”, OPM3 and OPM4: 3”, OPM5: 2”), QWP – quarter wave plate, WP – Wollaston prism, BPD – balanced photodiodes. Detection is performed via EOS in a 300-µm-thick <110> GaP crystal.

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As it is shown in Fig. 2, this source provides few-cycle THz pulses (Fig. 2(a)) with an emission spectrum extending beyond 3 THz (Fig. 2(b)). The dip located at 1.7 THz in the frequency spectrum is associated with a phonon mode of the HMQ-TMS crystal [28]. In the plane-wave non-depleted pump approximation and ignoring cascaded nonlinear effects, it is also possible to theoretically evaluate the THz spectrum retrieved via EOS in the GaP crystal, following a procedure similar to the one described in [24]. In these calculations, we took into account: the pulse duration of both the pump and probe pulses; the refractive index and absorption coefficient of HMQ-TMS at both optical and THz frequencies [28,31]; the GaP detector response function, considering its THz [39] and optical [40] characteristics. Note that the optimal phase matching wavelength for the electro-optic detection of THz radiation with a GaP crystal nearly coincides with the used probe wavelength (1030 nm). Therefore, a 300-µm-thick detection crystal does not considerably modify the spectrum up to about 5 THz. As it is possible to observe in Fig. 2(b), the experimental and theoretical results show a very good agreement, especially in terms of the overall emission band and the phonon dip position.

 

Fig. 2 (a) THz electric field waveform emitted by the 630-µm-thick HMQ-TMS crystal and retrieved via EOS using a GaP detection crystal. (b) Measured (solid) and theoretical (dashed) THz emission amplitude spectra, as retrieved via EOS.

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We then quantitatively estimated the strength of the THz peak electric field retrieved through EOS. For small modulations, the differential intensity measured by the balanced photodiodes (see Fig. 1) is directly proportional to the THz field strength, as shown by the following relation [41]:

 

Fig. 3 Peak electric field (a) and energy (b) of the THz pulses generated by the 630-µm-thick HMQ-TMS crystal as a function of the incident pump fluence. The inset of Fig. 3(a) shows the normalized absolute values of the measured THz field (blue) and of a waveform obtained by deconvoluting the measured trace with a Gaussian optical probe of 170 fs - FWHM (red). The formulas reported in both figures represent the best fit of the experimental data (dashed lines).

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As it is possible to observe, the maximum THz peak electric field that we measured was around 200 kV/cm. Note that the temporal duration of our optical probe pulse (FWHM of 170 fs) is relatively long and thus does not allow to fully resolve the amplitude of the oscillations of the generated THz electric field. To illustrate this, in the inset of Fig. 3(a) we show the absolute value of the measured electric field trace E_meas (blue) compared to the one of a THz waveform E_dec (red) obtained by deconvoluting the measured trace with a Gaussian optical probe G of 170 fs (FWHM), according to the formula: E_meas = E_dec * G. As it is evident from this evaluation, the effective THz peak value can be up to 1.8 times higher than the one extracted from our EOS measurement, which corresponds to a maximum peak electric field of about 350 kV/cm at the detection crystal position. We also measured the THz pulse energy by means of a pyroelectric detector (THZ-I-BNC from Gentec-EO). The generated THz energy is presented in Fig. 3(b), showing a super-linear dependence on the pump pulse fluence. At the maximum incident pump fluence of about 5.9 mJ/cm² (well below the damage threshold previously reported for the HMQ-TMS crystal, i.e. > 20 mJ/cm² [28]), the generated THz pulses reach an energy value of about 1.1 μJ per pulse (average power of 550 µW at 500 Hz), corresponding to a significant energy conversion efficiency of 0.26% (quantum efficiency of 56% at the THz central frequency of 1.35 THz). It is worth mentioning that the investigated THz generation process can be straightforwardly scaled up, in terms of both THz energy and peak electric field, through the use of larger aperture crystals and higher pump energies.

In order to demonstrate the potential of this source for nonlinear THz investigations, we performed an open-aperture Z-scan experiment on a 500-nm-thick n-doped InGaAs epilayer (carrier density n ~2 $\times$ 10¹⁸ cm⁻³) deposited on an InP substrate. Indeed, Z-scan is a very common nonlinear optical characterization technique that enables, for instance, the determination of the Kerr nonlinearity as well as the nonlinear absorption coefficients of a material from intensity-dependent transmission changes [42]. In our measurement, we recorded the THz energy transmitted through the sample while it was scanned along the propagation direction z across the focused THz beam (see Fig. 4(a)). For the selected sample, the strong THz field can induce an intervalley transition (from the Γ to the L valley) of the carriers within the InGaAs conduction band. The carrier mobility is lower in the satellite L valley, thus resulting in a lower conductivity of the film (i.e., a higher THz transmission) [43]. For each point of the scan along the z direction, we extracted the normalized transmission as the detected transmitted energy divided by the value measured at low THz intensity (i.e., away from the THz focus, at one extremity of the scanned range). The results of this measurement are shown in Fig. 4(b) (red circles). We observed a significant saturation of the THz absorption, with a maximum transmission increase of about 2.2 times at the focus. This transmission change is related with the change of the THz beam size (and the subsequent change in its intensity) along the z direction between OPM3 and OPM4. Such size was estimated by performing knife-edge measurements on the THz beam at different z positions, by monitoring the transmitted energy with the pyroelectric detector. The results of this characterization are also shown in Fig. 4(b) (blue squares). In this way, we retrieved a THz beam waist of 940 µm (radius at 1/e² of the intensity) at the focal position of OPM3. In a previous Z-scan experiment performed on the same sample [43] (using THz pulses generated via OR in a large-aperture ZnTe crystal pumped by 30 mJ, 30-fs-long optical pulses at 800 nm), a similar increase in THz transmission was found for a peak electric field of around 200 kV/cm. This value is in fair agreement with our EOS measurement. Indeed, considering the longer focal length of OPM3 (f = 3”) in comparison to OPM5 (f = 2”), the THz beam waist at the Z-scan sample position is 1.5 larger than the one at the GaP detection crystal (a value also confirmed by an additional knife-edge measurement, not shown). Thus, the THz peak electric field that we can estimate from our EOS characterization at the Z-scan sample position is about 230 kV/cm (taking into account the deconvolution factor mentioned above). A direct quantitative comparison with the experiment reported in [43] is however difficult, due to differences in the temporal and spectral shapes of the THz pulses employed in the two cases, which can also affect the nonlinear response of the doped InGaAs sample. That said, this characterization further confirms the significant electric field strength of the emitted THz pulses and shows how they can be effectively employed for nonlinear THz studies.

 

Fig. 4 (a) Schematic of the setup for the Z-scan measurement. (b) Normalized transmission of the InGaAs epilayer (red points) and THz beam size values (blue points) measured as a function of the z position (z = 0 corresponds to the THz focal position).

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3. Conclusion

Yb lasers surely represent the new frontier of ultrafast laser technology [32], but their exploitation for the efficient generation of THz radiation is still limited to complex pumping schemes, due to the fact that the most common, highly-nonlinear OR crystals do not offer a good phase-matching at 1030 nm. In this work, we have shown that the recently-developed organic crystal HMQ-TMS can be effectively employed for the collinear generation of high-peak-electric-field THz pulses using an amplified Yb laser as the optical pump. We have obtained THz peak electric fields greater than 200 kV/cm, a spectral emission extending beyond 3 THz, and a THz energy per pulse of 1.1 µJ, which corresponds to a significant energy conversion efficiency of 0.26%. We have also employed this THz source in a proof-of-principle nonlinear Z-scan experiment, inducing a significant THz absorption bleaching in an n-doped InGaAs thin film, thus showing the potential of this novel configuration for the exploration of THz nonlinear effects in condensed matter.