1. Introduction

Terahertz (THz) radiation is situated between the microwave and infrared frequency ranges and has been difficult to generate and detect until relatively recently, resulting in what is often called the "THz gap". One important class of THz radiation sources involves the use of mode-locked lasers to trigger currents on time scales of a picosecond or faster. These time-dependent currents create broadband THz-frequency pulses that are phase stable with respect to the laser pulse that triggers the process. This inherent phase stability can be exploited for so-called time-domain spectroscopy (TDS), where both the amplitude and phase of the THz-frequency light can be simultaneously measured. Various applications of THz TDS have been demonstrated, most notably in physics, material science, chemistry and biology [1–3].

A TDS measurement requires a method for measuring the electric field of light with time resolution sufficient to resolve sub-picosecond changes. Commonly applied techniques for such measurements include electro-optic sampling (EOS), measuring the transient current generated in a photoconductive antenna and monitoring second harmonic generation in a gas under electrical bias (air-biased coherent detection, or ABCD) [2–4]. Both EOS and photoconductive antennas are mainly suitable to detect lower THz frequencies since their bandwidth is ultimately limited by phonon absorption and dispersion in the material [5–7]. In the case of EOS, the commonly used nonlinear crystals ZnTe and GaP have an upper detection limit at $\sim$3.5 THz and $\sim$8 THz, respectively. This limitation can partially be relieved by resorting to thin crystals, which however leads to early Fabry-Pérot reflections that complicate the analysis of the data outside a narrow time window. Moreover, as the detection sensitivity scales linearly with the crystal thickness, thin crystals require large THz field strengths, limiting their use with high repetition rate laser systems where the peak electric field strength is typically low. The ABCD technique relies on the electric field induced second harmonic generation (EFISH) in gases and is therefore not affected by either phonon absorption or material dispersion. Fabry-Pérot reflections are also not a concern since the detection takes place in a gas. The EFISH process is a third order nonlinear interaction involving an optical probe pulse and the THz pulse which are mixed within an air region biased by an external bias field. This results in the generation of a new beam with a frequency at the second harmonic of the probe beam, the intensity of which is modulated by the THz field amplitude. The drawback of the ABCD technique is that it requires bias voltages on the order of kV and probe pulse energies on the order of tens of $\mathrm {\mu }$J [8,9].

Improvements in both sensitivity and bandwidth of coherent THz pulse detection is still a topic of ongoing research [10–13]. Recently, a new detection technique called solid-state-biased coherent detection (SSBCD) has been demonstrated. The SSBCD technique is similar to ABCD but replaces the gas with a thin layer of plasma-enhanced chemical vapor deposition (PECVD) grown silicon nitride (SiN). The SiN fills the gap in a 1 $\mathrm {\mu }$m wide gold slit [14–16]. By taking advantage of the high electric fields established across the micro-sized slit along with a 4-order of magnitude larger third order nonlinearity $\chi ^{(3)}$ of SiN compared to gases, the SSBCD technique has been proven operable at probe pulse energies of just a few tens of nJ, under a bias field of a few tens of volts. Additionally, the sub-wavelength size of the slit compared to THz wavelengths induces a non-resonant 6-fold field enhancement of the THz electric field in the gap, allowing for an augmented sensitivity across the entire THz frequency range. As with ABCD, the bandwidth is limited by the probe pulse duration and it is not affected by Fabry-Pérot reflections.

In the generation of coherent THz pulses similar bandwidth limitations arise as in the detection. The most commonly employed sources are based on optical rectification, photoconductive switches or two-color mixing in a plasma. While optical rectification in nonlinear crystals and photoconductive switches typically suffer from the same phonon absorptions that limit the detection [2–4], plasma sources generate THz pulses which can cover and even go beyond the 0.1-10 THz frequency range, but they require >100 $\mathrm {\mu }$J energy ultrashort optical pump pulses [17–19]. In recent years, a novel approach has emerged in the form of spintronic emitters, capable of covering the 0.1-30 THz frequency range (retrieved after correction for the EOS crystal response) when used with pump pulse durations of 10 fs [20–25]. In such an emitter, ultrashort pulses create an out-of-plane spin-polarized current in a ferromagnetic layer, which then propagates into a nonferromagnetic layer. Through the inverse spin-Hall effect this current is converted into an in-plane charge current, leading to the emission of a THz pulse. The performance of the spintronic emitter is improved further by employing a trilayer structure where a nonmagnetic layer sits between two ferromagnetic layers [20,21]. The spectral bandwidth of a THz pulse generated in a spintronic emitter is only dependent on the pump pulse duration, with a shorter pump pulse duration resulting in a broadening of the generated THz spectrum [24,25].

In high field THz setups, the combination of a two-color plasma source with the ABCD technique has been demonstrated to cover the 0.1-10 THz range. Such a setup can be further simplified through the use of SSBCD [14–16]. While the SSBCD technique has very successfully been used in high field setups driven by a plasma source at a repetition rate of 1 kHz [14–16], its suitability for setups with high repetition rates (>100 kHz) and low THz fields (<10 kV/cm) has not yet been demonstrated. In this work we examine the performance of an SSBCD device in a low THz field setup with a repetition rate of 250 kHz. We show that the combination of a spintronic emitter and the SSBCD method is a very promising approach to achieve a THz TDS setup covering the entire 0.1-10 THz region and we demonstrate use of the resulting TDS system to study the THz frequency optical properties of three different samples. We also discuss the installation and alignment procedure of the SSBCD device, which is significantly more challenging for low THz field setups.

2. Experimental methods

A schematic of the setup is shown in Fig. 1. The setup is based around the output of a high-repetition rate regenerative amplifier (250 KHz, 800 nm, 40 fs) with a maximum pulse energy of 6.2 $\mathrm {\mu }$J. The THz radiation was generated using a trilayer spintronic emitter: W(2  nm)/$\textrm {Co}_{\textrm {40}}\textrm {Fe}_{\textrm {40}}\textrm {B}_{\textrm {20}}$(1.8 nm)/Pt(2 nm), on 500 $\mathrm {\mu }$m of Sapphire. Previous work has shown that the absorption of high-energy 800 nm pulses with a duration of 40 fs by this layered structure generates broadband THz pulses with a spectrum covering 0.1 to 10 THz, as measured using EOS in a 10 $\mathrm {\mu }$m thick ZnTe crystal [23]. In our setup, we used polytetrafluoroethylene (PTFE) (thickness <100 $\mathrm {\mu }$m) to block the 800 nm residual pump pulse. The THz beam is focused first onto the sample position and then onto the detection position using off-axis parabolic mirrors. A peak THz amplitude of 4.5 kV/cm was measured at the detection position with EOS in a 300 $\mathrm {\mu }$m GaP crystal in a nitrogen-purged environment.

 

Fig. 1. Schematic of the THz TDS setup. An ultrafast laser pulse is divided into pump and probe beams by a 90:10 beamsplitter (BS). The pump (5.6 $\mathrm {\mu }$J) is focused onto a spintronic emitter (SE) to generate coherent THz radiation. The remaining 800 nm light is blocked by a polytetrafluoroethylene (PTFE) film. The THz beam is focused onto the sample position (where the different crystals presented in Section 3 are placed) and onto the detection using 90$^\circ$ off-axis parabolic mirrors. A short focal length lens (L1) is used to focus the probe beam onto the SSBCD device. A second harmonic (SH) beam is generated in the SSBCD device and detected in a photomultiplier tube (PMT). A bandpassfilter (BPF) rejects the residual 800 nm probe pulse. A data acquisition card (DAQ) acquires both the PMT signal and the AC waveform from the function generator. To use the setup with electro-optic sampling (EOS) in a 300 $\mathrm {\mu }$m thick GaP crystal, L1 is removed and a longer focal length lens is placed at the position marked L2.

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The SSBCD device was purchased from Ki3 Photonics [26]. It consists of three layers: a 500 $\mathrm {\mu }$m thick silica substrate; a 100 nm thick gold layer with a 1 $\mathrm {\mu }$m wide slit, where the interaction takes place, and which is filled with SiN; a 1 $\mathrm {\mu }$m thick SiN cover layer (Cr buffer layers were left out in this description). The design has been described in great detail by A. Tomasino et al. [14,15]. The nonlinear interaction between the THz, bias and probe fields in the SSBCD device generates an outgoing new beam, oscillating at the second harmonic of the probe field according to the EFISH process [14]. The total intensity $I_{\textrm {SH}}^{\textrm {total}}$ of the second harmonic of the probe beam is given by

The alignment of the SSBCD device depends critically on spatial overlap of the focal points of the probe and THz beams onto the 1 $\mathrm {\mu }$m wide slit of the device. Achieving spatial overlap for low THz field strengths only with the SSBCD device can be challenging and time-consuming, and a small misalignment can already lead to a complete disappearance of the THz interaction in the SSBCD device due to the low THz field. In order to circumvent this issue, we developed a robust alignment procedure. The THz and probe beams are initially aligned with EOS. In this configuration, the THz beam is focused by an off-axis parabolic mirror with a 2 inch effective focal length, and the probe beam is focused by a 600 mm focal length lens. The SSBCD device, however, requires a shorter focal length to be used for the probe beam (125 mm). We use a beam profiling camera, placed at the detection crystal position, to correct for any misalignment of the probe beam caused by changing to the shorter focal length lens. Following this procedure, we already start with an alignment where only very small optimization of the spatial overlap on the SSBCD device is necessary.

3. Results

A spectrum and the corresponding THz transient measured with the SSBCD device are shown in Fig. 2. A time-window (Tukey [28], $\alpha$ = 0.35) was used to smoothly bring the edges of the trace to zero before performing the Fourier transform. For a comparison, a spectrum obtained from the time transient generated by the spintronic emitter but measured using EOS in a 300 $\mathrm {\mu }$m thick GaP crystal is also shown in Fig. 2.

 

Fig. 2. Comparison of THz spectra generated by a spintronic emitter and measured with SSBCD and EOS (300 $\mathrm {\mu }$m GaP crystal). Both spectra are self-normalized. The SSBCD spectrum was acquired with 22 nJ probe pulses, $\pm$40 V bias voltage. The time-trace corresponding to the SSBCD spectrum is shown in the inset. The greyed out region around 6.1 THz indicates the PTFE absorption. The spectral intensity of the SSBCD spectrum drops to 10% at $\sim$5.5 THz and to 5% at $\sim$7 THz.

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To confirm the SH field dependencies predicted by the EFISH Eq. (2), namely quadratic scaling with probe pulse energy and linear scaling with bias voltage, we recorded THz transients using different probe pulse energies and bias voltages, as shown in Fig. 3. The probe pulse energy was varied from 8 nJ to 32 nJ while the bias voltage was varied from 25 V to 42 V. The error bars correspond to the standard deviation of the peak THz signal for an average of 10 measurements and an integration time of 0.5 s per time point. The data in Fig. 3 were fitted using two polynomial functions, $f_1(x) = ax^2$ (quadratic) and $f_2(x) = bx$ (linear). It is clear that the probe pulse energy measurements are better described by a quadratic function (Fig. 3(a)), whereas the bias energy measurements are better described by a linear function (Fig. 3(b)). This is as expected from Eq. (2): the induced modulation $\Delta I_{\textrm {SH}}^{\textrm {total}}$, which is linear in the THz electric field, scales quadratically with probe pulse energy $I_\omega$ ($a \propto 4 (\chi ^{(3)})^2 E_{\textrm {THz}}E_{\textrm {bias}}$) and linearly with bias voltage $E_{\textrm {bias}}$ ($b \propto 4 (\chi ^{(3)} I_\omega )^2 E_{\textrm {THz}}$). The fit parameters are discussed in detail in Supplement 1.

 

Fig. 3. Comparison of the measured peak THz induced modulation for (a) different probe pulse energies with constant 30  V bias voltage and (b) different bias voltages with constant 16 nJ probe pulse energy (black dots). The THz field incident onto the SSBCD detector was not changed between the two sets of data. The normalization is performed with respect to the largest THz induced modulation, which was obtained with 30 V bias voltage and 32 nJ probe pulse energy. Solid lines are fits to the quadratic function $f_1$ (red) and the linear function $f_2$ (blue) which are described in the main text. It is clear that (a) is better fitted by a quadratic function and (b) is better fitted by a linear function.

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To test the performance of the system we investigated the transmission of various crystals with well-known features in the 0.1-10 THz range [2,29,30]. The semiconductor compounds were placed at the sample position, indicated in Fig. 1. We investigated single-crystal samples of ZnTe (500 $\mathrm {\mu }$m thick), GaAs (625 $\mathrm {\mu }$m thick) and GaP (300 $\mathrm {\mu }$m thick) and the measured transmission spectra are shown in Fig. 4(a). A probe pulse energy of 16 nJ and $\pm$30 V bias voltage were used for ZnTe and GaP, while a probe pulse energy of 22 nJ and $\pm$40 V bias voltage were used for GaAs. The THz spectrum in the absence of the sample is used as a reference. The measurements are averaged over 20 runs with an integration time of 0.5 s per time point. The absorption coefficients $\alpha (\nu )$ can be directly extracted from the complex field transmission coefficient of the samples [2,3] and are shown in Fig. 4(b) alongside literature values [2,31,32]. The largest detectable absorption $\alpha _{\textrm {max}}(\nu )$ in the transmission measurements depends on the frequency dynamic range of the reference measurement, the sample thickness and the real part of the refractive index [33]. The largest detectable absorption coefficients $\alpha _{\textrm {max}}(\nu )$ for the investigated sample thicknesses reach 139 cm$^{-1}$ for ZnTe, 109 cm$^{-1}$ for GaAs and 231 cm$^{-1}$ for GaP at 1.45 THz, and are shown in detail in Supplement 1.

 

Fig. 4. THz TDS measurements of ZnTe (500 $\mathrm {\mu }$m), GaAs (625 $\mathrm {\mu }$m) and GaP (300 $\mathrm {\mu }$m). The area shaded in grey indicates the PTFE absorption around 6.1 THz. (a) Transmission amplitude $|\widetilde {E}_{\textrm {sample}}/ \widetilde {E}_{\textrm {reference}}|$. The area shaded in red indicates where the reference is below 7.5% of the peak value and the transmission is considered to be too close to the noise floor to be reliable. (b) Absorption coefficient $\alpha (\nu )$ obtained from the sample transmission. As a comparison, literature values [2,31,32] are included as dashed lines.

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4. Discussion

The spectrum shown in Fig. 2 exhibits frequency components as wide as 9 THz. Its bandwidth is therefore comparable to the one expected from a spintronic emitter pumped by an optical pulse of 40 fs duration [23,24]. More precisely, the spectral amplitude drops to 10% at $\sim$5.5 THz and to 5% at $\sim$7 THz, and exhibits tails up to $\sim$9 THz after which the amplitude drops below 2%, which corresponds to the noise floor. In contrast to the EOS detection, where the increasing phase-mismatch of GaP at higher frequencies [2] leads to a noticeable loss of sensitivity, we observe a flatter spectral response across the entire spectrum with the SSBCD technique. The sharp decrease around 6.1 THz can be attributed to absorption in PTFE due to a CF2 twisting mode [34]. This could be avoided by using a high resistivity silicon wafer instead of PTFE to separate the 800 nm residual pump pulse from the THz beam [35]. The advantage of using PTFE is the high transmission (85-90%) below 6 THz [34]. From the THz transient we calculated a SNR of 36 and a DR of 76 for the SSBCD technique and a SNR of 110 and DR of 283 for EOS in a 300 $\mathrm {\mu }$m thick GaP crystal. As the SNR and DR for the SSBCD technique both scale quadratically with the probe pulse energy and linearly with the THz field strength, such low SNR and DR values are expected for the combination of low values of both probe pulse energy and THz electric field used in this setup. Nonetheless, we have demonstrated that the SSBCD device can be used with low energy, high repetition rate lasers, and also that it can be set up using THz fields as low as a few kV/cm.

The dependence of the detected THz induced modulation on both probe pulse energy and bias voltage, as shown in Fig. 3, agrees very well with the expected behavior (quadratic and linear, respectively). A noticeable decrease in THz peak field value over time was observed for probe pulse energies above a relatively low 24 nJ threshold value. This decrease indicates the onset of competing high-order nonlinear processes occurring in the slit, such as carrier acceleration and dielectric breakdown. This limits the sensitivity of our SSBCD setup, which would benefit greatly from larger probe pulse energies. Compared to previous works reporting on the SSBCD technique [14–16], here we use a significantly shorter pulse duration (40 fs instead of 155 fs). While we expect the shorter pulse duration to be beneficial for the second harmonic generation, the larger peak intensities might lead us to reach the damage threshold of the device sooner. Another likely explanation is that the high repetition rate leads to larger heat accumulation. The average power of the probe beam is 8 mW for 32 nJ pulses at 250 kHz, which is significantly larger than the average power of 0.1 mW for 100 nJ pulses at 1 kHz, as used in previous publications [14–16]. Due to the small slit size, any thermal expansion effects might significantly impact the performance of the device.

Regarding the samples, ZnTe, GaAs and GaP were chosen as they exhibit features in the 0.1-10 THz region. The lowest transverse optical (TO) vibrational mode frequencies are at 5.3 THz, 8 THz and 11 THz, respectively [29]. The experimental sample transmissions evaluated through the SSBCD technique and shown in Fig. 4(a) are lower than the expected transmissions based on the lowest TO phonon only. However, the transmission through each of the samples studied in this work is additionally affected by multiphonon processes, which significantly contribute to absorption losses already at frequencies below the TO-phonon. For ZnTe the multiphonon processes are known to occur at 1.6 THz and 3.7 THz [2], for GaP at 3 THz and 4.3 THz [32], and for GaAs at 2.4 THz and 5 THz [31], as seen in Fig. 4(a). These features can be observed more clearly in Fig. 4(b) by comparing the absorption coefficient $\alpha (\nu )$ extracted from the TDS measurements to literature values [2,31,32]. The absorption coefficient of ZnTe matches well with the expected values overall, but there are some small discrepancies in the fine structure near 4 THz. The expected further increase in absorption due to the TO-phonon at 5.3 THz is not visible as it is clearly saturated, since the largest detectable absorption is reached at 4 THz (i.e. the transmission reaches the noise level in Fig. 4(a)). For GaAs, the measured absorption is significantly larger than that reported in the literature for all measured frequencies, by approximately a factor of 2-3. There is, however, qualitative agreement in that the absorption generally increases with frequency, with a sharp increase at $\sim$4.5 THz. For GaP, the measured absorption is again generally larger than literature reports, and in this case qualitatively agrees with the relatively constant absorption up to $\sim$4 THz. One possible reason for the discrepancies could be a higher concentration of carriers due to impurities in our samples. In the region around 6.1 THz the PTFE completely absorbs any THz radiation for both the sample and the reference measurements. Above the PTFE absorption frequency, the transmission for all samples decreases to a level comparable to the noise floor and the frequency dependent SNR [27] for all samples becomes essentially 1, which prevents a determination of the THz transmission above 6 THz.

Recently, an alternative approach to the bias field was presented by applying a DC voltage [16] instead of an AC voltage locked to the laser repetition rate [14,15]. By measuring two traces with opposite polarity of the DC field, one can reconstruct the THz trace. The advantage of the DC field [16] over the AC [14,15] scheme is the overall ease of implementation, the reduced noise level and the increased signal (since the bias field can effectively be doubled). We also tried this approach but could only partially reproduce the results demonstrated by A. Tomasino et al.[16]. While we observed a significant increase in second harmonic generation when the DC bias voltage was applied, the signal decayed slowly with time. It is unclear whether this may be a consequence of the higher repetition rate of the probe beam we are using, and further investigation would be required to clarify this issue. For the purpose of our work, however, we were able to recover the initial second harmonic intensity after switching the bias field polarity. We therefore settled for a 500 Hz modulation of the bias field, much slower than the kHz laser repetition rate but fast enough to prevent any significant decay of the second harmonic signal.

The combination of SSBCD with the broadband THz emission of the spintronic emitter is a very promising route to obtain an ultra-broadband THz TDS setup for low pulse energy, high repetition rate laser systems. To improve upon our measurements, we suggest further investigation into the design of the SSBCD device, specifically adapting it for high repetition rate lasers and shorter pulse durations. A possible approach would be to investigate the effect of different slit sizes. If the limit of the optical power is related to thermal effects on the small slit size, then a larger slit size should allow for larger probe pulse energies. This would also lead to a smaller THz field enhancement in the slit, which could, however, be rapidly compensated by increasing the probe pulse energy, since SNR and DR are expected to scale quadratically with probe pulse energy [15]. Alternatively one could also investigate smaller slit sizes, which would lead to a larger THz field enhancement and larger bias fields for the same bias voltage, but would require better focusing of the probe beam. Another possibility would be to investigate other nonlinear materials which might be more robust than SiN to exposure to high repetition rate pulses. An additional improvement of the device performance would be given by an investigation of the threshold associated with the amplitude of the bias voltage under high repetition rate probe beam exposure, which we have not attempted for fear of inducing irreversible damage to the SSBCD device.

5. Conclusion

We have demonstrated the suitability of the SSBCD technique for the coherent detection of ultra-broadband THz radiation generated in a spintronic emitter in combination with a high repetition rate, low energy laser setup. Specifically, our results show that such a detection scheme can be operated with probe beam energies of a few tens of nJ at a repetition rate of 250 kHz and 40 fs pulse duration and detect THz field strengths as low as a few kV/cm with a frequency content as wide as 9 THz. We have successfully shown its application in analyzing bulk samples of three different materials. We have observed limitations in terms of noise mainly related to the maximum applicable probe pulse energy, which are attributed to the high repetition rate and the short pulse duration. If these limitations could be overcome through a change in design or in the materials used in the SSBCD device, this technique would become a unique tool to detect the 0.1-10 THz range in THz TDS setups based on high repetition rate laser systems. A specific application would be to combine the SSBCD detection with high-repetition rate (>100 kHz) Ytterbium lasers, which have recently emerged as a successful approach to generate and detect coherent THz pulses [36]. The combination of the SSBCD technique with THz generation in a spintronic emitter would dramatically enhance and extend the spectral bandwidth to ultra-broadband regimes compared to common setups in which THz generation and detection are based on photoconductive antennas or nonlinear crystals such as ZnTe and GaP.