1. Introduction

Most conventional Terahertz (THz) setups, such as spectroscopy-, communication- and most imaging experiments, use a fairly low power. With the advent of free electron lasers (FELs), a new class of THz experiments became possible where non-linearities are probed with ultra-high power THz pulses. This class of experiments operates at extreme excitation conditions in order to reveal new physics [1, 2]. Such experiments include in particular pump-probe setups where either pump or probe (or even both) are intense THz pulses. The large spectral coverage of FELs permits probing physics over a large photon energy range. As an example, FELBE at the Helmholtz-Zentrum Dresden-Rossendorf offers two FELs with a total spectral coverage from 1.2 THz to 75 THz. A typical setup consists of a THz excitation (pump) laser, such as the free electron laser (FEL) [1, 3] and a phase locked visible or infrared (probe) laser, such as a Ti:sapphire laser that excites a sample under test with a well known temporal delay of the order of the pulse duration. Detectors for such applications have to fulfill quite different needs from those for table-top low power experiments: while low noise equivalent power (NEP) is the main criterion of low power detectors, detectors for pump-probe experiments should rather be able to withstand the extreme power levels and cover the huge frequency span of the FEL. Further, the detector should show response times on the time scale of the pulse durations, ideally being able to resolve the pulses, be sensitive to both pump and probe beams, and feature a high 1dB compression point for accurate pulse power evaluation. A particular problem is the timing between pump and probe pulses. For setups where one IR and one THz laser are involved, electro-optic sampling (EOS) is the state of the art method —given that there is a fixed delay between the IR laser and the THz laser with proper phase-locking. This is usually the case for (low power) table-top experiments, where the probe THz signal is generated with the very same laser pulse that is used for pumping. This natural locking does not occur for high power experiments, e.g. at FELs, where THz laser and IR laser are independent units. Though the repetition rates can be locked, the exact phase is unknown; jitters, drifts and even phase jumps aggravate the measurement. During the EOS measurement time, the pulses may already have drifted such that the obtained data are not valid any more. As a result, EOS is difficult to use for pump-probe setups including a FEL. Further, the EOS measurement requires an additional setup with electronic delay components and further optics, adding unnecessary complexity to the setup. In most cases, phase matching of the THz- and the NIR pulse in the non-linear crystal is only given for a certain frequency window that does not cover the whole FEL frequency span. Therefore, often two different detectors for each frequency range are used that cannot measure both pulses at the same time.

An alternative could be Schottky diodes [4], where the speed is mainly determined by post-detection electronics, and an excellent sensitivity with noise floors in the range of a few $\text{pW}/\sqrt{\text{Hz}}$ [5, 6] at the low end of the THz spectrum. However, Schottky diodes feature fairly low 1 dB compression points that are typically in the μW range [5], low destruction thresholds, and are very sensitive to electrostatic discharge. High attenuation and extreme care has to be taken when used at FELs and other high power facilities. Further, it is difficult to implement them as ultrafast optical/IR detectors since the contact area is blocked by the whisker contact electrode and hardly accessible for an optical signal. Antennas, as mostly used for Schottky diode detectors, are difficult to implement for frequencies above a few THz where the device size becomes comparable to the antenna length. In addition to the antenna limitation, the RC roll-off of the detection efficiency of Schottky diodes towards higher frequencies aggravates their implementation at the upper end of the THz band [7].

Field effect transistors have proven to be excellent THz detectors, with first THz cameras already demonstrated [8] or under development [9] using antenna-coupled devices. Large area field-effect transistors have been used to study the physical properties of 2DEGs such as plas-monics and THz absorption [10–12]. Unfortunately, there are only few publications investigating the frequency dependence of the responsivity of FETs. One reason is that antenna-coupled devices are mostly set up in a narrow-band configuration, such that for each frequency, a separate device has to be processed [13]. Here, we use antenna-less, large area devices with ultra-broadband performance. While designed for high speed operation and large video bandwidth, we have shown in a recent paper [14], that large area field effect transistor rectifiers (LA-FETs) are ideal alignment tools for pump-probe measurements: they feature a destruction threshold in the tens of kW peak power range, cover a large bandwidth and are sensitive to both IR and THz pulses with a temporal resolution of at least 30 ps for THz and from recent measurements ∼ 80 ps for IR pulses, and are simple to implement in the measurement setup without the need for many additional components.

In this paper, we investigate the THz frequency dependence of the response of LA-FETs, including roll-off, dynamic range and NEP for an extremely large frequency range of 0.1 to 22 THz. To the knowledge of the authors, this is the highest frequency and the largest frequency range where THz detection with FETs has yet been demonstrated and characterized. These high speed detectors are thus suitable for THz, FIR and NIR frequencies.

2. Setup

The detection is based on the rectification of a THz modulated current in the channel of the FET. An incident THz field modulates both the carrier velocity, v ∼ E_THz, and the carrier concentration under the gate n ∼ E_THz, at the same time. The current $I~nv~E_{\mathit{THz}}^2>0$ shows therefore a positive, rectified offset if the THz phases of v and n are similar [15]. The field-effect transistors rectify far above their f_τ and f_max for amplification. A detailed description of the theoretical background can be found elsewhere [9, 16–19]. Targeting for ultra broadband high power detectors, no antenna is used for coupling the THz power to the channel. Instead, the THz electric field couples directly to an array of very wide FETs (large area FET, LA-FET) as illustrated in Fig. 1. Therefore, the pure spectral response of the FETs is accessible that only depends on the device geometry. While for antenna-coupled devices all received power is concentrated on a single lumped element with micrometric dimensions, the power using a LA-FET is distributed on an area of the order of the THz spot size which is by about 1–2 orders of magnitude larger, ensuring a high damage threshold [20]. The fairly low radiation resistance of the large area can be tuned by the size of the array or its illuminated area and allows for detecting high power levels, preserving detector linearity. Due to the length of the individual FETs of several 100 μm and the parallel connection of all FETs in the LA-FET, the resistivity and parasitic serial resistance of the whole device is very low, typically far below 1Ω. This ensures high internal efficiency and high speed operation.

 

Fig. 1 a) Layout of the FET devices with the ohmic source (S) and drain (D) contacts as well as the Schottky gate (G) contact. The mesas are significantly longer compared to an antenna coupled device. At the same time, the individual mesas are all connected in parallel resulting in a very low overall access resistance. b) Packaged and silicon lens coupled LA-FET detector. c) Packaged LA-FET detector E with a horn antenna instead of a silicon lens.

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In this study, devices with different geometries as listed in Table 1 are evaluated. The length of the gate varies from 1 to 4 μm, the source-drain distance varies from 3.5 to 11 μm. The devices consist of high electron mobility FETs with a GaAs channel depth between 15 to 25nm where the barriers are Al_0.3Ga_0.7As. The samples are remotely doped in the barrier, leading to high mobilities in the range from 4300 up to 6000 cm²/Vs and carrier concentrations in the range of 1.8 – 5.3×10¹¹/cm². The size of the devices has been adjusted to the expected THz spot diameter at the lowest FEL frequency of 1.3 THz. The diffraction-limited beam diameter at 1.3 THz is d = 1.22λ_THz/NA = 1.1mm for NA = 0.25 for direct illumination from the air side, and 1.1mm/n_GaAs ≈ 310 μm for illumination through the GaAs substrate with a refractive index of GaAs of n_GaAs = 3.6. Therefore, backside coupled devices, where a hyper-hemispheric silicon lens is used for coupling the THz beam to the LA-FET, have an active area of 0.3 mm×0.3 mm, i.e. slightly smaller due to the square layout. Device E is designed for coupling from the front side and therefore has a larger active area of 1 mm×1 mm. It does not use a silicon lens. At 22 THz, a horn antenna was used to simplify the incoupling to the FET device E [as shown in Fig. 1(c)], however, the THz spot at 22 THz is already so small that the horn does not noticeably alter the THz coupling efficiency or device responsivity. It only simplifies the alignment procedure. Despite the large size of the devices, the gate leakage current remains in the low μA range for all designs and investigated gate biases.

Table 1. Parameters of the measured LA-FETs. All devices except E are silicon lens coupled.

View Table

The pulsed FEL experiments were carried out at the free electron laser FELBE (Helmholtz-Zentrum Dresden-Rossendorf, Germany). Two different undulators are available, the U100 radiating between 1.2 THz and 16 THz, and the U27 radiating between 14 THz and 75 THz. For the selection of THz frequencies, care was taken not to hit any water absorption lines. The LA-FETs were placed in the THz focus using a parabolic mirror. A maximum pulse peak power of 65 kW was used which could not damage the device. The detected signal is read out by a 30 GHz sampling oscilloscope (Tektronix DSA8200) with a coaxial SMA connection to drain (D) and source (S) of the FET. Another coaxial connection to gate (G) and source of the device allows for applying a gate bias. For a part of the measurements, an additional amplifier with a cut-off frequency around 10 GHz was introduced between LA-FET and oscilloscope in order to improve the signal to noise ratio (SNR). For determination of the pulse duration, the FEL spectra (in the frequency domain) are recorded and Fourier transformed. The FWHM pulse width is τ_FWHM = 31 ps at the lowest used frequency of 1.31 THz and becomes approximately inverse proportionally shorter with increasing frequency. At the highest used frequency of 22.3 THz the pulse width is 2 ± 0.5 ps. Such short pulses cannot be resolved by a 30 GHz oscilloscope which will measure an effective signal. The oscilloscope behaves approximately as a low pass filter with a response time of about 12 ps. Frequency components above 30 GHz are suppressed by a power law as discussed in the appendix. Further, the coaxial cables are also more lossy at higher GHz frequencies. Therefore, the signal amplitude shown by the oscilloscope will be smaller than the measured amplitude by the LA-FET.

The average THz power, P̄_THz, is measured with a thermal power meter. The peak power is determined by $P_{\mathit{THz}}^{\mathit{peak}}={\overline{P}}_{\mathit{THz}}/\left(f_{\mathit{rep}}{\tau }_{\mathit{FWHM}}\right)$, where τ_FWHM is the FWHM from the FEL spectra and f_rep = 13 MHz is the repetition rate of the FEL.

In addition to pulsed FEL measurements, the responsivity at 0.10 and 0.17 THz was measured in continuous-wave setups using a backward wave oscillator (Elva-1 BWO) or a frequency multiplied RF source and a focusing element with a higher NA ≈ 0.5 in order to assure efficient coupling. The 1 cm hyper-hemispheric silicon lens further focuses and increases the NA. The THz signal was electrically modulated or chopped for recording with a lock-in amplifier (EG&G 7265) for noise suppression.

3. Experimental results

The devices mentioned in Table 1 have been characterized at various frequencies between 1.3 and 22 THz at the FEL, complemented by CW measurements in the lower THz frequency range. A typical recorded pulse shape of the FEL measurement is depicted in the Inset of Fig. 2. For each FEL frequency, the optimum gate bias was first identified by measuring the THz peak signal at the oscilloscope vs. gate bias. At the gate bias where the largest signal is obtained, the devices featured approximately a 50Ω resistance, being impedance-matched to the oscilloscope. Then, the responsivity is determined by measuring the response of the device vs. incident THz power. The responsivity ℜ, the voltage noise level U_N and the 1 dB saturation power 1/P_1dB is determined with a saturation model [21]:

 

Fig. 2 Rectified THz Signal from LA-FET A at 2.87 THz. The 1dB compression point of the detector is 0.6kW (peak power) and 8.4mV, respectively, at this frequency. The responsivity is ℜ = 17 μV/W. The Inset shows the measured oscilloscope trace using FET E at 22.3 THz with a FWHM of 24 ps. The FWHM is limited by the temporal resolution of the oscilloscope.

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Figure 3 shows the fitted THz responsivities for various devices vs. frequency. The detectors work well above and below the Reststrahlen band of the GaAs wafer which peaks around 8.3 THz. However, already at 7.1 THz, i.e. in the tail of the Reststrahlenband, no THz power could be detected any more, potentially because of the large thickness of the GaAs substrate of 500 μm. Since the signal shape does not show any structural change vs. frequency and the frequency dependence does not show any kinks, we conclude that the dominant detection mechanism is indeed FET rectification over the whole frequency range. The LA-FETs feature a measured, extrinsic responsivity around 15mV/W (0.07 μV/W) for the low (high) frequency end of the investigated frequency range, namely at 0.1 THz (22 THz). The value of 0.07 μV/W at 22 THz corresponds to a current responsivity of 1.5 nA/W. The responsivity is fairly small since no antenna was used to efficiently couple the THz radiation to the device and the power is distributed amongst many parallely connected FETs. The large area features a radiation resistance that is at least three to four orders of magnitude smaller [22] than the radiation resistance of a dipole antenna on GaAs of around 30Ω. The THz coupling through the silicon lens (with a wave impedance of Z = 377Ω/n_Si = 110Ω) is therefore fairly mismatched. The intrinsic transistor responsivity is orders of magnitude higher. For the targeted application of a fast and easy to align THz detector for high power facilities, however, the LA-FET is ideally suited: the large area ensures easy alignment and high power carrying capabilities and the parallel connection of the FETs results in low access resistance and short time constant which is the key design criterion. For the available power levels at most FELs, the responsivity of the LA-FETs is indeed more than sufficient. Further, the absence of an antenna allows to use the LA-FETs over an unprecedented frequency range, covering the THz range and parts of the FIR range with a single LA-FET. The devices feature a f⁻² responsivity roll-off in the investigated range as for the case of Schottky diodes [4]. On a first glance, this f⁻² roll-off could be assigned to an RC roll-off, typical for most semiconductor-based THz detector concepts. But this does not take into account that the pulse duration of the FEL pulses is shorter than the response time of the oscilloscope for all frequencies but 1.3 THz, where they are comparable. Simply speaking, the oscilloscope cannot resolve the pulses and the peak voltage will be reduced, the pulse being smeared out. The shorter the THz pulse the stronger the filtering effects of the low-pass behavior of the oscilloscope. For FELBE, the pulse duration, τ_FWHM, scales roughly inverse proportionally with the FEL wavelength. That is, the oscilloscope records an increasingly suppressed pulse amplitude at higher THz frequencies. The dashed graph in Fig. 3 shows the corrected response, normalized to the CW data where no power reduction effects due to the measurement technique are expected, following approximately a f⁻¹ behavior. This agrees with the findings in ref. [16] where it has been shown that in an ideal FET (i.e. with negligible access resistance) the resistance and the capacitance by the channel should indeed cause a responsivity roll-off as f⁻¹. For the given LA-FETs, the access resistance is indeed so small that it can hardly be measured, usually below 1Ω.

 

Fig. 3 Measured responsivity of the large area field-effect transistors from 0.1 to 22 THz. The data above 1.3 THz were measured with the pulsed free electron laser FELBE, the data at the low frequency end are taken in a continuous wave setup. The individual devices show slightly different roll-offs around the f⁻² guide to the eye. The dashed line corresponds to a detector behavior corrected for the amplitude distortion from the oscilloscope. Error bars have been included exemplarily for device A, disappearing behind the markers except for the CW measurement at the low frequency end. The Inset shows the 1dB peak power compression for different LA-FET devices from 1.3 up to 22 THz. A f¹ guide to the eye is included.

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A similar effect could be mimicked if the high frequency components of the rectified signal generated by the LA-FET (with frequency components at approximately the inverse of the pulse duration) are above the cut-off frequency of the LA-FET (f_τ or f_max). The cut-off frequency, however, cannot be directly measured, since the LA-FET can hardly be integrated into a coplanar waveguide structure for S-parameter measurements. At this point, we cannot conclude whether the suggested less strong roll-off is due to the oscilloscope or the cut-off frequency of the FET. In either case, the data suggest that an ideal FET should roll-off less strongly than other semiconductor-based detectors, such as Schottky diodes, that typically feature a quadratic roll-off. The inset of Fig. 3 shows the 1dB peak compression power. P_1dB roughly increases linearly with frequency. The compression power of device A lies around the f¹ guide to the eye, the other devices show outliers due to focusing issues of the THz spot that may be (much) smaller than the device at the highest investigated frequencies.

In order to complete the characterization of the detector, dynamic range, noise equivalent power (NEP) and optimum operation conditions are discussed in the following. The bandwidth normalized dynamic range, measured from the noise floor to the 1dB compression point is $66\pm 3\hspace{0.17em}\text{dB}/\sqrt{\text{Hz}}$ at 1.3 THz. With an additional amplifier, however, the bandwidth normalized dynamic range increases to $69\pm 3\hspace{0.17em}\text{dB}/\sqrt{\text{Hz}}$ at 1.3 THz, showing that the noise originates from the oscilloscope. To the knowledge of the authors, this is the largest dynamic range presented for FET-based THz detectors so far.

Detector A shows a NEP of $2.7\hspace{0.17em}\mu \text{W}/\sqrt{\text{Hz}}$, $0.16\hspace{0.17em}\text{mW}/\sqrt{\text{Hz}}$ and $45\hspace{0.17em}\text{mW}/\sqrt{\text{Hz}}$ at 0.1 THz, 1.3 THz and 22 THz, respectively. However, in both CW and pulsed measurements, these values are still limited by noise from the post detection electronics.

The optimum gate bias is determined by the maximum responsivity vs. gate bias. The voltage responsivity of a FET increases when approaching the threshold [16, 23, 24], however, resistance and thermal noise increase as well. For the FEL measurements, the devices featured optimum SD resistance of 60 ± 20Ω, close to impedance matching to the 50Ω port impedance of the oscilloscope. When the device is connected to a high impedance Lock-in amplifier, in contrast, the responsivity further increases when approaching the threshold bias as there is no impedance matching and the device is then operated in the photovoltaic mode. The impedance of the device around 30 GHz (i.e. the input impedance of the device to the oscilloscope) differs from the impedance for the THz wave which has to be determined by a transmission line approach [16, 25, 26]. While the rectified signal is measured from drain to source, the THz signal gets rectified and is gone after a certain length in the gated area of the device. For all investigated devices and all frequencies under pulsed operation, the gate lengths are much longer than this effective rectification length [16], i.e. the penetration depth of the THz signal into the gated region, $L_{\mathit{eff}}\approx {\left[2/\left(\omega c_0{r}_0\right)\right]}^{1/2}={\left[\frac{e{d}_{\mathit{Ch}}{n}^{(2D)}\mu }{\pi {\epsilon }_0{\epsilon }_{r}f}\right]}^{1/2}$, where r₀ = (en^(2D)μ)⁻¹ is the channel resistance per unit length and c₀ = ε₀ε_r/d_Ch is the capacitance per unit length with d_Ch the depth of the channel. Resonant effects will alter the effective rectification length, however, the gates are so long that resonances are damped. For 1.3 THz (22 THz), the effective rectification length is in the range of 200 ± 100 nm (30 ± 20 nm) for all investigated devices, whereas the gate lengths, L_G, are at least 1 μm. That is, the devices feature an almost frequency-independent passive channel length of L_P = L_G − L_eff ≈ L_G that contributes to the device impedance for the rectified signal but does not impart in THz rectification or to the THz impedance. Due to the long channel, the responsivity-voltage characteristics do not show any resonant effects although the devices are operated in the plasma-resonant regime, ωτ ≫ 1, where τ is the momentum relaxation time. The critical frequency, where plasmons can be excited is for all samples between 1 and 1.5 THz.

The measurements show a smooth responsivity vs. bias curve as illustrated in the inset of Fig. 4. Figure 4 further shows the responsivity increase at the optimum bias vs. that at U_GS = 0V. At higher frequencies, the responsivity-voltage characteristics become flatter, with less responsivity increase at the optimum bias. That is, the gating influences the rectification lesser. This indicates that the rectification already takes place in the fringing fields at the edge of the gate that are roughly relevant within a distance L_F ≈ d_Ch outside the gated region [27]. Recalling that the penetration length of the THz wave, L_eff, is in the range of a few tens of nm at 22 THz, it is indeed comparable to the fringing field dimensions d_Ch = 15 – 25nm for all investigated samples. The detectors B and D, having longer gates, follow clearly a stronger reduction at high frequencies than the detectors A and C with a shorter gate length. The clarification on the origin of this behavior requires further research.

 

Fig. 4 Maximum signal with gate bias plotted against THz frequency. The Maximum signal with gate bias is normalized to the signal without gate bias. The straight line is a f^−0.3 fit to the data of device A. The Inset shows the measurements at the single frequencies of device A versus the gate bias. No sharp resonances can be seen.

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4. Conclusion

We presented experimental results for ultra broadband detection of THz radiation at room-temperature with rectifying FETs from 0.1 up to 22 THz with a post-detection limited temporal resolution of the available read-out 30 GHz oscilloscope. The pulses can simply be recorded with the oscilloscope on the time scale of seconds. Since LA-FETs can also detect NIR pulses with a temporal resolution around 80 ps, they are excellent detectors for very broadband pump-probe measurements at FELs. They may also be implemented in the future in CO₂-laser based setups that are just slightly higher in frequency (30 THz) than the highest frequency investigated in this paper (22 THz). The unique spectral coverage, their ultrafast response, compactness, the dynamic range of $69\pm 3\hspace{0.17em}\text{dB}/\sqrt{\text{Hz}}$, their durability and simple handling show that LA-FETs are excellent detectors for a variety of experimental applications in the THz, far IR and IR frequency range. The results shown here also give insight into the physics of the detection principle of rectifying FETs in general. The roll-off towards higher frequencies is less strong than expected from a pure RC roll-off. The data corrected for the low-pass behavior of the used oscilloscope suggest a 1/f responsivity roll-off, being less stringent for FETs as compared to other semiconductor-based detector types like Schottky diodes. Further research to support a 1/f roll-off of the responsivity is suggested, such as CW measurements with THz gas lasers where a fast oscilloscope is not needed, or measurements with an even faster oscilloscope where the THz peaks can be fully resolved.

5. Appendix

For most measurements, the FEL pulses are shorter than the rise time of the oscilloscope (12 ps) or the post detection amplifier (about a factor of 3 longer). Therefore, the pulse shape will be deteriorated, resulting in an increase of the pulse duration and a reduction of the pulse amplitude. For estimating this feature, we assume a simple low pass of second kind approximation that suppresses high frequency components to approximate the oscilloscope response. Due to Parseval’s theorem, the power in the time domain and in the frequency domain are the same. It is simplest to calculate the peak reduction in the frequency domain. For simplicity, we assume a Gaussian pulse shape for the FEL. The low pass of second kind reduces the power according to

(2)$$\eta \left({\tau }_{\mathit{FWHM}},f_{3\mathit{dB}}\right)=\frac{{\tau }_{\mathit{FWHM}}}{2\sqrt{\pi \text{ln}2}}{\int }_0^{\infty }\text{exp}\left(-\frac{f^2{\tau }_{\mathit{FWHM}}^2}{16\text{ln}2}\right)\frac{1}{1+{\left(f/f_{3\mathit{dB}}\right)}^2}\text{d}f$$

where f_3dB is the cut-off frequency of the oscilloscope and τ_FWHM the FEL FWHM pulse duration. The function is normalized such that η becomes unity for f_3dB ≫ 1/τ_FWHM. For f_3dB ≫ 1/τ_FWHM, the efficiency scales as η(τ_FWHM, f_3dB) ∼ τ_FWHM. For the pulses investigated within this paper, the pulse duration, τ_FWHM, becomes approximately inverse proportionally shorter with increasing frequency, f_THz, hence η(τ_FWHM, f_3dB) ∼ f⁻¹. The dashed line in Fig. 3 shows the corrected trend for an ideal oscilloscope with very high cut-off frequency, f_3dB, where η(τ_FWHM, f_3dB) ≈ 1.

An additional source for attenuation with increasing frequency of the rectified signal is the coaxial connection to the oscilloscope. The attenuation of the cables has been measured up to 50 GHz as illustrated in Fig. 5. As a result, there is an additional contribution to the low pass behavior of the oscilloscope in the detection path reducing the amplitudes of the different pulse lengths in the experiment.

 

Fig. 5 Attenuation from connecting cables including connectors to the oscilloscope with the used cable for devices B,C and D in blue and a cable with high quality connectors for reference in red. The cables show an additional frequency dependent damping of the signal in addition to the low pass behavior of the oscilloscope. The standing waves in the blue graph are due to small fabrication errors in the SMA connectors.

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Acknowledgments

The authors would like to thank Martin Nezadal, Jan Schür and Martin Vossiek from the Institute of Microwaves and Photonics (LHFT) at the University of Erlangen in Germany for their support with the continuous wave measurements at 0.17 THz. This work was supported by the Deutsche Forschungsgemeinschaft and by the LOEWE research initiative “Sensors Towards Terahertz” of the state of Hesse/Germany.

There are no competing financial interests.

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