1. Introduction

Terahertz (THz) pulsed radiation has been used to perform THz time-domain spectroscopy (THz-TDS), optical-pump THz-probe (OPTP), and THz-pump optical/THz-probe measurements to study properties of matter. A peak electric field of THz pulses higher than 100 kV/cm can be used for studying nonlinear THz effects, opening a new range of applications. High-field THz pulses have been used to study effective-mass anisotropy in semiconductors and ultrafast carrier dynamics and impact ionization in graphene [1–10]. High-field THz-driven particle accelerators have also shown a lot of potential to reduce the size and cost of the accelerator technology [11,12]. A detailed list of applications of high-field THz radiation is given in Ref. [13].

The generation of THz radiation, in general, has been difficult leading to the popular term THz-gap used for the 0.3–30 THz spectral band in the electromagnetic spectrum [14,15]. Generating THz pulses with high-field amplitudes is even more challenging and expensive. So far, gas plasmas and optical rectification are used to generate high-field THz pulses for table-top measurements of nonlinear THz effects. Optical rectification techniques using lithium niobate with tilted wave fronts, and organic crystals like DAST and DSTMS have successfully generated THz fields of the order of several MV/cm [14–16]. Despite the limitations in the maximum THz field generated, photoconductive emitters have become very popular for measurements where high THz fields are not essential. The feasibility of scattering-free and high-frequency electronic chopping for lock-in detection makes the data acquisition fast and clean. Photoconductive emitter can emit azimuthally and radially polarized fields of THz pulses [17,18]. Such THz pulses can have enormous applications in spectroscopy and particle accelerators [11,12]. This makes photoconductive emitters very unique compared to optical rectification and air-plasma techniques.

A photoconductive emitter needs to be optically pumped using sub-picosecond laser pulses with a photon energy higher than the semiconductor bandgap. The mode-locked Ti:Sapphire laser operating around 800 nm is one of the most common femtosecond lasers. This makes GaAs based photoconductive emitters a very popular choice, since they are compatible with 800 nm pumping. Despite continuous efforts during the last three decades to increase the THz field, photoconductive emitters have been rarely used to perform nonlinear THz experiments due to their inability to provide high THz field [19]. The large-area design with interdigitated electrodes makes these emitters compatible with high pulse-energy pumping without reaching saturation of the THz emission; and, unlike orthodox wide electrode-gap (∼ 1 cm) large area emitters, it does not require a very high bias voltage [20–23]. The interdigitated electrode emitter with moderate applied bias could provide the THz fields close to the minimum THz field required for the nonlinear measurements, which is of the order of 100 kV/cm [1–3]. Ewers et. al. used an interdigitated emitter yielding 15 kV/cm fields and demonstrate ionization of excitons, which is a highly nonlinear process. This can be regarded as an unusual system (at low temperature) where rather weak fields result in strong nonlinearities [24]. Recently a peak THz field of ∼ 120 kV/cm from an interdigitated electrode emitter fabricated on LT-GaAs on an insulating substrate has been reported [25]. Ropagnol et. al. have achieved a peak THz field as high as 331 kV/cm from ZnSe based photoconductive large area emitters [26,27]. The same group has also successfully demonstrated nonlinear THz studies on n-doped InGaAs by observing significant THz absorption bleaching [26]. However, due to the wide bandgap of the ZnSe, it has to be pumped at 400 nm, achieved by frequency doubling of 800 nm pump radiation originally from a Ti:Sapphire amplifier laser operating at a repetition rate of only 10 Hz. For practical applications it is useful to have the high-field THz emitter compatible with the operating wavelength of common amplifier laser systems at 800 nm, and a high repetition rate of THz pulses helps achieve better signal-to-noise ratio after averaging the THz signal. Considering the astonishing developments in femtosecond thin-disk lasers with extremely high average power and operating at few 10 MHz repetition rates [28,29], it could become possible to produce high-field and high-repetition-rate THz pulses for sensitive nonlinear THz experiments from a table-top source.

2. Device fabrication and characterization

In this paper, we demonstrate the emission of THz pulsed radiation from a semi-insulating GaAs large-area photoconductive emitter with high enough peak field to cause inter-valley scattering of conduction band electrons in GaAs. The emitter with interdigitated electrodes is fabricated on a ∼ 625 µm thick semi-insulating GaAs (SI-GaAs) substrate. The schematic diagram of the device structure is shown in Fig. 1(a). The electrode width is 10 µm, the gap between two electrodes is also 10 µm, and the emitter area is 1 cm². The device area is limited by fabrication yield. Each alternate gap area between the electrodes is covered to make sure that only the unidirectional field areas emit the THz radiation. The device is fabricated using phololithography techniques and the fabrication process is similar to the one in Refs. [20,21]. The relatively larger feature size of the device simplifies the fabrication process and chances of shorting the electrodes due to imperfections in the fabrication process are diminished. Although increased electrode and gap widths reduce the total number of strip-line emitters per unit area, increased efficiency of each individual strip line emitter due to wider anodes compensates the loss, and total THz emission efficiency is not affected [30,31]. The fabrication process of this emitter is much simpler than recently reported efficient photoconductive emitters [25,32]. The total current flowing through the device and subsequent heating of the emitter is a major concern for large-area interdigitated photoconductive emitters. This limits the maximum voltage that can be applied to the emitter. The dielectric breakdown field of GaAs is quite high, ∼ 400 kV/cm (∼ 150 kV/cm for SI-GaAs due to impact ionization of the EL2 deep donor level), hence a bias field of the order of ∼ 100 kV/cm can be applied to the emitter if a temperature increase in the emitter via Joule heating is avoided [33]. Joule heating depends on the total current flowing through the emitter and hence it also depends on imperfections in the emitter electrode structures that can short the electrodes partially or fully. Our emitter also has reduced dark resistance due to device imperfections/degradation. Therefore, mounting the emitter chip on the holder becomes crucial in order to avoid excessive heating of the device. We glued the emitter chip using thermally conductive glue on a metallic mount, which has a hole of the size ∼ 1 × 1 cm² for transmission of the THz radiation. We were able to apply 60 kV/cm (60 V over the 10 µm gap) d.c. field on the emitter, which is somewhat higher than the maximum field applied on comparable emitters [18,25].

 

Fig. 1. (a) The schematic diagram of the emitter electrodes. The width of electrodes is 10 µm and gap between them is also 10 µm. Each alternate gap region is covered with another metallic layer shown in partially transparent grey colour. There is an insulating layer of Si₃N₄ separating the electrode layer and covering layer. (b) The schematic diagram of the set up used for the measurements. The dotted red line shows the NIR beam path used to pump the GaAs wafer only for non-linear measurement.

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The emitter is pumped with a Ti:Sapphire amplifier laser operating at 800 nm with 1 kHz repetition rate and ∼ 45 fs pulse width. The pump beam diameter is expanded to ∼ 1.5 cm after collimation and passed through a 1 cm diameter aperture to obtain a relatively uniform optical density on the emitter. The emitter is pumped with 100 mW (0.1 mJ pulse energy) and 150 mW (0.15 mJ pulse energy) pump power. The pump beam is mechanically chopped for lock-in detection. The schematic diagram of the setup is shown in Fig. 1(b). The emitted THz pulse radiation is focused on a calibrated THz power meter (THZ20 SLT Sensor- und Lasertechnik GmbH) using an off-axis parabolic mirror of 5 cm effective focal length (f/5). A THz wire-grid polarizer is placed between the emitter and the power meter to discriminate unpolarized thermal radiation from the linearly polarized coherent THz radiation. The reading on the power meter is maximized (Polarizer perpendicular to THz field) and minimized (Polarizer parallel to THz field) by rotating the polarizer by 90° and the difference between them is taken as THz power. The finite extinction ratio (< 1000:1) of the polarizer will lead to under-estimation of THz power. The measured THz power and corresponding estimated peak electric field of the THz pulse are shown in Figs. 2(a) and (b), respectively. The THz power (field) shows quadratic (linear) increase with increasing applied bias field up to 60 kV/cm for both pumping conditions, 100 mW and 150 mW. The maximum THz pulse energy and corresponding peak field are ∼ 70 nJ and ≳230 kV/cm respectively. The emitter saturates at 150 mW pump power, i.e. ∼ 0.19 mJ/cm² optical density. The THz field is calculated from the measured power as it is done in Ref. [34]. To measure the THz focal spot diameter, apertures of 1.0 mm and 1.2 mm diameters are placed at the focus of the THz beam, which transmit ∼ 81% and 91% of the THz peak-to-peak field respectively. Assuming a Gaussian intensity distribution at the THz focus, the estimated full width at half maximum (FWHM) is ∼ 0.45 mm for both aperture measurements. Here we have ignored the diffraction caused by the aperture, and hence, total THz transmission through apertures could be more than the observed by the detector. Thus, 0.45 mm could be an over-estimation of the FWHM. This FWHM is used to calculate the THz peak fluence at the focus and the maximum THz field. The THz pulse width, which is also required to estimate the electric field, is determined by integrating the square of electric field of the complete THz pulse in the time domain; and it is found to be ∼ 0.41 ps. Since the pulse width estimation considers electric field distributed over the complete pulse, presence of a wider secondary peak broadens the pulse width. In our case the primary (positive) peak and second (negative) peak are both narrow and their peaks are just 0.33 ps apart. This resulted in an estimated pulse width as short as ∼ 0.41 ps.

 

Fig. 2. (a) Radiated THz power and (b) corresponding peak THz field, at different bias fields on the emitter at 100 mW and 150 mW optical pump. Dashed lines are guide to eyes to show the quadratic (a) and linear (b) behaviour of the data points. (c) THz pulse in time domain and corresponding spectrum in the inset.

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Since the FWHM of the THz spot may be overestimated, the peak THz field could even exceed 230 kV/cm. If we compare the relation between the peak field and the pulse energy for THz pulses reported in the literature (36 kV/cm for 6 nJ [21], 120 kV/cm for 113 nJ [25], 150 kV/cm for 800 nJ [22], and 350 kV/cm for 400 nJ [23]), one can see that in the present study we achieve a higher THz field for the respective pulse energy. This can be explained by a broader spectrum leading to shorter THz waveforms in time-domain. The broader spectral emission can be a consequence of comparatively smaller electrode width and a smaller gap between the electrodes in our emitter. In addition, the broader THz spectrum with more high-frequency components and the relatively short focal length of the parabolic mirror allow tighter focusing of the THz beam resulting in the enhanced peak THz field.

A standard THz time-domain spectroscopy (THz-TDS) setup is also used to record the THz pulse in the time domain and perform the THz transmission experiment using our emitter as THz source (see Fig. 1(b)). A 0.5 mm thick ZnTe crystal is used for electro-optic detection of the THz pulses. The THz pulse recorded in the time domain and corresponding spectra in the inset are shown in Fig. 2(c) for 60 kV/cm bias field and 100 mW pump power on the emitter. For electro-optic detection, the THz pulse is passed through a THz wire-grid polarizer before getting focused on the ZnTe detector working with the standard balanced-diode technique. For THz field of the order of 100 kV/cm, the detector enters the saturation region and the observed THz signal from the balanced photodiodes is not linearly proportional to the THz electric field anymore [35,36]. To avoid the detector saturation the THz polarizer is rotated to reduce the THz intensity to a value such that the detector is still in the linear regime.

3. Non-linear effect induced by a strong THz field

Finally, to demonstrate the capability of our emitter as a THz source for nonlinear THz experiments, we place a ∼ 0.6 mm thick SI-GaAs substrate at the focus of the THz beam in THz-TDS setup. The emitter is pumped with 100 mW near-infrared (NIR) power and bias on the emitter is varied to control the THz field. The observed THz signal in electro-optic sampling depends on several factors other than the THz field itself, e.g. alignment of the THz and probe pulse (polarization, propagation direction, focus), and electro-optic crystal (position, orientation and quality), detection response across the spectrum, etc. However, THz power measurement is much simpler and more reliable. Hence, we estimate the THz field by measuring the THz power. The front surface of the SI-GaAs substrate is also pumped (∼3 mm diameter) with 75 µJ pump at 800 nm from the same amplifier laser system which also pumps the THz emitter. The transmitted THz field (and peak electric fields in the inset) at different bias is plotted in Figs. 3(a) and (b) for the cases without and with photo-excitation of the SI-GaAs, respectively.

 

Fig. 3. THz pulses of varying field strength after passing through a GaAs substrate (a) without optical pumping, and, (b) with 75 mW optical pumping on GaAs front surface.

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The free-carrier density in SI-GaAs without optical pumping is so low that the carriers do not affect THz transmission and most of the THz radiation (up to 4 THz in this case) passes through the SI-GaAs [37]. Since the THz field increases linearly with applied bias, the peak field of the transmitted THz pulse also increases linearly as shown in the inset of Fig. 3(a). When the SI-GaAs is pumped with 75 mW optical pump, electrons are excited to the Γ-valley of the GaAs conduction band. In this case the generation of free electrons and holes increases the conductivity of the top layer of the SI-GaAs surface, which in turn reduces the THz transmission. The THz transmittance depends on conductivity, and the conductivity depends on the carrier density and mobility. Since electron mobility is much higher than hole mobility in GaAs, the conductivity is mainly determined by the electrons, hence we consider only electron dynamics. If electrons in the Γ-valley are accelerated enough to gain kinetic energy higher than the L-valley minima, scattering of the electrons from Γ-valley to L-valley starts taking place via absorption and emission of phonons.

The phonon scattering of the carriers to the side valleys is a well-studied phenomenon, and we show the schematic diagram of the scattering mechanism in Fig. 4(a). Since the effective mass of electrons in the L-valley is higher, the mobility drops and hence the THz transmittance increases. In Fig. 4(b) we plot the ratio between the THz peak-to-peak amplitudes of the THz pulses transmitted through the GaAs with/without the free carriers (i.e. without/with 75 mW pump on the GaAs substrate) for varying bias on the emitter (and hence varying THz fields). THz transmission is almost constant for the THz fields lower than 70 kV/cm. However, a clear increase in THz transmission is observed for peak THz fields above 100 kV/cm. This behavior is also evident from the super-linear increase of the peak field of the transmitted THz pulse shown in the inset of Fig. 3(b). The spectral transmission of THz radiation for low field (∼ 18 kV/cm) and high field is plotted in Fig. 4(c). We also calculate the optical conductivity (real part) of the top 1 µm thick layer of optically pumped GaAs [38]. The data for low (∼18 kV/cm) and high (∼143 kV/cm) THz field is shown in Fig. 4(d). The solid lines show the Drude model fitting of the data points. The d.c. conductivity (at zero frequency) is estimated from these fitting curves and it is plotted in Fig. 4(b) together with THz peak-to-peak field transmission ratio. As expected for fields higher than 100 kV/cm, the conductivity drops [37]. The significant drop in conductivity due to THz field also confirms that the THz field is of the order of or higher than 100 kV/cm at 40 kV/cm bias field and 100 mW pump.

 

Fig. 4. (a) A schematic diagram showing the GaAs band structure, and mechanism of excitation, acceleration and L-valley scattering of electrons. (b) THz transmission through optically pumped GaAs for varying THz fields. (c) Spectral transmission of low and high field THz radiation. (d) Optical conductivity (real part) of the optically pumped top 1 µm thick layer of GaAs.

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4. Conclusion

GaAs photoconductive emitters, which have undisputed dominance over other types of THz emitters for THz-TDS measurements requiring very high signal-to-noise ratio, are able to provide strong enough THz field to observe THz absorption bleaching in optically pumped GaAs. A peak THz field of ≳ 230 kV/cm at the focus is observed from a SI-GaAs large area photoconductive emitter biased with 60 kV/cm d.c. field and pumped with a 150 µJ NIR pulse at 1 kHz repetition rate. The synergy of high-frequency modulation of photoconductive THz emitters and high power high-repetition-rate pump lasers can dramatically improve the sensitivity of nonlinear THz measurements, and can provide additional experimental features like radially/longitudinally polarized THz fields.