Three-octave terahertz pulses from optical rectification of 20 fs, 1 μm, 78 MHz pulses in GaP

We demonstrate optical rectification of 1 μm pulses with a duration of 20 fs, a repetition-rate of 78 MHz and an average power of 5.5 W, in a 2 mm thick GaP crystal. The spectrum of the resulting far-infrared pulses is centered at 1.5 THz and extends to 5 THz at −50 dB intensity. In the absence of resonant absorption of GaP in this range, the spectrum has a well-behaved shape, facilitating spectroscopic applications. In the context of the recent rapid evolution of high-power Yb-based femtosecond laser systems, these results show a viable route towards sources of THz pulses combining broad bandwidth, high average power and a smooth spectral shape.


Introduction
The generation of coherent THz transients and the possibility to sample their electric fields-both processes using ultrashort near-infrared (NIR) laser pulses-have marked the birth of THz time-domain spectroscopy (THz-TDS) about three decades ago [1,2]. Since then, the coherent nature of this scheme, rendering it insensitive to thermal background and enabling the detection of very weak fields, has led to a rapid growth of the fields of THz spectroscopy and microscopy. Today, THz-TDS is widely employed in areas including nondestructive inspection, gas sensing, biological research and material science, to name a few examples [3][4][5][6][7]. The steadily increasing number of applications is accompanied by a growing demand for THz-TDS systems combing broadband spectral coverage with high average power and, preferably, a high-repetition-rate.
There are three main, well-established methods for ultrafast-laser-based THz generation and detection: laser-driven gas ionization [8][9][10][11][12], photoconductive switching in semiconductor-based antennas [13][14][15][16][17][18] and phase-matched optical rectification (OR) in crystals [19][20][21][22][23]. The first method relies on the ionization of gas atoms/molecules, leading to a current of photoelectrons with a steep temporal gradient [10,11]. While with this method, ultrabroadband THz spectra reaching deep in the mid-infrared range have been generated [9,12], photoionization of the gas requires peak intensities of the driving laser field on the order of 10 13 -10 15 W cm −2 . Such intensities are usually available only at repetition rates significantly below 1 MHz, limiting the average power of driving laser systems to the Watt level. Together with conversion efficiencies in the range of 10 −6 -10 −3 , this results in at most a few hundreds of μW of THz average powers [12].
Generation and detection of THz radiation using photoconductive antennas (PCAs) has been extensively studied after the first demonstration by Auston and Smith in 1983 [13], in particular with titanium-sapphire and erbium-doped fiber lasers. In 2003, Shen et al reported the generation and detection of THz radiation by using low-temperature-grown GaAs PCAs driven with a 12 fs titanium-sapphire laser, resulting in frequencies beyond 30 THz at −60 dB intensity [14], albeit suffering from the poor power scalability inherent to this laser technology. The central wavelength of erbiumdoped fiber lasers coincides with the minimum absorption in fused silica, providing ideal conditions for fiber-coupled PCAs, employing pulse durations around 100 fs for generation and detection [16]. While these systems reach impressive peak dynamic ranges of more than 100 dB, allowing the detection of frequency components up to 5 THz, the −30 dB spectral width is currently limited to 2.5 THz, with a THz average power of up to 100 μW, at 120 V bias voltage and 30 mW illumination power [16]. THz generation with PCAs driven by 1.0 μm lasers [17,18] has so far not surpassed these parameters.
The second-order nonlinear process of OR has been used in conjunction with a multitude of nonlinear crystals and driving wavelengths. High pulse energies (>100 μJ) were achieved by OR in LiNbO 3 using the tilted pulse front scheme and cryogenically cooled crystals, but the spectral emission is confined to 0.1-1 THz at −20 dB intensity [19,20]. Organic THz crystals, such as DAST [21], DSTMS [22], HMQ-TMS [23] can offer 10 THz broad spectra at room temperature. However, strong transverse optical (TO) phonon resonances at multiple THz frequencies [24] have several detrimental effects. Firstly, they limit the power scalability due to strong absorption [25]. Secondly, the strong absorption renders accurate spectroscopic measurements around these frequencies challenging. As an indirect bandgap zincblende crystal, GaP has a moderate electro-optic coefficient (d 14 =70.6 pmV −1 at 1.064 μm) and its first TO phonon frequency is lying as high as 11 THz, which potentially affords a smooth frequency response in the <10 THz range [26]. Figure 1 shows calculated OR spectra for 20 fs driving pulses and a 2 mm thick GaP crystal. An optimum with respect to the bandwidth and efficiency is reached for driving wavelengths around 1 μm. In addition, the absorption coefficients of GaP single crystals are low in both the THz wave (α ∼ 3 cm −1 at 1 THz) and NIR ranges (α<0.1 cm −1 at 1.064 μm). In particular, in the context of the rapidly progressing Yb-based high average-power laser technology [27][28][29][30][31][32][33][34], these aspects make OR of ultrashort ∼1 μm pulses in GaP a highly promising route towards the combination of high THz average power and broad bandwidth. So far, Chang et al reported THz generation in GaP pumped by a 210 fs, 10 W Yb-fiber laser, providing 6.5 μW average power with a −60 dB spectral width of 3.5 THz [35]. Li et al showed THz pulse generation in GaP driven with a chirp-tunable sub-60 fs Yb-fiber amplifier and an average power of 82.6 μW was obtained at 9 W pump power with negatively chirped pulses, at the cost of THz spectral bandwidth (2 THz at −10 dB intensity) [36].
In this work, we investigate the bandwidth scaling of OR in GaP, driven by ultrafast pulses spectrally centered at 1.05 μm. With a 78 MHz-repetition-rate train of 20 fs pulses with an average power of 5.5 W, we generated and detected a three-octave-spanning THz spectrum, centered at 1.5 THz and extending to 5 THz at −50 dB intensity, via OR in a 2 mm thick (110) GaP crystal. To the best of our knowledge, this is the broadest THz spectrum generated with a 1.0 μm, MHz-repetition-rate ultrafast pump source. Furthermore, the scheme is likely to be power scalable and the well-behaved shape of the spectrum is beneficial for applications in spectroscopy. Figure 2 shows the experimental setup for THz generation and field-resolved detection. The pump source is an Ytterbium-based master-oscillator-power-amplifier laser system. The Yb:KYW seeding oscillator delivers 170 fs pulses with an average power of 220 mW at a repetition frequency of  78 MHz. The pulses are amplified using a chirped-pulse amplifier (CPA) with a transmission-grating-based stretcher and compressor, and a two-stage fiber amplifier [31]. The output of the CPA is a train of 270 fs pulses which is launched to a large-mode-area photonic crystal fiber (LMA-25, NKT) for spectral broadening. Subsequent compression to a pulse duration of 20 fs is achieved with chirped mirrors. The maximum output power is 11 W. The spectrum and autocorrelation are shown in figure 3.

Experimental setup
The 20 fs pulses are split into a pump beam (5.5 W) for THz generation and a probe beam (400 mW) for detection. The pump beam is focused by a lens with 250 mm focal length into a 2 mm thick (110) GaP crystal (Egorov Scientific). The THz pulses are generated in transmission geometry by OR. The following four 90°off-axis parabolic mirrors are used to collect, collimate and focus the THz radiation for electro-optical detection. The probe beam is guided over a delay line and superimposed onto the THz beam through the hole in the third parabolic mirror. The THz beam and probe beams are focused on a 500 μm thick (110) GaP crystal for standard electro-optic sampling [37][38][39]. The pump beam is modulated by a mechanical chopper, operating at 3.8 kHz, and the signal is read out by a lock-in amplifier with 300 ms time constant. The output power of the THz wave is measured by a Golay cell (TYDEX). The entire setup is enclosed and purged with dry nitrogen to reduce water vapor absorption. The humidity was approximately 15% during all measurements.

Results and analysis
Broadband THz radiation is generated by OR in a 2 mm thick GaP crystal at an optical pump power of 5.5 W. The beam diameter on the GaP crystal is around 80 μm, and the peak intensity is 70 GW cm −2 , which is close to the damage threshold of GaP reported in [40]. The average power of the THz wave is 1.5 μW measured by a commercial Golay cell, which is comparable to the results in [35]. A black painted ceramic filter is used to block the residual IR beam. The transmission of this filter is measured to be ∼70% in the THz range. Figure 4 shows the measured THz transient electric field. The THz pulse duration determined from these data is ∼570 fs (intensity FWHM). The main pulse is followed by a series of oscillations extending to 10 ps, originating from water vapor absorption. Figure 5 shows the corresponding THz power spectrum and spectral phase calculated by Fourier transform. The THz spectrum is centered at 1.5 THz and extends to more than 5 THz with a 55 dB detection dynamic range. The dips in the spectrum stem from residual water vapor absorption along the THz wave path, as confirmed by comparison with the water absorption lines (plotted in pink line) from the HITRAN database [41]. The simulated spectral phase is calculated from the refractive index of GaP [42], taking into account the thickness of the crystal. The measured and simulated phase show excellent agreement. The spectral phase is almost flat for frequencies lower than 2 THz. Since GaP has a strong resonant TO phonon peak around 11 THz   [42], the material dispersion is relatively large in the THz range of a few THz, leading to a visible chirp on the pulse. By tuning the grating pair inside the Yb CPA system, the duration of the driving pulses is altered to 50 fs and 90 fs, respectively. Driving OR with longer pulses results in a significant decrease of the THz power spectral density at higher frequencies, as illustrated in figure 6.
To confirm the results theoretically, we carried out simulations of the THz generation and detection processes. The simulations are based on the nonlinear wave equation in the slowly-varying amplitude approximation, and account for the full dispersion and nonlinear propagation of broadband light pulses. The governing differential equation in the frequency domain reads [43]: where E ω is the complex amplitude of an individual spectral component, P NL w ( ) is the nonlinear polarization (here governed by a second-order susceptibility), and n(ω) is the frequency-dependent refractive index [37]. In figure 7, the simulated and detected spectra are compared, showing very good agreement when phase-matching and NIR-pulsedependence of both OR and EOS are considered.

Conclusion
In summary, we have presented broadband THz generation by OR of 20 fs pulses spectrally centered at 1 μm, with an average power of 5.5 W and a repetition frequency of 78 MHz, in a GaP crystal. With electro-optical sampling employing a 0.5 mm GaP crystal, frequencies up to 5 THz (at −50 dB intensity) are measured. To the best of our knowledge, this represents the most broadband THz spectrum generated with Yb-based laser systems. We show in theory and experiment that the short pulse duration is crucial for achieving this bandwidth. The power level in the few-μW range is consistent with previous experiments. Given the power scalability of OR in GaP [35,36] and the recent progress towards high-power Yb-based lasers [27][28][29][30][31][32][33][34], these results show a viable route towards the generation of highpower, broadband, high-repetition-rate THz pulses.