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Abstract
We demonstrate a table-top source delivering ultra-broadband THz pulses with electric field strength exceeding 100 kV/cm at a repetition rate of 200 kHz. The source is based on optical rectification of 23 fs pulses at 1030 nm delivered by a ytterbium-doped fiber laser followed by a nonlinear temporal compression stage. We generate THz pulses with a conversion efficiency of up to 0.11 % with a spectrum extending to 11 THz using a 1 mm thick GaP crystal and a conversion efficiency of 0.016 % with a spectrum extending to 30 THz using a 30 µm thick GaSe crystal. The essential features of the emitted THz pulse spectra are well captured by simulations of the optical rectification process relying on coupled nonlinear equations. Our ultrafast laser-based source uniquely satisfies an important requirement of nonlinear THz experiments, namely the emission of ultra-broadband THz pulses with high electric field amplitudes at high repetition rates, opening a route towards nonlinear time-resolved THz experiments with high signal-to-noise ratios.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) pulses provide a direct probe to explore low-energy elementary excitations in condensed matter as well as the electronic and structural dynamics of molecules and solids [1–3]. THz pulses associated with strong electric field also allow to investigate nonlinear regimes of THz light-matter interaction [4,5]. For instance, THz pulses with electric fields of strength larger than few tens of kV/cm have given rise to a wide variety of nonlinear physical processes such as high harmonic generation in bulk solids [6,7], in Dirac semimetals [8,9] and in semiconductor quantum wells [10], the manipulation of Dirac current in topological surface bands [11,12], the coherent control of atomic lattices [13–15], the ultrafast impact-ionization in narrow-gap semiconductors [16] , the nonlinear response of superconductors [17,18] and ultrafast phase transition [19,20]. Therefore, there is a strong and rising interest in ultrafast laser-based sources delivering intense THz pulses and in their implementation in time-domain and time-resolved spectroscopic techniques.
Current ultrafast laser-based sources of intense THz pulses, with high pulse energy or high electric field, are mainly based on optical rectification (OR) in nonlinear crystals [21–25], photoconductive antennas [26] or gas-ionization [27–30] driven by femtosecond optical pulses at low repetition rate (in the kHz or sub-kHz range). OR can generate electric fields of a few tens of MV/cm [22,24,31,32], photoconductive antennas provide THz electric fields of >230 kV/cm [26] and gas-ionization technique delivers peak field strengths exceeding several MV/cm over an extremely broad bandwidth [33]. Although a strong electric field can be generated, many applications demand a high signal-to-noise ratio that implies increasing the repetition rate of the ultrafast laser. To meet the demand to generate intense THz pulses (with electric field amplitude of at least a few tens of kV/cm) at higher repetition rate, the intermediate range between 100 kHz and 1 MHz, between conventional amplifiers and oscillators, is particularly interesting but has remained elusive. In this context, the availability of high-power femtosecond Ytterbium lasers that deliver optical pulses at 1030 nm wavelength with energies of tens of microjoules at repetition rates >100 kHz is of strong interest and is starting to enrich the THz domain. However, the emission of intense THz pulses using photoconductive antennas driven by high-energy optical pulses from Ytterbium lasers requires efficient photoconductive materials absorbing at 1030 nm and strategies to overcome saturation effects. On the other hand, gas-ionization techniques require millijoule energy range that is not provided by current high-power femtosecond Ytterbium lasers. The generation of THz pulses by OR of optical pulses at 1030 nm wavelength delivered by Ytterbium lasers at high repetition rate has resulted in electric field strength mostly limited to $\sim$10 kV/cm [34–40]. Only recently, using tilted-pump-pulse-front scheme at 1030 nm in LiNbO$_3$ crystal, electric fields exceeding 150 kV/cm at a repetition rate of 100 kHz have been reported [41,42] but with a spectral bandwidth lower than 3 THz and a central frequency centered at 0.6 THz. Using difference frequency mixing between signal and idler pulses, pulses with peak fields exceeding 13 MV/cm at a repetition rate of 190 kHz has been reported but at mid-infrared frequencies [43]. Therefore, generation of ultra-broadband THz pulses with electric field amplitude of at least few tens of kV/cm at elevated repetition rates (> 100 kHz) is still in its infancy.
Here, we report on a table-top THz source delivering ultrabroadband THz pulses with electric field strength exceeding 100 kV/cm at a repetition rate of 200 kHz. Our approach relies on collinear OR in GaP and GaSe crystals of 23 fs optical pulses at 1030 nm wavelength delivered by a ytterbium-doped fiber laser followed by a stage of nonlinear temporal compression in a gas-filled capillary. The spectral bandwidth of the emitted THz pulses is ultrabroad, extending to 11 THz using a GaP crystal and up to 30 THz using a GaSe crystal. The main properties of the emitted THz pulse spectra are well reproduced by a numerical model for optical rectification based on coupled nonlinear equations solved using the split-step Fourier technique. Our THz source that emits ultra-broadband pulses with strong electric field strength (in excess of $\sim$100 kV/cm) at high repetition rate (>100 kHz) addresses an important requirement of nonlinear time-resolved THz experiments to significantly improve their signal-to-noise ratios.
2. Experimental results
2.1 Post-compressed Yb-doped femtosecond source
Our driving laser system and the experimental setup are schematically depicted in Fig. 1(a). The ytterbium-doped fiber laser operating at 200 kHz delivers 210 $\mu$J (42 W average power) and 125 fs-long pulses centered at 1030 nm (Tangerine, Amplitude). The optical pulses, with an average power of 20 W, are first coupled to a 1-m long hollow core fiber capillary filled by krypton at a pressure of 5.8 bar that broadens the pulse spectrum through self-phase modulation, and then compressed by two chirped mirrors. This stage of nonlinear temporal compression results in optical pulses centered at 1033 nm wavelength with a spectral bandwidth of 120 nm, a pulse duration of 23 fs and an average power > 13 W (see Fig. 1(b)). Thus, our laser source provides hundreds of MW peak-power optical pulses with only a few watts of average power. The optical pulses are then sent into a THz time-domain spectroscopy setup. The optical beam is split by a 90:10 beamsplitter into pump and probe beams, respectively. The intensity of the optical beam in each path is controlled through the combination of a half-wave plate and a germanium window set at Brewster angle. The size of pump and probe beams are reduced by the insertion of beam condensers, made of a pair of concave and convex mirrors, and the laser radius of the pump and the probe beams at the nonlinear crystal position is $\approx$ 400 $\mu$m. We use a <011>-cut 1 mm thick GaP crystal and a <001>-cut 30 $\mu$m thick GaSe crystal for OR. The duration of the optical pulses incident on the nonlinear crystals is slightly increased to 25 fs. The emitted THz pulses are collected and focused into an electro-optic crystal by two off-axis parabolic mirrors. The residual optical pump is removed from the THz radiation optical path using a longpass filter. The electric field waveforms are then recorded using electro-optic sampling technique, together with a quarter-wave plate, a Wollaston prism and a Nirvana balanced optical receiver connected to a lock-in amplifier phase-locked to a chopper in the pump beam at 3.5 kHz. The average power of the probe beam incident on the electro-optic crystal is $\sim$ 200 mW. The whole THz radiation path is purged with dry air (humidity below 2 %) to reduce THz absorption due to water absorption in the air.
Fig. 1. Experimental setup consisting of the ytterbium-doped fiber laser followed by a stage of nonlinear temporal compression in a gas-filled capillary and the THz generation and detection setup. CM: chirped mirror, 1/2 WP: half wave-plate, GP: Germanium window, Cx. M: convex mirror, Cv. M: concave mirror, NLC: non-linear crystal, PM: parabolic mirror, 1/4 WP: quarter wave-plate, WP: Wollaston prism, BPD: balanced photodetector. The pump beam is chopped at 3.5 kHz with a mechanical chopper, which enables lock-in detection. (b) The spectrum of the optical pulses of 23 fs duration with 13.6 W average power.
2.2 Waveforms and spectra of the emitted THz pulses
Figure 2 shows the THz pulses generated by collinear OR in the non-organic crystals pumped by the 25 fs, 1030 nm, 200 kHz optical pulses. The average power of the optical pulses incident on the crystals is 2 W and their peak intensity is estimated to be $\sim$ 79 GW/cm$^2$. The typical waveform of the THz pulse generated in the <011>-cut 1 mm thick GaP crystal and its amplitude spectrum are reported in Figs. 2(a) and (b), respectively. We use a 100 $\mu$m thick GaP crystal for the electro-optic detection and a high pass filter made of a multilayer dielectric on a silicon substrate to block the residual optical pump. We observe a broadband spectrum extending up to 11 THz. The signal-to-noise ratio is >300 (i.e. $\sim$50 dB in power) for an integration time of the lock-in amplifier of 500 ms. The frequency spectrum shows two clear features; one expanding from the lowest detectable frequency up to $\sim$ 7.5 THz, where the nonlinear electro-optic constant of GaP, r$_{41}$, becomes 0 [44]. The other feature extends from 7.5 THz to $\sim$ 11 THz where the signal vanishes due to the combined effect of the mismatch between the group velocity of optical pump pulses and the phase velocity of the THz pulses, and the THz absorption by optical phonons of GaP crystal [45]. To explore a broader spectral range, we use a 30 $\mu$m thick GaSe crystal as emitter and a 20 $\mu$m thick ZnTe crystal for electro-optic detection. The typical THz waveform generated from OR in the GaSe crystal and its amplitude spectrum are reported in Figs. 2(c) and 2(d), respectively. The wavevector of the optical pump is set parallel to the $c-$ axis of the crystal and the azimuthal angle between the optical pump field direction and crystalline $x$-axis is set to 60 degrees to obtain both ordinary and extraordinary polarized components of the optical pump field. The residual pump beam is now blocked using a broadband germanium plate. We observe that the THz waveforms emitted by the GaSe crystal exhibit a low frequency envelope similar to those emitted by the GaP crystal, overlaid with additional high frequency modulation. On the amplitude spectrum, we clearly observe two distinct features: one extending from the lowest detectable frequency to 5 THz and a wider part spanning from 7 THz to beyond 30 THz. The very weak signal beyond 30 THz on the spectrum results from the OR of the extremities of the optical pump spectrum. The dip in the region between 5 THz to $\sim$ 7 THz is caused by ZnTe optical phonon absorption and the Reststrahlen band of GaSe material. The extra modulation observed on the spectrum results from multiple reflections of the THz beam inside the GaSe crystal. While many studies on OR of optical pulses centered at 800 nm wavelength in GaSe crystals have been reported to date [46,47], OR of optical pulses centered at 1030 nm wavelength in GaSe crystal remains unexplored until now.
Fig. 2. Optical rectification in non-organic crystals. Top panel (a) Waveform generated in a 1 mm thick GaP crystal, retrieved by electro-optic detection based on a 100 $\mu$m thick GaP crystal. (b) Corresponding normalized amplitude spectrum obtained by Fourier transform of the waveform in (a). Bottom panel (c) Waveform generated in a 30 $\mu$m thick GaSe crystal, retrieved by electro-optic detection based on a 20 $\mu$m thick ZnTe crystal. (d) Corresponding normalized amplitude spectrum obtained by Fourier transform of the waveform in (c).
2.3 Average THz power and efficiency
The emitted electric field amplitude is now investigated with respect to the average power of the optical pump. Figures 3(a) and 3(c) display the squared value of the peak-to-peak THz electric field ($|E_{pp}|^2$) emitted by OR in the GaP and GaSe crystals, respectively, as a function of the incident pump power. We observe a quadratic increase of $|E_{pp}|^2$ with the optical pump power, as expected for OR process, up to $\sim$2 W (peak intensity of $\sim$ 79 GW/cm$^2$) in the GaP crystal and to $\sim$1 W (peak intensity of $\sim$ 39 GW/cm$^2$) in the GaSe crystal. Beyond these regimes, the electric field amplitude increases quasi linearly with the pump power as two-photon absorption effects become substantial [21]. Note that up to the maximum power incident on our crystal (3.8 W) we did not observe any thermal effect. However, by further increasing the average power, thermal effects start to induce instability in the delivered THz power. Next, we measure the emitted THz average power by replacing the electro-optic detection crystals by a pyroelectric detector. The THz radiation is chopped at 10 Hz and the THz average power is recorded using a lock-in amplifier. To prevent detection of residual scattered light coming from the optical pump beam, an additional filter made of a thin black plastic is added in front of the pyroelectric detector. The transmission of each of the filters was measured from 0.2 THz to 6 THz using standard THz time domain spectroscopy system [48] and accounted for in the reported power values. We measure a THz average power of 1.66 mW (8.3 nJ per pulse) and of 325 $\mu$W (1.6 nJ per pulse) generated by OR in the GaP crystal and in the GaSe crystal, respectively, for an optical pump power of 2 W. From these calibrations, we deduce the conversion efficiency as a function of the optical pump average power for each crystal (right axis in Figs. 3(a) and 3(c)). The optical-to-THz conversion efficiency reaches up to 0.11 % and 0.016 % for OR in GaP and GaSe crystals, respectively, at the maximum optical pump power.
Fig. 3. THz power vs the average power of the optical pump. (a) Left axis shows the evolution of the squared value of the peak-to-peak THz electric field, $|E_{pp}|^2$, and right axis shows the optical-to-THz conversion efficiency of OR in the GaP crystal as a function of optical pump power. (b) THz spot image at focus. The sections of the THz beam along the x coordinate (y=0) and y coordinate (x=0) are shown on top hand side and right of the image, respectively. (c) THz peak electric field and conversion efficiency for OR in the GaSe crystal as a function of optical pump power. (d) The THz image at focus. The sections of the THz beam along the x coordinate (y=0) and y coordinate (x=0) are shown on top hand side and right of the image, respectively.
2.4 Beam intensity profile and THz electric field strength
Next, we focus the THz beam onto a RIGI uncooled micro-bolometer THz camera using a $f/1$ parabolic mirror to record the intensity profile, at the focal plane, of the THz pulses generated by OR in the GaP and GaSe crystals. The 2D spatial distributions in the focal plane of the emitted THz beams are reported in Fig. 3(b) and 3(d) for GaP and GaSe crystals, respectively. With the GaP crystal, the emitted THz beam shows a slight ellipticity along the x direction, attributed to aberrations introduced by the focusing parabolic mirror. The sections of the THz beam profile along the x coordinate (y=0) and y coordinate (x=0) (red curves) are very well overlapped by a Gaussian fit (black curves). The $1/e^2$ intensity radius of the focused THz beam is $w_x$ = 380 $\mu$m along $x$ direction and $w_y$ = 295 $\mu$m along $y$ direction. With the GaSe crystal, the image clearly shows a roughly circular cross-section of the THz beam profile at the focal plane (see Fig. 2(f)). The sections of the THz beam along the x coordinate (y=0) and y coordinate (x=0) (red curves) are very well overlapped by a Lorentzian fit (black curves) in contrast to the GaP crystal. The $1/e^2$ intensity radius of the focused THz beam is as small as 217 $\mu$m along $x$ direction and 214 $\mu$m along $y$ direction.
From the collected THz average power, the THz beam spot size together with the electro-optic measurements, we now estimate the peak electric field strength at the focal plane using the Poynting vector approach. For that, we calculate the peak intensity of the Gaussian THz pulses at the focus using $I_{peak} = 2P_{peak}/(\pi w_x w_y)$, where $P_{peak}$ is the THz peak power. The THz pulse duration is extracted from the intensity full width at half maximum (FWHM) of the temporal traces of the THz pulses reported in Figs. 2(a) and 2(c). We found a THz pulse duration emitted from the GaP crystal and the GaSe crystal of 400 fs and 155 fs, respectively. The peak electric field at the focus is then given by $E_0= \sqrt {\frac {2I_{peak}}{c \epsilon _{0}}}$, where $c$ is the speed of light and $\epsilon _{0}$ the vacuum permittivity. We determine a peak electric field of the THz pulses generated by the GaP crystal exceeding 150 kV/cm for an optical pump power of 3.85 W. This value exceeds the highest values reported so far with this nonlinear crystal [38]. The peak electric field emitted by the GaSe crystal is as high as 104 kV/cm for a pump power of 2 W. Also, such value has not yet been achieved with OR in GaSe crystal. These large values of THz pulse electric field strength at a 200 kHz repetition rate show that our ultra-broadband THz source is particularly well suited to sensitive THz nonlinear experiments.
3. Theoretical model for optical rectification
In order to more quantitatively interpret the observed experimental THz spectra we develop a numerical model based on coupled nonlinear propagation equations solved using the split-step Fourier method [49], which includes frequency-dependent nonlinear coefficients [50]. For the isotropic GaP crystal, the nonlinear part of the propagation is solved in the time domain according to the following differential equations:
For the uniaxial GaSe crystal, two wave mixing configurations are taken into account, namely THz (o) + pump (o) -> pump (e) and THz (e) + pump (o) -> pump (e), allowing the generation of THz radiation on both the ordinary (o) and extraordinary (e) polarization states. As a result, the nonlinear propagation equations are given by:
Fig. 4. Comparison between experimental and theoretical spectra for THz pulses generated with (a) a GaP crystal and (b) a GaSe crystal. In GaSe crystal, both extraordinary and ordinary THz waves are generated.
4. Conclusion
In conclusion, we provide a 200 kHz repetition rate source of ultra-broadband intense THz pulses based on OR driven by a femtosecond post-compressed ytterbium-doped fiber laser. We generate THz pulses with a conversion efficiency of 0.11 % and of 0.016 % using a GaP and GaSe crystal, respectively, with an electric field strength greater than 100 kV/cm. The spectra of the emitted THz pulses are well captured by simulations of the optical rectification process relying on coupled nonlinear equations. Our THz source, which delivers ultra-broadband THz pulses with high electric field amplitudes at high repetition rates, should enable more sensitive spectroscopy experiments of THz-induced nonlinear processes or pump-probe experiments.
Funding
H2020 European Research Council (ERC grant agreement No. 820133).
Acknowledgments
We thank Y. Zaouter, A.Maghraoui and F. Guichard for their assistance on the laser system.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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