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Abstract
We demonstrate a highly efficient method for the generation of a high-field terahertz (THz) pulse train via optical rectification (OR) in congruent lithium niobate (LN) crystals driven by temporally shaped laser pulses. A narrowband THz pulse has been successfully achieved with sub-percent level conversion efficiency and multi MV/cm peak field at 0.26 THz. For the single-cycle THz generation, we achieved a THz pulse with 373-μJ energy in a LN crystal excited by a 100-mJ laser pulse at room temperature. The conversion efficiency is further improved to 0.77 % pumped by a 20-mJ laser pulse with a smaller pump beam size (6 mm in horizontal and 15 mm in vertical). This method holds great potential for generating mJ-level narrow-band THz pulse trains, which may have a major impact in mJ-scale applications like terahertz-based accelerators and light sources.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, tremendous efforts have been concentrated on intense single-cycle terahertz pulse generation due to its increasing applications in fundamental sciences and advanced technologies [1]. For example, THz field-induced modifications of conductivity in materials [2,3], THz-driven electron bunch compression [4,5] and THz streaking [6,7]. However, for some emerging applications, such as THz-driven acceleration [8–12] and nonlinear THz spectroscopy [13–15], high energy, high-field THz pulse train with narrow bandwidth and low frequencies are in urgent demand. It holds the potential to overcome the limitations of plasma breakdown threshold in radio-frequency accelerators.
A well-established approach of generating narrowband THz pulse train is coherent radiation based on ultrashort electron bunches [16,17]. However, the compromise between electron bunch duration and bunch charge makes it difficult to enhance the field strength of THz pulses. With the development of joule-level ultrafast laser systems, OR driven by temporally shaped laser pulse has recently emerged as a promising route for the generation of high power, narrowband THz pulse trains. Various temporal pulse shaping methods have been explored for producing narrowband THz pulse train, such as spectrum modulated by liquid crystal light filter [18,19], frequency beating of two chirp-and-delay pulses [20–23] and purely beam splitter based on Michelson interferometer or etalon [24,25]. Among these, OR in cryogenically cooled periodically poled lithium niobite crystal with etalon-based chirp-and-delay pulse [22,23] has produced narrowband THz pulse with 0.6 mJ energy, 0.24 $\%$ conversion efficiency and $\sim$18 MV/m peak field strength. While, a chirp-and-delay method is also appropriate for homogeneous nonlinear crystals with larger nonlinear optical coefficients, such as organic crystal [20] and lithium niobite [21]. Though the chirp-and-delay method has shown its capability in generating optical pulse train with tunable periodicity and number, the conversion efficiency still needs to be improved which is currently limited by inherently high-order dispersion in the chirped pulses.
High efficiencies in nonlinear optical conversion processes require high pump energy and appropriate pulse duration. In 2013, OR with tilted pulse front (TPF) technique in cryogenically cooled LN crystal has produced 3.8 $\%$ optical-to-THz conversion efficiency by using a 1030 nm laser source with 680 fs pulse duration [26]. Recently, this approach has successfully obtained 1.4 mJ THz pulses by a Ti:sapphire laser system with pump energy of 214 mJ [27]. Alternatively, temporal shaping technique based on multi-stage Michelson interferometer [28] and birefringent crystal [29] can provide high energy optical pulse train with tunable pulse durations. Meanwhile, more pump laser energy in LN crystal can be employed without exceeding the optically induced damage threshold by dividing a pulse into several smaller pulses with uniform pulse durations. The combination of TPF excitation in LN crystal and Michelson interferometer-based temporal shaping method offers the opportunity to generate a high-field THz pulse train with high efficiency. In addition, this method has the potential for THz waveform synthesis by turning the amplitude and the temporal spacing of the pump laser pulses.
In this paper, we demonstrate an efficient method for high field THz pulse train generation in a bulk LN crystal with chirped Ti:sapphire laser pulses. High energy laser pulse trains are provided by a two-stage Michelson interferometer combined with a birefringent crystal to reduce the complexity of the optical configuration. To optimize the optical to THz conversion efficiency, a 2:1 relay-imaging telescope is applied with different pump beam sizes. A single-cycle THz pulse with 0.77 $\%$ conversion efficiency is obtained excited by a laser pulse with 28.3 mJ/cm2 (20 mJ) pump fluence and 700 fs pulse duration at room temperature. With this scheme, combining with temporally shaped optical waveforms, we obtain a uniform THz pulse train with $\sim$1.8 MV/cm peak electric field strength and 50 GHz bandwidth at 0.26 THz, and the conversion efficiency is comparable with that of the single-cycle case. With this method, mJ-level narrowband THz pules would be expected with an upgraded pump laser source, which may enable unexplored technologies and researches in terahertz-based accelerators and light sources.
2. Experimental setup
The experimental setup is shown in Fig. 1(a). A Ti:sapphire laser system was used as the pump laser with 1.2 J maximum output energy, 5 Hz repetition rate, and 100 fs Fourier transform-limited pulses duration at 790 nm central wavelength. A compressor in the laser system can provide both positive and negative chirp with tunable pulse duration by changing the grating spacing. The maximum pump laser energy used in our experiment was 100 mJ due to the damage limitation of the grating in non-vacuum condition and the LN crystal. A bit of pump laser was separated as probe pulse for electro-optical (EO) detection.
Fig. 1. (a) Experimental setup for high-field THz pulse train generation from congruent lithium niobate with TPF technique and EO sampling detection. TFP: thin-film polarizer; BS: beam splitter (50:50); HWP: Half-wave plate; cL: cylindrical lens; cLN: congruent lithium niobate; OAP: off-axis parabolic mirror; BPD: balanced photodiode. (b) The pump laser beam profile in the cLN.
An optical pulse train generation with multiple Michelson interferometers has been demonstrated with approximately 100 $\%$ efficiency [28], but with complex configuration. In our experimental setup, we used a relatively simple hybrid approach which consisted of a two-stage Michelson interferometer and a calcite crystal. A horizontally polarized laser pulse was separated by two beam splitters with 50:50 ratio, then polarizations were multiplexed via a half-wave plate (HWP) and a thin-film polarizer (TFP). The temporal spacing of the pulse train can be easily tuned by two optical delay lines. For simplicity, a 6.6-mm-thickness calcite crystal with 98 $\%$ calibrated transmission at 790 nm wavelength was placed after the TFP. We set the angle between the incident laser polarization (Orthogonal linear polarization) and the ordinary axis of the crystal to be $45^{\circ }$, which divides the pulse train into 8 pulses with uniform intensities and alternating polarizations at $45^{\circ }$. A linear polarizer oriented horizontally is then placed after the calcite crystal to form a pump laser pulse train of 8 pulses with horizontal polarization and $\sim$49 $\%$ of the incident light. The time delay between each adjacent pulses is 3.8 ps which can be calculated by ${{\bigtriangleup} \tau }=L\cdot [n_o(\lambda _0)-n_e(\lambda _0)]/c$, where $L=$ 6.6 mm is the thickness of calcite crystal, $n_o(\lambda _0)\approx 1.66$, $n_e(\lambda _0)\approx 1.49$ are the group velocity refractive indices of the ordinary and extraordinary axes [29], $c$ is the speed of light in vacuum.
In the TPF setup, a grating with 1800 lines/mm was used to tilt the intensity fronts of the pump pulses with an incidence angle of $41^{\circ }$, and the horizontal counterpart of the pump laser pulse train was diffracted (-1st order) from the grating with a diffraction angle of $50^{\circ }$. To improve the THz generation efficiency, a cylindrical imaging telescope was used to image the grating surface into the LN crystal, which has slight pulse front distortions compared with a single-lens imaging scheme [30–33]. The imaging system consists of two cylindrical lenses with focal length $f_1=200$ mm, $f_2=100$ mm, giving a demagnification factor of $-$ 0.5. The elliptic pump beam axis lengths on the LN crystal were 6 mm in horizontal and 15 mm in vertical as illustrated in Fig. 1(b). An HWP in front of the LN was used to rotate the polarization of the pump laser pulses to the optical axis of the LN crystal. The congruent LN crystal used for OR with 5 mol$\%$ MgO-doped, and cut into an isosceles triangle with two base angles of $63^{\circ }$, which can be a benefit to THz generation, such as reduce THz absorption in LN crystal [34], as well as improve the optical damage threshold of the crystal [35]. The input surface with an effective size of 22.7 $\times$ 35 mm$^2$ (horizontal $\times$ vertical) was anti-reflective (AR) coated at the pump laser wavelength. The THz output surface of the LN was coated with a polyimide layer of $\sim$70 $\mu$m thickness (Thorlabs, KAP22-075) to improve the THz transmission efficiency.
The generated THz pulses were collected and focused by an off-axis parabolic mirror (OAP) with 25.4-mm-focal length. The energy of THz pulse was measured near the focal plane by a calibrated Golay cell from TYDEX [36]. To avoid saturation of the Golay cell and block the residual pump laser, a THz attenuator with 2.8 $\%$ calibrated transmission and a low-pass filter (LPF 4.0-35, TYDEX) with 62 $\%$ transmission were placed in front of the detector. A $384\times 288$ pixels uncooled microbolometer FPA THz camera with 35 $\mu$m pixel pitch (model MICROXCAM-384i-THz, INO) was used to characterize THz beam profile. The temporal profile of the THz pulses was measured by means of electro-optic sampling (EOS) technique. The probe laser split from the single-cycle pump laser was spatio-temporally overlapped with THz pulses and focused onto a 300-$\mu m$-thick, $10\times 10$-mm$^2$-size, (110) cut ZnTe crystal. The EO signal was scanned by a balanced detection scheme [37] with an optical delay stage. A calibrated THz attenuator with $1\%$ transmission was placed after the LN to avoid the over-rotation of the induced birefringence in ZnTe [38].
3. Results and discussions
3.1 Optimization of single-cycle THz generation
Previous numerical models [39–42] and experimental studies [31,43–46] showed that THz conversion efficiency would be saturated in LN at intense Ti:sapphire lasers with the TPF technique. The main reasons include self-phase modulation (SPM) [42], free-carried absorption (FCA) induced by three-photon absorption (3PA) [39,40], and cascading effects in conjunction with group velocity dispersion due to angular dispersion (GVD-AD) [41,46]. Efficient methods to optimize the THz generation include optimizing the imaging system and pump laser parameters, such as tuning the pump laser pulse durations by spectral cutting and chirping, pump influence, and incident diameters.
At room temperature, we first investigated the THz generation efficiency at different pulse durations with negative or positive chirp for a fixed pump energy of 5 mJ. As illustrated in Fig. 2(a), for positive (left blue line) or negative chirp (right red line) cases, there exists an optimized pulse duration for maximizing the THz conversion efficiency. The maximum efficiencies excited by 900 fs positive and 700 fs negative chirped pulses are 0.56 % and 0.72 %, respectively. The main reason is the compromised relationship between the effective interaction length and three-photon absorption in the LN [39]. The effective interaction length is proportional to pump pulse duration. For shorter interaction length would limit the THz yield while longer interaction length would lead to increased THz absorption. This conversion efficiency is about two times higher than the previous experiment with similar ways by a 30 fs chirped Ti:sapphire laser pulses at room temperature [47]. However, the THz generation efficiencies for negative and positive chirp are asymmetric, and the conversion efficiency for negative chirp is higher than that of positive cases with the same pulse duration. This is attributed to the dispersion variation of chirped pulses with different spectrums in LN and imaging process, a negatively chirped laser pulse would undergo temporal compression in LN which has higher pump intensity for THz generation [45,48]. Figure 2(b) shows pump pulse spectra before and after interaction with the LN at pump energy of 5 mJ and a positively chirped pulse duration of 700 fs. Due to cascading effects in THz generation, obvious redshift from 790 nm to 801 nm can be seen as well as distinct spectrum broadening.
Fig. 2. (a) The THz generation efficiency as a function of the pump pulse duration for negative (right red line) and positive chirp (left blue line), respectively. (b) The transmitted pump spectra before and after interaction with the LN crystal.
The optimized setup is slightly different for different pump energies due to the compromise between the THz generation and absorption in the LN crystal [40]. Hence, the incident position of the pump beam on the LN, the chirped pulse duration as well as the imaging system were readjusted at each pump energies. Measurements of the THz pulse energy and conversion efficiency curves at room temperature are shown in Fig. 3(a) as function of pump laser energy and fluence measured before entering the LN. The maximum pump energy was 50 mJ and the corresponding peak pump fluence is 70 mJ/cm$^2$. The extracted THz pulse energy at the focal plane increases with the pump laser energy. At the maximum pump energy, we measured a 328 $\mu$J THz pulse energy and obtained 0.66 % conversion efficiency. In Fig. 3(a), the THz conversion efficiency first increases significantly with the pump fluence and starts to show saturation when the pump fluence exceeding 7.1 mJ/cm$^2$ (5 mJ). The THz efficiency goes on increasing again with the pump fluence from 12.7 mJ/cm$^2$ to 28.3 mJ/cm$^2$ and reaches a maximum THz conversion efficiency of 0.77 %. This is due to the saturation of free carrier generation when the pump fluence exceeding 12.7 mJ/cm$^2$. Free carrier saturation and its influence on THz generation have been modeled in LN crystal by 800 nm central wavelength and 700 fs pulse duration laser excitation at room temperature [40]. In this model, FCA induced by 3PA reduces THz conversion efficiency, but the concentration of free carrier in LN crystal is saturated ($\sim 4\times 10^{20}$ $m^{-3}$) when the pump fluence is 10 mJ/cm$^2$ and consequently increases the THz conversion efficiency. The THz efficiency decreases slowly when further increasing the pump fluence due to the joint effects of GVD-AD, material dispersion, SPM and the spatio-temporal distortions, etc [41,42]. Nonetheless, an efficiency of 0.77 % is achieved in LN via optical rectification pumped by a Ti:sapphire laser pulse at room temperature.
Fig. 3. The extracted THz energy and efficiency in dependence of the pulse energy and pump fluence with different pumped beam diameters. (a) 6 mm (horizontal) $\times$ 15 mm (vertical), (b) 11 mm (horizontal) $\times$ 26 mm (vertical).
To keep the pump fluence below the damage threshold of the LN crystal, we used a larger pump beam size with horizontal and vertical directions of 11 mm and 26 mm, respectively. The maximum pump energy is scaling up to 100 mJ, corresponding to a pump fluence of 44.5 mJ/cm$^2$. As shown in Fig. 3(b), the THz conversion efficiencies are lower than that in Fig. 3(a) with the same pump fluence. Due to the GVD-AD effects and the finite size of the cylindrical lenses, spatially chirped pump beam with larger beam size undergo more spectrum loss. In our experiment, the length of the cylindrical lenses (cL2) at the pump beam divergence direction is 30 mm, which is smaller than the diffraction beam size ($\sim$ 37 mm). Prior works have analytically expressed the deterioration of THz conversion efficiency at large beam sizes by GVD-AD with an undepleted model [41]. Moreover, the FCA in LN crystal may also lead to the reduction of conversion efficiency. In the case of a large pump beam, the terahertz pulse generated from the beam position farther from the phase-matching angle needs to be transmitted for a longer distance. Under the above conditions, though a highest THz pulse energy of 373 $\mu$J at 44.5 mJ/cm$^2$ pump fluence (100 mJ) is achieved at room temperature, but with a 0.38 % conversion efficiency. The saturation of THz conversion efficiency (0.46 %) requires a lower pump fluence of 3.6 mJ/cm$^2$ (pump energy 8 mJ) compared with the smaller pump beam size (Fig. 3(a)), which are in good agreement with the theoretical calculations in Ref. [40], the optimal pump fluence is nearly inversely proportional to the pump beam radius.
Figure 4 shows the spatial and temporal characteristics of THz pulse at the focal plane which is pumped by the larger beam size laser (11 mm $\times$ 26 mm) with 44.5 mJ/cm$^2$ pump fluence. The THz radiation exit of the LN crystal is focused by an OAP with 25.4-mm-focal length and measured with a THz camera (MICROXCAM-384i-THz). A THz attenuator with 1 % transmission is placed before the camera to avoid sensor damage. The spatial profile of THz focus and its cross-section intensity profiles are shown as Fig. 4(a) and Fig. 4(b), respectively. The horizontal and vertical beam diameters are both 0.6 mm (FWHM) which is close to the diffraction limit in our experimental configuration. Figure 4(c) illustrates the THz temporal waveform measured by the EOS, which is a 1.2 ps single-cycle pulse. By Fourier transformation, the spectrum depicted in Fig. 4(d) was obtained in the range of 0.1-1.2 THz centered at 0.3 THz. The THz peak electric field strength was calculated to be $\sim$9.1 MV/cm from the measured pulse energy, duration, and focal beam size.
Fig. 4. Spatial and temporal characteristics of THz focus. (a) The THz image at focal plane (25.4-mm-focal length, OAP) and (b) its Cross-section intensity profiles with Gaussian fits. (c) Temporal waveform of single-cycle THz pulse and (d) its Fourier transform spectrum.
3.2 Generation of a high-field THz pulse train
Figure 5(a) shows the cross-correlation measurement of the pump laser pulse train with a fixed energy of 20 mJ generated by a two-stage Michelson interferometer combined with a 6.6-mm-thickness calcite crystal. The sub-pulses of the train have a uniform pulse duration of 700 fs (FWHM) and 3.8 ps temporal spacing. Temporal waveform and frequency spectrum of the generated THz pulse train are shown in Fig. 5(b) and Fig. 5(c), respectively. The measured THz energy of the pulse train is $\sim$108 $\mu$J, corresponding to an optical to THz conversion efficiency of 0.54 %. In Fig. 5(c), the Fourier spectra of the THz pulses show a relatively narrow bandwidth of 50 GHz at 0.26 THz. The peak position is determined by the temporal spacing of the pump laser pulse train, which equal to the repetition rates of the laser pulse train (THz pulse train). The bandwidth is inversely proportional to the number of pulses. The spectra show harmonic frequency components at 0.53 THz and 0.79 THz. This THz pulse train is essentially temporally stacked by a train of single THz pulses ($\sim$13.5 $\mu$J, $\sim$1.2 ps) individually generated by an optical pulse train. We can see that the total conversion efficiency of the pulse train is similar to the efficiency (0.55 %) of the single-cycle THz pulse at 2.5 mJ pump energy in Fig. 3(c). The peak field strength of $\sim$1.8 MV/cm was calculated at the focus with a measured FWHM diameter of 0.56 mm.
Fig. 5. (a) Cross-correlation measurement of the pump laser pulse train with a pulse separation of 3.8 ps. (b) Temporal waveform and (c) frequency spectrum of the generated THz pulse train.
In order to quantitatively compare the THz conversion efficiencies between pulse train and single pulse, a two-stage Michelson interferometer was applied only for pulse shaping. A laser pulse train with 4 sub-pulses of uniform intensity and tunable temporal spacing was obtained by a two-stage Michelson interferometer. THz generation at different pump laser energies are given in Table 1. The temporal spacing of the pulse train is 4 ps. The measured THz energy is 143 $\mu$J by a laser pulse train with pump energy of 19.8 mJ. As shown in Table 1, although the pump fluence (28 mJ/cm$^2$) is 4 times larger than the sub-pulse, the conversion efficiency shows a similar value of 0.72 %. This shows that the efficiency of the THz pulse train is relies on the pump fluence of the sub-pulse with the same parameters rather than the pulse train. The THz output energy can be further improved by increasing the number and energy of sub-pulses as long as not to damage or saturate the crystal. Millijoule THz output energy would be expected as the pump energy of sub-pulses increased to 20 mJ in vacuum condition, which corresponds to a conversion efficiency of 0.77 %.
Table 1. THz generation at different pump lasers.
Meanwhile, with this pulse shaping configuration, we achieved THz pulse trains with tunable frequencies by changing the temporal spacing of the sub-pulses from 2 ps to 4 ps, as shown in Fig. 6. The normalized spectra are represented in Fig. 6(b), the peak frequencies are centered at 0.5 THz, 0.33 THz, and 0.26 THz, respectively. The central frequency has a reciprocal relationship with the temporal spacing of the sub-pulses. We can note that the spectra also show harmonic components. Nonetheless, high peak field strength exceeding $\sim$3.3 MV/cm was obtained. As shown in Fig. 6(a), the temporal profile of the THz pulse train with 2 ps pulse separation is more like a sinusoidal waveform. It is attributed to the terahertz pulses generated by each optical pulse of the train have a duration comparable to the temporal spacing and add up coherently. Therefore, the extracted THz energy and field strength were slightly decreased due to the coherent superposition of adjacent THz pulses.
Fig. 6. (a)Temporal waveforms and (b) frequency spectrums of the generated THz pulse trains with an adjustable temporal spacing from 2 ps to 4 ps.
4. Conclusion
In conclusion, we have demonstrated an efficient method for the generation of uniform high-field THz pulse train in LN crystal pumped by temporally modulated laser pulses in combination with TPF technique. Narrowband THz pulse train with peak electric field strength exceeding $\sim$1.8 MV/cm and 0.55 % optical to THz conversion efficiency were achieved at 0.26 THz with pump energy of 20 mJ. Specifically, it is observed that the THz generation efficiency is dependent on the pump laser fluence of the sub-pulse rather than the total pump fluence of the laser pulse train. Tunable THz pulse train with a THz conversion efficiency of 0.72 % and $\sim$140 $\mu$J THz pulse energy was also obtained at room temperature by using Michelson interferometer-based laser pulses with a sub-pulse fluence of 7 mJ/cm$^2$ (5 mJ pulse energy). With this efficient method, multi-mJ THz pulse train can be expected by further increasing the pump energy and cryogenic cooling of LN, which holds high promise for THz-pump/THz-probe spectroscopy and THz-based accelerations.
Moreover, enhancement of THz conversion efficiency by the saturation of free carries at intense pump fluence was observed in the single-cycle THz pulse generation. We have achieved an efficiency of 0.77 % in LN driven by Ti:sapphire laser system with the pump fluence of 28.3 mJ/cm$^2$ (20 mJ) and 700 fs pulse duration. By increasing the pump laser energy to 100 mJ and using a larger beam diameter, the excited THz pulse energy was measured up to 373 $\mu$J with a $\sim$9.1 MV/cm peak field strength. This method offers a feasible approach to achieving a table-top high-field THz source for beam manipulation in ultrafast electron diffraction and nonlinear THz applications.
Funding
National Natural Science Foundation of China (11835004).
Acknowledgements
We thank Prof. Qing Sun for help in the calibration of THz detector (Golay cell), and Zhanchang Huang and Qiang Yi for help with the laser system.
Disclosures
The authors declare no conflicts of interest.
References
1. J. A. Fülöp, S. Tzortzakis, and T. Kampfrath, “Laser-driven strong-field terahertz sources,” Adv. Opt. Mater. 8(3), 1900681 (2020). [CrossRef]
2. M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef]
3. B. D. O’Shea, G. Andonian, S. K. Barber, C. I. Clarke, P. D. Hoang, M. J. Hogan, B. Naranjo, O. B. Williams, V. Yakimenko, and J. B. Rosenzweig, “Conductivity induced by high-field terahertz waves in dielectric material,” Phys. Rev. Lett. 123(13), 134801 (2019). [CrossRef]
4. E. C. Snively, M. A. K. Othman, M. Kozina, B. K. Ofori-Okai, S. P. Weathersby, S. Park, X. Shen, X. J. Wang, M. C. Hoffmann, R. K. Li, and E. A. Nanni, “Femtosecond compression dynamics and timing jitter suppression in a THz-driven electron bunch compressor,” Phys. Rev. Lett. 124(5), 054801 (2020). [CrossRef]
5. D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A.-L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (STEAM),” Nat. Photonics 12(6), 336–342 (2018). [CrossRef]
6. L. Zhao, Z. Wang, C. Lu, R. Wang, C. Hu, P. Wang, J. Qi, T. Jiang, S. Liu, Z. Ma, F. Qi, P. Zhu, Y. Cheng, Z. Shi, Y. Shi, W. Song, X. Zhu, J. Shi, Y. Wang, L. Yan, L. Zhu, D. Xiang, and J. Zhang, “Terahertz streaking of few-femtosecond relativistic electron beams,” Phys. Rev. X 8(2), 021061 (2018). [CrossRef]
7. R. K. Li, M. C. Hoffmann, E. A. Nanni, S. H. Glenzer, M. E. Kozina, A. M. Lindenberg, B. K. Ofori-Okai, A. H. Reid, X. Shen, S. P. Weathersby, J. Yang, M. Zajac, and X. J. Wang, “Terahertz-based subfemtosecond metrology of relativistic electron beams,” Phys. Rev. Accel. Beams 22(1), 012803 (2019). [CrossRef]
8. L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top.--Accel. Beams 17(3), 031301 (2014). [CrossRef]
9. E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6(1), 8486 (2015). [CrossRef]
10. E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018). [CrossRef]
11. D. Zhang, M. Fakhari, H. Cankaya, A.-L. Calendron, N. H. Matlis, and F. X. Kärtner, “Cascaded multicycle terahertz-driven ultrafast electron acceleration and manipulation,” Phys. Rev. X 10(1), 011067 (2020). [CrossRef]
12. H. Xu, L. Yan, Y. Du, W. Huang, Q. Tian, R. Li, Y. Liang, S. Gu, J. Shi, and C. Tang, “Cascaded high-gradient terahertz-driven acceleration of relativistic electron beams,” arXiv:2005.11714 (2020).
13. H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. P. Jr., M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015). [CrossRef]
14. L. H. Coudert, “Optimal orientation of an asymmetric top molecule with terahertz pulses,” J. Chem. Phys. 146(2), 024303 (2017). [CrossRef]
15. Y. Huang, T. Xie, J. Li, J. Yu, and S. L. Cong, “Efficiently field-free orientation of CO molecules by a femtosecond pulse and a THz pulse train,” Laser Phys. 24(1), 016002 (2014). [CrossRef]
16. Y. Liang, Y. Du, X. Su, D. Wang, L. Yan, Q. Tian, Z. Zhou, D. Wang, W. Huang, W. Gai, C. Tang, I. V. Konoplev, H. Zhang, and G. Doucas, “Observation of coherent smith-purcell and transition radiation driven by single bunch and micro-bunched electron beams,” Appl. Phys. Lett. 112(5), 053501 (2018). [CrossRef]
17. X. Su, D. Wang, Q. Tian, Y. Liang, L. Niu, L. Yan, Y. Du, W. Huang, and C. Tang, “Widely tunable narrow-band coherent terahertz radiation from an undulator at THU,” J. Instrum. 13(01), C01020 (2018). [CrossRef]
18. J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486–2496 (2003). [CrossRef]
19. S. Vidal, J. Degert, J. Oberlé, and E. Freysz, “Femtosecond optical pulse shaping for tunable terahertz pulse generation,” J. Opt. Soc. Am. B 27(5), 1044–1050 (2010). [CrossRef]
20. J. Lu, H. Y. Hwang, X. Li, S.-H. Lee, O.-P. Kwon, and K. A. Nelson, “Tunable multi-cycle thz generation in organic crystal HMQ-TMS,” Opt. Express 23(17), 22723–22729 (2015). [CrossRef]
21. Z. Chen, X. Zhou, C. A. Werley, and K. A. Nelson, “Generation of high power tunable multicycle teraherz pulses,” Appl. Phys. Lett. 99(7), 071102 (2011). [CrossRef]
22. F. Ahr, S. W. Jolly, N. H. Matlis, S. Carbajo, T. Kroh, K. Ravi, D. N. Schimpf, J. Schulte, H. Ishizuki, T. Taira, A. R. Maier, and F. X. Kärtner, “Narrowband terahertz generation with chirped-and-delayed laser pulses in periodically poled lithium niobate,” Opt. Lett. 42(11), 2118–2121 (2017). [CrossRef]
23. S. W. Jolly, N. H. Matlis, F. Ahr, V. Leroux, T. Eichner, A.-L. Calendron, H. Ishizuki, T. Taira, F. X. Kärtner, and A. R. Maier, “Spectral phase control of interfering chirped pulses for high-energy narrowband terahertz generation,” Nat. Commun. 10(1), 2591 (2019). [CrossRef]
24. S. Adipa, A. L. Lytle, and E. Gagnon, “High efficiency, modular, optical pulse shaping technique for tunable terahertz generation from inas,” Appl. Phys. Lett. 102(8), 081106 (2013). [CrossRef]
25. K.-L. Yeh, J. Hebling, M. C. Hoffmann, and K. A. Nelson, “Generation of high average power 1kHz shaped thz pulses via optical rectification,” Opt. Commun. 281(13), 3567–3570 (2008). [CrossRef]
26. S.-W. Huang, E. Granados, W. R. Huang, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013). [CrossRef]
27. B. Zhang, Z. Ma, J. Ma, X. Wu, C. Ouyang, D. Kong, T. Hong, X. Wang, P. Yang, L. Chen, and Y. Li, “1.4-mJ high energy terahertz radiation from lithium niobates,” arXiv:2007.09322 (2020).
28. C. W. Siders, J. L. W. Siders, A. J. Taylor, S.-G. Park, and A. M. Weiner, “Efficient high-energy pulse-train generation using a 2n-pulse michelson interferometer,” Appl. Opt. 37(22), 5302–5305 (1998). [CrossRef]
29. B. Dromey, M. Zepf, M. Landreman, K. O’Keeffe, T. Robinson, and S. M. Hooker, “Generation of a train of ultrashort pulses from a compact birefringent crystal array,” Appl. Opt. 46(22), 5142–5146 (2007). [CrossRef]
30. J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mj energy,” Opt. Express 22(17), 20155–20163 (2014). [CrossRef]
31. S.-C. Zhong, J. Li, Z.-H. Zhai, L.-G. Zhu, J. Li, P.-W. Zhou, J.-H. Zhao, and Z.-R. Li, “Generation of 0.19-mJ THz pulses in LiNbO3 driven by 800-nm femtosecond laser,” Opt. Express 24(13), 14828–14835 (2016). [CrossRef]
32. M. Kunitski, M. Richter, M. D. Thomson, A. Vredenborg, J. Wu, T. Jahnke, M. Schöffler, H. Schmidt-Böcking, H. G. Roskos, and R. Dörner, “Optimization of single-cycle terahertz generation in LiNbO3 for sub-50 femtosecond pump pulses,” Opt. Express 21(6), 6826–6836 (2013). [CrossRef]
33. L. Tokodi, J. Hebling, and L. Pálfalvi, “Optimization of the Tilted-Pulse-Front Terahertz Excitation Setup Containing Telescope,” J. Infrared, Millimeter, Terahertz Waves 38(1), 22–32 (2017). [CrossRef]
34. L. Pálfalvi, J. Hebling, G. Almási, A. Péter, K. Polgár, K. Lengyel, and R. Szipöcs, “Nonlinear refraction and absorption of Mg doped stoichiometric and congruent LiNbO3,” J. Appl. Phys. 95(3), 902–908 (2004). [CrossRef]
35. L. Pálfalvi, J. Hebling, J. Kuhl, A. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005). [CrossRef]
36. Y. Wang, L. Yan, Z. Zhao, and Z. Chen, “Absolute energy measurement of single-shot terahertz pulse with a thermal detector,” International Photonics and Optoelectronics Meetings (Optical Society of America, 2012), p. STh4A.19.
37. G. Gallot and D. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16(8), 1204–1212 (1999). [CrossRef]
38. G. Sharma, K. Singh, I. Al-Naib, R. Morandotti, and T. Ozaki, “Terahertz detection using spectral domain interferometry,” Opt. Lett. 37(20), 4338–4340 (2012). [CrossRef]
39. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010). [CrossRef]
40. S.-C. Zhong, Z.-H. Zhai, J. Li, L.-G. Zhu, J. Li, K. Meng, Q. Liu, L.-H. Du, J.-H. Zhao, and Z.-R. Li, “Optimization of terahertz generation from LiNbO3 under intense laser excitation with the effect of three-photon absorption,” Opt. Express 23(24), 31313–31323 (2015). [CrossRef]
41. K. Ravi and F. Kärtner, “Analysis of terahertz generation using tilted pulse fronts,” Opt. Express 27(3), 3496–3517 (2019). [CrossRef]
42. K. Ravi, W. R. Huang, S. Carbajo, E. A. Nanni, D. N. Schimpf, E. P. Ippen, and F. X. Kärtner, “Theory of terahertz generation by optical rectification using tilted-pulse-fronts,” Opt. Express 23(4), 5253–5276 (2015). [CrossRef]
43. A. G. Stepanov, S. Henin, Y. Petit, L. Bonacina, J. Kasparian, and J.-P. Wolf, “Mobile source of high-energy single-cycle terahertz pulses,” Appl. Phys. B 101(1-2), 11–14 (2010). [CrossRef]
44. F. Blanchard, X. Ropagnol, H. Hafez, H. Razavipour, M. Bolduc, R. Morandotti, T. Ozaki, and D. G. Cooke, “Effect of extreme pump pulse reshaping on intense terahertz emission in lithium niobate at multimillijoule pump energies,” Opt. Lett. 39(15), 4333–4336 (2014). [CrossRef]
45. X. jun Wu, J. long Ma, B. long Zhang, S. su Chai, Z. ji Fang, C.-Y. Xia, D. yin Kong, J. guang Wang, H. Liu, C.-Q. Zhu, X. Wang, C.-J. Ruan, and Y.-T. Li, “Highly efficient generation of 0.2 mJ terahertz pulses in lithium niobate at room temperature with sub-50 fs chirped Ti:sapphire laser pulses,” Opt. Express 26(6), 7107–7116 (2018). [CrossRef]
46. X. Wu, S. Carbajo, K. Ravi, F. Ahr, G. Cirmi, Y. Zhou, O. D. Mücke, and F. X. Kärtner, “Terahertz generation in lithium niobate driven by ti:sapphire laser pulses and its limitations,” Opt. Lett. 39(18), 5403–5406 (2014). [CrossRef]
47. X. Wu, S. Chai, J. Ma, B. Zhang, C. Xia, Z. Fang, D. Kong, J. Wang, H. Liu, C. Zhu, X. Wang, C. Ruan, and Y. Li, “Optimization of highly efficient terahertz generation in lithium niobate driven by Ti:sapphire laser pulses with 30 fs pulse duration,” Chin. Opt. Lett. 16(4), 041901 (2018). [CrossRef]
48. D. Jang, C. Kang, S. K. Lee, J. H. Sung, C.-S. Kee, S. W. Kang, and K.-Y. Kim, “Scalable terahertz generation by large-area optical rectification at 80 TW laser power,” Opt. Lett. 44(22), 5634–5637 (2019). [CrossRef]
