Development of a 1 TW/35 fs Ti:sapphire Laser Amplifier and Generation of Intense THz Waves Using Two-Color Laser Filamentation
Development of a 1 TW/35 fs Ti:sapphire Laser Amplifier and Generation of Intense THz Waves Using...
Phung, Vanessa Ling Jen;Kang, Keekon;Jeon, Seongjin;Kim, Jinju;Roh, Kyungmin;Suk, Hyyong
hv photonics Communication Development of a 1 TW/35 fs Ti:sapphire Laser Ampliﬁer and Generation of Intense THz Waves Using Two-Color Laser Filamentation Vanessa Ling Jen Phung , Keekon Kang , Seongjin Jeon , Jinju Kim , Kyungmin Roh and Hyyong Suk * Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Buk-gu, Gwangju 61005, Korea; email@example.com (V.L.J.P.); firstname.lastname@example.org (K.K.); anfﬂdhkd418@gist.ac.kr (S.J.); email@example.com (J.K.); firstname.lastname@example.org (K.R.) * Correspondence: email@example.com † Current address: Advanced Photonics Research Institute (APRI), Gwangju Institute of Science and Technology, Buk-gu, Gwangju 61005, Korea. Abstract: We developed a compact Ti:sapphire laser ampliﬁer system in our laboratory, generating intense laser pulses with a peak power of >1 TW (terawatt), a pulse duration of 34 fs (femtosecond), a central wavelength of 800 nm, and a repetition rate of 10 Hz. The laser ampliﬁer system consists of a mode-locked Ti:sapphire oscillator, a regenerative ampliﬁer, and a single-side-pumped 4-pass ampliﬁer. The chirped-pulse ampliﬁcation (CPA)-based laser ampliﬁer was found to provide an energy of 49.6 mJ after compression by gratings in air, where the pumping ﬂuence of 1.88 J/cm was used. The ampliﬁed spontaneous emission (ASE) level was measured to be lower than 10 , and ps-prepulses were in 10 or lower level. The developed laser ampliﬁer system was used for the generation of intense THz (terahertz) waves by focusing the original (800 nm) and second harmonic (400 nm) laser pulses in air. The THz pulse energy was shown to be saturated in the high laser energy regime, and this phenomenon was conﬁrmed by fully electromagnetic, relativistic, and self-consistent particle-in-cell (PIC) simulations. Citation: Phung, V.L.J.; Kang, K.; Jeon, S.; Kim, J.; Roh, K.; Suk, H. Development of a 1 TW/35 fs Keywords: Ti:sapphire laser; laser ampliﬁer; fs CPA laser; high power laser; THz Ti:sapphire Laser Ampliﬁer and Generation of Intense THz Waves Using Two-Color Laser Filamentation. Photonics 2021, 8, 316. https:// 1. Introduction doi.org/10.3390/photonics8080316 Since the demonstration of the ﬁrst laser in 1960 , extensive efforts have been made to develop lasers with higher power/energy and shorter pulses . A breakthrough in laser Received: 24 June 2021 power was made by the invention of the chirped-pulse-ampliﬁcation (CPA) technique in Accepted: 2 August 2021 1985 , and since then, many TW laser systems and even PW laser systems have been de- Published: 5 August 2021 22 2 veloped, achieving a maximum focused intensity of 5.5 10 W/cm [4,5]. Thus far, most of them have been used for laser-plasma interaction studies, including high-energy electron Publisher’s Note: MDPI stays neutral acceleration [6–8], ion generation [9,10], X-ray/
-ray production [11,12], etc. In our labora- with regard to jurisdictional claims in tory at GIST (Gwangju Institute of Science and Technology), we also have a 20 TW/35 fs published maps and institutional afﬁl- Ti:sapphire laser system that is used mainly for high-energy electron acceleration and iations. related experiments. However, there is also a demand for lower power lasers of ~1 TW and a higher repetition rate for other researches. For example, they can be used for the generation of intense THz wave pulses , fs electron beam pulses for ultrafast electron diffraction (UED) , X-ray pulses for time-resolved X-ray crystallography and absorp- Copyright: © 2021 by the authors. tion spectroscopy [15,16], etc. Hence, we developed a 1 TW-class Ti:sapphire ampliﬁer Licensee MDPI, Basel, Switzerland. using some parts of the existing 20 TW laser system, allowing a separate beam line for This article is an open access article other researches. To build the separate laser beam line, we added a single-side-pumped distributed under the terms and 4-pass ampliﬁer and an in-air pulse compressor to the existing oscillator and regenerative conditions of the Creative Commons ampliﬁer, leading to a separate 1 TW laser system. The developed laser system turned out Attribution (CC BY) license (https:// to have a very good performance, for example, reaching an ASE level of less than 10 . creativecommons.org/licenses/by/ The laser ampliﬁer system has ps-prepulses, but their intensities are in 10 or lower levels. 4.0/). Photonics 2021, 8, 316. https://doi.org/10.3390/photonics8080316 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 316 2 of 10 The prepulse effect is not important in our laser-plasma-based THz research as we need laser-produced plasma in gas. The Ti:sapphire ampliﬁer system was designed and built by ourselves in-house, providing a unique laser facility for research. We used the laser ampliﬁer system to generate intense THz waves. Compared with other electromagnetic radiations, THz waves have some unique features. For example, they can interact strongly with chemical/biological molecules (in rotation and vibration modes). Furthermore, THz waves are reﬂected from conductors, but they can pass through dielectric materials easily. Based on these properties, THz waves have a wide range of important applications in science and technology, including THz imaging, spectroscopy, medical diagnostics, security, etc. [17,18]. To generate intense THz waves, we focused the original (800 nm) and second harmonic (400 nm) laser pulses in air, where an asymmetric net ﬁeld in the plasma produces a strong THz pulse. Our experimental result shows that the THz pulse energy increases sharply in the beginning as the laser energy increases, but it is saturated eventually in the high laser energy regime. As far as we know, this saturation phenomenon has not been explained by any rigorous theory or simulation. Hence, we performed fully electromagnetic and self-consistent particle-in-cell (PIC) simulations to investigate this phenomenon and found that the PIC simulation result also leads to saturation in the THz energy, which is in agreement with the experimental result. In this paper, we will report details of the Ti:sapphire laser ampliﬁer development and the experimental result for two-color-based intense THz wave generation together with the simulation results. 2. Development of the 1 TW/35 fs Ti:sapphire Laser Ampliﬁer System 2.1. Overall Conﬁguration Figure 1 illustrates the conﬁguration of the Ti:sapphire laser ampliﬁer system that was developed recently in our laboratory. It consists of a Ti:sapphire oscillator, a stretcher grat- ing, a Ti:sapphire regenerative ampliﬁer pumped by an Nd:YLF laser, a 4-pass Ti:sapphire ampliﬁer, and a pulse compressor. The Kerr-lens mode-locked oscillator (FemtoLasers Produktions GmbH, model Fusion 20) generates a train of broadband pulses at a repetition rate of 80 MHz, and the oscillator laser beam has a central wavelength of 796 nm, an energy of 3 nJ/pulse, and a pulse duration of 20 fs. The oscillator pulse is stretched to 312 ps (FWHM) by a grating with groove density 1100 lines/mm, and then it is injected into the re- generative ampliﬁer (Spectra-Physics, model Spitﬁre Pro) that is pumped by a Q-switched Nd:YLF laser (Spectra-Physics, model Empower 30) with a wavelength of 527 nm and 20 mJ/pulse at 1 kHz. The laser pulse is trapped in the cavity of the regenerative ampliﬁer and is ampliﬁed to 4 mJ over 12–15 round trips for enough energy, where two Pockels cells (PC1, PC2) are used for trapping and ejection of the laser pulse, as shown in Figure 1. After that, the laser beam from the regenerative ampliﬁer is sent to another Pockels cell (PC3, model QX-1020 by Gooch and Housego) for pulse cleaning, and then it is injected into the in-house 4-pass ampliﬁer for higher energy. The 4-pass amplifier consists of a Titanium-doped sapphire crystal with a diameter of 15 mm and a length of 20 mm, and it is single-side-pumped by the frequency-doubled (532 nm in wavelength) Nd:YAG laser (Continuum, model Surelite-EX) at 10 Hz. The injected laser pulse in the 4-pass amplifier passes through the Ti:sapphire crystal four times for enough amplification. The pump beam diameter was reduced from 10 mm to 5 mm using a Galilean telescope consisting of a pair of convex and concave lenses to increase the pump beam fluence up to 1.88 J/cm . The stretched, amplified laser pulse is sent at an incidence angle of 56 , to the Treacy configuration pulse compressor , which consists of a pair of Au-coated, reflective gratings with groove density 1500 lines/mm (produced by Spectrogon Inc.) and a vertical retro-reflector (VRR). To prevent potential damage on the gratings, especially from the compressed beam, the output laser beam from the 4-pass amplifier was expanded to 17 mm in diameter, resulting in a maximum energy fluence of 39 mJ/cm . This fluence will be adequate because the calculated damage threshold of the compressor grating is approximately 78 mJ/cm (800 nm, 10 Hz, 35 fs). In this way, we developed a high-power Ti:sapphire laser amplifier system that can deliver laser pulses with an energy Photonics 2021, 8, 316 3 of 10 of 49.6 mJ/pulse and a pulse duration of 34 fs, leading to more than 1 TW in peak power. More details for the development of the laser amplifier system are described below. Figure 1. Schematic of the 1 TW/35 fs Ti:sapphire laser ampliﬁer system. VRR: vertical retro-reﬂector, PPS: polarization periscope, TFP: thin ﬁlm polarizer, QWP: quarter-wave plate, M: mirror, BD: beam dump, BE: beam expander, BR: beam reducer, PS: periscope, PC: Pockels cell, CG: compressor grating, EM: exit mirror. 2.2. 4-pass Ti:sapphire Ampliﬁer and Pulse Compression Figure 2 shows the measured output energies after the 4-pass (blue squares) ampliﬁer when the pump beam energy changes. The result indicates that the maximum output pulse energy of 73 mJ can be obtained after 4-pass with an input pulse energy of 3.1 mJ and a pump beam energy of 370 mJ, leading to an ampliﬁcation factor of 23.5. Figure 2 also shows that the energy extraction efﬁciency is approximately 24%. Figure 2. Measured laser pulse energy after 4-pass ampliﬁcation (blue squares) and theoretical calculation using the Frantz–Nodvik equation [20,21] (black dotted line). The ampliﬁcation efﬁciency (slope of the ﬁtting line for the experimental data points) is 24%. The experimental result in Figure 2 can be compared with a theory. In the pulse ampliﬁcation process, the ampliﬁed output pulse energy for a single pass can be given by a simple relation E = E G , where the input seed energy E is ampliﬁed af- out in 0 in ter passing through the ampliﬁer, giving the ampliﬁed output energy E . Here, the out Photonics 2021, 8, 316 4 of 10 small-signal gain G is provided by G = exp( J / J ), where the saturation ﬂuence 0 0 sto sat J is the intrinsic parameter of the Ti:sapphire (Ti:Al O ) crystal (1 J/cm ) [21,22] and sat 2 3 J is the pump ﬂuence stored in the gain medium. The pump ﬂuence J stored in sto sto the medium can be deduced from experimental values from the expression given by J = (E / A)h h h , where E is the pump beam energy, A is the cross-section sto p QD QE ABS p of the pump beam, h = l /l = 532 nm/800 nm is the quantum defect fac- pum p QD l aser tor, h is the quantum efﬁciency of the ampliﬁcation process given by h = 0.81 at QE QE room-temperature , h is the experimentally measured absorption ratio of the pump ABS laser energy in the crystal (h = 0.92 in our 2-cm-long Ti:sapphire crystal). Hence, ABS 2 2 J results in 0.933 J/cm with the pump ﬂuence of 1.88 J/cm . Here, it should be noted sto that J includes the effect of the medium length, which is included in h . Considering sto ABS a back-of-envelope calculation here, the highest ampliﬁcation factor in a single-pass is calculated as G = exp(0.933) = 2.54. More generally, the output ﬂuence can be provided by the Frantz–Nodvik equation in J = J ln 1 + G exp 1 , (1) out sat sat where J and J are the input and output laser pulse ﬂuences, respectively. The output in out pulse energy calculated from Equation (1) gives 7.9 mJ when the input laser energy in the ampliﬁer is 3.1 mJ. Equation (1) can be applied successively for multiple passes, meaning the output of one pass becomes the input for the next pass. In this way, the output energy of the 4-pass ampliﬁer can be calculated, and the result is given by the dotted line in Figure 2. On the other hand, the experimentally measured energies after the 4-pass ampliﬁer are represented by the blue squares in the same ﬁgure. Figure 2 shows that the output laser pulse energy is slightly lower than the calculated value for pump energy >320 mJ, which corresponds to a pump ﬂuence of 1.63 J/cm . The deviation of the calculated result from the measured one in the ﬁgure may be due to the simple assumption of the Frantz–Nodvik theory, i.e., the theory is based on the assumption of uniform transverse distributions of the pump and seed laser beams, homogeneous broadening, and negligible loss in the system. The beam proﬁle of the ampliﬁed laser pulse for different output pulse energies was recorded using a beam proﬁler (OPHIR, model SP503U), as shown in Figure 3. From the ﬁgures, we can see the center of the output beam is saturated gradually as the output beam energy increases. The dimension of the beam with maximum output energy of 73 mJ is approximately 4.2 mm 5 mm. The ampliﬁed laser pulse energy will have shot-to-shot ﬂuctuations and the energy was measured to be 71.7 1.4 mJ (rms), as shown in Figure 4. The energy measurement also shows that the laser pulse energy from the 4-pass ampliﬁer drifts very little with only 0.44 mJ over 10 minutes. Figure 3. Beam proﬁle of the ampliﬁed uncompressed laser pulse with different output energies: (a) 21 mJ, (b) 44 mJ, (c) 60 mJ, and (d) 73 mJ. The beam dimension for 73 mJ is approximately 4.2 mm 5.0 mm and the central part of the beam is almost saturated already in this high-energy case. The ampliﬁed laser pulse from the 4-pass ampliﬁer is sent to the pulse compressor consisting of two gratings and a vertical retro-reﬂector. The gratings were optimized for the shortest pulse, and the compressed beam properties were characterized by the grating- eliminated no-nonsense observation of ultrafast incident laser light e-ﬁelds (GRENOUILLE; Photonics 2021, 8, 316 5 of 10 Swamp Optics, model 8-20-USB) based on the frequency-resolved optical grating (FROG) technique [24–26]. Figure 5a shows the spectrum measured at three locations, where the compressed beam has a central wavelength of 800 nm and an FWHM bandwidth of 41.6 nm. It should be noted here that the spectral bandwidth after 4-pass ampliﬁcation did not change signiﬁcantly by the gain-narrowing effect. It is important to preserve the compressible bandwidth throughout the ampliﬁcation stages because the bandwidth determines the ﬁnal laser pulse duration. The pulse duration after compression was measured to be 34 fs FWHM, as shown in Figure 5b. Figure 4. Measurement of the ampliﬁed laser pulse energy at a repetition rate of 10 Hz for more than 15 min. The measured energy shows 71.7 1.4 mJ (rms), and the energy drift is 0.44 mJ/10 min. Figure 5. (a) Spectra of the laser pulse from the oscillator (black squares), the ampliﬁed stretched pulse after the 4-pass ampliﬁer (blue circles) and the compressed laser pulse (red line). (b) Temporal intensity proﬁle after compression, showing a pulse duration of 34 fs FWHM. The ampliﬁed spontaneous emission (ASE) of the compressed laser pulse was mea- sured using a third-order cross-correlator (Amplitude Technologies, Sequoia). The temporal contrast ratio is deﬁned as the intensity ratio R of the peak intensity I to any prepulse peak or ASE/pedestal intensity I , i.e., R = I /I . The temporal contrast ratio of our ASE peak ASE 7 8 system was measured to be between 10 and 10 , as shown in Figure 6. This contrast ratio is high compared with typical CPA laser contrast ratios that are about 10 [27,28]. The ps-prepulses were also measured, and they were found to be in the level of 10 or less. Photonics 2021, 8, 316 6 of 10 The maximum energy of the compressed laser pulse was 49.6 mJ when 73 mJ laser energy was sent to the pulse compressor, leading to a grating compression efﬁciency of 68%. This is a reasonable result because we used rather old gratings. Figure 6. Ampliﬁed spontaneous emission (ASE) level of the compressed laser pulse measured by a third-order cross-correlator (Amplitude Technologies, Sequoia). 3. Experimental Results for Two-Color-Based Intense THz Wave Generation Using the Laser Ampliﬁer The generation of intense THz waves is a very important issue in science. Several ways were studied so far, and using a laser-produced plasma is a very promising way for high-energy THz wave generation. The two-color laser ﬁlamentation method [29–31], especially, is known to produce a strong THz pulse, where the fundamental and second harmonic laser pulses are focused together in the gas. We used the developed laser ampliﬁer system for the high-energy THz wave gen- eration experiment, which employs the two-color laser ﬁlamentation method, as shown in Figure 7. The original laser pulse with 800 nm wavelength is focused in air through a beta-barium-borate (BBO) nonlinear crystal, generating a second harmonic laser pulse of 400 nm wavelength. Focusing the fundamental and second harmonic laser pulses in air ionizes the air molecules and produces plasma ﬁlamentation, leading to the generation of an intense THz pulse. The THz generation mechanism from the two-color method is attributed to the transient electric current in the laser-produced plasma, where mixing the fundamental and second harmonic laser pulses leads to an asymmetric net ﬁeld in the plasma. The inserted image in Figure 7 shows an air plasma ﬁlament of about 30 mm in length, and the light is emitted mainly from nitrogen in the ultraviolet-visible range of bluish color . In Figure 7, the produced THz pulse passes through the 0.5 mm thick silicon wafer that is optically transparent for the THz wave but blocks the laser pulses. The collimated THz pulse is then focused on the pyro-detector (Gentec-EO, model: THZ5B-MT) for energy measurement. The pyro-detector is removed later for THz-TDS diagnostics. The THz-TDS (also known as an electro-optic sampling (EOS) technique) is one of the most common THz diagnostic methods . In this method, a ps-long THz pulse is sampled by a time-delayed fs-long probe pulse (800 nm), where the time delay relative to the THz pulse is scanned by a computer-controlled linear stage. When both the THz pulse and the probe laser pulse pass through the nonlinear ZnTe crystal [33–35], the polarization angle of the probe laser pulse changes by the birefringent ZnTe crystal in the THz ﬁeld. This way, the electric ﬁeld proﬁle of the THz pulse can be measured. Photonics 2021, 8, 316 7 of 10 Figure 7. Schematic diagram of the experimental setup for THz wave generation using the two-color ﬁlamentation method and the THz-TDS (time-domain spectroscopy) diagnostics system. The pump beam is focused in the air to produce a strong THz pulse and the probe beam is sent to the THz-TDS system for diagnostics of the THz pulse. OAP: off-axis parabolic mirror, QWP: quarter-wave plate, WP: Wollaston prism, M: mirror. (* indicates retractable). Figure 8a shows the THz pulse energy vs. the laser pulse energy (before frequency doubling), where the THz energy was before attenuation by the silicon wafer . The experimental result shows that the maximum THz energy of 480 nJ can be obtained with the laser energy of 18.8 mJ, which leads to the THz ﬁeld strength of 242 kV/cm. This result yields a THz conversion efﬁciency of 2.5 10 . It seems that the THz energy from our experiment is quite reasonable compared with other results [31,37]. Figure 8a also shows that the THz energy increases sharply in the beginning as the laser energy increases, but it is gradually saturated. Figure 8b shows the THz pulse form (in the inset) measured by the THz-TDS method and its Fourier transformation, yielding a spectrum of the THz pulse. It should be noted that the spectrum of the THz pulse from THz-TDS has a cut-off frequency around 5 THz. This frequency bandwidth is due to the limitation of the phonon-resonance properties of the ZnTe crystal . As Figure 8a shows, the THz pulse energy is saturated, and it does not increase anymore in the high laser energy regime. This saturation phenomenon has not been explained by any rigorous theory or simulation so far. To investigate this phenomenon seriously, therefore, we performed a series of two-dimensional (2D) particle-in-cell (PIC) simulations. For the PIC simulations, we used the EPOCH code  to model the interaction between the laser pulse and neutral gas/plasma, where a fully electromagnetic, relativistic, and self-consistent theory is employed. The simulation window of 200 m 300 m in size is a non-moving spatial domain which is discretized by 4000 750 cells with two particles per cell. For simplicity, neutral nitrogen species with an atmospheric density of 19 3 n = 2.68 10 cm was used in the simulation. We used linearly polarized Gaussian laser pulses with wavelengths of 800 nm and 400 nm and a pulse duration of 35 fs (FWHM). The laser pulses are focused on a focal plane with a beam waist of w = 10 m. Figure 9 shows the PIC simulation result, i.e., 2D plots of the THz wave for different laser pulse energies, implying that a stronger THz pulse is generated by a higher laser pulse energy. The THz pulse energy can be estimated from the simulation result (open circle) and compared with the experimental result (blue square) in Figure 8a. Here, it should be noted that the THz pulse energy from the PIC simulation result is also saturated in the high laser energy regime, which is consistent with the experimental result. This phenomenon can be understood by the fact that the plasma ﬁlament length, which is a critical factor Photonics 2021, 8, 316 8 of 10 in THz energy, does not increase linearly as the laser pulse energy increases. In fact, two factors play an important role in the formation of the laser ﬁlament when an intense laser pulse propagates in gas. One is the Kerr effect that provides a focusing force for the laser, and the other is a defocusing effect by the ionization-induced diffraction in addition to the ordinary diffraction. As the laser energy increases, more neutral atoms in the air are ionized, and the Kerr effect is reduced naturally, while the ionization-induced diffraction effect will be more dominant. Hence, the ﬁlament length can be limited although the laser energy increases, leading to the saturation in THz energy. Here, it should be noted that the relativistic self-focusing effect  does not have to be taken into account as it is too small in our case. The calculation with our laser and plasma parameters in this experiment shows that the normalized vector potential of the focused laser beam is a < 1 and the peak laser power is less than the critical power P for relativistic self-focusing, where a c 0 and P are given by a = 0.85 10 I[W/cm ]l[m] and P [GW] = 17.4 w/w in c 0 c p practical units, respectively . Here, I is the focused laser beam intensity, is the laser wavelength, w and w are the laser and plasma frequencies, respectively. Figure 8. (a) Measured THz pulse energy as a function of the laser energy (before frequency doubling). The simulation result (open circle) is normalized to the experimental result (blue square) for comparison. (b) Spectrum of the THz pulse obtained from Fast-Fourier Transform (FFT) of the THz pulse in the inset, where the THz pulse was directly measured from the THz-TDS method. Note that the spectrum is limited up to a maximum frequency of ~5 THz due to the intrinsic properties of the ZnTe crystal. Figure 9. 2D PIC simulation results for THz pulse generation by the two-color method: 2D-plot of the THz electric ﬁeld strength with a different laser pulse energy of (a) 5 mJ, (b) 10 mJ, (c) 15mJ, and (d) 20 mJ. The result shows that a stronger THz wave is generated by a higher laser pulse energy. In the ﬁgures, the black dashed line indicates the focal plane of the laser pulse, and the black arrows indicate the THz wave propagation. Photonics 2021, 8, 316 9 of 10 4. Conclusions In conclusion, we successfully developed a TW-class high-power ampliﬁer system using some existing parts in our laboratory, which consists of a mode-locked oscillator, a regenerative ampliﬁer, and a 4-pass Ti:sapphire ampliﬁer. The CPA-based laser ampliﬁer was characterized, and it was found to deliver an energy of 49.6 mJ/pulse and a pulse duration of 34 fs, resulting in more than 1 TW in power. The ASE and ps-prepulse levels 7 4 were measured to be quite low, i.e., less than 10 and 10 , respectively. We used this TW-class Ti:sapphire laser ampliﬁer to generate an intense THz wave by focusing the fundamental and second harmonic laser pulses in the air. It was found that the THz conversion efﬁciency is on the order of 10 , and the THz pulse energy is saturated as the laser energy increases. Fully electromagnetic, relativistic, and self-consistent PIC simulations were performed for comparison with the experimental result, and it turned out that both the simulation and experimental results show a similar saturation phenomenon. Author Contributions: H.S. conceived the idea. V.L.J.P., S.J., K.K., and J.K. prepared the laser ampliﬁer development and characterization. K.K., S.J., and K.R. prepared and performed the THz experiment. V.L.J.P. performed the 2D-PIC simulation, data analysis, and wrote the draft of the manuscript. All authors participated in preparatory discussions and manuscript improvement. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Research Foundation of Korea (NRF, Grant #: 2017R1A2B3010765). Data Availability Statement: The data presented in this paper are available on request from the corresponding author. Acknowledgments: The authors acknowledge H.J. Lee and H.I. Kim in the group for their tech- nical supports. The EPOCH code was developed under the UK EPSRC grants EP/G054950/1, EP/G056803/1, EP/G055165/1, and EP/M022463/1. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Maiman, T.H. Stimulated optical radiation in ruby. Nature 1960, 187, 493–494. [CrossRef] 2. Sixty years of lasers. Nat. Rev. Phys. 2020, 2, 221. [CrossRef] 3. Strickland, D.; Mourou, G. Compression of ampliﬁed chirped optical pulses. Opt. Commun. 1985, 55, 447–449. [CrossRef] 4. Yoon, J.W.; Jeon, C.; Shin, J.; Lee, S.K.; Lee, H.W.; Choi, I.W.; Kim, H.T.; Sung, J.H.; Nam, C.H. 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