Extending the cut-off energy of high-harmonic generation (HHG) to the soft x-ray range provides new opportunities in attosecond pump-probe studies, high-harmonic (HH) spectroscopy, recollision physics, selective x-ray spectroscopy, and biological or nanoscale imaging applications. Long-wavelength-driven HHG [1], that is HHG using driver pulses with wavelength longer than 800 nm, has been proven to be the most reliable way of reaching the water-window soft x-ray (280–520 eV) range [2,3] and even up to the keV region [4]. However, since HHG efficiency in the single-atom response scales unfavorably with drive wavelength, i.e., ${\lambda }^{-(5–6)}$, mostly due to quantum diffusion of electron trajectories [5–7], high-flux HHG using long-wavelength drivers is difficult to achieve. Macroscopic and constructive summation of harmonic light in a gas medium is necessary to overcome this drawback. Luckily, often reabsorption in medium is reduced at high photon energies, and phase matching between the driving pulse and the generated harmonics can be achieved at high gas pressure. In terms of the driver source specifications, the pulse energy up to multi-mJ is beneficial to avoid the phase mismatch induced by the Gouy phase shift because a tight focus is not necessary. Higher energy and repetition rates are always favorable to increase the flux of generated high-harmonics.

Optical parametric amplification (OPA) and optical parametric chirped pulse amplification (OPCPA) techniques have enabled us to generate energetic long-wavelength driving pulses at 1.3–4 μm [2–4,8–12]. Recently, phase-matched HHG covering the water window range with an efficiency of $\sim {10}^{-8}$ was experimentally demonstrated in Ne and He [2,3] using 10 Hz, multi-mJ OPA sources pumped by a Ti:sapphire laser. However, the generated soft x-ray photon number per second is still as low as $\sim {10}^6$ over 1% bandwidth, limiting potential applications. Increasing the repetition rate to kHz, therefore, can increase soft x-ray photon production by two orders of magnitude. Moreover, attosecond streaking experiments based on photoelectron measurement, which are commonly used for attosecond pulse characterization as well as time-resolved spectroscopy, cannot practically be performed at low repetition rates in the range of 10–20 Hz. There have been demonstrations of the soft x-ray HHG using kHz, sub-mJ, 1.5 μm OPA [9], and 1.6 μm OPCPA systems [12], pumped by a Ti:sapphire amplifier, which reached the cutoff of $\sim 300\mathrm{eV}$, but the photon flux has never been reported. In our previous report [11], we measured soft x-ray photon flux of $\sim 0.8\times {10}^8\text{photons}/\mathrm{s}$ over 1% bandwidth at 130 eV in Ar using a kHz, sub-mJ, 2.1 μm OPCPA system, pumped by a home-built cryogenic Yb:YAG chirped-pulse amplification (CPA) laser.

In this Letter, we report on a kHz, multi-mJ OPCPA system at 2.1 μm and its application to high-flux soft x-ray HHG up to 190 eV. First we describe the development of an OPCPA pump laser based on a kHz, three-stage, multi-ten-mJ picosecond cryogenic Yb:YAG CPA laser. Second, we scale up the energy of our OPCPA system from 0.85 mJ [13] to 2.6 mJ using this pump laser. Finally, we generate high-flux soft x-ray harmonics in Ar and N₂ gas cells driven by this high-energy kHz 2.1 μm source. HHG simulations with 3D pulse propagation are also performed to reveal the temporal structure of the attosecond soft x-ray pulses.

Although OPCPA is generally accepted as a more energy-scalable method than OPA, the energy scaling at high repetition rates in the kHz range is a nontrivial task without a suitable picosecond pump source. To do so, new high-power pump laser technologies based on Yb:YAG gain media at 1.03 μm have been explored. In 2009, Metgzer et al. [14] developed a 25 mJ $\sim 1\mathrm{ps}$ thin-disk Yb:YAG amplifier at 3 kHz, which recently enabled the generation of 1.2 mJ, 2.1 μm OPCPA pulses [15]. Most recently, amplification of 1.03 μm pulses to more than 40 mJ of energy from thin-disk amplifiers [16,17] have been reported. On the other hand, in 2010 Hong et al. [18] already demonstrated the amplification of uncompressed picosecond pulses to 40 mJ at 2 kHz from a two-stage cryogenic Yb:YAG CPA laser. A modified cryogenic Yb:YAG laser with 15 mJ of compressed output energy was used for pumping a sub-mJ, 2.1 μm OPCPA system at 1 kHz repetition rate [13].

In the current work, we have upgraded this pump laser by adding a single-pass amplifier stage and reconfiguring the amplifier chain. The system layout of the cryogenic Yb:YAG CPA laser system is illustrated in Fig. 1(a). The seed from a Ti:sapphire oscillator, which also provides the seed for the OPCPA stages, is preamplified in Yb-doped fiber amplifiers, stretched by a chirped volume Bragg grating (CVBG) pair to $\sim 560\mathrm{ps}$ with 0.7 nm of bandwidth at 1029 nm, and then amplified by a kHz 6 mJ regenerative amplifier and two multipass amplifiers, which are all based on cryogenically cooled Yb:YAG as gain medium. We used a 1% doped 10 mm long Yb:YAG crystal in the first two-pass amplifier and a 2% doped 20 mm long crystal in the second single-pass amplifier. Each crystal has 2 mm of an undoped YAG end cap on the pumping side. The crystals are indium-bonded to a heat sink and cooled to 77 K by liquid nitrogen in a vacuum chamber connected to an auto-refilling system. The beam size and the divergence at each stage have been carefully matched to the pump beams using telescopes. The periscope after the two-pass amplifier helps compensate the thermally induced astigmatism from both amplifiers. The maximum energy from the second and third amplifiers is 30 and 56 mJ, respectively, with excellent beam profiles as shown in Figs. 1(b) and 1(c). The pump power from two fiber-coupled cw $\sim 940\mathrm{nm}$ laser diodes at the maximum output energy are both 240 W, while the absorption is $\sim 75\%$ at Crystal 1 and $\sim 95\%$ at Crystal 2, respectively. The amplified pulse with a spectral bandwidth of 0.2 nm is compressed to 17 ps using a multilayer dielectric grating pair with a throughput efficiency of 75%, delivering a compressed energy of 42 mJ.

 

Fig. 1. (a) Optical layout of the three-stage kHz picosecond cryogenic Yb:YAG CPA laser and the beam profiles from the (b) two-pass and the (c) single-pass amplifiers. The circular fringes in the beam profiles are the measurement artifacts from neutral-density filters. Crystal 1, 1% doped, 10 mm long Yb:YAG; Crystal 2, 2% doped, 20 mm long, Yb:YAG; D, diameter; HR, high reflector; DM, dichroic mirror; TFP, thin-film polarizer; $\lambda /2$, half-wave plate; $\lambda /4$, quarter-wave plate; LD, laser diode at 940 nm.

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The improved pump laser is used for upscaling the energy of the ultrabroadband 2.1 μm OPCPA, whose optical layout is illustrated in Fig. 2. As described in previous reports [8,13], the OPCPA system is pumped by two independent picosecond lasers: (1) 1047 nm 11 ps Nd:YLF amplifier and (2) 1029 nm 17 ps cryogenic Yb:YAG amplifier. Both pump lasers are seeded by the same octave-spanning Ti:sapphire laser for achieving optical synchronization. The Nd:YLF CPA laser pumps the first two OPCPA stages [OPA1 and OPA2 in Fig. 2(a)] with a pump energy of 1 mJ. The 42 mJ cryogenic Yb:YAG laser pumps the final OPCPA stage for power amplification. Even though the energy from the Nd:YLF laser is only $\sim 2\%$ of that from the cryogenic Yb:YAG pump laser, we maintain this pump laser because the first two stages were carefully optimized for excellent superfluorescence (SF) suppression [19,20]. However, eventually the OPCPA system can be operated without the Nd:YLF pump laser.

 

Fig. 2. (a) Optical layout of the multi-mJ kHz 2.1 μm OPCPA system, (b) the amplified spectrum, (c) and the beam profile after compression with a 10 mm Gaussian diameter. The sharp line in (c) is owing to the damaged pixel elements. The beam is clipped due to the limited dimension of the pyroelectric detector. All the acronyms are spelled out in the text.

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The $\sim \mathrm{pJ}$ ultrabroadband 2.1 μm pulse is generated via intrapulse difference frequency generation (DFG) and stretched to $\sim 5\mathrm{ps}$ by an antireflection (AR) coated 30 mm long Si block and amplified in OPA1. And then it is further stretched to $\sim 9\mathrm{ps}$ using an acousto-optic programmable dispersive filter (AOPDF; Dazzler, Fastlite) before being amplified in OPA2. Ultrabroadband amplification is achieved by means of a degenerate OPA in periodically poled lithium niobate (MgO:PPLN) and periodically poled stoichiometric lithium tantalite (MgO:PPSLT) crystals. The details of the first two OPCPA stages are described in [19]. The $\sim 35\mathrm{\mu J}$ pulse from OPA2 is further stretched to $\sim 17\mathrm{ps}$ using an AR-coated 50 mm long Si block and then amplified in a 5 mm long type-I β-barium borate (BBO) crystal. The beam size of both seed and pump pulses is adjusted using two independent telescopes such that SF is minimized while generating high-energy output pulses. After optimization of the third OPCPA stage (OPA3), we obtained a maximum energy of 2.6 mJ with a gain of $\sim {10}^2$ at a pump intensity of $30–50\mathrm{GW}/{\mathrm{cm}}^2$. We installed a beam-pointing stabilizer for the Yb:YAG pump beam to actively stabilize beam pointing at the BBO crystal due to air fluctuations along the beam path. As a result, the pump-beam position fluctuation is $\sim 70\mathrm{\mu m}$ (rms) over $\sim 3.0\mathrm{mm}$ of beam diameter at the BBO crystal. The spectral bandwidth of the amplified pulses is 407 nm in FWHM centered at 2.1 μm, as shown in Fig. 2(b), and the compressed pulse duration is $\sim 40\mathrm{fs}$, measured with an interferometric autocorrelator, while the transform-limited pulse duration is 29 fs. The near-Gaussian beam profile measured after a telescope and the compressor using a pyroelectric camera reveals excellent quality as shown in Fig. 2(c). The average beam size on both axes is $\sim 10\mathrm{mm}$ in Gaussian ($1/e^2$) diameter. The compressor is composed of two Brewster-angled Suprasil 300 blocks with a total path length of 620 mm and is physically located next to the HHG chamber. The compression efficiency, including loss in the delivery optics (seven silver mirrors) between the third stage and the chamber, is $\sim 80\%$. As a result, the maximum energy available for the HHG experiment is $\sim 2.1\mathrm{mJ}$. The carrier-envelope phase (CEP) of the 2.1 μm pulses is passively stabilized [19], although the stability was not measured here because of the relatively long pulse duration of $\sim 6$ cycles, making CEP effects negligible in the HHG process. It also should be noted that, unlike Ti:sapphire laser-pumped 2 μm OPAs that generate 1.3 μm signal and 2 μm idler pulses, our degenerate OPCPA produces 2.1 μm idler pulses that have the same pulse energy and spectral bandwidth as those of the amplified signal pulses described above and could be independently compressed using Si blocks. Therefore the total energy available at 2.1 μm from signal and idler pulses is more than 4 mJ.

Using the kHz, 2.1 μm pulses we performed HHG experiment in Ar and N₂ gas cells. The gas cell is differentially pumped to keep the vacuum pressure in the HHG chamber below ${10}^{-2}$ mbar. The interaction length with a constant pressure is 6 mm and the 2.1-μm beam is focused at the center of the gas cell with a peak intensity of $\sim 3.1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Figures 3(a) and 3(b) show HH spectra from Ar and N₂ at a pressure of $\sim 200\mathrm{mbar}$ and $\sim 50\mathrm{mbar}$, respectively. Since both gases have similar ionization energies (15.8 eV for Ar and 15.6 eV for N₂), the cut-off photon energy at the same laser intensity is found to be almost the same at $\sim 190\mathrm{eV}$. The harmonic peaks are not well resolved in Fig. 3 because the entrance slit of the spectrometer was fully opened, and the harmonic peaks are dense. We also measured the soft x-ray photon flux using a calibrated x-ray photodiode (AXUV100, IRD). The photon flux at 160 eV from Ar harmonics is $\sim 2\times {10}^8\text{photons}/\mathrm{s}$ over 1% bandwidth while that at 140 eV from N₂ harmonics is $\sim 1\times {10}^7\text{photons}/\mathrm{s}$ over 1% bandwidth, which is 20 times lower. The driver energy of 2.1 μm used in these measurements is 0.9 mJ. The shape of each HH spectrum in the range of $>50\mathrm{eV}$ follows the transmission curve of Ar and $N_2$, respectively, indicating that the soft x-ray flux is limited by reabsorption in the gas.

 

Fig. 3. High-order harmonic spectra from Ar at (a) 200 mbar and (b) N₂ at 50 mbar. The transmission of x-ray filters used in the measurement is plotted on the right axis. Both spectra show the cut-off extension to 190 eV.

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In general, grating-based extreme ultraviolet/soft x-ray spectrometers have lower resolution at higher photon energies, which is disadvantageous to dense harmonics generated by long-wavelength drivers. Since the structure of the harmonics is not resolved in our experiment due to the resolution limit, as mentioned, numerical simulations are helpful to understand the detailed spectral and temporal structure of the experimentally generated soft x-ray pulses. Thus we have run a 3D propagation simulation [11,21] of HHG in Ar with the parameters given by the experimental condition. The recombination amplitude (or photo-recombination cross section) is considered in this simulation for accurate reconstruction of the spectral shape [11,22]. Figure 4 shows the simulated HH spectrum from Ar. The cut-off energy and the spectral shape are in excellent agreement with the experimental data shown in Fig. 3(a), while the simulation result shows the harmonic structure more clearly. The harmonic peaks in the plateau region are found to be not well defined, and they have moderate visibility ($\sim 50\%$), indicating the contribution of multiple electron trajectories to HHG. The corresponding on-axis electric-field profile in the inset of Fig. 4 shows the generation of sub-fs harmonic pulses in each half-cycle. The peak of the driving 2.1 μm pulse is located at time $t=0\mathrm{fs}$, so most of the harmonic light is found to be generated in the leading edge of the driver pulse due to the phase-matching condition from the relatively high intensity of the driver pulse. This simulation reveals that we have experimentally produced soft x-ray attosecond pulse trains.

 

Fig. 4. Calculated soft x-ray HH spectrum from Ar at 200 mbar based the 3D propagation simulation including the recombination amplitude calculation. The inset is the corresponding temporal profile with the sub-fs pulse train and the driving 2.1 μm laser field (red line), where the peak of laser field is at $t=0\mathrm{fs}$.

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In summary, we developed a multi-mJ, kHz, 2.1 μm OPCPA system, pumped by a 42 mJ picosecond cryogenic Yb:YAG amplifier, and demonstrated high-flux soft x-ray HHG via cut-off extension to 190 eV in Ar and N₂. We obtained $\sim 2\times {10}^8\text{photon}/\mathrm{s}$ over 1% bandwidth at 160 eV from Ar. Numerical simulations confirm the generation of soft x-ray attosecond pulse trains. This system is a promising light source for soft x-ray attosecond science as well as biological imaging applications. Further extension to the water-window region with high flux is possible using high-pressure Ne and He gas cells [4].