High average and peak powers are key technical indicators for the development of ultrafast laser technology, enabling a wide range of applications. With the rapid growth of ultrafast laser technologies, high-average-power lasers with ultrahigh repetition rates in the order of MHz have gained attention as fascinating secondary sources, such as the laser-like desktop source of high-order harmonic generation (HHG) in the extreme ultraviolet (XUV) regime with ultrahigh repetition rate, which has great potential in coherent diffraction imaging, coincidence detection, photoelectron spectroscopy, XUV optics metrology, and ultrafast atomic and molecular physics and chemistry. This is because of its excellent coherence, short wavelength, and femtosecond-to-attosecond pulse duration, making it an excellent supplementary source for synchrotron and free-electron lasers. However, high-average-power laser technologies with ultrahigh repetition rates are limited to pulse duration of hundreds of femtoseconds to a few picoseconds , which obstructs gas HHG. In this study, two different post-compression modules are developed to optimize HHG driving pulses. Sufficient driving conditions related to phase matching are comprehensively studied.

High-photon-flux coherent XUV sources are developed using a fiber laser with an ultrahigh repetition rate. In the experiment, two nonlinear post-compression systems are investigated: an argon-filled hollow-core fiber (HCF, Fig. 1) and a multi-pass cell (MPC, Fig. 2) filled with argon. Both approaches successfully broaden the laser spectrum and further reduce the pulse duration from 230 fs to below 40 fs after proper dispersion compensation with chirped mirrors. The ytterbium-doped fiber laser with a center wavelength of 1030 nm provides a maximum average power of 80 W with a pulse duration of 230 fs and supports flexible pulse repetition rates from 50 kHz to 19 MHz. The maximum pulse energy (400 μJ) is assigned at 200 kHz. As depicted in Fig. 4, the post-compressed pulses are subsequently focused by a gold-coated spherical mirror and interacted with the noble gases spurted out from a tapered gas jet. Because of the divergence difference between the infrared (IR) laser and the generated XUV beam, an iris is installed immediately after the gas jet to preliminarily reduce the residual driving pulse. Owing to the high average power driving conditions, a grazing incident plate is used to further diminish the residual IR, which allows reflectivity of 70% for the spectral range from 25 nm to 40 nm at a 7^o grazing incident angle. A relay imaging system is installed using an ellipsoidal mirror to set up a high-resolution XUV spectrometer and an application-friendly beamline. The tangential and sagittal radius of curvature of this relay imaging mirror are -12308.3 mm and -182.8 mm, respectively. To prevent heating due to ultrahigh-repetition-rate IR pulses, an aluminum filter (209.6 nm thick) is placed behind the ellipsoidal mirror, which ultimately stops the residual IR and any scattering light along the beamline. Pure XUV spectra are then detected using an in-house-built XUV flat-field spectrometer, which consists of a holographic grating and an X-ray charge-coupled device (CCD) camera. A removable silicon plate is used to switch between the spectrometer and the photon flux detector.

The two post-compression modules excellently reduce the laser pulse duration for subsequent HHG. The energy transmission efficiencies of HCF and MPC are over 60% and 90%, respectively. As shown in Fig. 3, the former module enables pulse compression from 230 fs to 27 fs, while the latter approach reaches 36 fs under optimal conditions. The improved pulses are then sent to the vacuum chamber to interact with Ar and Kr from the gas jet. Simulations and experiments on gas-based HHG are systematically performed. A variety of parameters related to important phase-matching conditions are investigated, such as driving pulse energy, pulse duration, gas type, gas pressure, and light-field coupling in the Z direction. By increasing the driving-pulse energy, the HHG signal becomes stronger. However, when the peak intensity is sufficiently high to induce overionization, the HHG exhibits a phase mismatch and the HHG signal decreases (Fig. 9). Because the gas density determines the neutral atom dispersion term and plasma dispersion term in phase matching, the gas pressure is one of the major tuning parameters for optimizing the HHG signal. Spatial splitting is observed in the HHG spectra when the gas jet is scanned along the beam path. This is mainly attributed to the contribution of electron trajectories in the HHG process. The long orbit tends to achieve phase matching at off-axis positions, whereas the short orbit favors phase matching at on-axis positions. Both experiments and simulations using a three-dimensional strong-field approximation code show good agreement on the above impacts on HHG optimization. A very bright harmonic signal between 21 nm and 40 nm is obtained at a 500 kHz repetition rate with a krypton gas jet backing pressure of 5.3 bar. The photon flux of each harmonic order exceeds 1.6×10¹⁰ photon/s, and the strongest harmonic order (35^th, the wavelength of 29.4 nm) is 1.8×10¹² photon/s ( the power of 12.2 μW), with an energy conversion efficiency of approximately 5×10^-7 (Fig. 7).

High-photon-flux HHG signals in the XUV regime (21?40 nm) are obtained with an ultra-high repetition rate femtosecond fiber laser associated with in-house developed HCF and MPC pulse post-compression systems. Under a loosely focusing configuration, the main impacts of the HHG process are investigated experimentally and through simulations, including the driving pulse energy and pulse width, gas type, gas pressure, and light field coupling conditions in the Z direction. Optimized photon flux of the 35^th harmonic order (29.4 nm) reaches 1.8×10¹² photon/s (12.2 μW), with a single harmonic order conversion efficiency of approximately 5×10^-7. Under the current experimental platform, further harmonic signals with higher brightness and shorter wavelengths (~10 nm) can be achieved by using a cascaded pulse post-compression system with MPC and HCF. Furthermore, fiber laser technology has successfully exceeded the average output power of 200 W and is an important driving laser for high-brightness XUV light source. For even shorter wavelengths, such as 6.7 nm and the water window, ultra-high-repetition-rate optical parametric chirped pulse amplification (OPCPA) mid-IR lasers (wavelength of 2.0?2.5 μm) are a viable option. The rapid development of disk laser technology has successfully surpassed the average output power by over kilowatts. When combined with a high-power MPC post-compression module, disk lasers are expected to be effective driving tools for milliwatt-level, short-wavelength (<10 nm) XUV light sources, with broad applications in nanostructure imaging, XUV metrology, ultrafast dynamics of atomic molecular physics, and component damage and system tests related to the lithography.