As a desktop-level extreme ultraviolet (EUV) coherent light source, high harmonic generation (HHG) becomes an indispensable tool in fundamental science fields such as atomic and molecular physics, biomedicine, materials chemistry, and precision spectroscopy. The maximum photon energy of high harmonics in gas extends to the soft X-ray spectral range. Based on the appropriate gating technique of high harmonics, it is possible to generate isolated attosecond pulses with tens of attoseconds pulse widths, providing feasibility for the study of electron motion in atomic and molecular systems on the attosecond time scale. In addition to being critical in basic science, HHG also serves as a coherent light source with wide industrial applications, especially in integrated circuit manufacturing and imaging detection in biomedicine. High harmonic extreme ultraviolet light sources for industrial applications require both high photon energy (100?500 eV) and higher average power (above mW). To obtain a shorter wavelength high harmonic, the mid-infrared femtosecond laser, combined with nonlinear pulse compression technology, realizes the output of keV photon energy harmonics. The shorter wavelength aids in improving imaging resolution and covering the absorption edge of high atomic number materials, which can be used for extreme ultraviolet spectrum analysis. To improve the average power of higher harmonics, it is better on one hand to use the higher repetition rate and higher power driving laser. On the other hand, improving the conversion efficiency of high harmonics is necessary, which can be realized by controlling the macroscopic propagation process of high harmonics to achieve phase matching.

In this study, we focus on the process of producing high harmonics directly in a single pass driven by high repetition rate lasers, and introduce the progress in repetition rate, single pulse energy, and average power improvement of HHG extreme ultraviolet light sources. The paper organizes in the following way: after a brief introduction in the first section, which includes the HHG three-step model, the second section reviews the work on HHG sources driven by high repetition rate lasers in recent years, with the femtosecond fiber laser being the main pump source for producing high repetition rate HHG. The main parameters from these experiments are listed in Table 1. With the development of femtosecond fiber laser techniques, such as nonlinear compression, coherent combination, and optical parametric chirped pulse amplification (OPCPA), high harmonic sources are evolving towards higher photon flux, higher cutoff photon energy, and higher repetition rates. Figures 1 and 2 present the experimental device diagrams and spectra of two significant high repetition HHG works. Figure 3 shows the distribution of the main optical parameters of HHG extreme ultraviolet sources driven by the most advanced fiber laser described in this section.

The third section discusses the key to improving high harmonic conversion efficiency, namely, phase matching in the macroscopic propagation process of HHG. By discussing the wave vector mismatch between the fundamental field and the high harmonic field, we determine how the phase-matched HHG photon energy threshold is influenced by different gas medium types, wavelengths, and pulse lengths of the driving laser, as shown in Fig.4. Considering the effect of nonlinear gas medium absorption, the effective phase matching conditions are presented in Fig.5. We introduce the scaling law that keeps HHG conversion efficiency constant by adjusting the global physical quantity under different focusing conditions, which is well utilized in the HHG experimental parameters design under tight focusing conditions for femtosecond fiber or disk lasers with high average power and relatively small pulse energy, as listed in Table 2. Then, combined with effective phase matching conditions and the scaling law, the macroscopic propagation process of two different bands of HHG in high-repetition-rate experiments is briefly discussed, as illustrated in Figs.6 and 7.

In section four, we introduce the main imaging technologies based on the extreme ultraviolet HHG source currently in use. Three different coherent diffraction imaging (CDI) techniques, conventional CDI for isolated samples, Fourier-transform holography (FTH), and ptychography are discussed in this section, as shown in Fig.8. The phase retrieval algorithm in the standard data processing procedure for CDI is also briefly introduced, as shown in Fig.9. Finally, we discuss EUV coherence tomography (ECT) technology used for object depth information detection. Figures 10 and 11 are sample reconstructions of ptychography and ECT, respectively.

With the advancement of high repetition rate and high power femtosecond laser technology, the repetition rate and photon flux of high harmonic sources continuously improve. The limitations of high power femtosecond fiber and solid-state lasers, such as long pulse widths, low single pulse energy, and narrow tuning ranges, are being overcome compared to the traditional Ti∶sapphire solid-state femtosecond laser. Various nonlinear compression techniques enable the compression of femtosecond fiber laser pulse widths to just a few cycles. With coherent combination technology, the pulse energy of high repetition rate femtosecond lasers can reach the tens of mJ level. OPCPA technology allows for tuning the driving laser wavelength over a wide range. By controlling the laser intensity and wavelength at the single-atom response level, and adjusting the self-absorption and phase matching of high harmonics during the macroscopic propagation process, new laser technologies now enable the production of extreme ultraviolet coherent light sources with the highest average power of 10 mW, the maximum photon energy of 100 eV, and the highest repetition rate of tens of MHz. Through high-repetition and high-flux extreme ultraviolet coherent sources, HHG is branching into various application scenarios beyond the scientific research laboratory, especially in the field of imaging detection. Coherent diffraction imaging and coherent tomography can achieve high spatial and material resolution of nanoscale three-dimensional structures, both transversely and longitudinally. Consequently, imaging technology and instruments based on the high photon flux HHG source are anticipated to find applications in the fields of integrated circuit manufacturing, nanomaterials, biomedicine, and more.