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High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to the ninth order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable$\le <\#comment/>12\mathrm{n}\mathrm{J}$, 100 fs pulses at 3 µm with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, among an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex highly nonlinear process. Accommodating the extreme spectral bandwidth, numerical simulations based on a single broadband envelope equation with only quadratic nonlinearity give estimates for the conversion efficiency within approximately 1 order of magnitude over a wide range of experimental parameters. From this comparison between theory and experiment, we identify a dimensionless parameter capturing the competition between three-wave mixing and group-velocity walk-off of the harmonics that governs the cascaded HHG physics. We also gain insights into spectral optimization via tuning the waveguide poling profile and pump pulse parameters. These results can inform cascaded HHG in a range of different platforms.

Vacuum-ultraviolet (VUV) light is critical for the study of molecules and materials, but the generation of femtosecond pulses in the VUV region at high repetition rates has proven difficult. Here we demonstrate the efficient generation of VUV light at megahertz repetition rates using highly cascaded four-wave mixing processes in a negative-curvature hollow-core fiber. Both even- and odd-order harmonics are generated up to the 15th harmonic (69 nm, 18.0 eV), with high energy resolution of$\sim <\#comment/>40\mathrm{m}\mathrm{e}\mathrm{V}$. In contrast to direct high harmonic generation, this highly cascaded harmonic generation process requires lower peak intensity and therefore can operate at higher repetition rates, driven by a robust$\sim <\#comment/>10\mathrm{W}$fiber-laser system in a compact setup. Additionally, we present numerical simulations that explore the fundamental capabilities and spatiotemporal dynamics of highly cascaded harmonic generation. This VUV source can enhance the capabilities of spectroscopies of molecular and quantum materials, such as photoionization mass spectrometry and time-, angle-, and spin-resolved photoemission.