  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 9th-order (333 nm) in chirped
periodically poled lithium niobate waveguides driven by phase-stable
$\leq$12-nJ, 100 fs pulses at 3 $\mu$m with 100 MHz repetition rate. A
mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is
observed, amongst 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. Numerical simulations based on a single
broadband envelope equation with quadratic nonlinearity give estimates for the
conversion efficiency within approximately 1 order of magnitude over a wide
range of experimental parameters. From this comparison 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.
These results can inform cascaded HHG in a range of different platforms.

Optics;Atomic Physics