  For the growing demand of frequency combs in mid-infrared (mid-IR), known as
the "molecular fingerprint" region of the spectrum [1], down conversion of
near-IR frequency combs through half- harmonic generation offers numerous
benefits including high conversion efficiency and intrinsic phase and frequency
locking to the near-IR pump [2]. Hence cascaded half-harmonic generation
promises a simple path towards extending the wavelength coverage of stable
frequency combs. Here, we report a two-octave down-conversion of a frequency
comb around 1 {\mu}m through cascaded half-harmonic generation with ~64%
efficiency in the first stage, and ~18% in the second stage. We obtain
broadband intrinsically-frequency-locked frequency combs with ~50-fs pulses at
~2 {\mu}m and ~110-fs pulses at ~4 {\mu}m. These results indicate the
effectiveness of half-harmonic generation as a universal tool for efficient
phase- and frequency-locked down-conversion, which can be beneficial for
numerous applications requiring long-wavelength coherent sources.
