  We report on the realization of a solid-state-based vacuum ultraviolet
frequency comb, using multi-harmonic generation in an external enhancement
cavity. Optical conversions in such arrangements were so-far reported only
using gaseous media. We present a theory that allows selecting the most suited
solid generation medium for specific target harmonics by adapting the bandgap
of the material. Consequently, we experimentally use a thin AlN film grown on a
sapphire substrate to realize a compact frequency comb multi-harmonic source in
the DUV/VUV spectral range. Extending our earlier VUV source [Opt. Exp. 26,
21900 (2018)] with the enhancement cavity, a sub-Watt level Ti:sapphire
femtosecond frequency comb is enhanced to 24 W stored average power, its 3rd,
5th and 7th harmonics are generated, and the target harmonic power at 160 nm
increased by two orders of magnitude. The emerging non-linear effects in the
solid medium together with suitable intra-cavity dispersion management support
optimal enhancement and stable locking. To demonstrate the spectroscopic
ability of the realized frequency comb, we report on the beat measurement
between the 3rd harmonic beam and a 266 nm CW laser reaching about 1 MHz
accuracy.
