  Using aluminum-nitride photonic-chip waveguides, we generate
optical-frequency-comb supercontinuum spanning from 500 nm to 4000 nm with a
0.8 nJ seed pulse, and show that the spectrum can be tailored by changing the
waveguide geometry. Since aluminum nitride exhibits both quadratic and cubic
nonlinearities, the spectra feature simultaneous contributions from numerous
nonlinear mechanisms: supercontinuum generation, difference-frequency
generation, second-harmonic generation, and third-harmonic generation. As one
application of integrating multiple nonlinear processes, we measure and
stabilize the carrier-envelope-offset frequency of a laser comb by direct
photodetection of the output light. Additionally, we generate ~0.3 mW in the
3000 nm to 4000 nm region, which is potentially useful for molecular
spectroscopy. The combination of broadband light generation from the visible
through the mid-infrared, combined with simplified self-referencing, provides a
path towards robust comb systems for spectroscopy and metrology in the field.
