  Quantum cascade laser (QCL) frequency combs are a promising candidate for
chemical sensing and biomedical diagnostics, requiring only milliseconds of
acquisition time to record absorption spectra without any moving parts. They
are electrically pumped and have a small footprint, making them an ideal
platform for on-chip integration. Until now, optical feedback is fatal for
frequency comb generation in QCLs and destroys intermodal coherence. This
property imposes strict limits on the possible degree of integration. Here, we
demonstrate coherent injection locking of the repetition frequency to a
stabilized RF oscillator. For the first time, we prove that the spectrum of the
injection locked QCL can be phase-locked, resulting in the generation of a
frequency comb. We show that injection locking is not only a versatile tool for
all-electrical frequency stabilization, but also mitigates the fatal effect of
optical feedback on the frequency comb. A prototype self-detected dual-comb
setup consisting only of an injection locked dual-comb chip, a lens and a
mirror demonstrates the enormous potential for on-chip dual-comb spectroscopy.
These results pave the way to miniaturized and all-solid-state mid-infrared
spectrometers.
